Right click here to get the supersized ... - Stephen Kinsella

EC4024 Financial Economics Course PackJan 14, 2008Dr Stephen Kinsella

Reflections_Leibowitz.fm Page 32 Monday, September 12, 2005 10:56 AMAlpha Hunters and Beta GrazersMartin L. LeibowitzActive alphas arederived fromexploiting acuteand chronicinefficiencies. Theyare hard to capture,but the greatinvestors have beenable to do so overmany, many years.There is a great philosophical divide between passive, efficiencybased“beta grazers” and active “alpha hunters.” The explosivegrowth of hedge funds, of both the traditional and the long-onlyformat, has contributed to this widening chasm between intenselyproactive investors and those funds that are indexed or semi-indexed.This Reflections article presents my personal observations onthe general subject of active investing and on the nature, persistence,and discernibility of various market inefficiencies that could give riseto such investment opportunities. Ironically, these behavioral biasescan act as frictions as well as opportunities, and this ambiguity mayhelp explain why a few notable investors appear to be almost continuouslysuccessful while other active investors fall well short oftheir alpha targets.At the outset, we should note that there is a middle ground whererelatively passive, non-zero-sum forms of alpha return can be found.As described in a series of articles (Leibowitz 2004; Leibowitz andBova 2005a, 2005c), these “allocation alphas” arise because the volatilityrisk of typical institutional portfolios is overwhelmingly dominatedby their home-market equity exposure. By tilting their strategicallocations toward a more balanced allocation, institutions can oftengarner enhanced expected returns with only modest increases inmarginal volatility. The level of expected benefit obviously dependson the institution’s specific return–risk assumptions.Unlike truly active alphas, allocation alphas are broadly accessiblethrough a semipassive process of moving toward an effectivestrategic allocation. As such, they are akin to the civilized sort ofprotein-seeking found in shopping at the local supermarket, with theselections determined by personal taste and dietary constraints.These readily available allocation alphas serve a critical and valuablerole in moving a fund toward optimal strategic allocation. Allocationalphas are quite distinct, however, from the truly active alphasderived from tracking down—and bagging—the fleeting and elusiveopportunities that arise from market inefficiencies. Both forms ofalpha offer the potential for enhanced return, and they can sometimesbe combined to create exceptional opportunities. They arequite different concepts, however, and are pursued in different ways.Having made this distinction, I focus the remainder of this article onthe truly active-skill-based investments that are intended to addalpha above and beyond the returns passively available in any assetclass or strategic portfolio.Martin L. Leibowitz is a managing director at Morgan Stanley, New York City.32 www.cfapubs.org ©2005, CFA Institute

Reflections_Leibowitz.fm Page 33 Friday, September 9, 2005 4:12 PMTruly Active AlphasMuch of the literature on truly active investing hasfocused on so-called anomalies—sources of incrementalreturn that appear to have some degree ofpersistence. In addition, a number of elegant formalizationshave been developed for incorporatingactive return–risk prospects into the investmentdecision process (Sharpe 1991; Grinold and Kahn2000; Waring and Siegel 2003; Asness 2004). Thisdiscussion should be broadened, however, toinclude consideration of all frictions and behavioralbiases—persistent as well as occasional—thatmight serve as fundamental sources of inefficiency.Such inefficiencies are not always exploitable: Theymay take the form of overshoots at certain timesand undershoots at other times, their exploitationmay be blocked by counterforces or technicalrestrictions of various sorts, or they may resolvethemselves very slowly—or never.We need to understand, however, that thesesources of inefficiency are multifold, broad based,and continually renewing themselves. Most importantly,we need to understand that they really doexist—even if they are not always available, discernible,or directionally consistent. Such pockets of inefficiencyat times become reasonably discernible andactionable—to certain active investors. Thus, theirvery existence becomes one facet of an argument(albeit an admittedly still incomplete argument) forthe possibility of successful active investing.Another argument (also incomplete) is the historicalfact that a handful of investors has producedextraordinary performance over a span of manyyears—often together with equally extraordinarycross-sectional success in their choices of disparateinvestments. The approaches of these greatinvestors—Warren Buffett, Bill Miller, Leon Levy,Dave Swensen, Jack Meyer—differ in numerousaspects, but as pointed out by Peter Bernstein(2005), the investors share the common feature ofnot being in the mainstream (i.e., they are all contrariansin one way or another). The great onesshare a number of positive characteristics—focus,patience, a clear-cut philosophy, a willingness to gobeyond the diversification mantra and accept highconcentration risks, an innovation-prone attitude,the organizational sponsorship and personal fortitudeto endure significant periods of underperformance,and a disciplined process for pursuing theirgoals. And in various ways and at various pointsin time, they have all been willing to stake significantchips on their convictions.With respect to this latter point, one might wellrecall Charles Ellis’s (1998) wonderful characterizationof most investors as playing what in tennisparlance is called “the loser’s game.” In the loser’sgame, weekend players, with their readily returnableforehands and backhands, square off againsteach other and the one who misses the last returnloses. The message is to play a consistent game andto avoid miss-hits. It is generally good advice for Bplayers—and beta grazers!The great ones, however—in tennis and ininvesting—go one big step beyond. They play adisciplined game until the moment they see whatlooks like a grand opportunity. At that moment,they move into carpe diem mode, gather up theirprowess, and take a calculated risk to proactivelyand aggressively force a win. 1Even the great Fischer Black was fascinated bythe potential for exploitable inefficiency, althoughhe certainly knew that such opportunities wouldnot be easy, widespread, or available to all. He oncefamously answered a question about how his viewof the investing world had evolved after movingfrom the Massachusetts Institute of Technology toGoldman Sachs with “the view is much clearerfrom the banks of the Charles than from the banksof the Hudson.” Earlier in his career, he had delivereda wonderful talk at the University of Chicagounder the title “Yes, Virginia, There Is Hope,”which was later published in the Financial AnalystsJournal (Black 1973). In that talk, he reported on hisstudy of the Value Line Ranking System, whichwould have produced superior performance overa long span of years if followed religiously (andwith transactional-cost efficiency!).Chronic and Acute InefficienciesSome of my pet sources of inefficiencies are behavioraland organizational distortions that I haveobserved over the years. I certainly do not mean toimply that they are exploitable anomalies, but theydo represent the raw nuclear material out of whichdiscernible opportunities could arise.In perfectly efficient markets, all informationwould be immediately embedded in prices. Themarket would go through a sequence of quantumleaps from one equilibrium value to another. Investorswould have no need to trade except for liquiditypurposes. It would be hard to make a livingSeptember/October 2005 www.cfapubs.org 33

Reflections_Leibowitz.fm Page 34 Friday, September 9, 2005 4:12 PMworking in such an idealized world. Fortunately,for those of us in the financial arena, the reality isthat the markets are always in transition from onestate of inefficiency to . . . maybe equilibrium but,more likely, a new state of inefficiency.Inefficiencies come in many forms and subforms,but they can be roughly classified as eitherchronic or acute. Acute inefficiencies are the discernibleopportunities that can be exploited by accessiblearbitrages. With acute inefficiencies, thesurrounding uncertainties can be hedged or minimized.Their resolution occurs quickly, well withinthe relevant time frame of arbitraging participants.Chronic inefficiencies tend to be less discernible,more ambiguous, more resistant to rapid resolutionfrom available market forces, and generallylonger term in nature. This distinction relates toJack Treynor’s (1976) wonderfully suggestive conceptof “fast ideas versus slow ideas.”Obviously, one would prefer to hurl fast ideasat acute inefficiencies, but by their very nature,fast ideas have a short half-life. And that half-lifemay be condensing with the explosive growth inhedge funds. But even in this era of the hedgefund, only a small minority of market participantsspend their days in a high-performance hunt foracute inefficiencies. The vast majority of investors,and certainly the bulk of the assets, swim with thebroad currents, while looking for less-fleetingincremental opportunities.Within this mainstream, one has expanses ofapparent efficiency coexisting with pockets ofchronic inefficiencies. Chronic inefficiencies arisefrom structural and behavioral sources, such astrading frictions, organizational barriers, imbalancesin capital flows, valuation ambiguities, lackof catalysts for resolution, convoy or herdingbehavior, artificial peer comparisons, rebalancinginconsistencies, compulsive confirmation seeking,filtering of conflicting data, misreading of marketsignals, inertia, formulaic action plans, and overlyrigid “policy portfolios.” These types of chronicinefficiencies can be quite persistent. Few arbitrageurshave mandates that allow them to pursuelong-term opportunities, and their absence contributesto the longevity of such inefficiencies. As thewell-known saying goes: The market can remainirrational far longer than you can hang onto yourposition—or your career.Process vs. Outcome. A much-discussedbehavioral bias is the tendency to overemphasizerecent historical results. As every mutual fund prospectusstates, “Past performance should not betaken as a guide to future performance.” Thatwarning, although true, is not much help when fewother hard facts are available. A more ominousrephrasing would be, “Past performance is noteven a good guide to the quality of the decisions thatwent into that past performance.” Yet, the ultimateissue is the soundness of the decision process itself:Was all knowable information incorporated? Wasthe reasoning thorough and sound? Were alternativescenarios considered and contrary viewssought? Was a well-planned implementation andmonitoring program established—and then followed?Was there a routine postmortem analysis oflessons learned? And are organizational disciplineand staff continuity sufficient to achieve consistencyin the decision process itself?Unfortunately, the sort of retrospective analysisthat includes these questions occurs more oftenwhen the outcomes are bad than when they aregood. Participants would be well advised to conductsuch postmortems even when the outcomesare happy ones, however, and to ask what really ledto success. Was the positive result achieved for thereasons thought, or was it simply good fortune inthis particular instance?Even when presented with a regime that hasevery evidence of success—but only a probabilisticsuccess—few investors are able to bring themselvesor their organizations to consistently follow its path.The pressures of benchmarks, peer comparisons,standard accounting, liability and expendituredemands, limited organizational risk tolerance,managerial self-doubt—all can lead to lurchingdepartures from prescribed disciplines, even oneswith a high—but probabilistic—success prospect.After all, even a strategy whose success is mathematicallyprovable will generate long runs ofunderperformance. Indeed, a topic in probabilitytheory deals specifically with the risk of ruin—andthe ultimate odds of ruin always favor the infinitelyresourced casino.Convoy Behavior. Traditional modes ofinvesting in the financial markets involve absoluteor relative valuations of various market segmentsor securities—a process in which ambiguities, complexities,and externalities abound. Inefficienciesand opportunities do exist in this area, but they arefar from clearly discernible and can only be seen“through a glass darkly.”34 www.cfapubs.org ©2005, CFA Institute

Reflections_Leibowitz.fm Page 35 Friday, September 9, 2005 4:12 PMMany chronic inefficiencies have their roots inthe behavioral biases of mainstream participants.For example, consider the herding behavior ofinstitutional funds. Participants in the financialmarkets find themselves on a sea of ambiguity.They may try to climb up the mast to see what liesahead, to look for islands of opportunity, but theyare always battered by the waves, the weather, andthe uncertainties of navigating in unchartedwaters. Is there any surprise that one sees so manysailing in convoys?It is no coincidence that most institutional portfoliosare tightly clustered, with total volatilitiesfalling in the 10–11 percent range—regardless ofthe fund’s mission, liability structure, sponsorstrength, or funding status (Leibowitz and Bova2004). When such ambiguity abounds, people naturallyassume that their peer groups might justhave the right idea. This behavior is not totallyirrational where theory is more art than science andwhere the expertise-to-luck ratio is often tilted infavor of luck. Moreover, a sufficient critical mass ofinvestors with a common belief, even an erroneousone, can forge a pricing consensus that becomes ade facto reality that must be taken seriously.Another issue is the valuation horizon of theaverage investor. The true efficient marketeermight argue that the market is continuously efficientover time. It is interesting to speculate, however,whether most investors have some specificspan of time—perhaps from six months to threeyears—on which they focus their investment andvaluation decisions. If so, then investors withlonger horizons may reap a somewhat larger riskpremium than average investors do. In terms ofTreynor’s fast–slow dichotomy, the advantagemight go to investors who are either faster orslower than this hypothetical norm.Another behavioral bias is the tendency to seekthe opinions of other “experts” who can confirmone’s own views, which results in what might becalled a “compounding consensus.” Actually,instead of seeking confirmation, one shouldactively solicit contrary views, hear them out, considerthem objectively, and then try to recognizethat the financial markets themselves always reflectsome balance of conflicting views. In theory, oneshould always start with the hypothesis that themarket is well priced. Then, before acting on anypotential opportunity, one should (1) try to ascertainwhy the market is priced where it is, (2) becomeconvinced that the basis for this current price doesnot fully reflect the true opportunities, (3) believethat there is some process whereby one’s views ofthe true state of affairs will eventually come to bewidely discernible (and in a more compelling fashionthan has obviously happened to date), and (4)conclude that this “discernment” will transpirewithin a relevant time span.Bayesian Rigidity. The compulsion to seekconfirmation also relates to how the unfolding ofevents is interpreted. The “rigid Bayesians” willrelentlessly try to retain their old views in the faceof new information. To help counter this all-toohumaninclination, one could write down theexplicit reasoning behind a projected outcome andthen establish the milestones that would have tooccur if events took the anticipated path. Such awrite-up would be akin to the contingency plansmilitary establishments routinely create for a widespectrum of geopolitical scenarios.A French marquis once said:He who makes detailed plans about everypotential course of action, and then decides—in advance and in great detail—how torespond to the various contingencies thatmight arise, and then further proceeds toaddress the subsequent situations that couldfollow each possible outcome, etc., etc.—thisman will make very few mistakes [actually, I’mnot sure that this part is true], but he will alsodo very little [I am sure that this part is true].Yet, although the market’s fast pace may limit howmuch contingency planning makes sense, theinvestment management profession surely coulddevote more effort in this direction.Price-Target Revisionism. Another area ofcurious behavior has to do with price targets. Whena long position is taken and the market movesfavorably, the price rise tends to be taken as aconfirmation of the wisdom of the purchase decision.To the extent that a price target was establishedat the outset, the investor may then betempted to find some rationale for revising thetarget upward. This revisionism has some ratherobvious dangers. A more rational approach wouldbe to assume that as the price moves toward theoriginal target, the prospect for further incrementalreturn decreases while the risk increases. So, as afirst cut, one should think in terms of selling off aportion of the position as it moves up. Thus, investorswould be well advised to have a plan to reduceSeptember/October 2005 www.cfapubs.org 35

Reflections_Leibowitz.fm Page 36 Friday, September 9, 2005 4:12 PMthe positions as the original target is approached—the burden of proof (or at least the burden of argument)being placed on the investor who wishes tomaintain the original position and/or revise theprice target upward.When the market moves against one’s position,one might reasonably conclude that the market isgiving a clear signal that one is wrong. A morecommon belief is that the market is wrong and thatgreater return is to be expected from the lower price.To counter the natural tendency to avoid a frontallook at deteriorating positions, a help, again, mightbe to have a series of adverse-event milestones thatcould act as trip wires to signal serious reconsideration.A substantive adverse move should be thebasis for asking what the market is trying to revealand for vigorously seeking those contrary views.The Ebullience Cycle. Another commonbehavior is the “unopened envelope” syndrome.Back in the old days when physical envelopes werethe primary delivery vehicle for individuals’ portfoliostatements, a persistently dreary marketwould lead to these envelopes being redelivered—unopened—into the “circular file.” Such a state ofdenial when the market moves against one is totallyhuman, especially when deciding what to do aboutit, if anything, is not easy. The unopened envelopereinforces individuals’ propensity for inaction inthe face of losing positions.The opposite phenomenon is, of course, thatwhen the markets are moving up, the incomingenvelope is eagerly awaited and ripped open withgreat vigor. High spirits are rampant, and risks aremore comfortable. In this ebullient atmosphere,both individual and institutional investors areinclined to hold on firmly to their winning positions,which are shining examples of their brilliance.They may even invest more aggressively,leading to the phenomenon that Jack Bogle (2005)cited of markets providing one return, the mutualfunds providing something less, and the investorsgetting even less (a number that is rarely measured,except by the individuals in pain). This problem ofmaking ever-greater investments as the marketrises is a classic cycle that is not likely to abate.Rebalancing Behavior. Market movementstypically elicit different responses from four typesof actors: holders, rebalancers, valuators, andshifters (Leibowitz and Hammond 2004).■ Holders. As noted, in a deteriorating market,individuals tend to leave their envelopesunopened and positions unchanged. This “holdingpattern” effectively reduces their equity allocations.■ Rebalancers. Institutions behave very differentlyfrom holders. When the market pushes aninstitutional fund away from its policy portfolioallocation, it usually quickly rebalances back to theoriginal percentage weights. In essence, institutionsact as “formulaic rebalancers.”■ Valuators. Valuators take positions basedon the belief that the market is either cheap (or rich)or that it will continue (or reverse) its recent direction.Valuators can obviously play in two directions.As the market moves down, they may, basedon the belief that the market has become cheap andwill reverse itself, act as contrarians. As momentumplayers, they may view the market’s decline—oneither a technical or a fundamental basis—as aharbinger of further downward pressure.■ Shifters. This category really represents atransient reaction rather than an ongoing style.Investors in any of the first three categories mayfind themselves becoming shifters at some point intime. Shifting occurs when a fundamental changein asset allocation is required because of circumstancesintrinsic to a fund’s or an individual’s situationrather than because of their assessment of themarket’s valuation. 2 That is, shifting is a fundamentalmove from one strategic stance to another. Forexample, individuals may increase their short-termfixed-income allocations when suddenly faced withan imminent liquidity need—loss of a job, anupcoming move, a looming major purchase, medicalcontingencies, and so on.Institutions are more resistant to shifting behavior.Most institutional funds have a policy portfoliothat serves as an anchor for their overall strategy.The policy portfolio is intended to be the best possiblepassive portfolio that encapsulates all relevantinformation about the nature of the fund, its purpose,and how it interacts with prospective returnsand risks in the financial markets. Policy portfolioshave great organizational value in forming a baselinefor structuring and controlling the investmentmanagement process. Following normal marketmovements, institutions try to rebalance back totheir policy portfolios. Significant shifts tend to takeplace only after a major reallocation study or underextreme organizational duress. A downside to policyportfolios is that they tend to be defined somewhatarbitrarily, to be specified in greater detail than36 www.cfapubs.org ©2005, CFA Institute

Reflections_Leibowitz.fm Page 37 Friday, September 9, 2005 4:13 PMis justified, to be sustained over a longer time thanis appropriate, and to form a high barrier for anytactical departure. Bill Jahnke (1999), Rob Arnott(2004), and Bernstein (2004) have written eloquentlyabout the behavioral distortions that can arise froman overly rigid commitment to policy portfolios.Market ImpactThese different responses may either exacerbate ormoderate market movements. Obviously, the holderswill have little effect on the market; they are outof the game, so to speak. The rebalancers will tendto have a smoothing effect: As the market goesdown, they buy more; as the market goes up, theysell. Within the valuator category, the contrariansand “reversionists” will act as moderators whereasthose pursuing momentum strategies will have anexacerbating effect. Because shifting tends tobecome more urgent (and probably more widespread)in adverse conditions, shifters will generallyexacerbate market moves.This four-part categorization also indicatessomething about how new flows are invested.Holders and rebalancers will usually invest theirnew funds congruently with their existing allocations.(However, individuals do seem to exhibitsomewhat more proactive flexibility in investingtheir new funds than with their existing allocations.This behavior is rather curious.) Valuators,of course, will make fresh decisions about whereto deploy new funds, but this type represents arelatively small part of overall new fund flows. Thebulk of flows is concentrated in holders and rebalancers—thosewith relatively rigid channels whotend to direct new investments largely towardtheir current allocations. 3Rebalancing and Market EfficiencyThe rebalancing behaviors themselves may becomesources of market inefficiency. Consider which ofthe behaviors really make sense. Suppose a fundstarts with a portfolio that mirrors the market as awhole. One could argue that, in a strictly efficientmarket, price movements would move the fund’sportfolio in concert with the evolving equilibrium,and in this case, holding behavior might make eminentsense. Most funds do not, however, have aportfolio that reflects the market as a whole (certainlynot on purpose). Moreover, at least in the caseof individuals, holding behavior is more likely tobe the result of inertia, not sophisticated reasoning.Some formulaic rebalancers believe they areadhering to an appropriate response in an efficientmarket. There is some inconsistency, however, inreestablishing the same allocation after an “efficientmarket” has made a major alteration in global assetweights. After all, a downward move reduces theasset’s weight in the market portfolio, which arguesfor rebalancing back to an allocation somewhatlower than the original policy portfolio weight.One sometimes hears the rationale for formulaicrebalancing presented in terms of buyingcheaper after a decline and selling expensiveassets after a rise. But if one really believes that themarket has become discernibly cheaper as a resultof a decline, shouldn’t the right move be to establishan even larger position rather than to rebalanceback to the original position? After all, if thepolicy allocation were done afresh, then (given thenewly cheaper valuation) the revised allocationshould be even more aggressive than before. Thus,one can reasonably argue that rebalancing should,in general, lead not to a resurrection of the originalallocation but, rather, to a higher or lower percentageweighting!Ideally, rational rebalancing should not be rigidlytethered to a fixed policy portfolio but shouldrespond more fluidly to market signals—to theextent they are interpreted either as an efficientrestructuring of the global portfolio or as a discerniblechange in valuation. The problem, of course, is thatlarge investment organizations are not designed tofacilitate such judgmental flexibility. And as oneastute chief investment officer put it, “Better to havea rigid rebalancing by prior agreement than a portfoliothat deteriorates into a holding pattern becausethe organization lacks the confidence or the will toreestablish the policy portfolio weightings—or toeven move back in that direction.”The behavior of valuators is integrally tied intothe issue of discernibility. To the extent that discerniblevaluation opportunities truly exist, why not tryto take advantage of them? Of course, with valuators,the big question is whether their businessmodels compel them to make tactical and timingdecisions even when no market opportunities meetthis test of “reasonable discernibility.”September/October 2005 www.cfapubs.org 37

Reflections_Leibowitz.fm Page 38 Friday, September 9, 2005 4:13 PMRisk as Risk to the Policy PortfolioA fund’s strong reluctance to being forced to shiftaway from its policy portfolio may play an underappreciatedrole in setting the fund’s risk toleranceand in shaping its policy portfolio in the first place.When an institution shifts to a lower-risk allocation,it departs from the policy portfolio that was previouslyconsidered to represent an optimal allocation.Institutional funds are understandablyreluctant to move away from pre-established policyportfolios. Indeed, their rebalancing behavior isspecifically geared toward sustaining this portfoliostructure. Most institutional managers view it asmost unfortunate if the fund is forced by an extrememarket movement—or by the fund’s investmentcommittee—to abandon the presumably optimalapproach and shift into a lower-risk strategy.Potential trigger points for such mandatedshifts lurk in the background of every investor’smind, however, acting as fence posts that define theouter limits of tolerable risk. These fence posts mayalso play a feedback role in setting the policy portfolio’soverall risk level in the first place. For example,suppose adverse movements of 15–20 percentare considered to be the tolerable outer limit of therisk envelope. Then, a fund might reasonably wishto control the prospect of any such triggering eventby reducing its probability to a minimal level (say,10 percent). This shortfall constraint implies a portfoliovolatility (risk) level in the 10–11 percentrange, which happens to be exactly where mostinstitutional funds are clustered.Two further observations on this issue of risk.One is that the standard measure of risk, volatility,is an estimate of the range of returns at a givenhorizon. As pointed out by Mark Kritzman (2000)and by Kritzman and Don Rich (2002), this end-ofhorizondistribution is not the same as thedistribution of outcomes that could occur at someintermediary time. That distribution is muchwider. And logically, this “riskier” intermediarydistribution should determine when triggerpoints might be activated. 4The Illusion of Growth EternalParticipants in the financial markets are intrinsicallyoriented toward an optimistic view of a worldwith a continuously compounding growth ofvalue. Reality reminds us, however, that wealth canalso be destroyed—both by “whimpers” and by“bangs.” Sidney Homer and I (2004) once posed thefollowing question: If a Roman soldier put just onedrachma in a savings account and let it compoundat 4 percent throughout the ages, how much moneywould his descendants have today? The answerturned out to be so many drachmas that, at virtuallyany exchange rate, it would amount to far morethan the total existing wealth in the world. Thisoutcome led to a follow-up question: What happenedto it all? The sobering answer is that wealthis destroyed by war, inflation, devaluation, pandemic,political collapse, repudiation, obsolescence,virulent competition, bankruptcy, financialdebacle, revolutionary technology, nonproductiveinvestment, and so on. The natural inclination todeny the phantom of such discontinuities may benecessary for moving things forward, but it mayalso be a chronic source of inefficiency.ConclusionParticipants in the financial markets often findthemselves sailing on a sea of ambiguity throughbroad patches of fog, bouts of heavy weather, andoccasional balmy periods that may prove only to bethe center of passing storms. One can elect thepassive approach—fly the beta flag and allow one’sportfolio to float on the “index currents.” Or onecan choose to be an active alpha-seeking investorand try to chip away at the many chronic inefficienciesand behavioral biases that we know exist, eventhough we can’t clearly discern how they are pricedand whether they will profitably regress towardequilibrium within a reasonable time. With chronicinefficiencies, by their very definition, discernibilitywill always be somewhat clouded. (Otherwise,they would become acute—and would be longgone.) So, with these opportunities, one is alwaysacting on imperfect knowledge and playing theodds. But without actively scanning the horizonand being poised to move on reasonably discernibleopportunities, investors will surely have nochance of reaping the incremental return inherentin the grand continuous march toward efficiency.The great investors are like the great sailors:They have the courage to set forth, they know wherethey want to go, they have a strong gyroscope tokeep them on course, they have appropriate respectfor the dangers of the sea and its potential for radicalshifts in weather and currents, and they are notafraid to be alone for long stretches.38 www.cfapubs.org ©2005, CFA Institute

Reflections_Leibowitz.fm Page 39 Friday, September 9, 2005 4:13 PMNotes1. Although I argue for the possibility of successful activeinvesting, I do not wish to suggest that everyone can be awinner. Indeed, they cannot. And the narrowness of the listof great investors attests to that dour fact. The great mass ofinvestors should treat the market as being highly efficientand should start with the null hypothesis that all assets arefairly priced.2. In some cases, market movements do ultimately lead to aportfolio shift. For example, a rule of thumb says that manyindividuals will let their allocations drift until a 15–20 percentdecline from some high-water mark forces them toseriously reconsider their risk tolerances. I am drawing adistinction, however, between shifts based on a marketdrivenchange in risk tolerance and those reallocations thatare directly valuation motivated.3. The large majority of existing dollar assets are also controlledby holders and formulaic rebalancers, which leadsto the interesting question of whether the key risk premiumsbetween asset classes are being priced by a relativelyminor segment of the investing universe.4. An even more severe criterion would be based on therange of declines from a high-water mark (Leibowitz andBova 2005b).ReferencesArnott, Robert D. 2004. “Managing Assets in a World of HigherVolatility and Lower Returns.” In Points of Inflection: NewDirections for Portfolio Management (Charlottesville, VA: CFAInstitute):39–52.Asness, Clifford. 2004. “An Alternative Future.” Journal ofPortfolio Management (Special Anniversary Issue):94–103.Bernstein, Peter L. 2004. “Overview: A Fifth Point of Inflection.”In Points of Inflection: New Directions for Portfolio Management(Charlottesville, VA: CFA Institute):1–5.———. 2005. “Alpha: The Real Thing, or Chimerical?” Economicsand Portfolio Strategy (15 March).Black, Fischer. 1973. “Yes, Virginia, There Is Hope: Tests of theValue Line Ranking System.” Financial Analysts Journal, vol. 29,no. 5 (September/October):10–14.Bogle, Jack. 2005. “The Mutual Fund Industry 60 Years Later:For Better or Worse?” Financial Analysts Journal, vol. 61, no. 1(January/February):15–24.Ellis, Charles. 1998. Winning the Loser’s Game. New York:McGraw-Hill.Grinold, Richard C., and Ronald N. Kahn. 2000. Active PortfolioManagement. 2nd ed. New York: McGraw-Hill.Homer, Sidney, and Martin L. Leibowitz. 2004. Inside the YieldBook. Princeton, NJ: Bloomberg Press.Jahnke, William. 1999. “Why Setting an Asset Allocation PolicyIs a Bad Idea.” Journal of Financial Planning (February).Available online at www.fpanet.org/journal/articles/1999_Issues/jfp0299-art5.cfm.Kritzman, Mark P. 2000. Puzzles of Finance. New York: JohnWiley & Sons.Kritzman, Mark P., and Don Rich. 2002. “The Mismeasurementof Risk.” Financial Analysts Journal, vol. 58, no. 3 (May/June):91–99.Leibowitz, Martin L. 2004. “The !-Plus Measure in AssetAllocation.” Journal of Portfolio Management, vol. 30, no. 3(Spring):26–36Leibowitz, Martin L., and Anthony Bova. 2004. “StructuralBetas: The Key Risk Factor in Asset Allocation.” Morgan StanleyResearch Notes (21 June).———. 2005a. “The Efficient Frontier Using ‘Alpha Cores’.”Morgan Stanley Research Notes (7 January).———. 2005b. “Convergence of Risk.” Morgan Stanley ResearchNote (April).———. 2005c. “Allocation Betas.” Financial Analysts Journal,vol. 61, no. 4 (July/August):70–82.Leibowitz, Martin L., and P. Brett Hammond. 2004. “TheChanging Mosaic of Investment Patterns.” Journal of PortfolioManagement, vol. 30, no. 3 (Spring):10–25.Sharpe, William F. 1991. “From the Board: The Arithmetic ofActive Management.” Financial Analysts Journal, vol. 47, no. 1(January/February):7–9.Treynor, Jack L. 1976. “Long-Term Investing.” Financial AnalystsJournal, vol. 32, no. 3 (May/June):56–59.Waring, M. Barton, and Laurence B. Siegel. 2003. “TheDimensions of Active Management.” Journal of PortfolioManagement, vol. 29, no. 3 (Spring):35–52.September/October 2005 www.cfapubs.org 39

Behavioral FinanceJay R. RitterCordell Professor of FinanceUniversity of FloridaP.O. Box 117168Gainesville FL 32611-7168http://bear.cba.ufl.edu/ritterjay.ritter@cba.ufl.edu(352) 846-2837Published, with minor modifications, in thePacific-Basin Finance Journal Vol. 11, No. 4, (September 2003) pp. 429-437.AbstractThis article provides a brief introduction to behavioral finance. Behavioral finance encompassesresearch that drops the traditional assumptions of expected utility maximization with rationalinvestors in efficient markets. The two building blocks of behavioral finance are cognitivepsychology (how people think) and the limits to arbitrage (when markets will be inefficient).The growth of behavioral finance research has been fueled by the inability of the traditionalframework to explain many empirical patterns, including stock market bubbles in Japan, Taiwan,and the U.S.JEL classification: G14; D81Keywords: Behavioral finance; arbitrage; psychology; market efficiencyA modified version of this paper was given as a keynote address at the July, 2002APFA/PACAP/FMA meetings in Tokyo. I would like to thank Ken Froot and Andrei Shleiferfor sharing their data and ideas, and Rongbing Huang for research assistance.

Behavioral Finance1. IntroductionBehavioral finance is the paradigm where financial markets are studied using models thatare less narrow than those based on Von Neumann-Morgenstern expected utility theory andarbitrage assumptions. Specifically, behavioral finance has two building blocks: cognitivepsychology and the limits to arbitrage. Cognitive refers to how people think. There is a hugepsychology literature documenting that people make systematic errors in the way that they think:they are overconfident, they put too much weight on recent experience, etc. Their preferencesmay also create distortions. Behavioral finance uses this body of knowledge, rather than takingthe arrogant approach that it should be ignored. Limits to arbitrage refers to predicting in whatcircumstances arbitrage forces will be effective, and when they won't be.Behavioral finance uses models in which some agents are not fully rational, eitherbecause of preferences or because of mistaken beliefs. An example of an assumption aboutpreferences is that people are loss averse - a $2 gain might make people feel better by as much asa $1 loss makes them feel worse. Mistaken beliefs arise because people are bad Bayesians.Modern finance has as a building block the Efficient Markets Hypothesis (EMH). The EMHargues that competition between investors seeking abnormal profits drives prices to their“correct” value. The EMH does not assume that all investors are rational, but it does assume thatmarkets are rational. The EMH does not assume that markets can foresee the future, but it doesassume that markets make unbiased forecasts of the future. In contrast, behavioral financeassumes that, in some circumstances, financial markets are informationally inefficient.Not all misvaluations are caused by psychological biases, however. Some are just due totemporary supply and demand imbalances. For example, the tyranny of indexing can lead todemand shifts that are unrelated to the future cash flows of the firm. When Yahoo was added tothe S&P 500 in December 1999, index fund managers had to buy the stock even though it had alimited public float. This extra demand drove up the price by over 50% in a week and over100% in a month. Eighteen months later, the stock price was down by over 90% from where itwas shortly after being added to the S&P.2

If it is easy to take positions (shorting overvalued stocks or buying undervalued stocks)and these misvaluations are certain to be corrected over a short period, then “arbitrageurs” willtake positions and eliminate these mispricings before they become large. But if it is difficult totake these positions, due to short sales constraints, for instance, or if there is no guarantee that themispricing will be corrected within a reasonable timeframe, then arbitrage will fail to correct themispricing. 1 Indeed, arbitrageurs may even choose to avoid the markets where the mispricing ismost severe, because the risks are too great. This is especially true when one is dealing with alarge market, such as the Japanese stock market in the late 1980s or the U.S. market fortechnology stocks in the late 1990s. Arbitrageurs that attempted to short Japanese stocks in mid-1987 and hedge by going long in U.S. stocks were right in the long run, but they lost hugeamounts of money in October 1987 when the U.S. market crashed by more than the Japanesemarket (because of Japanese government intervention). If the arbitrageurs have limited funds,they would be forced to cover their positions just when the relative misvaluations were greatest,resulting in additional buying pressure for Japanese stocks just when they were most overvalued!2. Cognitive BiasesCognitive psychologists have documented many patterns regarding how people behave.Some of these patterns are as follows:HeuristicsHeuristics, or rules of thumb, make decision-making easier. But they can sometimes leadto biases, especially when things change. These can lead to suboptimal investment decisions.When faced with N choices for how to invest retirement money, many people allocate using the1/N rule. If there are three funds, one-third goes into each. If two are stock funds, two-thirdsgoes into equities. If one of the three is a stock fund, one-third goes into equities. Recently,Benartzi and Thaler (2001) have documented that many people follow the 1/N rule.OverconfidencePeople are overconfident about their abilities. Entrepreneurs are especially likely to beoverconfident. Overconfidence manifests itself in a number of ways. One example is too littlediversification, because of a tendency to invest too much in what one is familiar with. Thus,1Technically, an arbitrage opportunity exists when one can guarantee a profit by, for example, going long in anundervalued asset and shorting an overvalued asset. In practice, almost all arbitrage activity is risk arbitrage—making trades where the expected profit is high relative to the risk involved.3

people invest in local companies, even though this is bad from a diversification viewpointbecause their real estate (the house they own) is tied to the company’s fortunes. Think of autoindustry employees in Detroit, construction industry employees in Hong Kong or Tokyo, orcomputer hardware engineers in Silicon Valley. People invest way too much in the stock of thecompany that they work for.Men tend to be more overconfident than women. This manifests itself in many ways,including trading behavior. Barber and Odean (2001) recently analyzed the trading activities ofpeople with discount brokerage accounts. They found that the more people traded, the worsethey did, on average. And men traded more, and did worse than, women investors.Mental AccountingPeople sometimes separate decisions that should, in principle, be combined. Forexample, many people have a household budget for food, and a household budget forentertaining. At home, where the food budget is present, they will not eat lobster or shrimpbecause they are much more expensive than a fish casserole. But in a restaurant, they will orderlobster and shrimp even though the cost is much higher than a simple fish dinner. If they insteadate lobster and shrimp at home, and the simple fish in a restaurant, they could save money. Butbecause they are thinking separately about restaurant meals and food at home, they choose tolimit their food at home.FramingFraming is the notion that how a concept is presented to individuals matters. Forexample, restaurants may advertise “early-bird” specials or “after-theatre” discounts, but theynever use peak-period “surcharges.” They get more business if people feel they are getting adiscount at off-peak times rather than paying a surcharge at peak periods, even if the prices areidentical. Cognitive psychologists have documented that doctors make differentrecommendations if they see evidence that is presented as “survival probabilities” rather than“mortality rates,” even though survival probabilities plus mortality rates add up to 100%.RepresentativenessPeople underweight long-term averages. People tend to put too much weight on recentexperience. This is sometimes known as the “law of small numbers.” As an example, whenequity returns have been high for many years (such as 1982-2000 in the U.S. and westernEurope), many people begin to believe that high equity returns are “normal.”4

ConservatismWhen things change, people tend to be slow to pick up on the changes. In other words,they anchor on the ways things have normally been. The conservatism bias is at war with therepresentativeness bias. When things change, people might underreact because of theconservatism bias. But if there is a long enough pattern, then they will adjust to it and possiblyoverreact, underweighting the long-term average.Disposition effectThe disposition effect refers to the pattern that people avoid realizing paper losses andseek to realize paper gains. For example, if someone buys a stock at $30 that then drops to $22before rising to $28, most people do not want to sell until the stock gets to above $30. Thedisposition effect manifests itself in lots of small gains being realized, and few small losses. Infact, people act as if they are trying to maximize their taxes! The disposition effect shows up inaggregate stock trading volume. During a bull market, trading volume tends to grow. If themarket then turns south, trading volume tends to fall. As an example, trading volume in theJapanese stock market fell by over 80% from the late 1980s to the mid 1990s. The fact thatvolume tends to fall in bear markets results in the commission business of brokerage firmshaving a high level of systematic risk. 2One of the major criticisms of behavioral finance is that by choosing which bias toemphasize, one can predict either underreaction or overreaction. This criticism of behavioralfinance might be called "model dredging." In other words, one can find a story to fit the facts toex post explain some puzzling phenomenon. But how does one make ex ante predictions aboutwhich biases will dominate? There are two excellent articles that address this issue: Barberisand Thaler (2002), and Hirshliefer (2001). Hirshliefer (p. 1547) in particular addresses the issueof when we would expect one behavioral bias to dominate others. He emphasizes that there is atendency for people to excessively rely on the strength of information signals and under-rely onthe weight of information signals. This is sometimes described as the salience effect.2During the bear market beginning in April 2000 in the U.S., aggregate stock market volume has not dropped. Thisis apparently due to increased trading by institutions, since stock trading by individuals has in fact declined. Thesignificant drop in transaction costs associated with the move to decimalization and technological advances partlyaccounts for this. Another reason is that many firms split their shares in late 1999 and the first half of 2000, which,ceteris paribus, would have resulted in higher trading volume. The drop in commission revenue from individuals(predicted by the disposition effect) has resulted in revenue declines for retail-oriented brokerage firms such asCharles Schwab & Co.5

3. The limits to arbitrageMisvaluations of financial assets are common, but it is not easy to reliably makeabnormal profits off of these misvaluations. Why? Misvaluations are of two types: those thatare recurrent or arbitrageable, and those that are nonrepeating and long-term in nature. For therecurrent misvaluations, trading strategies can reliably make money. Because of this, hedgefunds and others zero in on these, and keep them from ever getting too big. Thus, the market ispretty efficient for these assets, at least on a relative basis. For the long-term, nonrepeatingmisvaluations, it is impossible in real time to identify the peaks and troughs until they havepassed. Getting in too early risks losses that wipe out capital. Even worse, if limited partners orother investors are supplying funds, withdrawals of capital after a losing streak may actuallyresult in buying or selling pressure that exacerbates the inefficiency.Just who are these investors who make markets efficient? Well, one obvious class ofinvestors who are trying to make money by identifying misvaluations are hedge funds. Arelative value hedge fund takes long and short positions, buying undervalued securities and thenfinding highly correlated securities that are overvalued, and shorting them. A macro hedge fund,on the other hand, takes speculative positions that cannot be easily hedged, such as shortingNasdaq during the last two years.How well do efforts by arbitrageurs to make money work in practice at making marketsmore efficient? As Shleifer and Vishny argue in their 1997 "Limits to Arbitrage" article, theefforts of arbitrageurs to make money will make some markets more efficient, but they won'thave any effect on other markets.Let's look at an example, that of a giant hedge fund, Long Term Capital Management.LTCM was founded about nine years ago by Myron Scholes, Robert Merton, John Meriwether,and others. For their first three or four years, they were spectacularly successful. But then, fouryears ago, they had one bad quarter in which they lost $4 billion, wiping out their equity capitaland forcing the firm to liquidate. But they were right in the long run!LTCM mainly traded in fixed income and derivative markets. But one of the ways thatthey lost money was on the Royal Dutch/Shell equity arbitrage trade.In 1907, Royal Dutch of the Netherlands and Shell of the UK agreed to merge theirinterests on a 60-40 basis, and pay dividends on the same basis. It is easy to show that wheneverthe stock prices are not in a 60-40 ratio, there is an arbitrage profit opportunity. Finance theory6

has a clear prediction. Furthermore, these are large companies. Until July 2002, Royal Dutchwas in the S & P 500, and Shell is in the FTSE.How well does this prediction work?7

0.20.10-0.1-0.2-0.3Royal Dutch / Shell Deviation1/2/19801/2/19811/2/19821/2/19831/2/19841/2/19851/2/19861/2/19871/2/19881/2/19891/2/19901/2/19911/2/19921/2/19931/2/19941/2/19951/2/19961/2/19971/2/19981/2/19991/2/20001/2/2001Figure 1—Deviations from Royal Dutch/Shell parity from January 1980 to December 2001, as computed by Froot and Dabora (1999)and updated by Ken Froot.deviation from theoretical value

For the last 22 years, from 1980 to 2001, figure 1 demonstrates that there have been largedeviations from the theoretical relation. In 1998, LTCM shorted the expensive stock and boughtthe cheap one. Did they make money? No, they lost money when prices diverged further fromtheir theoretical values during the third quarter of 1998. To meet liquidity needs, LTCM andother hedge funds were forced to sell out their positions, and this selling pressure made marketsmore inefficient, rather than more efficient. So the forces of arbitrage failed.The data plotted in figure 1 end in December 2001, with the price ratio close to itstheoretical value. Has it stayed there? In July 2002, Standard and Poors announced that RoyalDutch would be dropped from the S&P 500 because they were deleting non-Americancompanies. Royal Dutch dropped by 17% in the week of the announcement, although there is nosuggestion that the present value of dividends changed.So what is the bottom line on market efficiency? It is useful to divide events into twocategories - high-frequency events, which occur often, and low-frequency events, which occuronly infrequently, and may take a long time to recover from.The high-frequency evidence supports market efficiency. It is hard to find a tradingstrategy that is reliably profitable. And mutual funds have difficulty beating their benchmarks.The low-frequency evidence, however, does not support market efficiency. Examples ofenormous misvaluations include:1) The undervaluation of world-wide stock markets from 1974-1982.2) The Japanese stock price and land price bubble of the 1980s.3) The Taiwanese stock price bubble that peaked in February 1990.4) The October 1987 stock market crash.5) The technology, media, and telecom (TMT) bubble of 1999-2000.4. Applications of behavioral financeI would now like to talk about some specific applications of behavioral finance. While Icould choose from many applications, I am going to briefly discuss two of my recentpublications. The first application concerns inflation and the stock market. I’m going to start outwith a simple valuation question. Below, I list some specific assumptions about a hypotheticalfirm, and the question is, “How much is the equity of this firm worth?”9

Assumptions: The inflation rate is 6%, and the equity risk premium is zero, so the nominal costof capital is 10% (a real cost of capital of 4%). The firm wants to keep the real value of its debtunchanged, so it must increase the nominal amount of debt by 6% each year. There is no realgrowth, and all free cash flow (if any) is paid out in dividends.Revenue $1,200,000Cost of Goods Sold $600,000Administrative Expenses $400,000Interest Expense $200,000Taxes $0After-tax profits $0Debt $2,000,000Book Equity $1,500,000Shares outstanding 10,000Interest rate on debt 10%With inflation at 6% and $2 million in debt, the firm must issue $120,000 more debt nextyear to keep the real value of its debt constant. This cash can be used to pay dividends. This is$12 per share, and using the growing perpetuity formulaP = Div 1 /(r – g)with r = 10% and g = 6%, P = $12/(0.10 – 0.06) = $300 per share.So the equity is worth $3 million, or $300 per share. Earnings are zero because theaccountants treat nominal interest expense as a cost, but they don't treat the inflation-induceddecrease in the real value of debt as a benefit to equity holders. In other words, the trueeconomic earnings are higher than the accounting earnings, because accountants measure thecost, but not the benefit to equityholders, of debt financing when there is inflation.This is an example of where framing makes a difference. Nominal interest expenseappears on the income statement. The decrease in the real value of nominal liabilities due toinflation does not appear on the income statement. Because it doesn’t appear, I would argue thatinvestors don’t take it into account, and hence undervalue equities when inflation is high. If youfind this implausible, ask yourself “how many finance professors with PhDs get the valuationcorrect?” If the market makes this mistake, then stocks become riskier, because they fall more10

than they should when inflation increases, and they rise more than they should when inflationdecreases. Over a full inflation cycle, these two effects balance out, which is why stocks are lessrisky in the long run than they are in the short run (Siegel (1998), Chapter 2).Modigliani and Cohn (1979) argued that the U.S. stock market was grossly undervaluedin the mid and late 1970s because investors had irrational beliefs about earnings, given the highinflation that existed then. Richard Warr and I, in our March 2002 JFQA article on the decline ofinflation and the bull market of 1982-1999, conduct an out-of-sample test of the Modigliani-Cohn hypothesis. We argue that part of the bull market of the 1980s was attributable to arecovery from the undervaluation. We also argue that the continued stock market rise in the1990s was an overshooting - the stock market became overvalued - and we predicted that 2000-2002 would have low stock returns. Fortunately, I believe in my research, and I've had much ofmy retirement assets in inflation-indexed bonds the last three years. These have been the bestperformingasset class.The second application of behavioral finance that I would like to briefly discuss concernsthe underpricing of IPOs.Prospect theory is a descriptive theory of choice under uncertainty. This is in contrast toexpected utility theory, which is normative rather than descriptive. Prospect theory focuses onchanges in wealth, whereas expected utility theory focuses on the level of wealth. Gains andlosses are measured relative to a reference point. Prospect theory also assumes loss aversion.Prospect theory also incorporates framing—if two related events occur, an individual has achoice of treating them as separate events (segregation) or as one (integration). For example, if aperson goes to the racetrack and makes two bets, winning one and losing one, the person mayintegrate the outcome and focus on the net payoff. If the net payoff is positive, a gain hasoccurred, and focusing on this makes the bettor happy. If there is a net loss, segregating the twobets allows the bettor to feel disappointed once, but happy once.Tim Loughran and I use prospect theory in our 2002 RFS paper "Why Don't Issuers GetUpset About Leaving Money on the Table in IPOs?" to explain the severe underpricing of someIPOs. If an IPO is underpriced, pre-issue stockholders are worse off because their wealth hasbeen diluted. We argue that if an entrepreneur receives the good news that he or she is suddenlyunexpectedly wealthy because of a higher than expected IPO price, the entrepreneur doesn'tbargain as hard for an even higher offer price. This is because the person integrates the good11

news of a wealth increase with the bad news of excessive dilution. The individual is better offon net. Underwriters take advantage of this mental accounting and severely underprice thesedeals. It is these IPOs where the offer price has been raised (a little) that leave a lot of money onthe table when the market price goes up a lot.5. ConclusionsThis brief introduction to behavioral finance has only touched on a few points. Moreextensive analysis can be found in Barberis and Thaler (2003), Hirshliefer (2001), Shefrin(2000), and Shiller (2000).It is very difficult to find trading strategies that reliably make money. This does notimply that financial markets are informationally efficient, however. Low frequencymisvaluations may be large, without presenting any opportunity to reliably make money. As anexample, individuals or institutions who shorted Japanese stocks in 1987-1988 when they weresubstantially overvalued, or Taiwanese stocks in early 1989 when they were substantiallyovervalued, or TMT stocks in the U.S., Europe, and Hong Kong in early 1999 when they weresubstantially overvalued, all lost enormous amounts of money as these stocks became even moreovervalued. Most of these shortsellers, who were right in the long run, were wiped out beforethe misvaluations started to disappear. Thus, the forces of arbitrage, which work well for highfrequency events, work very poorly for low frequency events.Behavioral finance is, relatively speaking, in its infancy. It is not a separate discipline,but instead will increasingly be part of mainstream finance.12

ReferencesBarber, Brad, and Terry Odean, 2001. “Boys will be boys: Gender, overconfidence, andcommon stock investment.” Quarterly Journal of Economics 116, 261-292.Barberis, Nicholas, and Richard Thaler, 2003. “A survey of behavioral finance.” in G.Constantinides, M. Harris, and R. Stulz (editors) Handbook of the Economics of FinanceNorth-Holland, Amsterdam.Benartzi, Shlomo, and Richard Thaler, 2001. “Naïve diversification strategies in definedcontribution savings plans.” American Economic Review 91, 79-98.Froot, Kenneth A., and Emil A. Dabora, 1999. “How are stock prices affected by the location oftrade?” Journal of Financial Economics 53, 189-216.Hirshleifer, David, 2001. “Investor psychology and asset pricing.” Journal of Finance 56,1533-1597.Loughran, Tim, and Jay R. Ritter, 2002. "Why don't issuers get upset about leaving money onthe table in IPOs?" Review of Financial Studies 15, 413-443.Modigliani, Franco, and Richard Cohn, 1979. “Inflation, rational valuation and the market.”Financial Analysts Journal 35, 24-44.Ritter, Jay R., and Richard Warr, 2002. “The decline of inflation and the bull market of 1982-1999.” Journal of Financial and Quantitative Analysis. 37, 29-61.Shefrin, Hersh, 2000. Beyond Greed and Fear Harvard Business School Press, Boston.Shiller, Robert J., 2000. Irrational Exuberance Princeton University Press, Princeton.Shleifer, Andrei, and Robert Vishny, 1997. “The limits of arbitrage.” Journal of Finance52, 35-55.Siegel, Jeremy J., 1998. Stocks for the Long Run, Second Edition McGraw-Hill, New York.13

The A Priori Problem of Observed ProbabilitiesNassim Nicholas TalebLife is not a laboratory in which we are suppliedprobabilities. Nor is it an exercise in textbooks onstatistics. Nor is it an urn. Nor is it a casino where thestate authorities monitor and enforce some probabilistictransparency.Alas we do not observe probabilities; we estimate themfrom observations and samples. This discussionpresents the principal problem of empirical probabilisticknowledge and discovery. The central problem is asfollows. Without a strong, necessarily normative, apriori specification of the underlying reality of aprocess, epistemic confidence is inversely proportionalto the consequences of the knowledge at hand. Themore events matter, the worse our empirical knowledgeabout their properties. Large deviations, the one thatcan have the most meaningful effect on the totalproperties, are far more error-prone in empiricalevaluation than regular ones.This note will also present the epistemologicaldifference between the nonscalable and scalabledistributions –as well as more minor issues oftenbundled under the archaic designation “Knightian”uncertainty.THE TELESCOPE PROBLEMAssume that there are series of discrete “events” i ofmagnitude ! i (taken as departures from a “norm”, a“mean”, or a center) and with probability " i (i can alsobe a “slice”, a discretizing interval for a continuousdistribution, in which case we assume equality in theslices). Assume further that ! i can take values on thereal line, with no known upper bounds or lower bounds,between minus infinity and infinity. (I am not assumingthat an upper or lower bound does not exist, only thatwe do not know where it is.) Assume that you areobserving samples in a finite set, and derivingproperties that are general, applying outside the sampleset (you could also be deriving a probability distributionof future events from past events). You observe a setof values ! i and make an inference about their possiblefrequency outside such set.Let me make it clear: You are not sampling within anurn, the composition of which you know. You aremaking statement outside of a sample set. This meansthat you are now subjected to the problem of induction.Now consider the moment contribution of every state ofthe world i, with M i,m = " i ! i m the moment contributionof order m. The total moment of order n would be thesummation of M over all possible values of i.M m=$" i# imLet us turn to the estimation of probabilities. How doesthe sample reveals the values " i ? Assume that you getthem by simply taking the sample of size n, and addingup the ! values of observations for a given !, here n ! /n ,where n ! are the number of observations of the eventof magnitude !.Let us call the “true” probabilities " i *, the probabilitiesthat can be obtained by having full knowledge of thegenerating process. We do not observe them, but theyare the ones that, in a world where they can bedesigned, the data is sampled from them.The constraint that all " i add up to 1 is not sufficient inmany situations. So the central problem is as follows.• The small probability estimationerror:The smaller the " i *, the larger weneed the sample n in order to be to besatisfied with our inference, and, for agiven sample size, the higher the error inusing " i as an estimator of "*.• The telescope problem: if the |!| issome decreasing function of ", for |!| largeenough, then the smaller the probability,the more consequential the impact of theerror on the total moment. Effectively thisis the case with unimodal distributions.So the errors in the smaller " are multiplied by a larger!. The pair " i ! i is a rectangle that gets thinner as "becomes smaller, but its surface is more stochastic." i" iThe Telescope Problem: Smaller probability "multiplies larger deviation !, with the error in the! i! i

!estimation of the product "! getting larger as " getssmaller.SAINT PETERSBURG COMPOUNDEDBut things can get worse for the “rectangle”. Let usnow consider the shape of the probability decrease,how the " need to drop as |!| rises. It is a fact thatthe " cannot decrease too slowly. The first intuition ofthe problem is in the well-known Saint Petersburgparadox (i.e., for n between 1 and infinity, a payoff ! iof 2 i with probability " i =1/2 i ), showing that no matterhow low the ", the increase in |!| can be such that themoment contributions of all M i are equal. Simply, thesituation in which" i= 1 K , where K is a constant,# imakes the computation of all moments >1 impossible.Generalization of the Saint Petersburg problemto higher ! momentsm. So more generally, for themoment M m to exist we need (in a unimodaldistribution) the slices of M i,m to decrease as a certainrate, i.e.,$" i< 1 '& K)%# i (So the problem is that it is hard for a probabilitydistribution to do the job for all moments m unless "falls faster than ! ! m for all m. For that to happen, theonly typical form is one with a characteristic scale, like" i= e #a$ i. It makes the product " i ! i m decrease forlarger values of !. What I call non-nonscalable is,simply, the situation in which we do not have thatexponential decline. See Note 1 for details.1/ mThe other solution is to give up on moments.THE A PRIORI PROBLEMLet us now look a the error rate in the estimation of " ,and the difficulty that for higher orders of M, there is acompounding effect of a higher error it multiplies largerand larger values of !. This is clearly intractable.This can be solved, of course, with an arbitrary functionthat decreases the moment contributions M i of the ! asthese become larger. In other words, by assuming apriori a certain class of distributions.Accordingly, we need one of the following threesolutions:Solution 1: A metaprobabilistic framework:allowing us to estimate the errors of the observed " isome measure of the difference between probabilitiesand perfect information. In other words, we wouldhave " * i,j for every probability i, making every momentcontribution M i,m stochastic. But here again there is therisk of regress as the metaprobability needs to bechecked as well for its own error –we need a model oferror measurement for that.Risk v/s Uncertainty: Note the difference betweenthe so-called “Knightian” risk and uncertainty can beexpressed as follows: risk is normatively set with*unitary metaprobabilities " i,j = 1 for all j (or nometaprobability). This makes the difference betweenthe two entirely normative, not empirical. In otherwords, the difference does not exist in an environmentwhere one cannot accept epistemological certaintiesabout probabilities without a priori.Solution 2: Assuming beforehand a probabilitydistribution: If distributions are popular, it is becausethey allow normatively to make inferences aboutprobabilities by analogy with other probabilities in placeof the metaprobabilistic framewor. Here the estimationerror concerns some parameters of the probabilitydistribution, but not the probabilities themselves.This option is problematic because there is nojustification for the derivation of probability distributionsinternally from the data, i.e. empirically, causinganother infinite regress argument. We need data forprobability distribution and a probability distribution toknow how much data we need. So we cannot do ameta-probability distribution. This is where it becomesnormative.Note that there are situations in which one can put asubordination: you sample between two probabilitydistributions, say two Gaussians. TheSolution 3: Truncation: of some values of the !allowing the integration and the finiteness of M m . This isnot done by assumption, but, rather, in eliminating thesensitivity of the variable above a certain amount.(Note one aspect of Saint-Petersburg: The use of utilityof payoff introduced a soft truncation. But you can setthe game in a way to truncate “organically”.)CONCLUSIONThere are no ways to deal with unbounded payoffsprobabilistically without making assumptions, andassuming that these assumptions are not subjected toprobabilistic judgment. This is the tragedy ofprobabilistic reasoning in modern domains, for whichwe cannot tolerate a priori probabilities.2© Copyright 2007 by N. N. Taleb.

MATHEMATICAL POINTSNote 1: Assume that "(x) is a continuous function.Assume x in the positive domain and p monotonic ineach domain “for x large enough”. We need M[n], i.e.,"(!) ! n to be a decreasing function of ! for all n. Tosatisfy the strict negativity of M’[n] the derivative of the“moment slice” with respect to !, we have! n-1 (n "(!) + ! "’(!))

Can Stock Market Forecasters Forecast?Alfred Cowles 3rdEconometrica, Vol. 1, No. 3. (Jul., 1933), pp. 309-324.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28193307%291%3A3%3C309%3ACSMFF%3E2.0.CO%3B2-SEconometrica is currently published by The Econometric Society.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/econosoc.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgFri Jan 4 10:47:40 2008

CAN STOCK MARKET FORECASTERS FORECAST?A paper read before a joint meeting of the Econometric Society and theAmerican Statistical Association, Cincinnati, Ohio, December 31, 1932INTRODUCTIONTHISpaper presents results of analyses of the forecasting efforts of 45professional agencies which have attempted, either to select specificcommon stocks which should prove superior in investment merit to thegeneral run of equities, or to predict the future movements of the stockmarket itself. The paper falls into two main parts. The first deals withthe attempts of two groups, 20 fire insurance companies and 16 financialservices, to foretell which specific securities would prove mostprofitable. The second part deals with the efforts of 25 financial publicationsto foretell the future course of the stock market. Various statisticaltests of these results are given.These investigations were instituted five years ago as a means oftesting the success of applied economics in the investment field. Itseemed a plausible assumption that if we could demonstrate the existencein individuals or organizations of the ability to foretell the elusivefluctuations, either of particular stocks, or of stocks in general, thismight lead to the identification of economic theories or statistical practiceswhose soundness had been established by successful prediction.The forecasters include well-known organizations in the differentfields represented, many of which are large and well financed, employingeconomists and statisticians of unquestioned ability. The names ofthese organizations are omitted, since their publication would be likelyto invite wholesale controversy over the interpretation of their records.Some of the forecasters seem to have taken a page from the book ofthe Delphic Oracle, expressing their prophecies in terms susceptible ofmore than one construction. It would frequently be possible, therefore,for an editor, after the event, to present a plausible challenge of ourinterpretation. Most of the forecasts appear through the medium ofweekly publications and each of these has been read and recorded onthe day it became available to us, which in practically every case wasbefore the event. In this way certain possible elements of bias havebeen eliminated. It was impossible that hindsight could influence ourjudgment, either in the selection of publications for analysis or in theinterpretations placed on their forecasts. In the case of the fire insurancecompanies, however, the analyses were made annually, based onthe transactions reported in Kimber's Record of Insurance CompanySecurity Pu~chases. The companies were selected as fairly representa-

tive of their class. The analysis of the 26-year forecasting record ofWilliam Peter Hamilton, former editor of the Tt'all Street Journal, alsofalls in a different category, in that it was undertaken because of thereputation for successful forecasting which he had established over along period of years.FORECASTING THE COURSE OF INDIVIDUAL STOCK PRICESWe turn first to the records of two groups, the financial services andthe fire insurance companies, which have attempted to select individualstocks that would prove more profitable for investment than the averageissue. The first part of this section deals with the records, over the44 years ending July, 1932, of 16 leading financial services which havemade a practice of regularly submitting to their subscribers selectedlists of common stocks for investment. Our analysis includes about7,500 separate recommendations, requiring approximately 75,000 entries.The first step was to record each week the name and price ofeach stock recommended for purchase or sale by each service. Nextcame the tabulation of the advice to sell or cover the commitmentpreviously advised. Reiterated advice was not considered, action beingassumed to have been taken as of the date when the recommendationwas first published. The percentage gain or loss on each such transactionwas recorded and, in a parallel column, the gain or loss of the stockmarket for the identical period. A balance was struck every six monthswhich summarized the total results secured by each service as comparedwith the action of the stock market. Proper corrections were, ofcourse, made to offset the effect of changes in capital structure resultingfrom the issue of rights, stock dividends, etc. Since a tendency existedamong some services to emphasize their conspicuously successful stockrecommendations and ignore more unfortunate commitments, weadopted a practice of automatically dropping a stock from the list sixmonths after it had been last recommended, when specific advice tosell was not given.A redistribution of funds in equal amounts among all stocks recommendedhas been assumed for each service at the beginning of every sixmonths' period analyzed. It could be maintained, of course, that thisequalizing process should take place as often as once a week, but thiswould increase the labor of computation to overwhelming proportions.Provisional experiments demonstrated that it would yield conclusionspractically identical with those secured by the shorter method. Compoundingthe successive six months' records gives the percentage bywhich each service's recommendations have exceeded, or fallen behind,the stock market, as shown in Table I.Only six of the 16 services achieved any success. To arrive at an

ALFRED COWLES ~ R D311average performance, the record of each service was reduced to an effectiveannual rate which was then weighted in accordance with thelength of the period represented. The average annual effective rate ofall the services, thus arrived at, is - 1.43 per cent.TABLEIRESULTSOF COMMITMENTSTOCKSIN RECOMMENDED BY 16 FINANCIALSERVICES (RELATED TO MARKET AVERAGES)Service W e e k s Per cent1. .....................234 ..................... +80.82. ....................234 ..................... +17.23. ....................234 ..................... +15.24. ..................... 234 ..................... f12.35. ..................... 234 ..................... + 8.46. ..................... 26 ..................... + 6.17. .................... 52 ..................... 0.8. .....................104 ..................... - 0.59. ..................... 234 - 1.910. . . . . . . . . . . . . . . . . . . . . 52 ..................... - 2.211. ..................... 52 ..................... - 3.012. ..................... 52 ..................... - 8.313. ..................... 78 ..................... -16.114. ..................... 104 ..................... -28.215. ..................... 104 . . . . . . . . . . . . . . . . . . . . -31.216. ..................... 156 ..................... -33.0PROBABILITY TESTSIn an attempt to determine whether the service having the best recordachieved its result through skill or chance, we resorted to the theoriesof compound and inverse probability. Our conclusion is thusrendered consistent by obtaining approximately the same answer intwo different ways.With the aid of various checks, involving 1250 computations of theaction of individual stocks selected at random, we derived a formula,A.D. (t) =5.42+1.5t (A.D. =average deviation, t, in units of 4 weeks,2 I), representing the deviation, for all periods from one month up toone year, of the average individual stock from the average of all stocks.Service Number 1, for the 9 six months' periods from January 1,1928 to July 1, 1932, was successful 7 times and unsuccessful 2 times.With the aid of the table referred to, the averages of "chances in 1000to do worse" for the 7 periods in which it was successful and the 2 periodsin which it was unsuccessful were found to be 842 and 66 respectively.By the theory of direct probabilities, the probability of asingle service being right at least 7 times in 9 is equal to the sum of thefirst 3 terms of the binomial (9+3)@.p = 1/29+9/2@+36/2@ =46/512 = .090The probability that a single service could in 9 predictions be 7 times

312 ECONOMETRICAon the positive side and in these 7 forecasts equal the achievement ofService Number 1 is,P=.090 X (1 - .842)= .014However, the record of the best service is marred by its failure in thetwo negative cases. The average of the two chances to do worse in thesecases is .066. We then have,as the probability of a single random service having a record worsethan that of Service Number 1. We therefore conclude that the probabilitythat a random service can, first, be on the right side of the market7 times out of 9, and second, equal in performance the record of ServiceNumber 1, isP = ,090X (1-.670) =.030.This means that in 16 services we should expect to find 16 X.030 = .48services which will equal the record of Service Number 1. That is to say,the chance is even that we should get at least one service as good asNumber 1.Because of the assumptions implied in this computation, we shall arguethis another way. We shall assume that the probability that a servicefor its total forecast shall be on the positive side of the market is1/2. Then the estimate of its success must be made by a differentevaluation of Q. For this purpose we shall adopt a formula suggestedby Bayes' rule in inverse probability in which the weights .9l0 and .090instead of 7/9 and 2/9 are used. We getHence, if a service was on the right side of the market, the probabilityof its achieving the success of Service Number 1would be 1-Q.Thus the compound probability would beP = 1/2 (1 - .901)= .050.Among the 16 services the probability of the most successful one equallingthe record of Service Number 1would be P= 16X .050 = 30, thatis to say, we should expect to get among 16 random services about oneservice which would equal Number 1. Since this answer is quite consistentwith our previous answer, our analysis suggests the conclusionthat the record of Service Number 1 could not be definitely attributedto skill.

ALFRED COTVLES ~ R D313TWENTY FIRE INSURANCE COhlPANIESThe second analysis deals with the common stock investments, from1028 to 1931 inclusive, of 20 of our leading fire insurance companies.Its significance lies in the fact that these companies are representativeof a class of common stock investor which has had long years of experienceand large amounts of capital at its disposal. Fire insurance datesfrom the Great London Fire of 1666, and active investment in stocksdeveloped during the nineteenth century. The fire insurance companiesare much older hands at the business of investment than either thefinancial services, which are a twentieth century product, or Americaninvestment trusts, which are largely a development of the last fewyears. The investment policies of these companies are based on theaccumulated knowledge of successive boards of directors whose judgmentmight be presumed, over the years, to have been well above thatof the average investor. The 20 companies which were selected foranalysis hold assets totalling several hundred million dollars, and seema fair sample of their kind.Fire insurance companies carry between 20 and 30 per cent of theirtotal investments in common stocks. Their average turnover amountsto only some 5 per cent a year. For this reason it was thought best toconfine our analysis to the record of the actual purchases and salesmade during the period under examination, rather than to computethe record of the entire common stock portfolio. To simplify the labor,all items of stock purchased were given equal weights, regardless of theamounts involved. While the conclusion does not exactly reflect theactual investment results secured by these companies, it should, however,provide a satisfactory test of the success of these organizationsin selecting stocks which performed better than the average.The method employed in the analysis is essentially the same as thatused in the case of the investment services. A second purchase of anitem was omitted from the record unless a sale of this item intervened.A record of the sale of an item, of course, determined the date as ofwhich it was dropped from the list. Also, any item of which there hadbeen no purchase recorded for 12 months was automatically consideredsold.The compounded records of the 20 companies for the 4-year periodare shown in Table 11.Six of the companies show evidence of success, and the average ofthe 20 is -4.72 per cent. The average record of the companies in thestocks which they selected for investment fell below the average of thestock market at the effective annual rate of 1.20 per cent. A comparableresult could have been achieved through a purely random selection of

314 ECONOMETRICAstocks. The analysis of the fire insurance companies' records thus confirmsthe results secured in appraising the records of the financial services.TABLEI1RESULTSOF COSIMITSIENTSSTOCKSIN MADEBY TWENTYFIRE INSURANCECOMPANIES (RELATEDTO STOCKMARKETAVERAGES)All companies 1928-31, inc.CompanyPer cent1. ..............................................+27.352. ..............................................$25.113. ..............................................+18.344. .............................................. $10.385. ..............................................+10.126. 3.207. ..............................................- 2.068. ............................................. - 3.639. .............................................- 5.0610. .............................................. - 6.6711. .............................................. -10.4412. .............................................. -10.5513. .............................................. -11.7614. .............................................. -12.9215. .............................................-13.8216. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -14.9617. .............................................-18.0318. -21.8919. -23.4420. .............................................. -33.72FORECASTING THE STOCK MARKET ACCORDING TO THE DOW THEORYHaving dealt with the efficiency of two great groups of professionals,fire insurance companies and financial services, in selecting commonstocks for investment, we turn now to a consideration of skill inpredicting the course of the stock market as a whole. This section alsois in two principal sub-divisions. First we consider the record of WilliamPeter Ramilton.This analysis was undertaken because several decades of editorialsin the country's leading financial newspaper have built up a great popularfollowing for the Dow Theory, of which Eamilton was the principalsponsor. The Dow Theory was the creation of Charles H . Dow, founderof the Dour Jones financial news service, founder and editor of the WallStred Journal. After Dour's death in 1902 Hamilton succeeded him aseditor of the Wall Street Journal, continuing in this position until hisdeath in December, 1929.During 26 years of his incumbency Hamilton wrote 255 editorialswhich presented forecasts for the stock market based on the Dow Theory.These were sufficiently definite to permit scoring as bullish, bearish,or doubtful. This we did by a majority vote of five readers. When

ALFRED COWLES ~ R D315doubtful we assumed that he abstained from trading. When bullish itwas assumed that he bought equal dollar amounts of the stocks includedin the Dour Jones railroad and industrial averages, and soldthem only when he became bearish or doubtful. When bearish we assumedthat he sold short equal dollar amounts of these stocks andcovered only when he became doubtful or bullish. The percentage gainor loss on each such transaction has been calculated, and the resultscompounded through the 26 years. Since the Dow Jones averages haveonly recently been corrected to offset the effect of stock rights, stockdividends, and stock splits, such adjustments have been made for allthe previous years on the basis of tables published by Dwight C. Rosein his book Investment Management. Corrections have also been madeto allow for the effect of brokerage charges, cash dividends, and theinterest presumably earned by Hamilton's funds when they were notin the stock market. The fully adjusted figures were then reduced toan effective annual rate of gain which is presented as a measure of theresult accomplished.From December 1903 to December 1929, Hamilton, through the applicationof his forecasts to the stocks composing the Dour Jones industrialaverages, would have earned a return, including dividend andinterest income, of 12 per cent per annum. In the same period thestocks composing the industrial averages showed a return of 15.5 percent per annum. Hamilton therefore failed by an appreciable marginto gain as much through his forecasting as he would have made by acontinuous outright investment in the stocks composing the industrialaverages. He exceeded by a wide margin, however, a supposedly normalinvestment return of about 5 per cent. Applying his forecasts tothe stocks composing the Dow Jones railroad averages, the result isan annual gain of 5.7 per cent while the railroad averages themselvesshow a return of 7.7 per cent.Hamilton was long of stocks 55 per cent, short 16 per cent, and outof the market 29 per cent, of the 26 years under review. Counting onlychanges of position, he made bullish forecasts 29 times. Applying theseto the industrial averages, 16 were profitable, 13 unprofitable. He announcedbearish forecasts 23 times, 10 were profitable, 13 unprofitable.He advised 38 times that funds be withdrawn from the stock market,19 of these withdrawals being profitable, 19 unprofitable. In all, 45 ofhis changes of position were unsuccessful, 45 successful. The applicationof the forecasts to the railroad averages confirms these conclusionsexcept that in this case 41 changes of position were successful and 49unsuccessful. For the period from 1909 to 1914 inclusive, when the industrialaverages displayed what, in effect, was a horizontal trend, hishypothetical fund shrank 7.8 per cent Der annum below what it would

316 ECONOMETRICAhave been if loaned at 5 per cent interest. The result of applying hisforecasts to the railroad averages deserves attention in view of the factthat this group displayed an almost horizontal secular trend for the26 years under consideration. His average annual pain of 5.7 per centin this group would have been approximately equalled, in the case ofa continuous outright investment, by the dividend income.STOCK NARKET FORECASTS OF TWENTY-FOUR FINANCIALPUBLICATIONSFor the analysis of other results secured in forecasting the course ofthe stock market, we selected during the period from January 1, 1928,to June 1, 1932, 24 publications (among which were 18 professionalfinancial services, 4 financial weeklies, one bank letter, and one investmenthouse letter). More than 3,300 forecasts were tabulated. Themethod used has been for each reader to ask himself the question, "Inthe light of what this particular bulletin says, would one be led to buystocks with all the funds at his disposal, or place a portion only of hisfunds in stocks, or withdraw entirely from the market?" The readergraded the advice in each instance by means of one of nine possibleentries, namely 100 per cent of funds in the market, 87$, 75, 62$, 50,374, 25, 124, or 0 per cent. The great majority of forecasters confinethemselves to general discussions of the investment situation, leavingto the reader the decision as to what proportion of his funds he shallplace in the market. The tabulation, therefore, cannot be mathematicallyconclusive. Our method, in general, has been to have the vote ofthree readers of c~mpetent intelligence determine the interpretation ofeach forecast. Marginal commitments have not been incorporated inour tabulations because in no case have they been advised by any ofthe forecasters. Similarly, short commitments are not in general assumedbecause, of the entire 24 forecasters, only one recommendedthem. His record has been computed on a special basis.The tabulated forecasts have been tested in the light of the actualfluctuations of the stock market as reflected by the Standard StatisticsCompany index of 90 representative stocks. If a forecast is 100 per centbullish and the market rises 10 per cent in the subsequent week, theforecaster is scored as +10 per cent. If the forecaster, after weighingthe favorable and unfavorable factors, leaves the decision hanging inthe balance, the score is $5 per cent or one-half of the market advance.This is on the assumption that the investor, being in doubt as to thefuture course of the market and being, by definition, committed tocommon stocks as a possible investment medium, would be led toadopt a hedged position with half of his funds in stocks and half inreserve. If the forecast is 100 per cent bearish, the score is zero, regard-

ALFRED COWLES ~ R D317less of the subsequent action of the mnrket, on the assumption that,under such conditions, the investor would withdraw all of his fundsfrom stocl\s. On the other hand, if the forecast is 100 per cent hullis11and the market drops 10 per cent in the ensuing weeli, the score is-10 per cent. If the forecast is doubtful when the market drops 10 percent, the score is -5 per cent. The compounding of all these weeklyscores for the period covered gives a cumulative record for each forecaster.This permits comparisons which reveal relative success andaverage performance. While it may be thought that accurate week-toweekforecasting is a hopeless ideal, it should be emphasized that ouranalysis of weekly results also measures accurately the efficiency oflong swing forecasts.A figure representing the average of all possible forecasting resultsfor the period was arrived at by compounding one-half of every weeklypercentage change in the level of the stock market. The final scoresgiven below for the 24 forecasters were computed by dividing theactual performance of each by the average of all possible results referredto above, and subtracting 100.TABLEI11RESULTSOF STOCKMARKETFORECASTSForecaster Weeks Per cent1. .....................105 ..................... f72.42. ..................... 230 ..................... +31.53. .....................230 ..................... +28.34. ..................... 21 ..................... $24.25. ..................... 157 ..................... + 9.06. ..................... 53 . . . . . . . . . . . . . . . . . . . . . + 3.07. ..................... 126 . . . . . . . . . . . . . . . . . . . . . + 2.48. ..................... 53 ..................... + 1.39. ..................... 105 ..................... - 1.710. . . . . . . . . . . . . . . . . . . . . . 157 ..................... - 2.111. ..................... 230 ..................... - 3.612. ..................... 43 ..................... - 6.013. ..................... 53 ..................... - 6.714. ..................... 131 ..................... - 6.915. . . . . . . . . . . . . . . . . . . . . . 230 ..................... -12.516. .....................230 . . . . . . . . . . . . . . . . . . . . . -13.517. ..................... 53 . . . . . . . . . . . . . . . . . . . . . -17.218. .....................230 ..................... -21.519. ..................... 69 ..................... -29.420. ..................... 230 ..................... -83.021. ..................... 230 ..................... -35.322. ..................... 230 ..................... -41.523. ..................... 157 ..................... -45.324. ..................... 230 . . . . . . . . . . . . . . . . . . . . . -49.1The records show that only one-third of the list met with any success.In order to derive a significant average of the performance of the

entire group the results listed above have been reduced to effectiveannual rates, and each has been given a weight to conform with thelength of the record analysed. After these adjustments, we are enabledto conclude that the average forecasting agency fell approximately4 per cent per annum below a record representing the average of allperformances achievable by pure chance. This would seem to indicatethat, in general, these stock market forecasters failed to accomplishtheir objective. The most that can be said in extenuation is that thelong-continued decline in securities has been, naturally, a handicap toa group which, taking warning from the experience of Cassandra, usuallyseems constrained to look on the bright side. During the 43 yearperiod under analysis the number of weeks in which the stock marketdeclined almost exactly equalled the number of weeks in which advanceswere recorded, and the total amount of the declines considerablyexceeded the total amount of the advances. Yet we recordedduring this period 2033 bullish, 804 bearish, and 479 doubtful forecasts.Further, we note that in 1028, the only year the market showeda net gain, the excess of bullish over bearish forecasts was smaller thanin any succeeding year. Taking a glaring example, in the rising marketof 1928 the ratio of bullish to bearish forecasts was only four to three.In 1931, when the market declined 54 per cent, there were sixteenbullish forecasts to every three bearish.STATISTICAL INTERPRETATIONS OF RESULTSIn an attempt to illuminate the problem of whether the records of allthese forecasters lay within the limits of pure chance, we compiled24 records, identical with those of the 24 forecasters as to the totalperiod covered, but having purely fortuitous advices applied to randomintervals within these perids. For example, to compile a purely chancerecord to compare with the actual record of a forecaster whose operationscovered 230 weeks from January 1,1928, to June 1,1932, we firstdetermined the average number of changes of advice for such a period,which was 33. Cards numbered from 1to 229 were shuffled, drawn, reshuffled,drawn, in all 33 times. Thus 33 random dates were selectedas of which forecasts were to be changed. The investment policieswhich were to apply to the intervals between those dates were derivedin similar fortuitous fashion, by drawing 33 times from nine cards oneach of which a different one of the nine possible investment policieswas noted.It only remained to relate these random advices to a stock marketindex, cumulate the results, relate them, as we had done with therecords of the actual forecasters, to the average of all chances for theperiod, and subtract 100. Thus we had a list of 21 purely chance fore-

ALFRED COWLES ~ R D 319casting records, shown in Table IV, to compare with the records of theactual prophet's.TABLEIVRESULTSOF RANDOMFORECASTSForecaster Weeks Per cent1. ..................... 230 ..................... f 7 1 . 12. .....................230 ..................... +37.23. .....................230 ..................... +24.24. ....................157 ..................... +19.15. ..................... 230 ..................... f 1 3 . 26. ..................... 105 .................... + 9.27. . . . . . . . . . . . . . . . . . . . . . 230 ..................... + 2 . 78. ..................... 53 ..................... + 2.59. . . . . . . . . . . . . . . . . . . . . . 131 .....................+ 1.3lo. .....................230 .................... f 1.111. ..................... 53 ..................... - .112. ..................... 54 ..................... - .613. ..................... 157 ..................... - 2.514. .....................230 ..................... - 4.615. . . . . . . . . . . . . . . . . . . . . . 43 ..................... - 5.416. ..................... 53 ..................... - 6.117. . . . . . . . . . . . . . . . . . . . . . 230 ..................... -10.518. ..................... 21 .................... -10.919. .....................157 ..................... -11.020. ..................... 105 ..................... -13.021. ..................... 230 ..................... -13.122. ..................... 230 ..................... -14.223. ..................... 69 -18.724. . . . . . . . . . . . . . . . . . . . . 126 ..................... -27.1For easy comparison of the two groups we have prepared Figure 1showing all the records, actual and hypothetical. The chart indicatesthat where forecasting agencies made gains, even the greatest of theselay within limits equalled by the best of our 24 imaginary recordsrepresenting random action at random intervals. But the extremerlosses of the forecasters tended to exceed the losses registered by theleast successful of our 2-1 records of purely chance operations.In any attempt at interpreting the significance of the performancesof the various stock market forecasters we are embarrased by our inabilityto determine how often economic developments occur of sufficientimportance to justify the revision of forecasts. This is tantamountto admitting that we do not know the true number of independentcases, or items, in the time series representing the various forecastingrecords. In these circumstances, probable errors for correlation coefficients,or for normal distributions, cannot constitute very exact measuresof probability JVe do know, however, since we are dealing withweekly publications, that the maximum possible number of forecastingopportunities is 32 a year. 5Ve also know that forecasts, on the average,undergo some degree of revision about 7 times a year. The correlation

320 ECONOMETRICAcoefficients and probable errors, which constitute one of our tests ofprobability, have been worked out on both of these bases.The record of Forecaster Kumber 1 was available to us for a periodof only two years, during which he did not once change his advice. Tiretherefore omitted his record from consideration in our statistical interpretationon the ground that inferences based on it would be relativelyinconclusive. For the correlation test therefore, Forecasters Number2, 3, 22 and 24 were chosen as representing the best and the worstwhose records covered the entire period under analysis. The weeklyforecasts of each of these four were correlated with the first differencesSTOCK MARKET FORECASTING1 24 professional Agenctes 1 ( 24 Random Records 1of the logarit'hms of t'he stock market averages over 44 years. ForecasterNumber 2 had a correlation coefficient of .I51 ;Forecaster Number3, of .107; and Forecast'ers Number 22 and 24, of -.I24 and -.I32respect'ively. The probable error of the best correlation coefficient, withn =230, was .043. The difference in r between Forecast'ers Numbers 1and 3 is about equal t'o this probable error, and r =.I97 is greater t'har4 times the probable error of .043. We have interpreted these data bjthe use of R. A. Fisher's technique, where z= tan h-lr. The best cor.relation r = .197, n =230, was first compared with a t'heoretical r = .000n =230; and then compared with r = -.132, n =230, t'hat is the loweslcorrelat'ion coefficient,.1' z n -3 1/n -31st sample .I97 .200 227 .0044 12nd sample ,000 ,000 227 .00441-Difference .200 Sum ,00882

ALFRED COWLES ~ R D321,188 is to be compared with .200. Since these figures are approximatelyequal, the presumption of skill is slight although the presumption doesexist because of the fact that .I88 is less than .200, the difference betweenthe two values for =. Using R. A. Fisher's technique in the secondcase, that is, comparing the best correlation coefficient r = .I97 withthe lowest correlation coefficient r= -.132, seems to indicate thatthere is a real difference between the two samples. If another samplewere taken from each of these two forecasters, we should expect to findn similar difference between them in favor of the first forecaster withinthe limits of the probable error.We then computed correlation coefficients and probd)le errors forthe data arrived at by taking as our items the periods during whicheach forecast was in force. We thus had 30 items for Forecaster Xumher2, which equalled the number of changes he made in his forecasts,instead of the 230 items which represented the number of weeks fortvhich his record was tabulated. On this basis Forecaster Sumber 2had a correlation coefficient of .479; Forecaster Kumber 3 had a correlationcoefficient of ,245; and Forecasters Number 22 and 24 had correlationcoefficients of -313 and -.206 respectively. The probable errorof the best correlation coefficient, with n=30, was found to be .095.Thus r =.479 was about five times the probable error of .005. The bestrandom forecast had r =.356$- .102, when his changes of position weretaken as the items of the series. When the number of weeks (230), overwhich his random record extends, was used, and this record correlatedwith the first differences of the logarithms of the stock market averages,r =.I25f,044.Deductions as to the significance of the relationships of the variouscorrelation coefficients to the probable errors are rendered inconclusive,not only by our inability to identify the true number of independentcases in each series, but also by the fact that we have not computed asufficient number of the correlation coefficients to enable us to determinethe character of their distribution.Having thus experimented with various correlation tests we thenresorted to measuring the spread of the performances of the individualforecasters by means of frequency distributions of the percentage~~eekly gains and losses of each of six forecasters divided by the averageresult of all possible forecasts. The six chosen were two of the bestactual records, two of the worst actual records, and the best andalmost the worst random records. The series thus arrived at were eachdistributed into several classes ranging from 92.50 per cent to 108.50per cent; these frequencies were plotted and appeared to be reasonablynormal. (See Figure 2.) Averages of each of the percentage frequencydistributions were computed and compared with a theoretical average

322 ECOXOMETRICAFREQUENCY OlSTRlBUTlONSForecaster 2 _ Forecaster 3125 - -too- 50rnqmwr-WOO -~m=3-nQtcao m=$v,~rcooo-arr,~v,~r-rnomaaoaoa""ppooppgA o o o o a o m p ~ g ~ p g p p ~ AForecaster 22 Forecaster 24 -I25100. 75m cn ~ on w r ~ namao m -~ N mg vg m~ a g + ~ w~ og g A%d%%6888szsdZ3h$%

ALFRED COWLES ~ R D323of 100, which represented the average of all random frequency distributions.The probable error of the latter was found to be .086. ForecastersNumber 2 and 3 showed averages of 100.098 and 100.103 respectively;each deviating from the theoretical average by amounts which wereslightly greater than the probable error .086, but considerably less thantwice this probable error. Forecasters Number 22 and 24 had averagesof 99.674 and 99.711 respectively; less than the theoretical average by3 2 6 and .289. Each of these differences was more than three, and lessthan four, times greater than the probable error .086. When a similarfrequency distribution is made for the best purely random forecaster,it is found that the average was equal to 100.213, which is greaterthan that of Forecasters 2 and 3. The deviation from the theoreticalaverage lies within three times the probable error of this theoreticalaverage.1. Sixteen financial services, in making some 7500 recommendationsof individual common stocks for investment during the period fromJanuary 1, 1928, to July 1, 1932, compiled an average record that wasworse than that of the average common stock by 1.43 per cent annually.Statistical tests of the best individual records failed to demonstratethat they exhibited skill, and indicated that they more probablywere results of chance.2. Twenty fire insurance companies in making a similar selection ofsecurities during the years 1928 to 1931, inclusive, achieved an averagerecord 1.20 per cent annually worse than that of the general run ofstocks. The best of these records, since it is not very much more impressivethan the record of the most successful of the sixteen financialservices, fails to exhibit definitely the existence of any skill in investment.3. William Peter Hamilton, editor of the U'all Street Journal, publishingforecasts of the stock market based on the Dow Theory over aperiod of 26 years, from 1904 to 1929, inclusive, achieved a result betterthan what would ordinarily be regarded as a normal investment return,but poorer than the result of a continuous outright investment in representativecommon stocks for this period. On 90 occasions he announcedchanges in the outlook for the market. Forty-five of thesepredictions were successful and 45 unsuccessful.4. Twenty-four financial publications engaged in forecasting thestock market during the 4$ years from January 1,1928, to June 1,1932,failed as a group by 4 per cent per annum to achieve a result as good asthe average of all purely random performances. A review of the variousstatistical tests, applied to the records for this period, of these 24 fore-

324 ECOBOMETRICAcasters, indicates that the most successful records are little, if any,better than what might be expected to result from pure chance. Thereis some evidence, on the other hand, to indicate that the least successfulrecords are worse than what could reasonably be attributed tochance.Cowles Commission foi. Research in Economics

1EFFICIENT MARKETS HYPOTHESISAndrew W. LoTo appear in L. Blume and S. Durlauf, The New Palgrave: A Dictionary of Economics,Second Edition, 2007. New York: Palgrave McMillan.The efficient markets hypothesis (EMH) maintains that market prices fullyreflect all available information. Developed independently by Paul A.Samuelson and Eugene F. Fama in the 1960s, this idea has been appliedextensively to theoretical models and empirical studies of financial securitiesprices, generating considerable controversy as well as fundamental insightsinto the price-discovery process. The most enduring critique comes frompsychologists and behavioural economists who argue that the EMH is basedon counterfactual assumptions regarding human behaviour, that is,rationality. Recent advances in evolutionary psychology and the cognitiveneurosciences may be able to reconcile the EMH with behaviouralanomalies.There is an old joke, widely told among economists, about an economist strolling down thestreet with a companion. They come upon a $100 bill lying on the ground, and as thecompanion reaches down to pick it up, the economist says, ‘Don’t bother – if it were agenuine $100 bill, someone would have already picked it up’. This humorous example ofeconomic logic gone awry is a fairly accurate rendition of the efficient markets hypothesis(EMH), one of the most hotly contested propositions in all the social sciences. It isdisarmingly simple to state, has far-reaching consequences for academic theories andbusiness practice, and yet is surprisingly resilient to empirical proof or refutation. Even afterseveral decades of research and literally thousands of published studies, economists have notyet reached a consensus about whether markets – particularly financial markets – are, in fact,efficient.The origins of the EMH can be traced back to the work of two individuals in the 1960s:Eugene F. Fama and Paul A. Samuelson. Remarkably, they independently developed thesame basic notion of market efficiency from two rather different research agendas. Thesedifferences would propel the them along two distinct trajectories leading to several otherbreakthroughs and milestones, all originating from their point of intersection, the EMH.

2Like so many ideas of modern economics, the EMH was first given form by PaulSamuelson (1965), whose contribution is neatly summarized by the title of his article: ‘Proofthat Properly Anticipated Prices Fluctuate Randomly’. In an informationally efficient market,price changes must be unforecastable if they are properly anticipated, that is, if they fullyincorporate the information and expectations of all market participants. Having developed aseries of linear-programming solutions to spatial pricing models with no uncertainty,Samuelson came upon the idea of efficient markets through his interest in temporal pricingmodels of storable commodities that are harvested and subject to decay. Samuelson’s abidinginterest in the mechanics and kinematics of prices, with and without uncertainty, led him andhis students to several fruitful research agendas including solutions for the dynamic assetallocationand consumption-savings problem, the fallacy of time diversification and logoptimalinvestment policies, warrant and option-pricing analysis and, ultimately, the Blackand Scholes (1973) and Merton (1973) option-pricing models.In contrast to Samuelson’s path to the EMH, Fama’s (1963; 1965a; 1965b, 1970)seminal papers were based on his interest in measuring the statistical properties of stockprices, and in resolving the debate between technical analysis (the use of geometric patternsin price and volume charts to forecast future price movements of a security) and fundamentalanalysis (the use of accounting and economic data to determine a security’s fair value).Among the first to employ modern digital computers to conduct empirical research infinance, and the first to use the term ‘efficient markets’ (Fama, 1965b), Fama operationalizedthe EMH hypothesis – summarized compactly in the epigram ‘prices fully reflect all availableinformation’ – by placing structure on various information sets available to marketparticipants. Fama’s fascination with empirical analysis led him and his students down a verydifferent path from Samuelson’s, yielding significant methodological and empiricalcontributions such as the event study, numerous econometric tests of single- and multi-factorlinear asset-pricing models, and a host of empirical regularities and anomalies in stock, bond,currency and commodity markets.The EMH’s concept of informational efficiency has a Zen-like, counter-intuitiveflavour to it: the more efficient the market, the more random the sequence of price changesgenerated by such a market, and the most efficient market of all is one in which price changesare completely random and unpredictable. This is not an accident of nature, but is in fact thedirect result of many active market participants attempting to profit from their information.Driven by profit opportunities, an army of investors pounce on even the smallestinformational advantages at their disposal, and in doing so they incorporate their information

3into market prices and quickly eliminate the profit opportunities that first motivated theirtrades. If this occurs instantaneously, which it must in an idealized world of ‘frictionless’markets and costless trading, then prices must always fully reflect all available information.Therefore, no profits can be garnered from information-based trading because such profitsmust have already been captured (recall the $100 bill on the ground). In mathematical terms,prices follow martingales.Such compelling motivation for randomness is unique among the social sciences and isreminiscent of the role that uncertainty plays in quantum mechanics. Just as Heisenberg’suncertainty principle places a limit on what we can know about an electron’s position andmomentum if quantum mechanics holds, this version of the EMH places a limit on what wecan know about future price changes if the forces of economic self-interest hold.A decade after Samuelson’s (1965) and Fama’s (1965a; 1965b; 1970) landmark papers,many others extended their framework to allow for risk-averse investors, yielding a‘neoclassical’ version of the EMH where price changes, properly weighted by aggregatemarginal utilities, must be unforecastable (see, for example, LeRoy, 1973; M. Rubinstein,1976; and Lucas, 1978). In markets where, according to Lucas (1978), all investors have‘rational expectations’, prices do fully reflect all available information and marginal-utilityweightedprices follow martingales. The EMH has been extended in many other directions,including the incorporation of non-traded assets such as human capital, state-dependentpreferences, heterogeneous investors, asymmetric information, and transactions costs. But thegeneral thrust is the same: individual investors form expectations rationally, marketsaggregate information efficiently, and equilibrium prices incorporate all available informationinstantaneously.The random walk hypothesisThe importance of the EMH stems primarily from its sharp empirical implications many ofwhich have been tested over the years. Much of the EMH literature before LeRoy (1973) andLucas (1978) revolved around the random walk hypothesis (RWH) and the martingale model,two statistical descriptions of unforecastable price changes that were initially taken to beimplications of the EMH. One of the first tests of the RWH was developed by Cowles andJones (1937), who compared the frequency of sequences and reversals in historical stockreturns, where the former are pairs of consecutive returns with the same sign, and the latterare pairs of consecutive returns with opposite signs. Cootner (1962; 1964), Fama (1963;1965a), Fama and Blume (1966), and Osborne (1959) perform related tests of the RWH and,

4with the exception of Cowles and Jones (who subsequently acknowledged an error in theiranalysis – Cowles, 1960), all of these articles indicate support for the RWH using historicalstock price data.More recently, Lo and MacKinlay (1988) exploit the fact that return variances scalelinearly under the RWH – the variance of a two-week return is twice the variance of a oneweekreturn if the RWH holds – and construct a variance ratio test which rejects the RWH forweekly US stock returns indexes from 1962 to 1985. In particular, they find that variancesgrow faster than linearly as the holding period increases, implying positive serial correlationin weekly returns. Oddly enough, Lo and MacKinlay also show that individual stocksgenerally do satisfy the RWH, a fact that we shall return to below.French and Roll (1986) document a related phenomenon: stock return variances overweekends and exchange holidays are considerably lower than return variances over the samenumber of days when markets are open. This difference suggests that the very act of tradingcreates volatility, which may well be a symptom of Black’s (1986) noise traders.For holding periods much longer than one week – fcor example, three to five years –Fama and French (1988) and Poterba and Summers (1988) find negative serial correlation inUS stock returns indexes using data from 1926 to 1986. Although their estimates of serialcorrelation coefficients seem large in magnitude, there is insufficient data to reject the RWHat the usual levels of significance. Moreover, a number of statistical artifacts documented byKim, Nelson and Startz (1991) and Richardson (1993) cast serious doubt on the reliability ofthese longer-horizon inferences.Finally, Lo (1991) considers another aspect of stock market prices long thought to havebeen a departure from the RWH: long-term memory. Time series with long-term memoryexhibit an unusually high degree of persistence, so that observations in the remote past arenon-trivially correlated with observations in the distant future, even as the time span betweenthe two observations increases. Nature’s predilection towards long-term memory has beenwell-documented in the natural sciences such as hydrology, meteorology, and geophysics,and some have argued that economic time series must therefore also have this property.However, using recently developed statistical techniques, Lo (1991) constructs a test forlong-term memory that is robust to short-term correlations of the sort uncovered by Lo andMacKinlay (1988), and concludes that, despite earlier evidence to the contrary, there is littlesupport for long-term memory in stock market prices. Departures from the RWH can be fullyexplained by conventional models of short-term dependence.

5Variance bounds testsAnother set of empirical tests of the EMH starts with the observation that in a world withoutuncertainty the market price of a share of common stock must equal the present value of allfuture dividends, discounted at the appropriate cost of capital. In an uncertain world, one cangeneralize this dividend-discount model or present-value relation in the natural way: themarket price equals the conditional expectation of the present value of all future dividends,discounted at the appropriate risk-adjusted cost of capital, and conditional on all availableinformation. This generalization is explicitly developed by Grossman and Shiller (1981).LeRoy and Porter (1981) and Shiller (1981) take this as their starting point incomparing the variance of stock market prices to the variance of ex post present values offuture dividends. If the market price is the conditional expectation of present values, then thedifference between the two, that is, the forecast error, must be uncorrelated with theconditional expectation by construction. But this implies that the variance of the ex postpresent value is the sum of the variance of the market price (the conditional expectation) andthe variance of the forecast error. Since volatilities are always non-negative, this variancedecomposition implies that the variance of stock prices cannot exceed the variance of ex postpresent values. Using annual US stock market data from various sample periods, LeRoy andPorter (1981) and Shiller (1981) find that the variance bound is violated dramatically.Although LeRoy and Porter are more circumspect about the implications of such violations,Shiller concludes that stock market prices are too volatile and the EMH must be false.These two papers ignited a flurry of responses which challenged Shiller’s controversialconclusion on a number of fronts. For example, Flavin (1983), Kleidon (1986), and Marshand Merton (1986) show that statistical inference is rather delicate for these variance bounds,and that, even if they hold in theory, for the kind of sample sizes Shiller uses and underplausible data-generating processes the sample variance bound is often violated purely due tosampling variation. These issues are well summarized in Gilles and LeRoy (1991) andMerton (1987).More importantly, on purely theoretical grounds Marsh and Merton (1986) andMichener (1982) provide two explanations for violations of variance bounds that are perfectlyconsistent with the EMH. Marsh and Merton (1986) show that if managers smooth dividends– a well-known empirical phenomenon documented in several studies of dividend policy –and if earnings follow a geometric random walk, then the variance bound is violated intheory, in which case the empirical violations may be interpreted as support for this versionof the EMH.

6Alternatively, Michener constructs a simple dynamic equilibrium model along the linesof Lucas (1978) in which prices do fully reflect all available information at all times butwhere individuals are risk averse, and this risk aversion is enough to cause the variancebound to be violated in theory as well.These findings highlight an important aspect of the EMH that had not been emphasizedin earlier studies: tests of the EMH are always tests of joint hypotheses. In particular, thephrase ‘prices fully reflect all available information’ is a statement about two distinct aspectsof prices: the information content and the price formation mechanism. Therefore, any test ofthis proposition must concern the kind of information reflected in prices, and how thisinformation comes to be reflected in prices.Apart from issues regarding statistical inference, the empirical violation of variancebounds may be interpreted in many ways. It may be a violation of EMH, or a sign thatinvestors are risk averse, or a symptom of dividend smoothing. To choose among thesealternatives, more evidence is required.Overreaction and underreactionA common explanation for departures from the EMH is that investors do not always react inproper proportion to new information. For example, in some cases investors may overreact toperformance, selling stocks that have experienced recent losses or buying stocks that haveenjoyed recent gains. Such overreaction tends to push prices beyond their ‘fair’ or ‘rational’market value, only to have rational investors take the other side of the trades and bring pricesback in line eventually. An implication of this phenomenon is price reversals: what goes upmust come down, and vice versa. Another implication is that contrarian investmentstrategies – strategies in which ‘losers’ are purchased and ‘winners’ are sold – will earnsuperior returns.Both of these implications were tested and confirmed using recent US stock marketdata. For example, using monthly returns of New York Stock Exchange (NYSE) stocks from1926 to 1982, DeBondt and Thaler (1985) document the fact that the winners and losers inone 36-month period tend to reverse their performance over the next 36-month period.Curiously, many of these reversals occur in January (see the discussion below on the ‘Januaryeffect’). Chopra, Lakonishok and Ritter (1992) reconfirm these findings after correcting formarket risk and the size effect. And Lehmann (1990) shows that a zero-net-investmentstrategy in which long positions in losers are financed by short positions in winners almostalways yields positive returns for monthly NYSE/AMEX stock returns data from 1962 to

71985.However, Chan (1988) argues that the profitability of contrarian investment strategiescannot be taken as conclusive evidence against the EMH because there is typically noaccounting for risk in these profitability calculations (although Chopra, Lakonishok andRitter, 1992 do provide risk adjustments, their focus was not on specific trading strategies).By risk-adjusting the returns of a contrarian trading strategy according to the capital assetpricing model, Chan (1988) shows that the expected returns are consistent with the EMH.Moreover, Lo and MacKinlay (1990c) show that at least half of the profits reported byLehmann (1990) are not due to overreaction but rather the result of positive crossautocorrelationsbetween stocks. For example, suppose the returns of two stocks A and B areboth serially uncorrelated but are positively cross-autocorrelated. The lack of serialcorrelation implies no overreaction (which is characterized by negative serial correlation), butpositive cross-autocorrelations yields positive expected returns to contrarian tradingstrategies. The existence of several economic rationales for positive cross-autocorrelation thatare consistent with EMH suggests that the profitability of contrarian trading strategies is notsufficient evidence to conclude that investors overreact.The reaction of market participants to information contained in earningsannouncements also has implications for the EMH. In one of the earliest studies of theinformation content of earnings, Ball and Brown (1968) show that up to 80 per cent of theinformation contained in the earnings ‘surprises’ is anticipated by market prices.However, the more recent article by Bernard and Thomas (1990) argues that investorssometimes underreact to information about future earnings contained in current earnings.This is related to the ‘post-earnings announcement drift’ puzzle first documented by Ball andBrown (1968), in which the information contained in earnings announcement takes severaldays to become fully impounded into market prices. Although such effects are indeedtroubling for the EMH, their economic significance is often questionable – while they mayviolate the EMH in frictionless markets, very often even the smallest frictions – for example,positive trading costs, taxes – can eliminate the profits from trading strategies designed toexploit them.AnomaliesPerhaps the most common challenge to the EMH is the anomaly, a regular pattern in anasset’s returns which is reliable, widely known, and inexplicable. The fact that the pattern isregular and reliable implies a degree of predictability, and the fact that the regularity is

8widely known implies that many investors can take can advantage of it.For example, one of the most enduring anomalies is the ‘size effect’, the apparentexcess expected returns that accrue to stocks of small-capitalization companies – in excess oftheir risks – which was first discovered by Banz (1981). Keim (1983), Roll (1983), andRozeff and Kinney (1976) document a related anomaly: small capitalization stocks tend tooutperform large capitalization stocks by a wide margin over the turn of the calendar year.This so-called ‘January effect’ seems robust to sample period, and is difficult to reconcilewith the EMH because of its regularity and publicity. Other well-known anomalies includethe Value Line enigma (Copeland and Mayers, 1982), the profitability of short-term returnreversalstrategies in US equities (Rosenberg, Reid and Lanstein,1985; Chan, 1988;Lehmann, 1990; and Lo and MacKinlay, 1990c), the profitability of medium-termmomentum strategies in US equities (Jegadeesh, 1990; Chan, Jegadeesh and Lakonishok,1996; and Jegadeesh and Titman, 2001), the relation between price/earnings ratios andexpected returns (Basu, 1977), the volatility of orange juice futures prices (Roll, 1984), andcalendar effects such as holiday, weekend, and turn-of-the-month seasonalities (Lakonishokand Smidt, 1988).What are we to make of these anomalies? On the one hand, their persistence in the faceof public scrutiny seems to be a clear violation of the EMH. After all, most of theseanomalies can be exploited by relatively simple trading strategies, and, while the resultingprofits may not be riskless, they seem unusually profitable relative to their risks (see,especially, Lehmann, 1990).On the other hand, EMH supporters might argue that such persistence is in factevidence in favour of EMH or, more to the point, that these anomalies cannot be exploited toany significant degree because of factors such as risk or transactions costs. Moreover,although some anomalies are currently inexplicable, this may be due to a lack of imaginationon the part of academics, not necessarily a violation of the EMH. For example, recentevidence suggests that the January effect is largely due to ‘bid–ask bounce’, that is, closingprices for the last trading day of December tend to be at the bid price and closing prices forthe first trading day of January tend to be at the ask price. Since small-capitalization stocksare also often low-price stocks, the effects of bid-ask bounce in percentage terms are muchmore pronounced for these stocks – a movement from bid to ask for a $5.00 stock on theNYSE (where the minimum bid-ask spread was $0.125 prior to decimalization in 2000)represents a 2.5 per cent return.Whether or not one can profit from anomalies is a question unlikely to be settled in an

9academic setting. While calculations of ‘paper’ profits of various trading strategies comeeasily to academics, it is virtually impossible to incorporate in a realistic manner importantfeatures of the trading process such as transactions costs (including price impact), liquidity,rare events, institutional rigidities and non-stationarities. The economic value of anomaliesmust be decided in the laboratory of actual markets by investment professionals, over longperiods of time, and even in these cases superior performance and simple luck are easilyconfused.In fact, luck can play another role in the interpretation of anomalies: it can account foranomalies that are not anomalous. Regular patterns in historical data can be found even if noregularities exist, purely by chance. Although the likelihood of finding such spuriousregularities is usually small (especially if the regularity is a very complex pattern), itincreases dramatically with the number of ‘searches’ conducted on the same set of data. Suchdata-snooping biases are illustrated in Brown et al. (1992) and Lo and MacKinlay (1990b) –even the smallest biases can translate into substantial anomalies such as superior investmentreturns or the size effect.Behavioural critiquesThe most enduring critiques of the EMH revolve around the preferences and behaviour ofmarket participants. The standard approach to modelling preferences is to assert that investorsoptimize additive time-separable expected utility functions from certain parametric families –for example, constant relative risk aversion. However, psychologists and experimentaleconomists have documented a number of departures from this paradigm, in the form ofspecific behavioural biases that are ubiquitous to human decision-making under uncertainty,several of which lead to undesirable outcomes for an individual’s economic welfare – forexample, overconfidence (Fischoff and Slovic, 1980; Barber and Odean, 2001; Gervais andOdean, 2001), overreaction (DeBondt and Thaler, 1985), loss aversion (Kahneman andTversky, 1979; Shefrin and Statman, 1985; Odean, 1998), herding (Huberman and Regev,2001), psychological accounting (Tversky and Kahneman, 1981), miscalibration ofprobabilities (Lichtenstein, Fischoff and Phillips, 1982), hyperbolic discounting (Laibson,1997), and regret (Bell, 1982). These critics of the EMH argue that investors are often – if notalways – irrational, exhibiting predictable and financially ruinous behaviour.To see just how pervasive such behavioural biases can be, consider the followingexample which is a slightly modified version of an experiment conducted by twopsychologists, Kahneman and Tversky (1979). Suppose you are offered two investment

10opportunities, A and B: A yields a sure profit of $240,000, and B is a lottery ticket yielding$1 million with a 25 per cent probability and $0 with 75 per cent probability. If you had tochoose between A and B, which would you prefer? Investment B has an expected value of$250,000, which is higher than A’s payoff, but this may not be all that meaningful to youbecause you will receive either $1 million or zero. Clearly, there is no right or wrong choicehere; it is simply a matter of personal preferences. Faced with this choice, most subjectsprefer A, the sure profit, to B, despite the fact that B offers a significant probability ofwinning considerably more. This behaviour is often characterized as ‘risk aversion’ forobvious reasons. Now suppose you are faced with another two choices, C and D: C yields asure loss of $750,000, and D is a lottery ticket yielding $0 with 25 per cent probability and aloss of $1 million with 75 per cent probability. Which would you prefer? This situation is notas absurd as it might seem at first glance; many financial decisions involve choosing betweenthe lesser of two evils. In this case, most subjects choose D, despite the fact that D is morerisky than C. When faced with two choices that both involve losses, individuals seem to be‘risk seeking’, not risk averse as in the case of A versus B.The fact that individuals tend to be risk averse in the face of gains and risk seeking inthe face of losses can lead to some very poor financial decisions. To see why, observe that thecombination of choices A and D is equivalent to a single lottery ticket yielding $240,000 with25 per cent probability and ! $760,000 with 75 per cent probability, whereas thecombination of choices B and C is equivalent to a single lottery ticket yielding $250,000 with25 per cent probability and ! $750,000 with 75 per cent probability. The B and Ccombination has the same probabilities of gains and losses, but the gain is $10,000 higher andthe loss is $10,000 lower. In other words, B and C is formally equivalent to A and D plus asure profit of $10,000. In light of this analysis, would you still prefer A and D?A common response to this example is that it is contrived because the two pairs ofinvestment opportunities were presented sequentially, not simultaneously. However, in atypical global financial institution the London office may be faced with choices A and B andthe Tokyo office may be faced with choices C and D. Locally, it may seem as if there is noright or wrong answer – the choice between A and B or C and D seems to be simply a matterof personal risk preferences – but the globally consolidated financial statement for the entireinstitution will tell a very different story. From that perspective, there is a right and wronganswer, and the empirical and experimental evidence suggests that most individuals tend toselect the wrong answer. Therefore, according to the behaviouralists, quantitative models of

11efficient markets – all of which are predicated on rational choice – are likely to be wrong aswell.Impossibility of efficient marketsGrossman and Stiglitz (1980) go even farther – they argue that perfectly informationallyefficient markets are an impossibility for, if markets are perfectly efficient, there is no profitto gathering information, in which case there would be little reason to trade and marketswould eventually collapse. Alternatively, the degree of market inefficiency determines theeffort investors are willing to expend to gather and trade on information, hence a nondegeneratemarket equilibrium will arise only when there are sufficient profit opportunities,that is, inefficiencies, to compensate investors for the costs of trading and informationgathering. The profits earned by these attentive investors may be viewed as ‘economic rents’that accrue to those willing to engage in such activities. Who are the providers of these rents?Black (1986) gave us a provocative answer: ‘noise traders’, individuals who trade on whatthey consider to be information but which is, in fact, merely noise.The supporters of the EMH have responded to these challenges by arguing that, whilebehavioural biases and corresponding inefficiencies do exist from time to time, there is alimit to their prevalence and impact because of opposing forces dedicated to exploiting suchopportunities. A simple example of such a limit is the so-called ‘Dutch book’, in whichirrational probability beliefs give rise to guaranteed profits for the savvy investor. Consider,for example, an event E , defined as ‘the S&P 500 index drops by five per cent or more nextMonday’, and suppose an individual has the following irrational beliefs: there is a 50 per centprobability that E will occur, and a 75 per cent probability that E will not occur. This isclearly a violation of one of the basic axioms of probability theory – the probabilities of twomutually exclusive and exhaustive events must sum to 1 – but many experimental studieshave documented such violations among an overwhelming majority of human subjects.These inconsistent subjective probability beliefs imply that the individual would bewilling to take both of the following bets B1and B2:B 1 =" $1 if E#$ ! $1 otherwise, B 2 =c" $1 if E#$ ! $3 otherwisewherecE denotes the event ‘not E ’. Now suppose we take the opposite side of both bets,placing $50 on B1and $25 on B2. If E occurs, we lose $50 on B1but gain $75 on B2,yielding a profit of $25. IfcE occurs, we gain $50 on B1and lose $25 on B2, also yielding a

12profit of $25. Regardless of the outcome, we have secured a profit of $25, an ‘arbitrage’ thatcomes at the expense of the individual with inconsistent probability beliefs. Such beliefs arenot sustainable, and market forces – namely, arbitrageurs such as hedge funds and proprietarytrading groups – will take advantage of these opportunities until they no longer exist, that is,until the odds are in line with the axioms of probability theory. (Only when these axioms aresatisfied is arbitrage ruled out. This was conjectured by Ramsey, 1926, and proved rigorouslyby de Finetti, 1937, and Savage, 1954.) Therefore, proponents of the classical EMH arguethat there are limits to the degree and persistence of behavioural biases such as inconsistentprobability beliefs, and substantial incentives for those who can identify and exploit suchoccurrences. While all of us are subject to certain behavioural biases from time to time,according to EMH supporters market forces will always act to bring prices back to rationallevels, implying that the impact of irrational behaviour on financial markets is generallynegligible and, therefore, irrelevant.But this last conclusion relies on the assumption that market forces are sufficientlypowerful to overcome any type of behavioural bias, or equivalently that irrational beliefs arenot so pervasive as to overwhelm the capacity of arbitrage capital dedicated to takingadvantage of such irrationalities. This is an empirical issue that cannot be settledtheoretically, but must be tested through careful measurement and statistical analysis. Theclassic reference by Kindleberger (1989) – where a number of speculative bubbles, financialpanics, manias, and market crashes are described in detail – suggests that the forces ofirrationality can overwhelm the forces of arbitrage capital for months and, in several wellknowncases, years.So what does this imply for the EMH?The current state of the EMHGiven all of the theoretical and empirical evidence for and against the EMH, what can weconclude? Amazingly, there is still no consensus among economists. Despite the manyadvances in the statistical analysis, databases, and theoretical models surrounding the EMH,the main result of all of these studies is to harden the resolve of the proponents of each side ofthe debate.One of the reasons for this state of affairs is the fact that the EMH, by itself, is not awell-defined and empirically refutable hypothesis. To make it operational, one must specifyadditional structure, for example, investors’ preferences or information structure. But then atest of the EMH becomes a test of several auxiliary hypotheses as well, and a rejection of

13such a joint hypothesis tells us little about which aspect of the joint hypothesis is inconsistentwith the data. Are stock prices too volatile because markets are inefficient, or due to riskaversion, or dividend smoothing? All three inferences are consistent with the data. Moreover,new statistical tests designed to distinguish among them will no doubt require auxiliaryhypotheses of their own which, in turn, may be questioned.More importantly, tests of the EMH may not be the most informative means of gaugingthe efficiency of a given market. What is often of more consequence is the efficiency of aparticular market relative to other markets – for example, futures vs. spot markets, auctionvs. dealer markets. The advantages of the concept of relative efficiency, as opposed to the allor-nothingnotion of absolute efficiency, are easy to spot by way of an analogy. Physicalsystems are often given an efficiency rating based on the relative proportion of energy or fuelconverted to useful work. Therefore, a piston engine may be rated at 60 per cent efficiency,meaning that on average 60 per cent of the energy contained in the engine’s fuel is used toturn the crankshaft, with the remaining 40 per cent lost to other forms of work, such as heat,light or noise.Few engineers would ever consider performing a statistical test to determine whether ornot a given engine is perfectly efficient – such an engine exists only in the idealizedfrictionless world of the imagination. But measuring relative efficiency – relative, that is, tothe frictionless ideal – is commonplace. Indeed, we have come to expect such measurementsfor many household products: air conditioners, hot water heaters, refrigerators, and so on.Therefore, from a practical point of view, and in light of Grossman and Stiglitz (1980), theEMH is an idealization that is economically unrealizable, but which serves as a usefulbenchmark for measuring relative efficiency.The desire to build financial theories based on more realistic assumptions has led toseveral new strands of literature, including psychological approaches to risk-taking behaviour(Kahneman and Tversky, 1979; Thaler, 1993; Lo, 1999), evolutionary game theory(Friedman, 1991), agent-based modelling of financial markets (Arthur et al., 1997; Chan etal., 1998), and direct applications of the principles of evolutionary psychology to economicsand finance (Lo, 1999; 2002; 2004; 2005; Lo and Repin, 2002). Although substantiallydifferent in methods and style, these emerging sub-fields are all directed at newinterpretations of the EMH. In particular, psychological models of financial markets focus onthe the manner in which human psychology influences the economic decision-makingprocess as an explanation of apparent departures from rationality. Evolutionary game theorystudies the evolution and steady-state equilibria of populations of competing strategies in

14highly idealized settings. Agent-based models are meant to capture complex learningbehaviour and dynamics in financial markets using more realistic markets, strategies, andinformation structures. And applications of evolutionary psychology provide a reconciliationof rational expectations with the behavioural findings that often seem inconsistent withrationality.For example, in one agent-based model of financial markets (Farmer, 2002), the marketis modelled using a non-equilibrium market mechanism, whose simplicity makes it possibleto obtain analytic results while maintaining a plausible degree of realism. Market participantsare treated as computational entities that employ strategies based on limited information.Through their (sometimes suboptimal) actions they make profits or losses. Profitablestrategies accumulate capital with the passage of time, and unprofitable strategies lose moneyand may eventually disappear. A financial market can thus be viewed as a co-evolvingecology of trading strategies. The strategy is analogous to a biological species, and the totalcapital deployed by agents following a given strategy is analogous to the population of thatspecies. The creation of new strategies may alter the profitability of pre-existing strategies, insome cases replacing them or driving them extinct.Although agent-based models are still in their infancy, the simulations and relatedtheory have already demonstrated an ability to understand many aspects of financial markets.Several studies indicate that, as the population of strategies evolves, the market tends tobecome more efficient, but this is far from the perfect efficiency of the classical EMH. Pricesfluctuate in time with internal dynamics caused by the interaction of diverse tradingstrategies. Prices do not necessarily reflect ‘true values’; if we view the market as a machinewhose job is to set prices properly, the inefficiency of this machine can be substantial.Patterns in the price tend to disappear as agents evolve profitable strategies to exploit them,but this occurs only over an extended period of time, during which substantial profits may beaccumulated and new patterns may appear.The adaptive markets hypothesisThe methodological differences between mainstream and behavioural economics suggest thatan alternative to the traditional deductive approach of neoclassical economics may benecessary to reconcile the EMH with its behavioural critics. One particularly promisingdirection is to view financial markets from a biological perspective and, specifically, withinan evolutionary framework in which markets, instruments, institutions and investors interactand evolve dynamically according to the ‘law’ of economic selection. Under this view,

15financial agents compete and adapt, but they do not necessarily do so in an optimal fashion(see Farmer and Lo, 1999; Farmer, 2002; Lo, 2002; 2004; 2005).This evolutionary approach is heavily influenced by recent advances in the emergingdiscipline of ‘evolutionary psychology’, which builds on the seminal research of E.O. Wilson(1975) in applying the principles of competition, reproduction, and natural selection to socialinteractions, yielding surprisingly compelling explanations for certain kinds of humanbehaviour, such as altruism, fairness, kin selection, language, mate selection, religion,morality, ethics and abstract thought (see, for example, Barkow, Cosmides and Tooby, 1992;Gigerenzer, 2000). ‘Sociobiology’ is the rubric that Wilson (1975) gave to these powerfulideas, which generated a considerable degree of controversy in their own right, and the sameprinciples can be applied to economic and financial contexts. In doing so, we can fullyreconcile the EMH with all of its behavioural alternatives, leading to a new synthesis: theadaptive markets hypothesis (AMH).Students of the history of economic thought will no doubt recall that Thomas Malthusused biological arguments – the fact that populations increase at geometric rates whereasnatural resources increase at only arithmetic rates – to arrive at rather dire economicconsequences, and that both Darwin and Wallace were influenced by these arguments (seeHirshleifer, 1977, for further details). Also, Joseph Schumpeter’s view of business cycles,entrepreneurs and capitalism have an unmistakeable evolutionary flavour to them; in fact, hisnotions of ‘creative destruction’ and ‘bursts’ of entrepreneurial activity are similar in spirit tonatural selection and Eldredge and Gould’s (1972) notion of ‘punctuated equilibrium’. Morerecently, economists and biologists have begun to explore these connections in several veins:direct extensions of sociobiology to economics (Becker, 1976; Hirshleifer, 1977);evolutionary game theory (Maynard Smith, 1982); evolutionary economics (Nelson andWinter, 1982); and economics as a complex system (Anderson, Arrow and Pines, 1988). Andpublications like the Journal of Evolutionary Economics and the Electronic Journal ofEvolutionary Modeling and Economic Dynamics now provide a home for research at theintersection of economics and biology.Evolutionary concepts have also appeared in a number of financial contexts. Forexample, Luo (1995) explores the implications of natural selection for futures markets, andHirshleifer and Luo (2001) consider the long-run prospects of overconfident traders in acompetitive securities market. The literature on agent-based modelling pioneered by Arthur etal. (1997), in which interactions among software agents programmed with simple heuristicsare simulated, relies heavily on evolutionary dynamics. And at least two prominent

16practitioners have proposed Darwinian alternatives to the EMH. In a chapter titled ‘TheEcology of Markets’, Niederhoffer (1997, ch. 15) likens financial markets to an ecosystemwith dealers as ‘herbivores’, speculators as ‘carnivores’, and floor traders and distressedinvestors as ‘decomposers’. And Bernstein (1998) makes a compelling case for activemanagement by pointing out that the notion of equilibrium, which is central to the EMH, israrely realized in practice and that market dynamics are better explained by evolutionaryprocesses.Clearly the time is now ripe for an evolutionary alternative to market efficiency.To that end, in the current context of the EMH we begin, as Samuelson (1947) did, withthe theory of the individual consumer. Contrary to the neoclassical postulate that individualsmaximize expected utility and have rational expectations, an evolutionary perspective makesconsiderably more modest claims, viewing individuals as organisms that have been honed,through generations of natural selection, to maximize the survival of their genetic material(see, for example, Dawkins, 1976). While such a reductionist approach can quicklydegenerate into useless generalities – for example, the molecular biology of economicbehaviour – nevertheless, there are valuable insights to be gained from the broader biologicalperspective. Specifically, this perspective implies that behaviour is not necessarily intrinsicand exogenous, but evolves by natural selection and depends on the particular environmentalthrough which selection occurs. That is, natural selection operates not only upon geneticmaterial but also upon social and cultural norms in homo sapiens; hence Wilson’s term‘sociobiology’.To operationalize this perspective within an economic context, consider the idea of ‘boundedrationality’ first espoused by Nobel-prize-winning economist Herbert Simon. Simon (1955)suggested that individuals are hardly capable of the kind of optimization that neoclassicaleconomics calls for in the standard theory of consumer choice. Instead, he argued that,because optimization is costly and humans are naturally limited in their computationalabilities, they engage in something he called ‘satisficing’, an alternative to optimization inwhich individuals make choices that are merely satisfactory, not necessarily optimal. In otherwords, individuals are bounded in their degree of rationality, which is in sharp contrast to thecurrent orthodoxy – rational expectations – where individuals have unbounded rationality(the term ‘hyper-rational expectations’ might be more descriptive). Unfortunately, althoughthis idea garnered a Nobel Prize for Simon, it had relatively little impact on the economicsprofession. (However, his work is now receiving greater attention, thanks in part to thegrowing behavioural literature in economics and finance. See, for example, Simon, 1982;

17Sargent, 1993; A. Rubinstein, 1998; Gigerenzer and Selten, 2001.) Apart from thesociological factors discussed above, Simon’s framework was commonly dismissed becauseof one specific criticism: what determines the point at which an individual stops optimizingand reaches a satisfactory solution? If such a point is determined by the usual cost–benefitcalculation underlying much of microeconomics (that is, optimize until the marginal benefitsof the optimum equals the marginal cost of getting there), this assumes the optimal solution isknown, which would eliminate the need for satisficing. As a result, the idea of boundedrationality fell by the wayside, and rational expectations has become the de facto standard formodelling economic behaviour under uncertainty.An evolutionary perspective provides the missing ingredient in Simon’s framework.The proper response to the question of how individuals determine the point at which theiroptimizing behaviour is satisfactory is this: such points are determined not analytically butthrough trial and error and, of course, natural selection. Individuals make choices based onpast experience and their ‘best guess’ as to what might be optimal, and they learn byreceiving positive or negative reinforcement from the outcomes. If they receive no suchreinforcement, they do not learn. In this fashion, individuals develop heuristics to solvevarious economic challenges, and, as long as those challenges remain stable, the heuristicswill eventually adapt to yield approximately optimal solutions to them.If, on the other hand, the environment changes, then it should come as no surprise thatthe heuristics of the old environment are not necessarily suited to the new. In such cases, weobserve ‘behavioural biases’ – actions that are apparently ill-advised in the context in whichwe observe them. But rather than labelling such behaviour ‘irrational’, it should berecognized that suboptimal behaviour is not unlikely when we take heuristics out of theirevolutionary context. A more accurate term for such behaviour might be ‘maladaptive’. Theflopping of a fish on dry land may seem strange and unproductive, but under water the samemotions are capable of propelling the fish away from its predators.By coupling Simon’s notion of bounded rationality and satisficing with evolutionarydynamics, many other aspects of economic behaviour can also be derived. Competition,cooperation, market-making behaviour, general equilibrium, and disequilibrium dynamics areall adaptations designed to address certain environmental challenges for the human species,and by viewing them through the lens of evolutionary biology we can better understand theapparent contradictions between the EMH and the presence and persistence of behaviouralbiases.Specifically, the adaptive markets hypothesis can be viewed as a new version of the

18EMH, derived from evolutionary principles. Prices reflect as much information as dictated bythe combination of environmental conditions and the number and nature of ‘species’ in theeconomy or, to use the appropriate biological term, the ecology. By ‘species’ I mean distinctgroups of market participants, each behaving in a common manner. For example, pensionfunds may be considered one species; retail investors, another; market-makers, a third; andhedge-fund managers, a fourth. If multiple species (or the members of a single highlypopulous species) are competing for rather scarce resources within a single market, thatmarket is likely to be highly efficient – for example, the market for 10-Year US TreasuryNotes reflects most relevant information very quickly indeed. If, on the other hand, a smallnumber of species are competing for rather abundant resources in a given market, that marketwill be less efficient – for example, the market for oil paintings from the Italian Renaissance.Market efficiency cannot be evaluated in a vacuum, but is highly context-dependent anddynamic, just as insect populations advance and decline as a function of the seasons, thenumber of predators and prey they face, and their abilities to adapt to an ever-changingenvironment.The profit opportunities in any given market are akin to the amount of food and waterin a particular local ecology – the more resources present, the less fierce the competition. Ascompetition increases, either because of dwindling food supplies or an increase in the animalpopulation, resources are depleted which, in turn, causes a population decline eventually,decreasing the level of competition and starting the cycle again. In some cases cyclesconverge to corner solutions, that is, certain species become extinct, food sources arepermanently exhausted, or environmental conditions shift dramatically. By viewing economicprofits as the ultimate food source on which market participants depend for their survival, thedynamics of market interactions and financial innovation can be readily derived.Under the AMH, behavioural biases abound. The origins of such biases are heuristicsthat are adapted to non-financial contexts, and their impact is determined by the size of thepopulation with such biases versus the size of competing populations with more effectiveheuristics. During the autumn of 1998, the desire for liquidity and safety by a certainpopulation of investors overwhelmed the population of hedge funds attempting to arbitragesuch preferences, causing those arbitrage relations to break down. However, in the years priorto August 1998 fixed-income relative-value traders profited handsomely from these activities,presumably at the expense of individuals with seemingly ‘irrational’ preferences (in fact,such preferences were shaped by a certain set of evolutionary forces, and might be quiterational in other contexts). Therefore, under the AMH, investment strategies undergo cycles

19of profitability and loss in response to changing business conditions, the number ofcompetitors entering and exiting the industry, and the type and magnitude of profitopportunities available. As opportunities shift, so too will the affected populations. Forexample, after 1998 the number of fixed-income relative-value hedge funds declineddramatically – because of outright failures, investor redemptions, and fewer start-ups in thissector – but many have reappeared in recent years as performance for this type of investmentstrategy has improved.Even fear and greed – the two most common culprits in the downfall of rationalthinking according to most behaviouralists – are the product of evolutionary forces, adaptivetraits that enhance the probability of survival. Recent research in the cognitive neurosciencesand economics, now coalescing into the discipline known as ‘neuroeconomics’, suggests animportant link between rationality in decision-making and emotion (Grossberg and Gutowski,1987; Damasio, 1994; Elster, 1998; Lo and Repin, 2002; and Loewenstein, 2000), implyingthat the two are not antithetical but in fact complementary. For example, contrary to thecommon belief that emotions have no place in rational financial decision-making processes,Lo and Repin (2002) present preliminary evidence that physiological variables associatedwith the autonomic nervous system are highly correlated with market events even for highlyexperienced professional securities traders. They argue that emotional responses are asignificant factor in the real-time processing of financial risks, and that an importantcomponent of a professional trader’s skills lies in his or her ability to channel emotion,consciously or unconsciously, in specific ways during certain market conditions.This argument often surprises economists because of the link between emotion andbehavioural biases, but a more sophisticated view of the role of emotions in human cognitionshows that they are central to rationality (see, for example, Damasio, 1994; Rolls, 1999). Inparticular, emotions are the basis for a reward-and-punishment system that facilitates theselection of advantageous behaviour, providing a numeraire for animals to engage in a ‘cost–benefit analysis’ of the various actions open to them (Rolls, 1999, ch. 10.3). From anevolutionary perspective, emotion is a powerful adaptation that dramatically improves theefficiency with which animals learn from their environment and their past (see Damasio,1994). These evolutionary underpinnings are more than simple speculation in the context offinancial market participants. The extraordinary degree of competitiveness of global financialmarkets and the outsize rewards that accrue to the ‘fittest’ traders suggest that Darwinianselection – ’survival of the richest’, to be precise – is at work in determining the typicalprofile of the successful trader. After all, unsuccessful traders are eventually eliminated from

20the population after suffering a certain level of losses.The new paradigm of the AMH is still under development, and certainly requires agreat deal more research to render it ‘operationally meaningful’ in Samuelson’s sense.However, even at this early stage it is clear that an evolutionary framework is able toreconcile many of the apparent contradictions between efficient markets and behaviouralexceptions. The former may be viewed as the steady-state limit of a population with constantenvironmental conditions, and the latter involves specific adaptations of certain groups thatmay or may not persist, depending on the particular evolutionary paths that the economyexperiences. More specific implications may be derived through a combination of deductiveand inductive inference – for example, theoretical analysis of evolutionary dynamics,empirical analysis of evolutionary forces in financial markets, and experimental analysis ofdecision-making at the individual and group level.For example, one implication is that, to the extent that a relation between risk andreward exists, it is unlikely to be stable over time. Such a relation is determined by therelative sizes and preferences of various populations in the market ecology, as well asinstitutional aspects such as the regulatory environment and tax laws. As these factors shiftover time, any risk–reward relation is likely to be affected. A corollary of this implication isthat the equity risk premium is also time-varying and path-dependent. This is not sorevolutionary an idea as it might first appear – even in the context of a rational expectationsequilibrium model, if risk preferences change over time, then the equity risk premium mustvary too. The incremental insight of the AMH is that aggregate risk preferences are notimmutable constants, but are shaped by the forces of natural selection. For example, untilrecently US markets were populated by a significant group of investors who had neverexperienced a genuine bear market – this fact has undoubtedly shaped the aggregate riskpreferences of the US economy, just as the experience since the bursting of the technologybubble in the early 2000s has affected the risk preferences of the current population ofinvestors. In this context, natural selection determines who participates in marketinteractions; those investors who experienced substantial losses in the technology bubble aremore likely to have exited the market, leaving a markedly different population of investors.Through the forces of natural selection, history matters. Irrespective of whether prices fullyreflect all available information, the particular path that market prices have taken over thepast few years influences current aggregate risk preferences. Among the three fundamentalcomponents of any market equilibrium – prices, probabilities, and preferences – preferencesis clearly the most fundamental and least understood. Several large bodies of research have

21developed around these issues – in economics and finance, psychology, operations research(also called ‘decision sciences’) and, more recently, brain and cognitive sciences – and manynew insights are likely to flow from synthesizing these different strands of research into amore complete understanding of how individuals make decisions (see Starmer, 2000, for anexcellent review of this literature). Simon’s (1982) seminal contributions to this literature arestill remarkably timely and their implications have yet to be fully explored.ConclusionsMany other practical insights and potential breakthroughs can be derived from shifting ourmode of thinking in financial economics from the physical to the biological sciences.Although evolutionary ideas are not yet part of the financial mainstream, the hope is that theywill become more commonplace as they demonstrate their worth – ideas are also subject to‘survival of the fittest’. No one has illustrated this principal so well as Harry Markowitz, thefather of modern portfolio theory and a Nobel laureate in economics in 1990. In describinghis experience as a Ph.D. student on the eve of his graduation, he wrote in his Nobel address(Markowitz, 1991, p. 476):. . . [W]hen I defended my dissertation as a student in the Economics Department ofthe University of Chicago, Professor Milton Friedman argued that portfolio theory wasnot Economics, and that they could not award me a Ph.D. degree in Economics for adissertation which was not Economics. I assume that he was only half serious, sincethey did award me the degree without long debate. As to the merits of his arguments, atthis point I am quite willing to concede: at the time I defended my dissertation,portfolio theory was not part of Economics. But now it is.In light of the sociology of the EMH controversy (see, for example, Lo, 2004), thedebate is likely to continue. However, despite the lack of consensus in academia and industry,the ongoing dialogue has given us many new insights into the economic structure of financialmarkets. If, as Paul Samuelson has suggested, financial economics is the crown jewel of thesocial sciences, then the EMH must account for half the facets.Andrew W. LoSee also asset price anomalies; bounded rationality; financial market anomalies; information

22economics; rational expectationsI thank John Cox, Gene Fama, Bob Merton, and Paul Samuelson for helpful discussions.BibliographyAnderson, P. Arrow, K. and Pines, D.eds. 1988. The Economy as an Evolving ComplexSystem. Reading, MA: Addison-Wesley Publishing Company.Arthur, B. Holland, J. LeBaron, B. Palmer R. and P. Tayler. 1997. Asset pricing underendogenous expectations in an artificial stock market. In The Economy as an EvolvingComplex System II, ed. B. Arthur, S. Durlauf, and D. Lane Reading, MA: Addison Wesley.Ball, R. and Brown, P. 1968. An empirical evaluation of accounting income numbers.Journal of Accounting Research 6, 159–78.Banz, R. 1981. The relationship between return and market value of common stock. Journalof Financial Economics 9, 3–18.Barber, B. and Odean, T. 2001. Boys will be boys: gender, overconfidence, and commonstock investment. Quarterly Journal of Economics 116, 261–29.Barkow, J. Cosmides, L. and Tooby, J. 1992. The Adapted Mind: Evolutionary Psychologyand the Generation of Culture. Oxford: Oxford University Press.Basu, S. 1977. The investment performance of common stocks in relation to their price–earnings ratios: a test of the efficient market hypothesis. Journal of Finance 32, 663–82.Becker, G. 1976. Altruism, egoism, and genetic fitness: economics and sociobiology.Journal of Economic Literature 14, 817–26.Bell, D. 1982. Risk premiums for decision regret. Management Science 29, 1156–66.Bernard, V. and Thomas, J. 1990. Evidence that stock prices do not fully reflect theimplications of current earnings for future earnings. Journal of Accounting and Economics13, 305–40.Bernstein, P. 1998. Why the efficient market offers hope to active management. InEconomics and Portfolio Strategy, 1 October. New York: Peter Bernstein, Inc.Black, F. 1986. Noise. Journal of Finance 41, 529–44.Black, F. and Scholes, M. 1973. Pricing of options and corporate liabilities. Journal ofPolitical Economy 81, 637–54.

23Brown, S. Goetzmann, W. Ibbotson, R. and Ross, S. 1992. Survivorship bias in performancestudies. Review of Financial Studies 5, 553–80.Campbell, J. and Shiller, R. 1988. The dividend–price ratio and expectations of futuredividends and discount factors. Review of Financial Studies 1, 195–228.Chan, K. 1988. On the contrarian investment strategy. Journal of Business 61, 147–64.Chan, L., Jegadeesh, N. and Lakonishok, J. 1996. Momentum strategies. Journal of Finance51, 1681–713.Chan, N., LeBaron, B., Lo, A. and Poggio, T. 1998. Information Dissemination andAggregation in Asset Markets with Simple Intelligent Traders. Laboratory TechnicalMemorandum No. 1646. Cambridge, MA: MIT Artificial Intelligence.Chopra, N. Lakonishok, J. and Ritter, J. 1992. Measuring Abnormal Performance: Do StocksOverreact? Journal of Financial Economics 31, 235–86.Cootner, P. 1962. Stock prices: random vs. systematic changes. Industrial ManagementReview 3, 24–45.Cootner, P. 1964. The Random Character of Stock Market Prices. London: RiskPublications.Copeland, T. and Mayers, D. 1982. The Value Line enigma (1965–1978): a case study ofperformance evaluation issues. Journal of Financial Economics 10, 289–322.Cowles, A. 1960. A revision of previous conclusions regarding stock price behavior.Econometrica 28, 909–15.Cowles, A. and Jones, H. 1937. Some a posteriori probabilities in stock market action.Econometrica 5, 280–294.Damasio, A. 1994. Descartes’ Error: Emotion, Reason, and the Human Brain. New York:Avon Books.Dawkins, R. 1976. The Selfish Gene. Oxford: Oxford University Press.de Finetti, B. 1937. La Prévision: Ses Lois Logiques, Ses Sources Subjectives. Annales del’Institut Henri Poincaré 7, 1–68. English translation in Studies in Subjective Probability, ed.H. Kyburg and H. Smokler. New York: John Wiley & Sons, 1964.DeBondt, W. and Thaler, R. 1985. Does the stock market overreact?. Journal of Finance 40,793–807.Eldredge, N. and Gould, S. 1972. Punctuated equilibria: an alternative to phyletic gradualism.In Models in Paleobiology, ed. T. Schopf. San Francisco: Freeman, Cooper.Elster, J. 1998. Emotions and economic theory. Journal of Economic Literature 36, 47–74.Fama, E. 1963. Mandelbrot and the stable Paretian hypothesis. Journal of Business 36, 420–

2429.Fama, E. 1965a. The behavior of stock market prices. Journal of Business 38, 34–105.Fama, E. 1965b. Random walks in stock market prices. Financial Analysts Journal 21, 55–9.Fama, E. 1970. Efficient capital markets: a review of theory and empirical work. Journal ofFinance 25, 383–417.Fama, E. and Blume, M. 1966. Filter rules and stock market trading profits. Journal ofBusiness 39, 226–41.Fama, E. and French, K.1988. Permanent and temporary components of stock prices.Journal of Political Economy 96, 246–73.Farmer, D. 2002. Market force, ecology and evolution. Industrial and Corporate Change11, 895–953.Farmer, D. and Lo, A. 1999. Frontiers of finance: evolution and efficient markets.Proceedings of the National Academy of Sciences 96, 9991–2.Fischoff, B. and Slovic, P. 1980. A little learning...: confidence in multicue judgment tasks.In Attention and Performance, VIII, ed. R. Nickerson Hillsdale, NJ: Erlbaum.Flavin, M. 1983. Excess volatility in the financial markets: a reassessment of the empiricalevidence. Journal of Political Economy 91, 929–56.French, K. and Roll, R. 1986. Stock return variances: the arrival of information and thereaction of traders. Journal of Financial Economics 17, 5–26.Friedman, D. 1991. Evolutionary games in economics. Econometrica 59, 637–66.Gervais, S. and Odean, T. 2001. Learning to be overconfident. Review of Financial Studies14, 1–27.Gigerenzer, G. 2000, Adaptive Thinking: Rationality in the Real World. Oxford: OxfordUniversity Press.Gigerenzer, G. and Selten, R. 2001, Bounded Rational: The Adaptive Toolbox. Cambridge,MA: MIT Press.Gilles, C. and LeRoy, S. 1991. Econometric aspects of the variance-bounds tests: a survey.Review of Financial Studies 4, 753–92.Grossberg, S. and Gutowski, W. 1987. Neural dynamics of decision making under risk:affective balance and cognitive-emotional interactions. Psychological Review 94, 300–18.Grossman, S. and Shiller, R. 1981. The determinants of the variability of stock market prices.American Economic Review 71, 222–7.Grossman, S. and Stiglitz, J. 1980. On the impossibility of informationally efficient markets.

25American Economic Review 70, 393–408.Hirshleifer, J. 1977. Economics from a biological viewpoint. Journal of Law and Economics20, 1–52.Hirshleifer, D. and Luo, G. 2001. On the survival of overconfident traders in a competitivesecurities market. Journal of Financial Markets 4, 73–84.Huberman, G. and Regev, T. 2001. Contagious speculation and a cure for cancer: a noneventthat made stock prices soar. Journal of Finance 56, 387–96.Jegadeesh, N. 1990. Evidence of predictable behavior of security returns. Journal ofFinance 45, 881–98.Jegadeesh, N. and Titman, S. 2001. Profitability of momentum strategies: an evaluation ofalternative explanations. Journal of Finance 56, 699–720.Kahneman, D. and Tversky, A. 1979. Prospect theory: an analysis of decision under risk.Econometrica 47, 263–91.Keim, D. 1983. Size-related anomalies and stock return seasonality: further empiricalevidence. Journal of Financial Economics 12, 13–32.Kim, M., Nelson, C. and Startz, R. 1991. Mean reversion in stock prices? a reappraisal of theempirical evidence. Review of Economic Studies 58, 515–28.Kindleberger, C. 1989. Manias, Panics, and Crashes: A History of Financial Crises. NewYork: Basic Books.Kleidon, A. 1986. Variance bounds tests and stock price valuation models. Journal ofPolitical Economy 94, 953–1001.Laibson, D. 1997. Golden eggs and hyperbolic discounting. Quarterly Journal of Economics62, 443–77.Lakonishok, J. and Smidt, S. 1988. Are seasonal anomalies real? A ninety-year perspective.Review of Financial Studies 1, 403–25.Lehmann, B. 1990. Fads, martingales, and market efficiency. Quarterly Journal ofEconomics 105, 1–28.Leroy, S. 1973. Risk aversion and the martingale property of stock returns. InternationalEconomic Review 14, 436–46.LeRoy, S. and Porter, R.1981. The present value relation: tests based on variance bounds.Econometrica 49, 555–74.Lichtenstein, S., Fischoff, B. and Phillips, L. 1982. Calibration of probabilities: the state ofthe art to 1980. In Judgment Under Uncertainty: Heuristics and Biases, ed. D. Kahneman, P.Slovic and A. Tversky. Cambridge: Cambridge University Press.

26Lo, A. 1991. Long-term memory in stock market prices. Econometrica 59, 1279–313.Lo, A., ed. 1997. Market Efficiency: Stock Market Behavior in Theory and Practice, 2 vols.Cheltenham: Edward Elgar Publishing Company.Lo, A. 1999. The three P’s of total risk management. Financial Analysts Journal 55, 87–129.Lo, A. 2001. Risk management for hedge funds: introduction and overview. to appear inFinancial Analysts Journal 57, 16–33.Lo, A. 2002. Bubble, rubble, finance in trouble? Journal of Psychology and FinancialMarkets 3, 76–86.Lo, A. 2004. The adaptive markets hypothesis: market efficiency from an evolutionaryperspective. Journal of Portfolio Management 30, 15–29.Lo, A. 2005. Reconciling efficient markets with behavioral finance: the adaptive marketshypothesis. Journal of Investment Consulting 7, 21–44.Lo, A. and MacKinlay, C. 1988. Stock market prices do not follow random walks: evidencefrom a simple specification test. Review of Financial Studies 1, 41–66.Lo, A. and MacKinlay, C. 1990a. An econometric analysis of nonsynchronous trading.Journal of Econometrics 45, 181–212.Lo, A. and MacKinlay, C. 1990b. Data snooping biases in tests of financial asset pricingmodels. Review of Financial Studies 3, 431–68.Lo, A. and MacKinlay, C. 1990c. When are contrarian profits due to stock marketoverreaction? Review of Financial Studies 3, 175–206.Lo, A. and MacKinlay, C. 1999. A Non-Random Walk Down Wall Street. Princeton, NJ:Princeton University Press.Lo, A. and Repin, D. 2002. The psychophysiology of real-time financial risk processing.Journal of Cognitive Neuroscience 14, 323–39.Loewenstein, G. 2000. Emotions in economic theory and economic behavior. AmericanEconomic Review 90, 426–32.Lucas, R. 1978. Asset prices in an exchange economy. Econometrica 46, 1429–46.Luo, G. 1995. Evolution and market competition. Journal of Economic Theory 67, 223–50.Markowitz, H. 1991. Foundations of portfolio theory. Journal of Finance 46, 469–77.Marsh, T. andMerton, R. 1986. Dividend variability and variance bounds tests for therationality of stock market prices. American Economic Review 76, 483–98.Maynard Smith, J. 1982, Evolution and the Theory of Games. Cambridge: CambridgeUniversity Press.

27Merton, R. 1973. Theory of rational option pricing. Bell Journal of Economics andManagement Science 4, 141–83.Merton, R. 1987. On the current state of the stock market rationality hypothesis. InMacroeconomics and Finance: Essays in Honor of Franco Modigliani, ed. R. Dornbusch, S.Fischer and J. Bossons. Cambridge, MA: MIT Press.Michener, R. 1982. Variance bounds in a simple model of asset pricing. Journal of PoliticalEconomy 90, 166–75.Nelson, R. and Winter, S. 1982. An Evolutionary Theory of Economic Change. Cambridge,MA: Belknap Press of Harvard University Press.Niederhoffer, V. 1997. Education of a Speculator. New York: John Wiley & Sons.Odean, T. 1998. Are investors reluctant to realize their losses?. Journal of Finance 53,1775–98.Osborne, M. 1959. Brownian motion in the stock market. Operations Research 7, 145–73.Poterba, J. and Summers, L. 1988. Mean reversion in stock returns: evidence andimplications. Journal of Financial Economics 22, 27–60.Ramsey, F. 1926. Truth and probability. In Foundations of Mathematics and Other LogicalEssays, ed. R. Braithwaite. New York: Harcourt Brace & Co.Richardson, M. 1993. Temporary components of stock prices: a skeptic’s view. Journal ofBusiness and Economics Statistics 11, 199–207.Roberts, H. 1959. Stock-market ‘patterns’ and financial analysis: methodologicalsuggestions. Journal of Finance 14, 1–10.Roberts, H. 1967. Statistical versus clinical prediction of the stock market. Unpublishedmanuscript, Center for Research in Security Prices, University of Chicago.Roll, R. 1983. Vas is das? The turn-of-the-year effect and the return premia of small firms.Journal of Portfolio Management 9, 18–28.Roll, R. 1984. Orange juice and weather. American Economic Review 74, 861–80.Rolls, E. 1999. The Brain and Emotion. Oxford: Oxford University Press.Rosenberg, B., Reid, K. and Lanstein, R. 1985. Persuasive evidence of market inefficiency.Journal of Portfolio Management 11, 9–17.Rozeff, M. and Kinney, W., Jr. 1976. Capital market seasonality: the case of stock returns.Journal of Financial Economics 3, 379–402.Rubinstein, A. 1998. Modeling Bounded Rationality. Cambridge, MA: MIT Press.Rubinstein, M. 1976. The valuation of uncertain income streams and the pricing of options.Bell Journal of Economics 7, 407–25.

28Samuelson, P. 1947. Foundations of Economics Analysis. Cambridge, MA: HarvardUniversity Press.Samuelson, P. 1965. Proof that properly anticipated prices fluctuate randomly. IndustrialManagement Review 6, 41–9.Sargent, T. 1993. Bounded Rationality in Macroeconomics. Oxford: Clarendon Press.Savage, L. 1954. Foundations of Statistics. New York: John Wiley & Sons.Schumpeter, J. 1939. Business Cycles: A Theoretical, Historical, And Statistical Analysis ofthe Capitalist Process. New York: McGraw-Hill.Shefrin, M. and Statman, M. 1985. The disposition to sell winners too early and ride loserstoo long: theory and evidence. Journal of Finance 40, 777–90.Shiller, R. 1981. Do stock prices move too much to be justified by subsequent changes individends? American Economic Review 71, 421–36.Simon, H. 1955. A behavioral model of rational choice. Quarterly Journal of Economics 69,99–118.Simon, H. 1982. Models of Bounded Rationality, 2 vols. Cambridge, MA: MIT Press.Starmer, C. 2000. Developments in non-expected utility theory: the hunt for a descriptivetheory of choice under risk. Journal of Economic Literature 38, 332–82.Thaler, R., ed. 1993, Advances in Behavioral Finance. New York: Russell Sage Foundation.Tversky, A. and Kahneman, D.1981. The framing of decisions and the psychology of choice.Science 211, 453–8.Wilson, E. 1975, Sociobiology: The New Synthesis. Cambridge, MA: Belknap Press ofHarvard University Press.

Maps of Bounded Rationality: Psychology for Behavioral EconomicsDaniel KahnemanThe American Economic Review, Vol. 93, No. 5. (Dec., 2003), pp. 1449-1475.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28200312%2993%3A5%3C1449%3AMOBRPF%3E2.0.CO%3B2-%23The American Economic Review is currently published by American Economic Association.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/aea.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgMon Jan 14 13:57:31 2008

Maps of Bounded Rationality:Psychology for Behavioral ~conomics~The work cited by the Nobel committee wasdone jointly with Amos Tversky (1937-1996)during a long and unusually close collaboration.Together, we explored the psychology of intuitivebeliefs and choices and examined theirbounded rationality. Herbert A. Simon (1955,1979) had proposed much earlier that decisionmakers should be viewed as boundedly rational,and had offered a model in which utility maximizationwas replaced by satisficing. Our researchattempted to obtain a map of boundedrationality, by exploring the systematic biasesthat separate the beliefs that people have and thechoices they make from the optimal beliefs andchoices assumed in rational-agent models. Therational-agent model was our starting point andthe main source of our null hypotheses, butTversky and I viewed our research primarily asa contribution to psychology, with a possiblecontribution to economics as a secondary benefit.We were drawn into the interdisciplinaryconversation by economists who hoped thatpsychology could be a useful source of assumptionsfor economic theorizing, and indirectly asource of hypotheses for economic research(Richard H. Thaler, 1980, 1991, 1992). TheseThis article is a revised version of the lecture DanielKahneman delivered in Stockholm, Sweden, on December8, 2002, when he received the Bank of Sweden Prize inEconomic Sciences in Memory of Alfred Nobel. The articleis copyright 0The Nobel Foundation 2002 and is publishedhere with the permission of the Nobel Foundation.* Woodrow Wilson School, Princeton University,Princeton, NJ 08544 (e-mail: Kahneman@princeton.edu).This essay revisits problems that Amos Tversky and Istudied together many years ago, and continued to discuss ina conversation that spanned several decades. It builds on ananalysis of judgment heuristics that was developed in collaborationwith Shane Frederick (Kahneman and Frederick,2002). A different version was published in American Psychologistin September 2003. For detailed comments on thisversion I am grateful to Angus Deaton, David Laibson,Michael Rothschild, and Richard Thaler. The usual caveatsapply. Geoffrey Goodwin, Amir Goren, and Kurt Schoppeprovided helpful research assistance.hopes have been realized to some extent, givingrise to an active program of research by behavioraleconomists (Thaler, 2000; Colin Camereret al., forthcoming; for other examples, seeKahneman and Tversky, 2000).My work with Tversky comprised three separateprograms of research, some aspects ofwhich were carried out with other collaborators.The first explored the heuristics that people useand the biases to which they are prone in varioustasks of judgment under uncertainty, includingpredictions and evaluations of evidence(Kahneman and Tversky, 1973; Tversky andKahneman, 1974; Kahneman et al., 1982). Thesecond was concerned with prospect theory, amodel of choice under risk (Kahneman andTversky, 1979; Tversky and Kahneman, 1992)and with loss aversion in riskless choice (Kahnemanet al., 1990, 1991 ; Tversky and Kahneman,1991). The third line of research dealt withframing effects and with their implications forrational-agent models (Tversky and Kahneman,1981, 1986). The present essay revisits thesethree lines of research in light of recent advancesin the psychology of intuitive judgmentand choice. Many of the ideas presented herewere anticipated informally decades ago, butthe attempt to integrate them into a coherentapproach to judgment and choice is recent.Economists often criticize psychological researchfor its propensity to generate lists oferrors and biases, and for its failure to offer acoherent alternative to the rational-agent model.This complaint is only partly justified: psychologicaltheories of intuitive thinking cannotmatch the elegance and precision of formal normativemodels of belief and choice, but this isjust another way of saying that rational modelsare psychologically unrealistic. Furthermore,the alternative to simple and precise models isnot chaos. Psychology offers integrative conceptsand mid-level generalizations, which gaincredibility from their ability to explain ostensiblydifferent phenomena in diverse domains. Inthis spirit, the present essay offers a unified

1450 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003treatment of intuitive judgme'nt and choice,which builds on an earlier study of the relationshipbetween preferences and attitudes (Kahnemanet al., 1999) and extends a model ofjudgment heuristics recently proposed by Kahnemanand Shane Frederick (2002). The guidingideas are (i) that most judgments and mostchoices are made intuitively; (ii) that the rulesthat govern intuition are generally similar to therules of perception. Accordingly, the discussionof the rules of intuitive judgments and choiceswill rely extensively on visual analogies.Section I introduces a distinction betweentwo generic modes of cognitive function, correspondingroughly to intuition and reasoning.Section 11 describes the factors that determinethe relative accessibility of different judgmentsand responses. section-111 relates prospect theoryto the general proposition that changes anddifferences are more accessible than absolutevalues. Section IV explains framing effects interms of differential salience and accessibility.Section V reviews an attribute substitutionmodel of heuristic judgment. Section VI describesa particular family of heuristics, calledprototype heuristics. Section VII discusses theinteractions between intuitive and deliberatethought. Section VIII concludes.I. The Architecture of Cognition: Two SystemsThe present treatment distinguishes twomodes of thinking and deciding, which correspondroughly to the everyday concepts of reasoningand intuition. Reasoning is what we dowhen we compute the product of 17 by 258, fillan income tax form, or consult a map. Intuitionis at work when we read the sentence "BillClinton is a shy man" as mildly amusing, orwhen we find ourselves reluctant to eat a pieceof what we know to be chocolate that has beenformed in the shape of a cockroach (Paul Rozinand Carol Nemeroff, 2002). Reasoning is donedeliberately and effortfully, but intuitive thoughtsseem to come spontaneously to mind, withoutconscious search or computation, and withouteffort. Casual observation and systematic researchindicate that most thoughts and actionsare normally intuitive in this sense (Daniel T.Gilbert, 1989, 2002; Timothy D. Wilson, 2002;Seymour Epstein, 2003).Although effortless thought is the norm,some monitoring of the quality of mental oper-ations and overt behavior also goes on. We donot express every passing thought or act onevery impulse. But the monitoring is normallylax, and allows many intuitive judgments to beexpressed, including some that &e erroneous(Kahneman and Frederick, 2002). Ellen J.Langer et al. (1978) provided a well-knownexample of what she called "mindless behavior."In her experiment, a confederate tried tocut in line at a copying machine, using variouspreset "excuses." The conclusion was that statementsthat had the form of an unqualified requestwere rejected (e.g., "Excuse me, may I usethe Xerox machine?')), but almost any statementthat had the general form of an explanation wasaccepted, including "Excuse me, may I use theXerox machine because I want to make copies?"The superficiality is striking.Frederick (2003, personal communication)has used simple puzzles to study cognitive selfmonitoring,as in the following example: "A batand a ball cost $1.10 in total. The bat costs $1more than the ball. How much does the ballcost?'AAlmost everyone reports an initial tendencyto answer "10 cents" because the sum$1.10 separates naturally into $1 and 10 cents,and 10 cents is about the right magnitude. Frederickfound that many intelligent people yield tothis immediate impulse: 50 percent (47193) of agroup of Princeton students and 56 percent(1641293) of students at the University of Michigangave the wrong answer. Clearly, these respondentsoffered their response without firstchecking it. The surprisingly high rate of errorsin this easy problem illustrates how lightly theoutput of effortless associative thinking is monitored:people are not accustomed to thinkinghard. and are often content to trust a plausiblejudgment that quickly comes to mind. Remarkably,Frederick has found that errors inthis puzzle and in others of the same typewere- significant predictors of high discountrates.In the examples discussed so far, intuitionwas associated with poor performance, but intuitivethinking can also be powerful and accurate.High skill is acquired by prolongedpractice, and the performance of skills is rapidand effortless. The proverbial master chessplayer who walks past a game and declares"white mates in three" without slowing is performingintuitively (Simon and William G.Chase, 1973), as is the experienced nurse who

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONALITYEPERCEPTIONSYSTEMFastParallelAutomaticEffortlessAssociativeSlow-learningEmotional1- --rSYSTEM 2SerialControlledEffortfulRule-governedFlexibleNeutralPerceptsCurrent stimulationStimulus-boundConceptual representationsPast, Present and FutureCan be evoked by languagedetects subtle signs of impending heart failure(Gary Klein, 1998; Atul Gawande, 2002).The distinction between intuition and reasoninghas recently been a topic of considerableinterest to psychologists (see, e.g., ShellyChaiken and Yaacov Trope, 1999; Gilbert,2002; Steven A. Sloman, 2002; Keith E.Stanovich and Richard F. West, 2002). There issubstantial agreement on the characteristics thatdistinguish the two types of cognitive processes,for which Stanovich and West (2000) proposedthe neutral labels of System 1 and System 2.The scheme shown in Figure 1 summarizesthese characteristics. The operations of System1 are fast, automatic, effortless, associative, andoften emotionally charged; they are also governedby habit, and are therefore difficult tocontrol or modify. The operations of System 2are slower, serial, effortful, and deliberatelycontrolled; they are also relatively flexible andpotentially rule-governed.The difference in effort provides the mostuseful indications of whether a given mentalprocess should be assigned to System 1 or System2. Because the overall capacity for mentaleffort is limited, effortful processes tend to disrupteach other, whereas effortless processesneither cause nor suffer much interference whencombined with other tasks. For example, a driver'sability to conduct a conversation is a sensitiveindicator of the amount of attentioncurrently demanded by the driving task. Dualtasks have been used in hundreds of psychologicalexperiments to measure the attentional demandsof different mental activities (for areview, see Harold E. Pashler, 1998). Studiesusing the dual-task method suggest that the selfmonitoringfunction belongs with the effortfuloperations of System 2. People who are occupiedby a demanding mental activity (e.g., attemptingto hold in mind several digits) aremuch more likely to respond to another task byblurting out whatever comes to mind (Gilbert,1989). The phrase that "System 2 monitors theactivities of System 1" will be used here asshorthand for a hypothesis about what wouldhappen if the operations of System 2 were disrupted.For example, it is safe to predict that thepercentage of errors in the bat-and-ball questionwill increase, if the respondents are asked thisquestion while attempting to keep a list ofwords in their active memory.In the language that will be used here, theperceptual system and the intuitive operations

1452 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003of System 1 generate impressions of the attributesof objects of perception and thought.These impressions are not voluntary and neednot be verbally explicit. In contrast, judgmentsare always explicit and intentional, whether ornot they are overtly expressed. Thus, System 2is involved in all judgments, whether they originatein impressions or in deliberate reasoning.The label "intuitive" is applied to judgmentsthat directly reflect impressions.Figure 1 illustrates an idea that guided theresearch that Tversky and I conducted from itsearly days: that intuitive judgments occupy aposition-perhaps corresponding to evolutionaryhistory-between the automatic operationsof perception and the deliberate operations ofreasoning. All the characteristics that studentsof intuition have attributed to System 1 are alsoproperties of perceptual operations. Unlike perception,however, the operations of System 1are not restricted to the processing of currentstimulation. Like System 2, the operations ofSystem 1 deal with stored concepts as well aswith percepts, and can be evoked by language.This view of intuition suggests that the vaststore of scientific knowledge available aboutperceptual phenomena can be a source of usefulhypotheses about the workings of intuition. Thestrategy of drawing on analogies from perceptionis applied in the following section.11. The Accessibility DimensionA defining property of intuitive thoughts isthat they come to mind spontaneously, like percepts.The technical term for the ease withwhich mental contents come to mind is accessibility(E. Tory Higgins, 1996). To understandintuition, we must understand why somethoughts are accessible and others are not. Theremainder of this section introduces the conceptof accessibility by examples drawn from visualperception.Consider Figures 2a and 2b. As we look atthe object in Figure 2a, we have immediateimpressions of the height of the tower, the areaof the top block, and perhaps the volume of thetower. Translating these impressions into unitsof height or volume requires a deliberate operation,but the impressions themselves are highlyaccessible. For other attributes, no perceptualimpression exists. For example, the total areathat the blocks would cover if the tower were,' /F~gurc 2a Figt~rc ?b Figure 2cdismantled is not perceptually accessible,though it can be estimated by a deliberate procedure,such as multiplying the area of a blockby the number of blocks. Of course, the situationis reversed with Figure 2b. Now the blocksare laid out and an impression of total area isimmediately accessible, but the height of thetower that could be constructed with theseblocks is not.Some relational properties are accessible.Thus, it is obvious at a glance that Figures 2aand 2c are different, but also that they are moresimilar to each other than either is to Figure2b. And some statistical properties of ensemblesare accessible, while others are not. For anexample, consider the question "What is theaverage length of the lines in Figure 3?' Thisquestion is easy. When a set of objects of thesame general kind is presented to an observerwhethersimultaneously or successively-a representationof the set is computed automatically,which includes quite precise information aboutthe average (Dan Ariely, 2001; Sang-ChulChong and Anne Treisman, 2003). The representationof the prototype is highly accessible,and it has the character of a percept: we fo'im animpression of the typical line without choosingto do so. The only role for System 2 in this taskis to map the impression of typical length ontothe appropriate scale. In contrast, the answer tothe question "What is the total length of thelines in the display?' does not come to mindwithout considerable effort.As the example of averages and sums illustrates,some attributes are more accessible thanothers, both in perception and in judgment. Attributesthat are routinely and automaticallyproduced by the perceptual system or by System

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONALITY14531, without intention or effort, have been callednatural assessments (Tversky and Kahneman,1983). Kahneman and Frederick (2002) compileda partial list of these natural assessments.In addition to physical properties such as size,distance, and loudness, the list includes moreabstract properties such as similarity, causalpropensity, surprisingness, affective valence,and mood.The evaluation of stimuli as good or bad is aparticularly important natural assessment. Theevidence, both behavioral (John A. Bargh,1997; Robert B. Zajonc, 1998) and neurophysiological(e.g., Joseph E. LeDoux, 2000), isconsistent with the idea that the assessment ofwhether objects are good (and should be approached)or bad (should be avoided) is carriedout quickly and efficiently by specialized neuralcircuitry. A remarkable experiment reported byBargh (1997) illustrates the speed of the evaluationprocess, and its direct link to approach andavoidance. Participants were shown a series ofstimuli on a screen, and instructed to respond toeach stimulus as soon as it appeared, by movinga lever that blanked the screen. The stimuli wereaffectively charged words, some positive (e.g.,LOVE) and some aversive (e.g., VOMIT), butthis feature was irrelevant to the participant'stask. Half the participants responded by pullingthe lever toward themselves, half responded bypushing the lever away. Although the responsewas initiated within a fraction of a second, wellbefore the meaning of the stimulus was consciouslyregistered, the emotional valence of theword had a substantial effect. Participants wererelatively faster in pulling a lever toward themselves(approach) for positive words, and relativelyfaster pushing the lever away when theword was aversive. The tendencies to approachor avoid were evoked by an automatic processthat was not under conscious voluntary control.Several psychologists have commented on theinfluence of this primordial evaluative system(here included in System 1) on the attitudes andpreferences that people adopt consciously anddeliberately (Zajonc, 1998; Kahneman et al.,1999; Paul Slovic et al., 2002; Epstein, 2003).The preceding discussion establishes a dimensionof accessibility. At one end of thisdimension we find operations that have thecharacteristics of perception and of the intuitiveSystem 1: they are rapid, automatic, and effortless.At the other end are slow. serial. andeffortful operations that people need a specialreason to undertake. Accessibility is a continuum,not a dichotomy, and some effortful operationsdemand more effort than others. Someof the determinants of accessibility are probablygenetic; others develop through experience. Theacquisition of skill gradually increases the accessibilityof useful responses and of productiveways to organize information, until skilled performancebecomes almost effortless. This effectof practice is not limited to motor skills. Amaster chess player does not see the same boardas the novice, and visualizing the tower in anmay of blocks would also become virtuallyeffortless with prolonged practice.The impressions that become accessible inany particular situation are mainly determined,of course, by the actual properties of the objectof judgment: it is easier to see a tower in Figure2a than in Figure 2b, because the tower in thelatter is only virtual. Physical salience also determinesaccessibility: if a large green letter anda small blue letter are shown at the same time,"green" will come to mind first. However, saliencecan be overcome by deliberate attention:an instruction to look for the small object willenhance the accessibility of all its features.Analogous effects of salience and of spontaneousand voluntary attention occur with moreabstract stimuli. For example, the statements"Team A beat team B" and "Team B lost to

1454 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003team A" convey the same information, but becauseeach sentence draws attention to its grammaticalsubject, they make different thoughtsaccessible. Accessibility also reflects temporarystates of associative activation. For example, themention of a familiar social category temporarilyincreases the accessibility of the traits associatedwith the category stereotype, as indicated by alowered threshold for recognizing behaviors asindications of these traits (Susan T. Fiske, 1998).As designers of billboards know well, motivationallyrelevant and emotionally arousingstimuli spontaneously attract attention. Billboardsare useful to advertisers because payingattention to an object makes all its featuresaccessible-including those that are not linkedto its primary motivational or emotional significance.The "hot" states of high emotional andmotivational arousal greatly increase the accessibilityof thoughts that relate to the immediateemotion and to the current needs, and reduce theaccessibility of other thoughts (George Loewenstein.1996. 2000: Jon Elster. 1998). Aneffect of emotional significance on accessibilitywas demonstrated in an important study by YuvalRottenstreich and Christopher K. Hsee(2001), which showed that people are less sensitiveto variations of probability when valuingchances to receive emotionally loaded outcomes(kisses and electric shocks) than whenthe outcomes are monetary.Figure 4 (adapted from Jerome S. Bruner andA. Leigh Minturn, 1955) includes a standarddemonstration of the effect of context on accessibility.An ambiguous stimulus that is perceivedas a letter within a context of letters isinstead seen as a number when placed within acontext of numbers. More generally, expectations(conscious or not) are a powerful determinantof accessibility.Another important point that Figure 4 illustratesis the complete suppression of ambiguityin conscious perception. This aspect of the demonstrationis spoiled for the reader who sees thetwo versions in close proximity, but when thetwo lines are shown separately, observers willnot spontaneously become aware of the alternativeinterpretation. They "see" the interpretationof the object that is the most likely in its context,but have no subjective indication that itcould be seen differently. Ambiguity and uncertaintyare suppressed in intuitive judgment aswell as in perception. Doubt is a phenomenon ofSystem 2, an awareness of one's ability to thinkincompatible thoughts about the same thing.The central finding in studies of intuitive decisions,as described by Klein (1998), is thatexperienced decision makers working underpressure (e.g., firefighting company captains)rarely need to choose between options because,in most cases, only a single option comes to mind.The compound cognitive system that hasbeen sketched here is an impressive computationaldevice. It is well-adapted to its environmentand has two ways of adjusting to changes:a short-term process that is flexible and effortful,and a long-term process of skill acquisitionthat eventually produces highly effective responsesat low cost. The system tends to seewhat it expects to see-a form of Bayesianadaptation-and it is also capable of respondingeffectively to surprises. However, this marvelouscreation differs in important respects fromanother paragon, the rational agent assumed ineconomic theory. Some of these differences areexplored in the following sections, which reviewseveral familiar results as effects of accessibility.Possible implications for theorizing in behavioraleconomics are explored along the way.111. Changes or States: Prospect TheoryA general property of perceptual systems isthat they are designed to enhance the accessibilityof changes and differences. Perception isreference-dependent: the perceived attributesof a focal stimulus reflect the contrast betweenthat stimulus and a context of prior and concurrentstimuli. This section will show that

VOL. 93 NO. 5 XAHNEMAN: MAPS OF BOUNDED RATIONALITY 1455FIGURE 5. REFERENCE-DEPENDENCE IN THE PERCEF'TION OF BRIGHTNESSintuitive evaluations of outcomes are alsoreference-dependent.The role of ~rior stimulation is familiar in thedomain of temperature. Immersing the hand inwater at 20°C will feel pleasantly warm afterprolonged immersion in much colder water, andpleasantly cool after immersion in muchwarmer water. Figure 5 illustrates referencedependencein vision. The two enclosed squareshave the same luminance, but they do not appearequally bright. The point of the demonstrationis that the brightness of an area is not asingle-parameter function of the light energythat reaches the eye from that area, just as theexperience of temperature is not a single-parameterfunction of the temperature to which one iscurrently exposed. An account of perceivedbrightness ortemperature also requires a parameterfor a reference value (often called adaptationlevel), which is influenced by the context ofcurrent and prior stimulation.From the vantage point of a student of perception,it is quite surprising that in standardeconomic analyses the utility of decision outcomesis assumed to be determined entirely bythe final state of endowment, and is thereforereference-independent. In the context of riskychoice, this assumption can be traced to thebrilliant essay that first defined a theory of expectedutility (Daniel Bernoulli, 1738). Bernoulliassumed that states of wealth have aspecified utility, and proposed that the decisionrule for choice under risk is to maximize theexpected utility of wealth (the moral expectation).The language of Bernoulli's essay is prescriptive-itspeaks of what is sensible orreasonable to do-but the theory was also intendedas a description of the choices of reasonablemen (Gerd Gigerenzer et al., 1989). As inmost modem treatments of decision-making,Bernoulli's essay does not acknowledge anytension between prescription and description.The proposition that decision makers evaluateoutcomes by the utility of final asset positionshas been retained in economic analyses for almost300 vears. This is rather remarkable. becausethe idea is easily shown to be wrong; Icall it Bernoulli's error.Tversky and I constructed numerous thoughtexperiments when we began the study of riskychoice that led to the formulation of prospecttheory (Kahneman and Tversky, 1979). Examplessuch as Problems 1 and 2 below convincedus of the inadequacy of the utility function forwealth as an explanation of choice.Problem 1Would you accept this gamble?50% chance to win $15050% chance to lose $100Would your choice change if youroverall wealth were lower by $loo?

1456 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003There will be few takers of the gamble in Problem1. The experimental evidence shows thatmost people will reject a gamble with evenchances to win and lose, unless the possible winis at least twice the size of the possible loss(e.g., Tversky and Kahneman, 1992). The answerto the second question is, of course, negative.Next consider Problem 2:1OSst.SVALUECAMProblem 2Which would you choose?lose $100 with certaintyor50% chance to win $5050% chance to lose $200Would your choice change if youroverall wealth were higher by $loo?In Problem 2, the gamble appears much moreattractive than the sure loss. Experimental resultsindicate that risk-seeking preferences areheld by a large majority of respondents in problemsof this kind (Kahneman and Tversky,1979). Here again, the idea that a change of$100 in total wealth would affect preferencescannot be taken seriously.We examined many choice pairs of thistype in our early explorations, and concludedthat the very abrupt switch from risk aversionto risk seeking could not plausibly be explainedby a utility function for wealth. Preferencesappeared to be determined byattitudes to gains and losses, defined relativeto a reference point, but Bernoulli's theoryand its successors did not incorporate a referencepoint. We therefore proposed an alternativetheory of risk, in which the carriers ofutility are gains and losses-changes ofwealth rather than states of wealth. One noveltyof prospect theory was that it was explicitlypresented as a formal descriptive theoryof the choices that people actually make, notas a normative model. This was a departurefrom a long history of choice models thatserved double duty as normative logics and asidealized descriptive models.The distinctive predictions of prospect theoryfollow from the shape of the value function,which is shown in Figure 6. The valuefunction is defined on gains and losses and isIFIGURE 6. ASCHEMATICVALUEFUNCTION FOR CHANGEScharacterized by three features: (1) it is concavein the domain of gains, favoring riskaversion; (2) it is convex in the domain oflosses, favoring risk seeking; (3) most important,the function is sharply kinked at thereference point, and loss-averse-steeper forlosses than for gains by a factor of about2-2.5 (Kahneman et al., 1991; Tversky andKahneman, 1992).If Bernoulli's formulation is transparentlyincorrect as a descriptive model of riskychoices, as has been argued here, whyhas this model been retained for so long?The answer appears to be that the assignmentof utility to wealth is an aspect of rationality,and therefore compatible with thegeneral assumption of rationality in economictheorizing (Kahneman, 2003a). ConsiderProblem 3:Problem 3Two persons get their monthly reportfrom a broker:A is told that her wealth went from4M to 3MB is told that her wealth went fromIM to I.1MWho of the two individuals has morereason to be satisfied with her financialsituation?Who is happier today?

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONAUTY1457Problem 3 highlights the contrasting interpretationsof utility in theories that define outcomesas states or as changes. In Bernoulli's analysisonly the first of the two questions of Problem 3is relevant, and only long-term consequencesmatter. Prospect theory, in contrast, is concernedwith short-term outcomes, and the valuefunction presumably reflects an anticipation ofthe valence and intensity of the emotions thatwill be experienced at moments of transitionfrom one state to another (Kahneman, 2000a, b;Barbara Mellers, 2000). Which of these conceptsof utility is more useful? The culturalnorm of reasonable decision-making favors thelong-term view over a concern with transient emotions.Indeed, the adoption of a broad perspectiveand a long-term view is an aspect of the meaningof rationality in everyday language. The finalstatesinterpretation of the utility of outcomes istherefore a good fit for a rational-agent model.These considerations support the normativeand prescriptive status of the Bernoullian definitionof outcomes. On the other hand, an exclusiveconcern with the long term may beprescriptively sterile, because the long term isnot where life is lived. Utility cannot be divorcedfrom emotion, and emotions are triggeredby changes. A theory of choice thatcompletely ignores feelings such as the pain oflosses and the regret of mistakes is not onlydescriptively unrealistic, it also leads to prescriptionsthat do not maximize the utility ofoutcomes as they are actually experiencedthatis, utility as Bentham conceived it (Kahneman,1994, 2000a; Kahneman et al., 1997).Bernoulli's error-the idea that the carriersof utility are final states-is not restricted todecision-making under risk. Indeed, the incorrectassumption that initial endowments do notmatter is the basis of Coase's theorem and of itsmultiple applications (Kahneman et al., 1990).The error of reference-independence is builtinto the standard representation of indifferencemaps. It is puzzling to a psychologist that thesemaps do not include a representation of thedecision maker's current holdings of variousgoods-the counterpart of the reference point inprospect theory. The parameter is not included,of course, because consumer theory assumesthat it does not matter.The core idea of prospect theory-that thevalue function is kinked at the reference pointand loss averse-became useful to economicswhen Thaler (1980) used it to explain risklesschoices. In particular, loss aversion explained aviolation of consumer theory that Thaler identifiedand labeled the "endowment effect": the sellingprice for consumption goods is much higher thanthe buying price, often by a factor of 2 or more.The value of a good to an individual appears to behigher when the good is viewed as something thatcould be lost or given up than when the same goodis evaluated as a potential gain (Kahneman et al.,1990, 1991; Tversky and Kahneman, 1991).When half the participants in an experimentalmarket were randomly chosen to be endowedwith a good (a mug) and trade was allowed, thevolume of trade was about half the amount thatwould be predicted by assuming that value wasindependent of initial endowment (Kahnemanet al., 1990). Transaction costs did not explainthis counterexample to the Coase theorem, becausethe same institution produced no indicationof reluctance to trade when the objects oftrade were money tokens. The results suggestthat the participants in these experiments did notvalue the mug as an object they could have andconsume, but as something they could get, orgive up. Interestingly, John A. List (2003a, b)found that the magnitude of the endowmenteffect was substantially reduced for participantswith intense experience in the trading of sportscards.Experienced traders (who are also consumers)showed less reluctance to trade onegood for another-not only sportscards, but alsomugs and other goods-as if they had learned tobase their choice on long-term value, rather thanon the immediate emotions associated with gettingor giving up objects.Reference-dependence and loss aversion helpaccount for several phenomena of choice. Thefamiliar observation that out-of-pocket lossesare valued much more than opportunity costs isreadily explained, if these outcomes are evaluatedon different limbs of the value function.The distinction between "actual" losses andlosses of opportunities is recognized in manyways in the law (David Cohen and Jack L.Knetsch, 1992) and in lay intuitions about rulesof fairness in the market (Kahneman et al.,1986). Loss aversion also contributes to thewell-documented status-quo bias (WilliamSamuelson and Richard Zeckhauser, 1988). Becausethe reference point is usually the statusquo, the properties of alternative options areevaluated as advantages or disadvantages

1458 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003relative to the current situation, and the disadvantagesof the alternatives loom larger thantheir advantages. Other applications of the conceptof loss aversion are documented in severalchapters in Kahneman and Tversky (2000).IV. Framing EffectsIn the display of blocks in Figure 2, the sameproperty (the total height of a set of blocks) washighly accessible in one display and not in another,although both displays contained thesame information. This observation is entirelyunremarkable-it does not seem shocking thatsome attributes of a stimulus are automaticallyperceived while others must be computed, orthat the same attribute is perceived in one displayof an object but must be computed inanother. In the context of decision-making,however, similar observations raise a significantchallenge to the rational-agent model.The assumption that preferences are not affectedby inconsequential variations in thedescription of outcomes has been called extensionality(Kenneth J. Arrow, 1982) and invariance(Tversky and Kahneman, 1986), and isconsidered an essential aspect of rationality.Invariance is violated in framing effects, whereextensionally equivalent descriptions lead todifferent choices by altering the relative salienceof different aspects of the problem. Tversky andKahneman (1981) introduced their discussion offraming effects with the following problem:The Asian diseaseImagine that the United States is preparingfor the outbreak of an unusualAsian disease, which is expected to kill600 people. Two alternative programs tocombat the disease have been proposed.Assume that the exact scientific estimatesof the consequences of the programs areas follows:If Program A is adopted, 200 peoplewill be savedIf Program B is adopted, there is aone-third probability that 600 people willbe saved and a two-thirds probability thatno people will be savedIn this version of the problem, a substantialmajority of respondents favor Program A, indicatingrisk aversion. Other respondents, selectedat random, receive a question in whichthe same cover story is followed by a differentdescription of the options:If Program A' is adopted, 400 people willdieIf Program B' is adopted, there is a onethirdprobability that nobody will die anda two-thirds probability that 600 peoplewill dieA substantial majority of respondents nowfavor Program B', the risk-seeking option. Althoughthere is no substantive difference betweenthe versions, they evoke differentassociations and evaluations. This is easiest tosee in the certain option, because outcomes thatare certain are overweighted relative to outcomesof high or intermediate probability (Kahnemanand Tversky, 1979). Thus, the certaintyof saving people is disproportionately attractive,while accepting the certain death of people isdisproportionately aversive. These immediateaffective responses respectively favor A over Band B' over A'. As in Figures 2a and 2b, thedifferent representations of the outcomes highlightsome features of the situation and maskothers.In an essay about the ethics of policy,Thomas C. Schelling (1984) presented a compellinglyrealistic example of the dilemmasraised by framing. Schelling reports asking hisstudents to evaluate a tax policy that wouldallow a larger child exemption to the rich thanto the poor. Not surprisingly, his students foundthis proposal outrageous. Schelling then pointedout that the default case in the standard tax tableis a childless family, with special adjustmentsfor families with children, and led his class toagree that the existing tax schedule could berewritten with a family with two children as thedefault case. In this formulation, childless familieswould pay a surcharge. Should this surchargebe as large for the poor as for the rich?Of course not. The two versions of the questionabout how to treat the rich and the poor bothtrigger an intuitive preference for protecting the

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONAWTY1459poor, but these preferences are incoherent.Schelling's problem highlights an importantpoint. Framing effects are not a laboratory curiosity,but a ubiquitous reality. The tax tablemust be framed one way or another, and eachframe will increase the accessibility of someresponses and make other responses less likely.There has been considerable interest amongbehavioral economists in a particular type offraming effect, where a choice between twooptions A and B is affected by designatingeither A or B as a default option. The optiondesignated as the default has a large advantagein such choices, even for decisions that haveconsiderable significance. Eric J. Johnson et al.(1993) described a compelling example. Thestates of Pennsylvania and New Jersey bothoffer drivers a choice between an insurancepolicy that allows an unconstrained right to sue,and a less expensive policy that restricts theright to sue. The unconstrained right to sue isthe default in Pennsylvania, the opposite is thedefault in New Jersey, and the takeup of fullcoverage is 79 percent and 30 percent in the twostates, respectively. Johnson and Daniel G.Goldstein (2003) estimate that Pennsylvaniadrivers spend 450 million dollars annually onfull coverage that they would not purchase iftheir choice were framed as it is for New Jerseydrivers.Johnson and Goldstein (2003) also comparedthe proportions of the population enrolled inorgan donation programs in seven Europeancountries in which enrollment was the defaultand four in which nonenrollment was the default.Averaging over countries, enrollment indonor programs was 97.4 percent when thiswas the default option, 18 percent otherwise.The passive acceptance of the formulationgiven has significant consequences in thiscase. as it does in other recent studies wherethe selection of the default on the form thatworkers completed to set their 401(k) contributionsdominated their ultimate choice(Brigitte Madrian and Dennis Shea, 2001;James J. Choi et al., 2002).The basic principle of framing is the passiveacceptance of the formulation given. Because ofthis passivity, people fail to construct a canonicalrepresentation for all extensionally equivalentdescriptions of a state of affairs. They donot spontaneously compute the height of atower that could be built from an array ofblocks, and they do not spontaneously transformthe representation of puzzles or decisionproblems. Obviously, no one is able to recognize"137 X 24" and "3,288" as "the same"number without going through some elaboratecomputations. Invariance cannot be achieved bya finite mind.The impossibility of invariance raises significantdoubts about the descriptive realism ofrational-choice models (Tversky and Kahneman,1986). Absent a system that reliably generatesappropriate canonical representations,intuitive decisions will be shaped by the factorsthat determine the accessibility of different featuresof the situation. Highly accessible featureswill influence decisions, while features of lowaccessibility will be largely ignored-and thecorrelation between accessibility and reflectivejudgments of relevance in a state of completeinformation is not necessarily high.A particularly unrealistic assumption of therational-agent model is that agents make theirchoices in a comprehensively inclusive context,which incorporates all the relevant details of thepresent situation, as well as expectations aboutall future opportunities and risks. Much evidencesupports the contrasting claim that people'sviews of decisions and outcomes arenormally characterized by "narrow framing"(Kahneman and Daniel Lovallo, 1993), and bythe related notions of "mental accounting"(Thaler, 1985, 1999) and "decision bracketing"(Daniel Read et al., 1999).The following are some examples of theprevalence of narrow framing. The decision ofwhether or not to accept a gamble is normallyconsidered as a response to a single opportunity,not as an occasion to apply a general policy(Gideon Keren and Willem A. Wagenaar, 1987;Tversky and Donald A. Redelmeier, 1992; Kahnemanand Lovallo, 1993; Shlomo Benartzi andThaler, 1999). Investors' decisions about particularinvestments appear to be considered inisolation from the remainder of the investor'sportfolio (Nicholas Barberis et al., 2003). Thetime horizon that investors adopt for evaluatingtheir investments appears to be unreasonablyshort-an observation that helps explain theequity-premium puzzle (Benartzi and Thaler,1995). Finally, the prevalence of the gain~lossframing of outcomes over the wealth frame,which was discussed in the previous section,can now be seen as an instance of narrow

1460 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003framing. A shared feature of all these examplesis that decisions made in narrow frames departfar more from risk neutrality than decisions thatare made in a more inclusive context.The prevalence of narrow frames is an effectof accessibility, which can be understood byreferring to the displays of blocks in Figure2. The same set of blocks is framed as a towerin Figure 2a, and as a flat array in Figure 2b. Althoughit is possible to "see" a tower in Figure2b, it is much easier to do so in Figure 2a. Narrowframes generally reflect the structure of theenvironment in which decisions are made. Thechoices that people face arise one at a time, andthe principle of passive acceptance suggests thatthey will be considered as they arise. The problemat hand and the immediate consequences ofthe choice will be far more accessible than allother considerations, and as a result decisionproblems will be framed far more narrowly thanthe rational model assumes.V. Attribute Substitution: A Model of JudgmentHeuristicsThe first research program that Tversky and Iundertook together consisted of a series of studiesof various types of judgment about uncertainevents, including numerical predictions and assessmentsof the probabilities of hypotheses.Our conclusion in a review of this work was that"people rely on a limited number of heuristicprinciples which reduce the complex tasks ofassessing probabilities and predicting values tosimpler judgmental operations. In general, theseheuristics are quite useful, but sometimes theylead to severe and systematic errors" (Tverskyand Kahneman, 1974, p. 1124). The article introducedthree heuristics-representativeness,availability, and anchoring-that were used toexplain a dozen systematic biases in judgmentunder uncertainty, including nonregressive prediction,neglect of base-rate information, overconfidence,and overestimates of the frequencyof events that are easy to recall. Some of thebiases were identified by systematic errors inestimates of known quantities and statisticalfacts. Other biases were defined by discrepanciesbetween the regularities of intuitivejudgments and the principles of probabilitytheory, Bayesian inference, and regressionanalysis.FIGURE 7. AN ILLUSION OF ATTRIBUTE SUBSTITUTIONSource: Photo by Lenore Shoharn, 2003.Kahneman and Frederick (2002) recently revisitedthe early studies of judgment heuristics,and proposed a formulation in which the reductionof complex tasks to simpler operations isachieved by an operation of attribute substitution."Judgment is said to be mediated by aheuristic when the individual assesses a specifiedtarget attribute of a judgment object bysubstituting another property of that object-theheuristic attribute-which comes more readilyto mind" (p. 53). Unlike the early work, Kahnemanand Frederick's conception of heuristicsis not restricted to the domain of judgmentunder uncertainty.For a perceptual example of attribute substitution,consider the question: "What are thesizes of the two horses in Figure 7, as they aredrawn on the page?' The images are in factidentical in size, but the figure produces a compellingillusion. The target attribute that 0bse~ersintend to evaluate is objective twodimensionalsize, but they are unable to do thisveridically. Their judgments map an impressionof three-dimensional size (the heuristic attribute)onto units of length that are appropriateto the target attribute, and scaled to the sizeof the page. This illusion is caused by thedifferential accessibility of competing interpretationsof the image. An impression of three-

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONAWTY1461dimensional size is the only impression of sizethat comes to mind for ndive observers-paintersand experienced photographers are able todo better-and it produces an illusion in theperception of picture size.A study by Fritz Strack et al. (1988) illustratesthe role of attribute substitution in a differentcontext. College students responded to asurvey which included the two following questionsin immediate succession: "How happy areyou with your life in general?" and "How manydates did you have last month?" The correlationbetween the two questions was 0.12 when theyappeared in the order shown. Among respondentswho received the same questions in reverseorder, the correlation was 0.66. Thepsychological interpretation of the high correlation'is inferential, but straightforward. The datingquestion undoubtedly evoked in manyrespondents an emotionally charged evaluationof their romantic life. This evaluation washighly accessible when the question abouthappiness was encountered next, and it wasmapped onto the scale of general happiness.In the interpretation offered here, the respondentsanswered the happiness question by reportingwhat came to their mind, and failed tonotice that they were answering a questionthat had not been asked-a cognitive illusionthat is analogous to the visual illusion ofFigure 7.The most direct evidence for attribute substitutionwas reported by Kahneman and Tversky(1973), in a task of categorical prediction. Therewere three experimental groups in their experiment.Participants in a base-rate group evaluatedthe relative frequencies of graduatestudents in nine categories of ~pecialization.~Mean estimates ranged from 20 percent for Humanitiesand Education to 3 percent for LibraryScience.Two other groups of participants were shownthe same list of areas of graduate specialization,and the following description of a fictitiousgraduate student.' The observed value of 0.66 underestimates the truecorrelation between the variables of interest, because ofmeasurement error in all variables.The categories were Business Administration; ComputerScience; Engineering; Humanities and Education;Law; Library Science; Medicine; Physical and Life Sciences;Social Sciences and Social Work.Tom W. is of high intelligence, althoughlacking in true creativity. He has a needfor order and clarity, and for neat andtidy systems in which every detail findsits appropriate place. His writing israther dull and mechanical, occasionallyenlivened by somewhat corny punsand by flashes of imagination of thesci-ji type. He has a strong drive forcompetence. He seems to have little feeland little sympathy for other people anddoes not enjoy interacting with others.Self-centered, he nonetheless has a deepmoral sense.Participants in a similarity group ranked thenine fields by the degree to which Tom W."resembles a typical graduate student" (in thatfield). The description of Tom W, was deliberatelyconstructed to make him more representativeof the less populated fields, and thismanipulation was successful: the correlation betweenthe averages of representativeness rank-ing~ and of estimated base rates was -0.62.Participants in the probabilily group ranked thenine fields according to the likelihood that TomW. would have specialized in each. The respondentsin the latter group were graduate studentsin psychology at major universities. They weretold that the personality sketch had been writtenby a psychologist when Tom W. was in highschool, on the basis of personality tests of dubiousvalidity. This information was intended todiscredit the description as a source of validinformation.The statistical logic is straightforward. A descriptionbased on unreliable information mustbe given little weight, and predictions made inthe absence of valid evidence must revert tobase rates. This reasoning implies that judgmentsof probability should be highly correlatedwith the corresponding base rates in the TomW. problem.The psychology of the task is also straightforward.The similarity of Tom W. to variousstereotypes is a highly accessible natural assessment,whereas judgments of probability are difficult.The respondents are therefore expected tosubstitute a judgment of similarity (representa-tiveness) for the required judgment of probability.The two instructions-to rate similarity or

THE AMERICAN ECONOMIC REVIEW DECEMBER 2003(4 (b)Tom W.Lindamean rank (similarity)mean rank (similarity)probability-should therefore elicit similarjudgments.The scatterplot of the mean judgments of thetwo groups is presented in Figure 8a. As thefigure shows, the correlation between judgmentsof probability and similarity is nearlyperfect (0.98). The correlation between judgmentsof probability and base rates is -0.63.The results are in perfect accord with the hypothesisof attribute substitution. They also confirma bias of base-rate neglect in thisprediction task. The results are especially compellingbecause the responses were rankings.The large variability of the average rankings ofboth attributes indicates highly consensual responses,and nearly total overlap in the systematicvariance.Figure 8b shows the results of another studyin the same design, in which respondents wereshown the description of a woman namedLinda, and a list of eight possible outcomesdescribing her present employment and activities.The two critical items in the list were #6("Linda is a bank teller") and the conjunctionitem #8 ("Linda is a bank teller and active inthe feminist movement"). The other six possibilitieswere unrelated and miscellaneous(e.g., elementary school teacher, psychiatricsocial worker). As in the Tom W. problem,some respondents ranked the eight outcomesby the similarity of Linda to the categoryprototypes; others ranked the same outcomesby probability.Linda is 31 years old, single, outspokenand very bright. She majored in philosophy.As a student she was deeply concernedwith issues of discrimination andsocial justice and also participated in antinucleardemonstrations.As might be expected, 85 percent of respondentsin the similarity group ranked the conjunctionitem (#8) higher than its constituent,indicating that Linda resembles the image of afeminist bank teller more than she resembles astereotypical bank teller. This ordering of thetwo items is quite reasonable for judgments ofsimilarity. However, it is much more problematicthat 89 percent of respondents in the probabilitygroup also ranked the conjunction higherthan its constituent. This pattern of probabilityjudgments violates monotonicity, and has beencalled the "conjunction fallacy" (Tversky andKahneman, 1983).The observation that biases of judgment aresystematic was quickly recognized as relevantto the debate about the assumption of rationality

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONALITY1463in economics (see, e.g., Peter A. Diamond,1977; David M. Grether, 1978; Howard Kunreuther,1979; Arrow, 1982). There has alsobeen some discussion of the role of specificjudgment biases in economic phenomena, especiallyin finance (e.g., Werner F. M. De Bondtand Thaler, 1985; Robert J. Shiller, 2000; AndreiShleifer, 2000; Matthew Rabin, 2002). Recentextensions of the notion of heuristics to thedomain of affect may be of particular relevanceto the conversation between psychology andeconomics, because they bear on the core conceptof a preference. As was noted earlier, affectivevalence is a natural assessment, which isautomatically computed and always accessible.This basic evaluative attribute (good/bad, like/dislike, approachfavoid) is therefore a candidatefor substitution in any task that calls for a favorableor unfavorable response. Slovic and hiscolleagues (see, e.g., ~lovic et al., 2002) introducedthe concept of an aSfect heuristic. Theyshowed that affect (liking or disliking) is theheuristic attribute for numerous target attributes,including the evaluation of the costsand benefits of various technologies, the safeconcentration of chemicals, and even the predictedeconomic performance of various industries.In an article aptly titled "Risk asFeelings," Loewenstein et al. (2001) documentedthe related proposition that beliefs aboutrisk are often expressions of emotion.If different target attributes are strongly influencedby the same affective reaction, thedimensionality of decisions and judgmentsabout valued objects may be expected to beunreasonably low. Indeed, Melissa L. Finucaneet al. (2000) found that people's judgments ofthe costs and benefits of various technologiesare negatively correlated, especially when thejudgments are made under time pressure. Atechnology that is liked is judged to have lowcosts and large benefits. These judgments aresurely biased, because the correlation betweencosts and benefits is generally positive in theworld of real choices. In the same vein, Kahnemanet al. (1997) presented evidence that differentresponses to public goods (e.g.,willingness to pay, ratings of moral satisfactionfor contributing) yielded essentially interchangeablerankings of a set of policy issues.Here again, a basic affective response appearedto be the common factor.Kahneman et al. (1997) suggested that peo-ple's decisions often express affective evaluations(attitudes), which do not conform to thelogic of economic preferences. To understandpreferences, then, we may need to understandthe psychology of emotions. And we cannottake it for granted that preferences that are controlledby the emotion of the moment will beinternally coherent, or even reasonable by thecooler criteria of reflective reasoning. In otherwords, the preferences of System 1 are notnecessarily consistent with the preferences ofSystem 2. The next section will show that somechoices are not appropriately sensitive to variationsof quantity and cost-and are better describedas expressions of an affective responsethan as economic preferences.VI. Prototype HeuristicsThe results summarized in Figure 8 showedthat the judgments that subjects made about theTom W. and Linda problems substituted themore accessible attribute of similarity (representativeness)for the required target attribute ofprobability. The goal of the present section is toembed the representativeness heuristic in abroader class of prototype heuristics, whichshare a common psychological mechanismtherepresentation of categories by their prototypes-anda remarkably consistent pattern ofbiases.In the display of lines in Figure 3, the average(typical) length of the lines was highly accessible,but the sum of their lengths was not. Bothobservations are quite general. Classic psychologicalexperiments have established the followingproposition: whenever we look at orthink about a set (ensemble, category) which issufficiently homogeneous to have a prototype,information about the prototype is automaticallyaccessible (Michael I. Posner and StephenW. Keele, 1968; Eleanor Rosch and Carolyn B.Mewis, 1975). The prototype of a set is characterizedby the average values of the salientproperties of its members. The high accessibilityof prototype information serves an importantadaptive function. It allows new stimuli to becategorized efficiently, by comparing their featuresto those of category prototypes.3 ForStored information about individual exemplars alsocontributes to categorization.

1464 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003example, the stored prototype of a set of linesallows a quick decision about a new line-doesit belong with the set? There is no equallyobvious function for the automatic computationof sums.The low accessibility of sums and the highaccessibility of prototypes have significant consequencesin tasks that involve judgments ofsets, as in the following examples:(i) category prediction (e.g., the probabilitythat the category of bank tellers containsLinda as a member);(ii) pricing a quantity of public or privategoods (e.g., the personal dollar value ofsaving a certain number of migratory birdsfrom drowning in oil ponds);(iii) global evaluation of a past experience thatextended over time (e.g., the overall aversivenessof a painful medical procedure);(iv) assessment of the support that a sample ofobservations provides for a hypothesis(e.g., the probability that a sample of coloredballs has been drawn from one specijiedurn rather than another).The objects of judgment in these tasks aresets or categories, and the target attributes havea common logical structure. Extensional attributesare governed by a general principle ofconditional adding, which dictates that each elementwithin the set adds to the overall value anamount that depends on the elements alreadyincluded. In simple cases, the value is additive:the total length of the set of lines in Figure 3 isjust the sum of their separate lengths. In othercases, each positive element of the set increasesthe aggregate value, but the combination rule isnonadditive (typically ~ubadditive).~ The attributesof the category prototype are not extensional-theyare averages, whereas extensionalattributes are alun to sums.The preceding argument leads to the hypothesisthat tasks that require the assessment ofIf the judgment is monotonically related to an additivescale (such as the underlying count of the number of birds),the formal structure is known in the measurement literatureas an "extensive structure" (R. Duncan Luce et at., 1990,Ch. 3). There also may be attributes that lack an underlyingadditive scale, in which case the structure is known in theliterature as a "positive concatenation structure" (Luce etal., 1990, Ch. 19, volume 3, p. 38).extensional variables will be relatively difficult,and that intuitive responses may be generatedby substituting an attribute of the prototype forthe extensional target attribute. Prototype heuristicsinvolve a target attribute that is extensional,and a heuristic attribute which is acharacteristic of the category prototype. Prototypeheuristics are associated with two majorbiases, which generalize the biases of representativenessthat were introduced in the precedingsection:(i) Violations of monotonicity. Adding elementsto a set may lower the average andcause the judgment of the target variable todecrease, contrary to the logic of extensionalvariables. The prevalent judgmentthat Linda is less likely to be a bank tellerthan to be a feminist bank teller illustratesthis bias.(ii) Extension neglect. Other things equal, anincrease in the extension of a category willincrease the value of its extensional attributes,but leave unchanged the values ofits prototype attributes. The apparent neglectof the base rates of areas of specializationin judgments about Tom W, is anexample.Studies that have examined the two biases indifferent contexts are described next.A. Pricing GoodsThe price of a set of goods is an extensionalvariable. If price is evaluated by the attractivenessof a prototypical element of the set, violationsof monotonicity and extension neglect arepredicted.Scope Neglect.-Complete or almost completeneglect of extension has often been observedin studies of the willingness to pay forpublic goods, where the effect is called "neglectof scope." The best known example is a studyby William H. Desvousges et al. (1993) inwhich respondents indicated their willingness tocontribute money to prevent the drowning ofmigratory birds. The number of birds that wouldbe saved was varied for different subsamples.The estimated amounts that households werewilling to pay were $80, $78, and $88, to save2,000, 20,000, or 200,000 birds, respectively.

VOL. 93 NO. 5KAHNEMAN. MAPS OF BOUNDED RATIONAUTY1465The target attribute in this case is willingness topay (WTP), and the heuristic attribute appearsto be the emotion associated with the image ofa bird drowning in oil, or perhaps with theimage of a bird being saved from drowning(Kahneman et al., 1999).Frederick and Baruch Fischhoff (1998) reviewednumerous demonstrations of such scopeneglect in studies of willingness to pay for publicgoods. For example, Kahneman and Knetschfound that survey respondents in Toronto werewilling to pay almost as much to clean up thelakes in a small region of Ontario or to clean upall the lakes in that province (reported by Kahneman,1986). The issue of scope neglect iscentral to the application of the contingent valuationmethod (CVM) in the assessment of theeconomic value of public goods, and it has beenhotly debated (see, e.g., Richard T. Carson,1997). The proponents of CVM have reportedexperiments in which there was some sensitivityto scope, but even these effects are minute,far too small to satisfy the economic logic ofpricing (Diamond, 1996; Kahneman et al.,1999).Violations of Monotonicity.-List (2002) reportedan experiment that confirmed, in a realmarket setting, violations of dominance thatHsee (1998) had previously reported in a hypotheticalpricing task. In List's experiment, tradersof sportscards assigned significantly highervalue to a set of ten sportscards labeled "Mint1near mint condition" than to a set that includedthe same ten cards and three additional cardsdescribed as "poor condition." In a series offollow-up experiments, Jonathan E. Alevy et al.(2003) also confirmed an important difference(originally suggested by Hsee) between theprices that people will pay when they see onlyone of the goods (separate evaluation), or whenthey price both goods at the same time (jointevaluation). The goods were similar to thoseused in List's experiment. The predicted violationof dominance was observed in separateevaluation, especially for relatively inexperiencedmarket participants. These individualsbid an average of $4.05 for the small set ofcards, and only $1.82 for the larger set. Theviolations of dominance were completelyeliminated in the joint evaluation condition,where the bids for the small and large setsaveraged $2.89 and $3.32, respectively.Alevy et al. (2003) noted that System 1 appearsto dominate responses in separate evaluation,whereas System 2 conforms to thedominance rule when given a chance to do so.There was a definite effect of market experience,both in this study and in List (2002): thebids of highly experienced traders alsoshowed violations of monotonicity in separateevaluation, but the effect was much smaller.B. Evaluations of Extended EpisodesThe global utility of an experience that extendsover time is an extensional attribute (Kahneman,1994,20OOa, b; Kahneman et al., 1997),and the duration of the experience is a measureof its extension. The corresponding prototypeattribute is the experienced utility associatedwith a representative moment of the episode. Aspredicted by attribute substitution, global evaluationsof the episode exhibit both durationneglect and violations of monotonicity.Duration Neglect.-In a study described byRedelmeier and Kahneman (1996), patients undergoingcolonoscopy reported the intensity ofpain every 60 seconds during the procedure (seeFigure 9), and subsequently provided a globalevaluation of the pain they had suffered. Thecorrelation of global evaluations with the durationof the procedure (which ranged from 4 to66 minutes in that study) was 0.03. On the otherhand global evaluations were correlated (r =0.67) with an average of the pain reported attwo points of time: when pain was at its peak,and just before the procedure ended. For example,patient A in Figure 9 reported a more negativeevaluation of the procedure than patient B.The same pattern of duration neglect and PeaklEnd evaluations has been observed in otherstudies (Barbara L. Fredrickson and Kahneman,1993; see Kahneman, 2000a, for a discussion).These results are consistent with the hypothesisthat the extended episode (which can be consideredan ordered set of moments) is representedin memory by a typical moment of theexperience.Violations of Dominance.-A randomizedclinical experiment was conducted followingthe colonoscopy study described above. For halfthe patients, the instrument was not immediatelyremoved when the clinical examination

1466 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003Patlent APatient B0 10 20 0Tlrne (minutes)10 20Tlrne (rnlnuter)FIGURE 9. PAIN INTENSITY REPORTED BY TWO COLONOSCOPY PATIENTSended. Instead, the physician waited for about aminute, leaving the instrument stationary. Theexperience during the extra period was uncomfortable,but the procedure guaranteed that thecolonoscopy never ended in severe pain. Patientsreported significantly more favorableglobal evaluations in this experimental conditionthan in the control condition (Redelmeier etal., 2003).Violations of dominance have also beenconfirmed in choices. Kahneman et al. (1993)exposed participants to two cold-pressor experiences,one with each hand: a "short" episode(immersion of one hand in 14°C waterfor 60 seconds), and a "long" episode (theshort episode, plus an additional 30 secondsduring which the water was gradually warmedto 15°C). When they were later asked whichof the two experiences they preferred to repeat,a substantial majority chose the longtrial. This pattern of choices is predicted fromthe PeaklEnd rule of evaluation that was describedearlier. Similar violations of dominancewere observed with unpleasant soundsof variable loudness and duration (Charles A.Schreiber and Kahneman, 2000). These violationsof dominance suggest that choices betweenfamiliar experiences are made in anintuitive process of "choosing by liking." Extendedepisodes are represented in memory bya typical moment-and the desirability oraversiveness of the episode is dominated bythe remembered utility of that moment (Kah-neman, 1994). When a choice is to be made,the option that is associated with the higherremembered utility (more liked) is chosen.This mode of choice is likely to yield choicesthat do not maximize the utility that willactually be experienced (Kahneman et al.,1997).C. Other Prototype HeuristicsThe pattern of results observed in diversestudies of prototype heuristics suggests the needfor a unified interpretation, and raises a significantchallenge to treatments that deal only withone domain. A number of authors have offeredcompeting interpretations of base-rate neglect(Leda Cosmides and John Tooby, 1996;Jonathan Jay Koehler, 1996), insensitivity toscope in WTP (Raymond Kopp, 1992), andduration neglect (Ariely and Loewenstein,2000). In general however, these interpretationsare specific to a particular task, and would notcarry over to demonstrations of extension neglectin the other tasks that have been discussed.In contrast, the account offered here(and developed in greater detail by Kahnemanand Frederick, 2002) is equally applicable todiverse tasks that require an assessment of anextensional target attribute.The cases that have been discussed are onlyillustrations, not a comprehensive list of prototypeheuristics. For example, the same form ofnonextensional thinking explains why the me-

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONALITY1467dian estimate of the annual number of murdersin Detroit is twice as high as the estimate of thenumber of murders in Michigan (Kahnemanand Frederick, 2002). It also explains whyprofessional forecasters assigned a higherprobability to "an earthquake in Californiacausing a flood in which more than 1,000people will drown" than to "a flood somewherein the United States in which more than1,000 people will drown" (Tversky and Kahneman,1983).As these examples illustrate, there is no guaranteeddefense against violations of monotonicity.How could a forecaster who assigns aprobability to a lethal flood ensure (in finitetime) that there is no subset of that event whichwould have appeared even more probable?More generally, the results reviewed in thissection suggest a profound incompatibility betweenthe capabilities and operational rules ofintuitive judgment and choice and the normativestandards for beliefs and preferences. Thelogic of belief and choice requires accurateevaluation of extensional variables. In contrast,intuitive thinking operates with exemplars orprototypes that have the dimensionality of individualinstances and lack the dimension ofextension.VII. The Boundaries of Intuitive ThinkingThe judgments that people express, the actionsthey take, and the mistakes they commitdepend on the monitoring and corrective functionsof System 2, as well as on the impressionsand tendencies generated by system 1. Thissection reviews a selection of findings and ideasabout the functioning of System 2. A moredetailed treatment is given in Kahneman andFrederick (2002) and Kahneman (2003b).Judgments and choices are normally intuitive,skilled, unproblematic, and reasonablysuccessful (Klein, 1998). The prevalence offraming effects, and other indications of superficialprocessing such as the bat-and-ball problem,suggest that people mostly do not thinkvery hard and that System 2 monitors judgmentsquite lightly. On some occasions, however,the monitoring of System 2 will detect apotential error, and an effort will be made tocorrect it. The question for this section can beformulated in terms of accessibility: when dodoubts about one's intuitive judgments come tomind? The answer, as usual in psychology, is alist of relevant factors.Research has established that the ability toavoid errors of intuitive judgment is impairedby time pressure (Finucane et al., 2000), byconcurrent involvement in a different cognitivetask (Gilbert, 1989, 1991, 2002), by performingthe task in the evening for "morning people"and in the morning for "evening people" (GalenV. Bodenhausen, 1990), and, surprisingly, bybeing in a good mood (Alice M. Isen et al.,1988; Herbert Bless et al., 1996). Conversely,the facility of System 2 is positively correlatedwith intelligence (Stanovich and West, 2002),with the trait that psychologists have labeled"need for cognition" (which is roughly whetherpeople find thinking fun) (Eldar Shafir andRobyn A. LeBoeuf, 2002), and with exposure tostatistical thinking (Richard E. Nisbett et al.,1983; Franca Agnoli and David H. Krantz,1989; Agnoli, 1991).The question of the precise conditions underwhich errors of intuition are most likely to beprevented is of methodological interest to psychologists,because some controversies in theliterature on cognitive illusions are resolvedwhen this factor is considered (see Kahnemanand Frederick, 2002; Kahneman, 2003b). Oneof these methodological issues is also of considerablesubstantive interest: this is the distinctionbetween separate evaluation and jointevaluation (Hsee, 1996).In the separate evaluation condition of List'sstudy of dominance violations, for example,different groups of traders bid on two sets ofbaseball cards; in joint evaluation each traderevaluated both sets at the same time. The resultswere drastically different. Violations of monotonicity,which were very pronounced in thebetween-groups comparison, were eliminated inthe joint evaluation condition. The participantsin the latter condition evidently realized that oneof the sets of goods included the other, and wastherefore worth more. Once they had detectedthe dominance relation, the participants constrainedtheir bids to follow the rule. Thesedecisions are mediated by System 2. Thus, thereappear to be two distinct modes of choice:"choosing by liking" selects the most attractiveoption; "choosing by rule" conforms to an explicitconstraint.Prospect theory introduced the same distinctionbetween modes of choice (Kahneman and

1468 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003Tversky, 1979). The normal process correspondsto choice by liking: the decision makerevaluates each gamble in the choice set, thenselects the gamble of highest value. In prospecttheory, this mode of choice can lead to theselection of a dominated option5 However, thetheory also introduced the possibility of choiceby rule: if one option transparently dominatesthe other, the decision maker will select thedominant option without further evaluation. Totest this model, Tversky and Kahneman (1986)constructed a pair of gambles that satisfied threecriteria: (i) !gamble A dominated gamble B; (ii)the prospect-theory value of B was higher thanthe value of A; (iii) the gambles were complex,and the dominance relation only became apparentafter grouping outcomes. As expected fromother framing results, most participants in theexperiment evaluated the gambles as originallyformulated, failed to detect the relation betweenthem, chose the option they liked most, andexhibited the predicted violation of dominance.The cold-pressor experiment that was describedearlier (Kahneman et al., 1993) isclosely analogous to the study of nontransparentdominance that Tversky and Kahneman (1986)reported. A substantial majority of participantsviolated dominance in a direct and seeminglytransparent choice between cold-pressor experiences.However, postexperimental debriefingsindicated that the dominance was not in facttransparent. The participants in the experimentdid not realize that the long episode included theshort one, although they did notice that theepisodes differed- in duration. Because theyfailed to detect that one option dominated theother, the majority of participants chose as peoplecommonly do when they select an experienceto be repeated: they "chose by liking,"selected the option that had the higher rememberedutility, and thereby agreed to exposethemselves to a period of unnecessary pain(Kahneman, 1994; Kahneman et al., 1997).The complex pattern of results in the studiesof dominance in the joint-evaluation designsuggests three general conclusions: (i) choicesthat are governed by rational rules do exist, but(ii) these choices are restricted to unusual circumstances,and (iii) the activation of the rulesCumulative prospect theory (Tversky and Kahneman,1992) does not have this feature.depends on the factors of attention and accessibility.The fact that System 2 "knows" the dominancerule and "wants" to obey it onlyguarantees that the rule will be followed if apotential violation is explicitly detected.System 2 has the capability of correctingother errors, besides violations of dominance. Inparticular, the substitution of one attribute foranother in judgment inevitably leads to errorsin the weights assigned to different sourcesof information, and these could-at least inprinciple-be detected and corrected. For example,a participant in the Tom W. study (seeFigure 8a) could have reasoned as follows:"Tom W. looks very much like a library sciencestudent, but there are very few of those. I shouldtherefore adjust my impression of probabilitydownward." Although this level of reasoningshould not have been beyond the reach of thegraduate students who answered the Tom W.question, the evidence shown in Figure 8 showsthat few, if any, of these respondents had theidea of adjusting their predictions to allow forthe different base rates of the alternative outcomes.The explanation of this result in terms ofaccessibility is straightforward: the experimentprovided no explicit cues to the relevance ofbase rates.Base-rate information was not completely ignoredin experiments that provided strongercues, though the effects of this variable wereconsistently too small relative to the effect ofthe case-specific information (Jonathan St. B. T.Evans et al., 2002). The evidence of numerousstudies supports the following conclusions: (i)the likelihood that the subject will detect a misweightingof some aspect of the informationdepends on the salience of cues to the relevanceof that factor; (ii) if the misweighting is detected,there will be an effort to correct it; (iii)the correction is likely to be insufficient, and thefinal judgments are therefore likely to remainanchored on the initial intuitive impression(Gretchen B. Chapman and Johnson, 2002).Economists may be struck by the emphasison salient cues and by the absence of financialincentives from the list of major factors thatinfluence the quality of decisions and judgments.However, the claim that high stakeseliminate departures from rationality is not supportedby a careful review of the experimentalevidence (Camerer and Robin M. Hogarth,1999). A growing literature of field research and

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONALITY1469field experiments documents large and systematicmistakes in some of the most consequentialfinancial decisions that people make, includingchoices of investments (Brad M. Barber andTerrance Odean, 2000; Benartzi and Thaler,2001), and actions in the real estate market(David Genesove and Christopher J. Mayer,2001). The daily paper provides further evidenceof poor decisions with large outcomes.The present analysis helps explain why theeffects of incentives are neither large nor robust.High stakes surely increase the amount of attentionand effort that people invest in theirdecisions. But attention and effort by themselvesdo not purchase rationality or guaranteegood decisions. In particular, cognitive effortexpended in bolstering a decision already madewill not improve its quality, and the evidencesuggests that the share of time and effort devotedto such bolstering may increase when thestakes are high (Jennifer S. Lerner and Philip E.Tetlock, 1999). Effort and concentration arelikely to bring to mind a more complete set ofconsiderations, but the expansion may yield aninferior decision unless the weighting of thesecondary considerations is appropriately low.In some instances-including tasks that requirepredictions of one's future tastes-too muchcognitive effort actually lowers the quality ofperformance (Wilson and Jonathan W.Schooler, 1991). Klein (2003, Ch. 4) has arguedthat there are other situations in which skilleddecision makers do better when they trust theirintuitions than when they engage in detailedanalysis.VIII. Concluding RemarksThe rational agent of economic theory wouldbe described, in the language of the presenttreatment, as endowed with a single cognitivesystem that has the logical ability of a flawlessSystem 2 and the low computing costs of System1. Theories in behavioral economics havegenerally retained the basic architecture of therational model, adding assumptions about cognitivelimitations designed to account for specificanomalies. For example, the agent may berational except for discounting hyperbolically,evaluating outcomes as changes, or a tendencyto jump to conclusions.The model of the agent that has been presentedhere has a different architecture, whichmay be more difficult to translate into the theoreticallanguage of economics. The core ideasof the present treatment are the two-systemstructure, the large role of System 1 and theextreme context-dependence that is implied bythe concept of accessibility. The central characteristicof agents is not that they reason poorlybut that they often act intuitively. And the behaviorof these agents is not guided by whatthey are able to compute, but by what theyhappen to see at a given moment.These propositions suggest heuristic questionsthat may guide attempts to predict or explainbehavior in a given setting: "What wouldan impulsive agent be tempted to do?"'Whatcourse of action seems most natural in thissituation?" The answers to these questions willoften identify the judgment or course of actionto which most people will be attracted. Forexample, it is more natural to join a group ofstrangers running in a particular direction thanto adopt a contrarian destination. However, thetwo-system view also suggests that other questionsshould be raised: "Is the intuitively attractivejudgment or course of action in conflictwith a rule that the agent would endorse?" If theanswer to that question is positive, then "Howlikely is it in the situation at hand that therelevant rule will come to mind in time to overrideintuition?" Of course, this mode of analysisalso allows for differences between individuals,and between groups. What is natural and intuitivein a given situation is not the same foreveryone: different cultural experiences favordifferent intuitions about the meaning of situations,and new behaviors become intuitive asskills are acquired. Even when these complexitiesare taken into account, the approach to theunderstanding and prediction of behavior thathas been sketched here is simple and easy toapply, and likely to yield hypotheses that aregenerally plausible and often surprising. Theorigins of this approach are in an importantintellectual tradition in psychology, which hasemphasized "the power of the situation" (LeeRoss and Nisbett, 1991).The present treatment has developed severalthemes: that intuition and reasoning are alternativeways to solve problems, that intuition resemblesperception, that people sometimesanswer a difficult question by answering aneasier one instead, that the processing of informationis often superficial, that categories are

1470 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003represented by prototypes. All these features ofthe cognitive system were in our minds in someform when Amos Tversky and I began our jointwork in 1969, and most of them were in HerbertSimon's mind much earlier. However, the roleof emotion in judgment and decision makingreceived less attention in that work than it hadreceived before the beginning of the cognitiverevolution in psychology in the 1950's. Morerecent developments have restored a central roleto emotion, which is incorporated in the view ofintuition that was presented here. Findingsabout the role of optimism in risk taking, theeffects of emotion on decision weights, the roleof fear in predictions of harm, and the role ofliking and disliking in factual predictions-allindicate that the traditional separation betweenbelief and preference in analyses of decisionmaking is psychologically unrealistic.Incorporating a common sense psychology ofthe intuitive agent into economic models willpresent difficult challenges, especially for formaltheorists. It is encouraging to note, however,that the challenge of incorporating the firstwave of psychological findings into economicsappeared even more daunting 20 years ago, andthat challenge has been met with considerablesuccess.REFERENCESAgnoli, Franca. "Development of JudgmentalHeuristics and Logical Reasoning: TrainingCounteracts the Representativeness Heuristic."Cognitive Development, April-June1991, 6(2), pp. 195-217.Agnoli, Franca and Krantz, David H. "SuppressingNatural Heuristics by Formal Instruction:The Case of the Conjunction Fallacy." CognitivePsychology, October 1989, 21(4), pp.515-50.Alevy, Jonathan E.; List, John A. and Adamowicz,Wiktor. "More is Less: Preference Reversalsand Non-Market valuations." Workingpaper, University of Maryland, 2003.Ariely, Dan. "Seeing Sets: Representation byStatistical Properties." Psychological Science,March 2001, 12(2), pp. 157-62.Ariely, Dan and Loewenstein, George. "WhenDoes Duration Matter in Judgment and DecisionMaking?" Journal of ExperimentalPsychology: General, December 2000,129(4), pp. 508-23.Arrow, Kenneth J. "Risk Perception in Psychologyand Economics." Economic Inquiry, January1982, 20(1), pp. 1-9.Barber, Brad M. and Odean, Terrance. "Tradingis Hazardous to Your Wealth: The CommonStock Investment Performance of IndividualInvestors." Journal of Finance, April 2000,55(2), pp. 773-806.Barberis, Nicholas; Huang, Ming and Thaler,Richard H. "Individual Preferences, MonetaryGambles and the Equity Premium." NationalBureau of Economic Research(Cambridge, MA) Working Paper No.W9997, May 2003.Bargh, John A. "The Automaticity of EverydayLife," in Robert S. Wyer, Jr., ed., The automaticityof everyday life: Advances in socialcognition, Vol. 10. Mahwah, NJ: Erlbaum,1997, pp. 1-61.Benartzi, Shlomo and Thaler, Richard H. "MyopicLoss Aversion and the Equity PremiumPuzzle." Quarterly Journal of Economics,February 1995, 110(1), pp. 73-92.."Risk Aversion or Myopia? Choices inRepeated Gambles and Retirement Investments."Management Science, March 1999,47(3), pp. 364-81.. "NaYve Diversification Strategies inDefined Contribution Saving Plans." ArnericanEconomic Review, March 2001, 91(1),pp. 79-98.Bernoulli, Daniel. "Exposition of a New Theoryon the Measurement of Risk." Econometrica,January 1954, 22(1), pp. 23-36. (Originalwork published 1738.)Bless, Herbert; Clore, Gerald L.; Schwarz, Norbert;Golisano, Verana; Rabe, Christian andWolk, Marcus. "Mood and the Use of Scripts:Does a Happy Mood Really Lead to Mindlessness?'Journalof Personality and SocialPsychology, October 1996, 71(4), pp. 665-79.Bodenhausen, Galen V. "Stereotypes as JudgmentalHeuristics: Evidence of CircadianVariations in Discrimination." PsychologicalScience, September 1990, 1(5), pp. 3 19-22.Bruner, Jerome S. and Minturn, A. Leigh. "PerceptualIdentification and Perceptual Organization."Journal of General Psychology, July1955, 53, pp. 21-28.Camerer, Colin F. and Hogarth, Robin M. "TheEffect of Financial Incentives." Journal ofRisk and Uncertainty, December 1999,19(1-3), pp. 7-42.

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONALITY1471Camerer, Colin F.; Loewenstein, George andRabin, Matthew, eds. Advances in behavioraleconomics. Princeton, NJ: Princeton UniversityPress (forthcoming).Carson, Richard T. "Contingent Valuation Surveysand Tests of Insensitivity to Scope," inR. J. Kopp, W. W. Pommerhene, and N.Schwartz, eds., Determining the value of nonmarketedgoods: Economic, psychological,and policy relevant aspects of contingent valuationmethods. Boston, MA: Kluwer, 1997,pp. 127-63.Chaiken, Shelly and Trope, Yaacov, eds. Dualprocesstheories in social psychology. NewYork: Guilford Press, 1999.Chapman, Gretchen B. and Johnson, Eric J. "Incorporatingthe Irrelevant: Anchors in Judgmentsof Belief and Value," in ThomasGilovich, Dale Griffin, and Daniel Kahneman,eds., Heuristics and biases: The psychologyof intuitive thought. New York:Cambridge University Press, 2002, pp. 120-38.Choi, James J.; Laibson, David; Madrian, Brigitteand Metrick, Andrew. "Defined ContributionPensions: Plan Rules, Participant Decisionsand the Path of Least Resistance," in JamesM. Poterba, ed., Tax policy and the economy,Vol. 16. Cambridge, MA: MIT Press, 2002,pp. 67-113.Chong, Sang-Chul and Treisman, Anne. "Representationof Statistical Properties." Vision Research,February 2003, 43(4), pp. 393-404.Cohen, David and Knetsch, Jack L. "JudicialChoice &d Disparities Between Measures ofEconomic Value." Osgoode Hall Law Review,1992, 30(3), pp. 737-70.Cosmides, Leda and Tooby, John. "Are HumansGood Intuitive Statisticians After All? RethinkingSome Conclusions From the Literatureon Judgment and Uncertainty."Cognition, January 1996, 58(1), pp. 1-73.De Bondt, Werner F. M. and Thaler, Richard H."Does the Stock Market Overreact?'Journalof Finance, July 1985, 40(3), pp. 793-808.Desvousges, William H.; Johnson, F. Reed; Dunford,Richard W.; Hudson, Sara P.; Wilson, K.Nichole and Boyle, Kevin J. "Measuring NaturalResource Damages with Contingent Valuation:Tests of Validity and Reliability," inJeny A. Hausman, ed., Contingent valuation:A critical assessment. Amsterdam: North-Holland, 1993, pp. 91-164.Diamond, Peter A. "A Framework for SocialSecurity Analysis." Journal of Public Economics,December 1977, 8(3), pp. 275-98.. "Testing the Internal Consistency ofContingent Valuation Surveys." Journal ofEnvironmental Economics and Management,May 1996, 30(3), pp. 155-73.Elster, Jon. "Emotions and Economic Theory."Journal of Economic Literature, March 1998,26(1), pp. 47-74.Epstein, Seymour. "Cognitive-Experiential Self-Theory of Personality," in Theodore Millonand Melvin J. Lerner, eds., Comprehensivehandbook of psychology, volume 5: Personalityand social psychology. Hoboken, NJ:Wiley & Sons, 2003, pp. 159-84.Evans, Jonathan St. B. T.; Handley, Simon J.;Over, David E. and Perham, Nicholas. "BackgroundBeliefs in Bayesian Inference." Memoryand Cognition, March 2002, 30(2), pp.179 -90.Finucane, Melissa L.; Alhakami, Ali; Slovic, Pauland Johnson, Stephen M. "The Affect Heuristicin Judgments of Risks and Benefits."Journal of Behavioral Decision Making, JanuaryMarch2000, 13(1), pp. 1-17.Fiske, Susan T. "Stereotyping, Prejudice, andDiscrimination," in Daniel T. Gilbert, SusanT. Fiske, and Gardner Lindzey, eds., Thehandbook of social psychology, 4th Ed., Vol.1. New York: McGraw-Hill, 1998, pp. 357-41 1.Frederick, Shane W. and Fischhoff, Baruch."Scope (1n)sensitivity in Elicited Valuations."Risk, Decision, and Policy, August1998, 3(2), pp. 109-23.Fredrickson, Barbara L. and Kahneman, Daniel."Duration Neglect in Retrospective Evaluationsof Affective Episodes." Journal of Personalityand Social Psychology, July 1993,65(1), pp. 45-55.Gawande, AN. Complications: A surgeon'snotes on an imperfect science. New York:Metropolitan Books, 2002.Genesove, David and Mayer, Christopher J."Loss Aversion and Seller Behavior: Evidencefrom the Housing Market." QuarterlyJournal of Economics, November 2001,II6(4), pp. 1233-60.Gigerenzer, Gerd; Swijtink, Zeno; Porter, Theodore;Daston, Lorraine; Beatty, John andKmger, Lorenz. The empire of chance: Howprobability changed science and everyday

1472 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003life. Cambridge: Cambridge University Press,1989.Gilbert, Daniel T. "Thinlung Lightly About Others:Automatic Components of the Social InferenceProcess," in James S. Uleman andJohn A. Bargh, eds., Unintended thought.Englewood Cliffs, NJ: Prentice-Hall, 1989,pp. 189-211.. "How Mental Systems Believe."American Psychologist, February 199 1,46(2),pp. 107-19.. "Inferential Correction," in ThomasGilovich, Dale Griffin, and Daniel Kahneman,eds., Heuristics and biases: The psychologyof intuitive thought. New York:Cambridge University Press, 2002, pp. 167-84.Grether, David M. "Recent Psychological Studiesof Behavior Under Uncertainty." AmericanEconomic Review, May 1978 (Papersand Proceedings), 68(2), pp. 70-74.Higgins, E. Tory. "Knowledge Activation: Accessibility,Applicability, and Salience," in E.Tory Higgins and Arie W. Kruglanski, eds.,Social psychology: Handbook of basic principles.New York: Guilford Press, 1996, pp.133-68.Hsee, Christopher K. "The Evaluability Hypothesis:An Explanation of Preference ReversalsBetween Joint and Separate Evaluations ofAlternatives." Organizational Behavior andHuman Decision Processes, September 1996,67(3),pp. 247-57.."Less is Better: When Low-Value Op-tions are Valued More Highly Than High-Value Options." Journal of BehavioralDecision Making, June 1998, 11(2), pp. 107-21.Isen, Alice M.; Nygren, Thomas E. and Ashby, F.Gregory. "Influence of Positive Affect on theSubjective Utility of Gains and Losses: It isJust Not Worth the Risk." Journal of Personalityand Social Psychology, November1988, 55(5), pp. 710-17.Johnson, Eric J. and Goldstein, Daniel G. "DoDefaults Save Lives?'Working paper, Centerfor Decision Sciences, Columbia University,2003.Johnson, Eric J.; Hershey, John; Meszaros, Jacquelineand Kunreuther, Howard. "Framing,Probability Distortions, and Insurance Decisions."Journal of Risk and Uncertainty, August1993, 7(1), pp. 35-51.Kahneman, Daniel. "Comment," in Ronald G.Cumrnings, David S. Brookshire, and WilliamD. Schultze, eds., Valuing environmen-tal goods. Totowa, NJ: RowmanandAllenheld, 1986, pp. 185-93.. "New Challenges to the RationalityAssumption." Journal of Institutional andTheoretical Economics, March 1994, 150(1),pp. 18-36.. "Evaluation by Moments: Past and Future,"in Daniel Kahneman and Amos Tversky,eds., Choices, values, and frames. NewYork: Cambridge University Press, 2000a,pp. 693-708.."Experienced Utility and Objective Happiness:A Moment-Based Approach," in DanielKahneman and Amos Tversky, eds., Choices,values, and frames. New York: CambridgeUniversity Press, 2000b, pp. 673-92.. "A Psychological Perspective on Economics."American Economic Review, May2003a (Papers and Proceedings), 93(2), pp.162-68.. "A Perspective on Judgment andChoice: Mapping Bounded Rationality."American Psychologist, September 2003b,56(9),pp. 697-720.Kahneman, Daniel and Frederick, Shane. "RepresentativenessRevisited: Attribute Substitutionin Intuitive Judgment," in ThomasGilovich, Dale Griffin, and Daniel Kahneman,eds., Heuristics and biases: The psychologyof intuitive thought. New York:Cambridge University Press, 2002, pp. 49-81.Kahneman, Daniel; Fredrickson, Barbara L.;Schreiber, Charles A. and Redelmeier, DonaldA. "When More Pain is Preferred to Less:Adding a Better End." Psychological Science,November 1993, 4(6), pp. 401-05.Kahneman, Daniel; Knetsch, Jack and Thaler,Richard. "Fairness as a Constraint on Profitseeking:Entitlements in the Market." AmericanEconomic Review, September 1986,76(4),pp. 728-41.. "Experimental Tests of the EndowmentEffect and the Coase Theorem." Journalof Political Economy, December 1990,98(6),pp. 1325-48.. "The Endowment Effect, Loss Aversion,and Status Quo Bias: Anomalies." Journalof Economic Perspectives, Winter 1991,5(1),pp. 193-206.

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATIONALITY1473Kahneman, Daniel and Lovallo, Daniel. "TimidChoices and Bold Forecasts: A CognitivePerspective on Risk Taking." ManagementScience, January 1993, 39(1), pp. 17-31.Kahneman, Daniel; Ritov, Ilana and Schkade,David. "Economic Preferences or AttitudeExpressions? An Analysis of Dollar Responsesto Public Issues." Journal of Riskand Uncertainty, December 1999, 19(1-3),pp. 203-35.Kahneman, Daniel; Slovic, Paul and Tversky,Amos, eds. Judgment under uncertainty: Heuristicsand biases. New York: CambridgeUniversity Press, 1982.Kahneman, Daniel and Tversky, Amos. "On thePsychology of Prediction." PsychologicalReview, July 1973, 80(4), pp. 237-51.. "Prospect Theory: An Analysis of DecisionsUnder Risk." Econometrica, March1979, 47(2), pp. 263-91.-, eds. Choices, values, andframes. NewYork: Cambridge University Press, 2000.Kahneman, Daniel; Wakker, Peter P. and Sarin,Rakesh. "Back to Bentham? Explorations ofExperienced Utility." Quarterly Journal ofEconomics, May 1997,112(2), pp. 375-405.Keren, Gideon and Wagenaar, Willem A. "Violationsof Utility Theory in Unique and RepeatedGambles." Journal of ExperimentalPsychology: Learning, Memory, and Cognition,July 1987, 13(3), pp. 387-91.Klein, Gary. Sources of power: How peoplemake decisions. Cambridge, MA: MIT Press,1998.. Intuition at work: Why developingyour gut instincts will make you better atwhat you do. New York: Doubleday, 2003.Koehler, Jonathan Jay. "The Base-Rate FallacyReconsidered: Descriptive, Normative, andMethodological Challenges." Behavioral andBrain Sciences, March 1996, 19, pp. 1-53.Kopp, Raymond. "Why Existence Value Shouldbe Used in Cost-Benefit Analysis." Journalof Policy Analysis and Management, Winter1992, 11(1), pp. 123-30.Kunreuther, Howard. "The Changing SocietalConsequences of Risks From Natural Hazards."Annals of the American Academy ofPolitical and Social Science, May 1979,443(443), pp. 104-16.Langer, Ellen J.; Blank, Arthur and Chanowitz,Benzion. "The Mindlessness of OstensiblyThoughtful Action: The Role of 'Placebic'Information in Interpersonal Interaction."Journal of Personality and Social Psychology,June 1978, 36(6), pp. 635-42.LeDow, Joseph E. "Emotion Circuits in theBrain." Annual Review of Neuroscience,March 2000, 23, pp. 155-84.Lerner, Jennifer S. and Tetlock, Philip E. "Accountingfor the Effects of Accountability."Psychological Bulletin, March 1999, 125(2),pp. 255-75.List, John A. "Preference Reversals of a DifferentKind: The 'More Is Less' Phenomenon."American Economic Review, December2002, 92(5), pp. 1636-43.. "Does Market Experience EliminateMarket Anomalies?'Quarterly Journal ofEconomics, February 2003a, 118(1), pp. 47-71.. "Neoclassical Theory Versus ProspectTheory: Evidence From the Marketplace."National Bureau of Economic Research(Cambridge, MA) Working Paper No.W9736, 2003b; Econometrica, 2004 (forthcoming).Loewenstein, George. "Out of Control: VisceralInfluences on Behavior." Organizational Behaviorand Human Decision Processes,March 1996, 65(3), pp. 272-92.. "Emotions in Economic Theory andEconomic Behavior." American EconomicReview, May 2000 (Papers and Proceedings),90(2), pp. 426-32.Loewenstein, George; Weber, Elke U.; Hsee,Christopher K. and Welch, N. "Risk as Feelings."Psychological Bulletin, March 2001,127(2), pp. 267-86.Luce, R. Duncan; Krantz, David H.; Suppes,Patrick and Tversky, Amos. Foundations ofmeasurement, volume 3: Representation, axiomatization,and invariance. San Diego, CA:Academic Press, 1990.Madrian, Brigitte and Shea, Dennis. "The Powerof Suggestion: Inertia in 40 1 (k) Participationand Savings Behavior." Quarterly Journal ofEconomics, November 200 1, 116(4), pp.1149-87.Mellers, Barbara. "Choice and the RelativePleasure of Consequences." PsychologicalBulletin, November 2000, 126(6), pp. 910-24.Nisbett, Richard E.; Krantz, David H.; Jepson,Christopher and Kunda, Ziva. "The Use ofStatistical Heuristics in Everyday Inductive

1474 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003Reasoning." Psychological Review, October1983, 90(4), pp. 339-63.Pashler, Harold E. The psychology of attention.Cambridge, MA: MIT Press, 1998.Posner, Michael I. and Keele, Stephen W. "On theGenesis of Abstract Ideas." Journal of ExperimentalPsychology, Pt. 1, 1968, 77(3), pp.353-63.Rabin, Matthew. "Inference by Believers in theLaw of Small Numbers." Quarterly Journalof Economics, August 2002, 17(3), pp. 775-816.Read, Daniel; Loewenstein, George and Rabin,Matthew. "Choice Bracketing." Journal ofRisk and Uncertainty, December 1999,19(1-3), pp. 171-97.Redelmeier, Donald A. and Kahneman, Daniel."Patients' Memories of Painful MedicalTreatments: Real-time and RetrospectiveEvaluations of Two Minimally Invasive Procedures."Pain, July 1996, 66(1), pp. 3-8.Redelmeier, Donald A.; Katz, Joel and Kahneman,Daniel. "Memories of Colonoscopy: ARandomized Trial." Pain, July 2003, 104(1-2), pp. 187-94.Rosch, Eleanor and Mervis, Carolyn B. "FamilyResemblances: Studies in the Internal Structureof Categories." Cognitive Psychology,October 1975, 7(4), pp. 573-605.Ross, Lee and Nisbett, Richard E. The person andthe situation. New York: McGraw-Hill,1991.Rottenstreich, Yuval and Hsee, Christopher K."Money, Kisses and Electric Shocks: On theAffective Psychology of Risk." PsychologicalScience, May 2001, 12(3), pp. 185-90.Rozin, Paul and Nemeroff, Carol. "SympatheticMagical Thinking: The Contagion and SimilarityHeuristics," in Thomas Gilovich, DaleGriffin, and Daniel Kahneman, eds., Heuristicsand biases: The psychology of intuitivethought. New York: Cambridge UniversityPress, 2002, pp. 201-16.Samuelson, William and Zeckhauser, Richard."Status Quo Bias in Decision Making." Journalof Risk and Uncertainty, March 1988,](I), pp. 7-59.Schelling, Thomas C. Choice and consequence:Perspectives of an errant economist.Cambridge, MA: Harvard UniversityPress, 1984.Schreiber, Charles A. and Kahneman, Daniel."Determinants of the Remembered Utility ofAversive Sounds." Journal of ExperimentalPsychology: General, March 2000, 129(1),pp. 27-42.Shafir, Eldar and LeBoeuf, Robyn A. "Rationality."Annual Review of Psychology, February2002, 53(1), pp. 419-517.Shiller, Robert J. Irrational exuberance. Princeton,NJ: Princeton University Press, 2000.Shleifer, Andrei. InefJicient markets: An introductionto behavioral jnance. New York:Oxford University Press, 2000.Simon, Herbert A. "A Behavioral Model of RationalChoice." Quarterly Journal of Economics,February 1955, 69(1), pp. 99-1 18.. "Information Processing Models ofCognition." Annual Review of Psychology,February 1979, 30, pp. 363-96.Simon, Herbert A. and Chase, William G. "Skillin Chess." American Scientist, July 1973,61(4), pp. 394-403.Sloman, Steven A. "Two Systems of Reasoning,"in Thomas Gilovich, Dale Griffin, and DanielKahneman, eds., Heuristics and biases: Thepsychology of intuitive thought. New York:Cambridge University Press, 2002, pp. 379-96.Slovic, Paul; Finucane, Melissa; Peters, Ellen andMacGregor, Donald G. "The Affect Heuristic,"in Thomas Gilovich, Dale Griffin, andDaniel Kahneman, eds., Heuristics and biases:The psychology of intuitive thought.New York: Cambridge University Press,2002, pp. 397-420.Stanovich, Keith E. and West, Richard F. "IndividualDifferences in Reasoning: Implicationsfor the Rationality Debate?" Behavioraland Brain Sciences, October 2000,23(5), pp.645-65.. "Individual Differences in Reasoning:Implications for the Rationality Debate?" inThomas Gilovich, Dale Griffin, and DanielKahneman, eds., Heuristics and biases: Thepsychology of intuitive thought. New York:Cambridge University Press, 2002, pp. 421-40.Strack, Fritz; Martin, Leonard and Schwarz,Norbert. "Priming and Communication: SocialDeterminants of Information Use inJudgments of Life Satisfaction." EuropeanJournal of Social Psychology, October-November 1988, 18(5), pp. 429-42.Thaler, Richard H. "Toward a Positive Theoryof Consumer Choice." Journal of Economic

VOL. 93 NO. 5KAHNEMAN: MAPS OF BOUNDED RATlONALITY1475Behavior and Organization, March 1980,1(1), pp. 36-90.. "Mental Accounting and ConsumerChoice." Marketing Science, Summer 1985,4(3), pp. 199-214.. Quasi rational economics. New York:Russell Sage Foundation, 1991.. The winner's curse: Paradoxes andanomalies of economic life. New York: FreePress, 1992.."Mental Accounting Matters." Journalof Behavioral Decision Making, July 1999,12(3), pp. 183-206.. "Toward a Positive Theory of ConsumerChoice," in Daniel Kahneman andAmos Tversky, eds., Choices, values, andframes. New York: Cambridge UniversityPress, 2000, pp. 268-87.Tversky, Amos and Kahneman, Daniel. "Judgmentunder Uncertainty: Heuristics andBiases." Science, September 1974,185(4157), pp. 1124-31.. "The Framing of Decisions and thePsychology of Choice." Science, January1981,211(4481), pp. 453-58.-."Extensional Versus Intuitive Reasoning:The Conjunction Fallacy in ProbabilityJudgment." Psychological Review, October1983, 90(4), pp. 293-315.. "Rational Choice and the Framing ofDecisions." Journal of Business, October1986, 59(4), pp. S251-78.. "Loss Aversion in Riskless Choice: AReference-Dependent Model." QuarterlyJournal of Economics, November 1991,106(4), pp. 1039-61.. "Advances in Prospect Theory: CumulativeRepresentation of Uncertainty." Journalof Risk and Uncertainty, October 1992,5(4), pp. 297-323.Tversky, Amos and Redelmeier, Donald A. "Onthe Framing of Multiple Prospects." PsychologicalScience, May 1992, 3(3), pp. 191-93.Wilson, Timothy D. Strangers to ourselves:Discovering the adaptive unconscious.Cambridge, MA: Harvard University Press,2002.Wilson, Timothy D. and Schooler, Jonathan W."Thinking Too Much: Introspection Can Reducethe Quality of Preferences and Decisions."Journal of Personality and SocialPsychology, ~ebn&y 1991, 60(2), pp. 181-92.Zajonc, Robert B. "Emotions," in Daniel T. Gilbert,Susan T. Fiske, and Gardner Lindzey,eds., Handbook of socialpsychology, 4th Ed.,Vol. 1. New York: Oxford University Press,1998, pp. 591-632.

http://www.jstor.orgLINKED CITATIONS- Page 1 of 5 -You have printed the following article:Maps of Bounded Rationality: Psychology for Behavioral EconomicsDaniel KahnemanThe American Economic Review, Vol. 93, No. 5. (Dec., 2003), pp. 1449-1475.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28200312%2993%3A5%3C1449%3AMOBRPF%3E2.0.CO%3B2-%23This article references the following linked citations. If you are trying to access articles from anoff-campus location, you may be required to first logon via your library web site to access JSTOR. Pleasevisit your library's website or contact a librarian to learn about options for remote access to JSTOR.ReferencesTrading Is Hazardous to Your Wealth: The Common Stock Investment Performance ofIndividual InvestorsBrad M. Barber; Terrance OdeanThe Journal of Finance, Vol. 55, No. 2. (Apr., 2000), pp. 773-806.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28200004%2955%3A2%3C773%3ATIHTYW%3E2.0.CO%3B2-FMyopic Loss Aversion and the Equity Premium PuzzleShlomo Benartzi; Richard H. ThalerThe Quarterly Journal of Economics, Vol. 110, No. 1. (Feb., 1995), pp. 73-92.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28199502%29110%3A1%3C73%3AMLAATE%3E2.0.CO%3B2-TRisk Aversion or Myopia? Choices in Repeated Gambles and Retirement InvestmentsShlomo Benartzi; Richard H. ThalerManagement Science, Vol. 45, No. 3. (Mar., 1999), pp. 364-381.Stable URL:http://links.jstor.org/sici?sici=0025-1909%28199903%2945%3A3%3C364%3ARAOMCI%3E2.0.CO%3B2-UNaive Diversification Strategies in Defined Contribution Saving PlansShlomo Benartzi; Richard H. ThalerThe American Economic Review, Vol. 91, No. 1. (Mar., 2001), pp. 79-98.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28200103%2991%3A1%3C79%3ANDSIDC%3E2.0.CO%3B2-8

http://www.jstor.orgLINKED CITATIONS- Page 2 of 5 -Exposition of a New Theory on the Measurement of RiskDaniel BernoulliEconometrica, Vol. 22, No. 1. (Jan., 1954), pp. 23-36.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28195401%2922%3A1%3C23%3AEOANTO%3E2.0.CO%3B2-XDoes the Stock Market Overreact?Werner F. M. De Bondt; Richard ThalerThe Journal of Finance, Vol. 40, No. 3, Papers and Proceedings of the Forty-Third Annual MeetingAmerican Finance Association, Dallas, Texas, December 28-30, 1984. (Jul., 1985), pp. 793-805.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28198507%2940%3A3%3C793%3ADTSMO%3E2.0.CO%3B2-QEmotions and Economic TheoryJon ElsterJournal of Economic Literature, Vol. 36, No. 1. (Mar., 1998), pp. 47-74.Stable URL:http://links.jstor.org/sici?sici=0022-0515%28199803%2936%3A1%3C47%3AEAET%3E2.0.CO%3B2-9Loss Aversion and Seller Behavior: Evidence from the Housing MarketDavid Genesove; Christopher MayerThe Quarterly Journal of Economics, Vol. 116, No. 4. (Nov., 2001), pp. 1233-1260.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28200111%29116%3A4%3C1233%3ALAASBE%3E2.0.CO%3B2-JRecent Psychological Studies of Behavior under UncertaintyDavid M. GretherThe American Economic Review, Vol. 68, No. 2, Papers and Proceedings of the Ninetieth AnnualMeeting of the American Economic Association. (May, 1978), pp. 70-74.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28197805%2968%3A2%3C70%3ARPSOBU%3E2.0.CO%3B2-Z

http://www.jstor.orgLINKED CITATIONS- Page 3 of 5 -A Psychological Perspective on EconomicsDaniel KahnemanThe American Economic Review, Vol. 93, No. 2, Papers and Proceedings of the One HundredFifteenth Annual Meeting of the American Economic Association, Washington, DC, January 3-5,2003. (May, 2003), pp. 162-168.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28200305%2993%3A2%3C162%3AAPPOE%3E2.0.CO%3B2-5Fairness as a Constraint on Profit Seeking: Entitlements in the MarketDaniel Kahneman; Jack L. Knetsch; Richard ThalerThe American Economic Review, Vol. 76, No. 4. (Sep., 1986), pp. 728-741.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28198609%2976%3A4%3C728%3AFAACOP%3E2.0.CO%3B2-IExperimental Tests of the Endowment Effect and the Coase TheoremDaniel Kahneman; Jack L. Knetsch; Richard H. ThalerThe Journal of Political Economy, Vol. 98, No. 6. (Dec., 1990), pp. 1325-1348.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28199012%2998%3A6%3C1325%3AETOTEE%3E2.0.CO%3B2-WAnomalies: The Endowment Effect, Loss Aversion, and Status Quo BiasDaniel Kahneman; Jack L. Knetsch; Richard H. ThalerThe Journal of Economic Perspectives, Vol. 5, No. 1. (Winter, 1991), pp. 193-206.Stable URL:http://links.jstor.org/sici?sici=0895-3309%28199124%295%3A1%3C193%3AATEELA%3E2.0.CO%3B2-VTimid Choices and Bold Forecasts: A Cognitive Perspective on Risk TakingDaniel Kahneman; Dan LovalloManagement Science, Vol. 39, No. 1. (Jan., 1993), pp. 17-31.Stable URL:http://links.jstor.org/sici?sici=0025-1909%28199301%2939%3A1%3C17%3ATCABFA%3E2.0.CO%3B2-IProspect Theory: An Analysis of Decision under RiskDaniel Kahneman; Amos TverskyEconometrica, Vol. 47, No. 2. (Mar., 1979), pp. 263-292.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197903%2947%3A2%3C263%3APTAAOD%3E2.0.CO%3B2-3

http://www.jstor.orgLINKED CITATIONS- Page 4 of 5 -Back to Bentham? Explorations of Experienced UtilityDaniel Kahneman; Peter P. Wakker; Rakesh SarinThe Quarterly Journal of Economics, Vol. 112, No. 2, In Memory of Amos Tversky (1937-1996).(May, 1997), pp. 375-405.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28199705%29112%3A2%3C375%3ABTBEOE%3E2.0.CO%3B2-FWhy Existence Value Should Be Used in Cost-Benefit AnalysisRaymond J. KoppJournal of Policy Analysis and Management, Vol. 11, No. 1. (Winter, 1992), pp. 123-130.Stable URL:http://links.jstor.org/sici?sici=0276-8739%28199224%2911%3A1%3C123%3AWEVSBU%3E2.0.CO%3B2-VThe Changing Societal Consequences of Risks from Natural HazardsHoward KunreutherAnnals of the American Academy of Political and Social Science, Vol. 443, Risks and Its Treatment:Changing Societal Consequences. (May, 1979), pp. 104-116.Stable URL:http://links.jstor.org/sici?sici=0002-7162%28197905%29443%3C104%3ATCSCOR%3E2.0.CO%3B2-WPreference Reversals of a Different Kind: The "More Is Less" PhenomenonJohn A. ListThe American Economic Review, Vol. 92, No. 5. (Dec., 2002), pp. 1636-1643.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28200212%2992%3A5%3C1636%3APROADK%3E2.0.CO%3B2-UEmotions in Economic Theory and Economic BehaviorGeorge LoewensteinThe American Economic Review, Vol. 90, No. 2, Papers and Proceedings of the One HundredTwelfth Annual Meeting of the American Economic Association. (May, 2000), pp. 426-432.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28200005%2990%3A2%3C426%3AEIETAE%3E2.0.CO%3B2-LThe Power of Suggestion: Inertia in 401(k) Participation and Savings BehaviorBrigitte C. Madrian; Dennis F. SheaThe Quarterly Journal of Economics, Vol. 116, No. 4. (Nov., 2001), pp. 1149-1187.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28200111%29116%3A4%3C1149%3ATPOSII%3E2.0.CO%3B2-%23

http://www.jstor.orgLINKED CITATIONS- Page 5 of 5 -A Behavioral Model of Rational ChoiceHerbert A. SimonThe Quarterly Journal of Economics, Vol. 69, No. 1. (Feb., 1955), pp. 99-118.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28195502%2969%3A1%3C99%3AABMORC%3E2.0.CO%3B2-AMental Accounting and Consumer ChoiceRichard ThalerMarketing Science, Vol. 4, No. 3. (Summer, 1985), pp. 199-214.Stable URL:http://links.jstor.org/sici?sici=0732-2399%28198522%294%3A3%3C199%3AMAACC%3E2.0.CO%3B2-8Judgment under Uncertainty: Heuristics and BiasesAmos Tversky; Daniel KahnemanScience, New Series, Vol. 185, No. 4157. (Sep. 27, 1974), pp. 1124-1131.Stable URL:http://links.jstor.org/sici?sici=0036-8075%2819740927%293%3A185%3A4157%3C1124%3AJUUHAB%3E2.0.CO%3B2-MThe Framing of Decisions and the Psychology of ChoiceAmos Tversky; Daniel KahnemanScience, New Series, Vol. 211, No. 4481. (Jan. 30, 1981), pp. 453-458.Stable URL:http://links.jstor.org/sici?sici=0036-8075%2819810130%293%3A211%3A4481%3C453%3ATFODAT%3E2.0.CO%3B2-3Rational Choice and the Framing of DecisionsAmos Tversky; Daniel KahnemanThe Journal of Business, Vol. 59, No. 4, Part 2: The Behavioral Foundations of Economic Theory.(Oct., 1986), pp. S251-S278.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28198610%2959%3A4%3CS251%3ARCATFO%3E2.0.CO%3B2-CLoss Aversion in Riskless Choice: A Reference-Dependent ModelAmos Tversky; Daniel KahnemanThe Quarterly Journal of Economics, Vol. 106, No. 4. (Nov., 1991), pp. 1039-1061.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28199111%29106%3A4%3C1039%3ALAIRCA%3E2.0.CO%3B2-O

Theory of Finance from the Perspective of Continuous TimeRobert C. MertonThe Journal of Financial and Quantitative Analysis, Vol. 10, No. 4, 1975 Proceedings. (Nov.,1975), pp. 659-674.Stable URL:http://links.jstor.org/sici?sici=0022-1090%28197511%2910%3A4%3C659%3ATOFFTP%3E2.0.CO%3B2-5The Journal of Financial and Quantitative Analysis is currently published by University of Washington School of BusinessAdministration.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/uwash.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgThu Nov 1 06:11:33 2007

JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSISNovember 1975THEORY OF FINANCE FROM THE PERSPECTIVE OF CONTINUOUS TIMERobert C. Merton*It is not uncommon on occasions such as this to talk about the shortcomings in thetheory of Finance, and to emphasize how little progress has been made in answering thebasic questions in Finance, despite enormous research efforts. Indeed, it is not uncommonon such occasions to attack our basic "mythodology," particularly the "Ivory Tower" natureof our assumptions, as the major reasons for our lack of progress. Like a Sunday morningsermon, such talks serve many useful functions. For one, they serve to deflate our professionalegos. For another, they serve to remind us that the importance of a contributionas judged by our professional peers (the gold we really work for) is often not closelyaligned with its operational importance in the outside world. Also, such talks serve tocomfort those just entering the field, by letting them know that there is much left to dobecause so little has been done. While such talks are not uncommon, this is not what mytalk is about. Rather, my discussion centers on the positive progress made in the developmentof a theory of Finance using the continuous-time mode of analysis.Hearing this in 1975, amidst an economic recession with a baffling new disease called"stagflation" and with our financial markets only beginning to recover from the worstturmoil in almost 40 years, some will say that I am embarked on a fool's errand. Perhaps.At any rate, on this errand, I shall discuss the continuous-time solutions to some of thebasic problems of Finance: portfolio selection, capital market equilibrium, and the pricingof capital assets; the derived functions of financial intermediaries and instruments;and the pricing of corporate liabilities. Rather than dwelling on the technical aspectsof obtaining these solutions, I will discuss the substantive results and why they seem todiffer from those obtained in other modes of analysis. While my main interest is in thesubstantive results, some methodological discussion is necessary because the continuoustimemode is relatively new. However, I will attempt to keep this discussion to a minimumby emphasizing only those assumptions that differ from its discrete-time counterpart, andleave those assumptions common to both types of analysis as understood.The natural beginning point for the development of a theory of Finance is the problemof lifetime consumption and portfolio selection for the individual consumer or householdunder uncertainty. There is a long standing tradition in economic theory to take the existenceof households and their tastes as 'tgivens," as exogenous to the theory. But thistradition does not extend to economic organizations and institutions: that is, they areregarded as existing primarily because of the functions they serve instead of functioningprimarily because they exist. Economic organizations and institutions, unlike householdsand their tastes, are endogenous to the theory. To derive the functions of these financial* Massachusetts Institute of Technology. Aid from the Natural Science Foundation isqra tef ull y acknowledged.

organizations and institutions, therefore, we must first derive the behavior of individualhouseholds.The basic lifetime consumption-portfolio selection problem can be stated as follows:at each point in time, the consumer must make two types of decisions: (1) How much ofhis wealth to consume (the "consumption choice"); (2) How to allocate that part of hiswealth that he does not consume, across alternative assets (the "portfolio choice"). Itis assumed that he makes these decisions so as to maximize the expected value of hisutility of lifetime consumption. This function is usually represented as a sum (or inthe case of continuous-time, a time integral) of strictly concave von-Neumann-Morgensternutility functions for consumption at each date plus possibly an end-of-life utility func-tion of wealth representing any bequest motives.So formulated, a set of stochastic processes for the state variables, typically thereturns on assets, are posited, either as objective probability distributions for thefuture course of returns or as representations of the investor's subjective beliefs, andthe problem is solved by stochastic dynamic programming. A complete solution containsthe individual's demands for consumption and assets as a function of age, wealth, and theother relevant state variables. To this point, of course, the discussion is consistentwith either a discrete-time or continuous-time formulation.While there are differing assumptions about the continuous-time formulation of theproblem depending upon the stochastic processes posited, there are three assumptions com-mon to all such formulations: Namely,(1) The capital markets are assumed to be open all the time, and therefore economicagents have the opportunity to trade continuously.(2) Prices of assets traded in speculative markets satisfy the "Efficient Markets Hypo-thesis" of Fama and samue1son.l Namely, assets are priced so that the stochasticprocesses describing the unanticipated parts of their returns (i.e.1 the actual returnsminus their expected value) are a martingale. This assumption does not imply an independentincrements process although such a process satisfies this assumption.(3) The stochastic processes generating the state variables can be described as either:[I] Diffusion processes with continuous sample paths. Simply described,the state variables generated by these processes are changing all thetime but the magnitude of such changes are small over a short timeperiod.[2] Compound Poisson processes with step function type sample paths.Simply described, the state variables generated by these processeswill, almost certainly, over a short enough time interval have nochange, or with a very small probability, a radical change or"jump" will occur.[31 A mixture of both types.While all three types have been used in the Finance literaturet2 most of the best-known'see Fama [51 and Samuelson [23].*see Merton [lo-171 ; Black and Scholes [I, 21 ; Cox and Ross [41; Merton and Samuelson[181.

esults from continuous-time analysis have come from restricting the state variabledynamics to being diffusion processes with continuous sample paths. Indeed, since vir-tually any reasonable stochastic process arising in an economics context can be adequatelyapproximated by some mixture of these two types, I would expect any serious disagreementwith the stochastic process assumption would be on the use of a special form of theseprocesses, rather than with the processes themselves.The basic assumptions established, let us return to the consumption-portfolio prob-lem, leaving for later the discussion of the merits of the assumptions. In its simplestfoAI3 the continuous-time version of the problem assumes that the only source of uncer-tainty facing the consumer is the rate of return on assets. It is further assumed thatthese returns are generated by diffusion processes with continuous sample paths and thatreturns are serially independent and identically distributed through time, i.e., thatprices follow a geometric Brownian motion and hence,the prices are lognormally distributed.Also, it is assumed that there is a single consumption good.In solving this problem, as in more general forms of the continuous time analysis,the first-order conditions for optimal demands for assets are linear, and hence the demandfunctions can be solved for explicitly by matrix inversion. Moreover, in this problem,the relative demands for risky assets, i.e., the demand for, say, risky asset i dividedby the demand for risky asset j, is independent of the investor's preferences of wealthlevel, and indeed, depend only on the instantaneous means, variances, and covariances ofthe returns. From this, it is a short step to prove a mutual fund or separation theorem:namely, that all investors agreeing on the distribution of returns will be indifferentbetween choosing their portfolios from among the basic securities or from just two mutualfunds. Further, the separation is complete because the compositions of two funds can bedetermined solely from the "technological" data about returns without knowledge of inves-tors' preferences, wealth levels, or time horizons. Moreover, if one of the assets isriskless, then one fund can be that asset and the other need only have risky assets, andin this case, the risky fund is called the "optimal combination of risky assets."though these results are identical in structure to the classic Markowitz-Tobin mean-variance findings, their derivation here comes from a quite different set of assumptions.The classic mean-variance results are deduced in a static framework by hypothesizingthat mean and variance are sufficient statistics for making decisions. Indeed, when itwas shown that the only conditions under which this hypothesis is consistent with expectedutility maximization are if returns are normally distributed or if utility functions arequadratic, economists (with the exception of those in Finance) lost interest in this ap-proach (except for example purposes) and returned to the more general framework of expectedutility maximization.In contrast, the continuous-time results come from an intertemporal model, are con-sistent with any concave utility function, and assume a return structure consistent withlimited liability: namely, the lognormal distribution which has for a long time been a4prototype distribution for security returns.3~eeMerton [I01 and [ll, section 51.*~tshould be emphasized that the lognormality assumption applies only in the simpleform of the continuous time formulation, and is not essential to the basic simplificationsgained from this mode of analysis.Al-

The natural question to ask is: "Why does it work here, when it didn't in discretetime?" What rabbits went into the hat? Indeed, one should be suspicious about any resultsthat obtain in a continuous-time formulation but not in its discrete counterpart.There are two "rabbits": one, the assumption that investors can revise their portfoliosfrequently, and two, that prices can only change by small amounts in short periods oftime. Moreover, the continuous-time result is consistent with the discrete-time solutionwhen the appropriate comparison is made.To see this, I make a short digression: There are three time intervals or horizonsinvolved in the consumption-portfolio problem. (1) The trading horizon, is the minimumlength of time between which successive transactions by economic agents can be made inthe market. This is determined by the structure of the markets in the economy. For example,how frequently the market is open, and this time scale is not determined by theindividual investor. (2) The decision horizon, is the length of time between which theinvestor makes successive decisions. So, for example, an investor with a fixed decisioninterval of one month, who makes a consumption decision and portfolio allocation todaywill under no conditions make any new decisions or take any action prior to one monthfrom now. (3) The planning horizon, is the maximum length of time for which the investorgives any weight in his utility function. Typically, this time period would correspondto the balance of the consumer's lifetime. Actually, there is a fourth time interval,not directly related to the problem's solution but related to empirical testing of thederived behavior. I call this the observation horizon. It is the length of time betweensuccessive observations of the data by the tester, and is typically, either daily, weekly,monthly, quarterly, or annually. It is useful to keep these three or four different timeintervals in mind when evaluating the relative merits of alternative formulations for thesame problem. Indeed, the choice of time intervals has a significant impact on the derivedbehavior: a fact too often neglected in many analyses.The one-period or static approach to portfolio selection implicitly assumes that thedecision and planning horizons are the same: "one-period." Moreover, when such modelsare aggregated to determine market equilibrium relationships, it is further implicitlyassumed that these intervals are the same for all investors, and therefore, correspondto the trading interval. Further, when such models are tested, the tester usually assumesthat these three intervals are in turn equal to the observation interval from whichhe has chosen his data.In the typical multiperiod, discrete-time analysis, the trading and decision intervalsare assumed equal and the same for all participants. However, the actual time lengthof these intervals is left unspecified. Hence, while usually not recognized explicitly,every such solution derived has as an implicit argument the length of the time interval,denoted here by "h." Clearly, if one were to vary the "h" in such solutions, the derivedbehavior of the investors would change, as indeed would any deduced equilibrium relationship.Moreover, for any derived behavior to be true for an arbitrary discrete-time model(i.e., one where "h" is not specified), it would have to be invariant to "h." Think aboutwhat this means: such a result would have to obtain whether investors had the opportunityto revise their portfolios every day or were "frozen" into their investments for tenyears. In this light, it is not surprising that there are few results from these arbitrary

discrete-time models, and those that do obtain are for the most part a qualitative na-ture such as: "risk-averse investors diversify."By contrast, the continuous-time model is very explicit about the value of "h":namely, h = 0.Of course, this is only a theoretical abstraction since actual continuoustrading is not possible. However, with a few technical exceptions the continuous-timesolution is the valid continuous limit of the discrete-time solution as the trading in-terval h tends to zero. I.e., given a delta, I can always find an "h" small enough sothat the difference between the continuous-time solution and its discrete counterpartfor that h is less than delta, using a reasonable metric for measuring "difference."Thus, the continuous-time solution is a valid approximation to the discrete-time solu-tion, and its accuracy is a function of the actual structure of returns and the lengthof the "true" discrete time interval. And it is in this sense that the continuous-timeand discrete-time results are consistent.While I thought this correspondence was clear from the derivations in my papers, ithas periodically been rediscovered. Indeed, six years after my first paper appeared inprint, a new twist in its rediscovery has been to use it to argue for the superiority ofdiscrete-time analysis over the continuous analysis because discrete-time includes con-5tinuous time as a limiting case.While I am on the subject of such comparisons, the major substantive results ob-tained in discrete-time analysis have required the assumption of a specific utility func-tion or family of functions (for example, the HARA family). Quite aside from the issueof whether assuming a specific family of utility functions is superior to assuming aspecific family of stochastic processes, the limited results of sharing rules and separa-tion theorems in the discrete case not only require investors to have the same utilityfunctions but they also must have the same decision interval (what I have called "h").Indeed, for such results to be empirically testable, the tester will have to settle onwhat that interval is. In this sense, the discrete analysis is operationally no moregeneral than the continuous analysis. Moreover, having looked at the data on stock andbond returns, if that interval is less than a month, then the discrete and continuoussolutions will be virtually the same.A more serious criticism of the realism of the continuous-model is that with trans-actions costs investors cannot trade continuously. This is certainly true. Indeed, onereason often given for finite trading-intervals is to give implicit, if not explicit,recognition to these costs. I have argued that this is unsatisfactory because thelength of time between trades in the presence of such costs will almost certainly be"action-oriented" and therefore stochastic in nature, and the proper way to handle thisproblem is to start with the continuous-time model and deduce the optimal intervals. Ina recent paper, Magill and Constantinides [9] have deduced such solutions, and the op-timal trading intervals are discrete and stochastic. Indeed, the investor could end uptrading more than once in a day or not for many months, depending on the ex-post timepath followed by prices. The derived behavior for investors is to trade when the gainfrom better diversification offsets the cost of transactinq. Their analysis also castslight on an issue raised earlier: namely, there are some cases where the limit of thediscrete-time solution is not the continuous solution. For example, if an investor has5~ee Rubinstein [22, p. 51.

an isoelastic utility function and if security returns are lognormally distributed,then in a standard discrete-time analysis, such an investor will never choose to borrowor shortHowever, in a continuous-time analysis, the same investor may wellchoose to borrow or short sell. Which is the more "reasonable" description? The Magill-Constantinides analyses demonstrate that even though the trading intervals are discretewith probability one, investors with utility functions in the HARA family may wellchoose to borrow or short sell. The reason for the difference in derived behavior be-tween the standard discrete-time and the stochastic discrete-time analyses is clear.In the former, the investor is "frozen" into holding his portfolio until the end of theperiod, and hence by shortselling, or borrowing, risks ruin. In the latter, the investorcan revise his portfolio at any time (although he incurs a cost to do so) and hence hewill readjust his portfolio, when necessary, to avoid ruin. I submit that the latter be-havior is a better description of how investors behave, and it illustrates why using dis-crete-time analysis as an implicit method of recognizing transactions costs is a poorsubstitute for its explicit recognition in a continuous-time framework.In summary, the continuous-time solution is consistent with its discrete-timecounterpart when the trading interval is "small," and to my mind, the assumptions re-quired are descriptive of capital markets as they actually function. Moreover, thecontinuous-time analysis has all the virtues of simplicity and empirical tractabilityfound in the classic mean-variance analysis but without its objectionable assumptions.~eturning to the substantive findings of the basic consumption-portfolio selec-tion problem, once the separation or mutual fund theorem is proven, it is straight-forward to derive a continuous-time version of the Capital Asset Pricing Model. Indeed,in any model where all investors hold risky assets in the same relative proportions,it follows immediately that this "optimal combination of risky assetso' must be the marketportfolio for equilibrium to obtain. For if all investors want to hold risky assetsin the same relative proportions, then there is only one way in which this is possible:namely, these relative proportions must he identical to those in the market portfolio.It therefore follows that among all possible investment strategies, the only one thatall investors could follow is the one that says hold all assets in proportion to theirmarket value.Let me remark, somewhat parenthetically, that if among the soothsayers and strate-gists of Wall Street, there were one best investment strategy, and if this "best" strate-gy became widely known, then whatever the original statement of the strategy, it mustlead to simply this imperative: hold all assets in proportion to their market value.For suppose such a strategy required that the investor hold equal amounts of Ford andGeneral Motors. How could all investors following this best strategy do so, unless thetotal value of each were the same?Having established that the optimal combination of risky assets is the market portfolio,the Security Market Line relationship follows directly. However, in the continuous-6~hereason is that the lognormal distribution has the full range of nonnegativeoutcomes and the expected value of the marginal utility of an isoelastic utility functionis infinite if there is a positive probability of zero wealth, and undefined fornegative wealth.

time model, it will only hold for short observation intervals, while in the originalstatic version, the observation interval is never specified.This simple version of the continuous-time model has been attacked on the groundsthat it is not consistent with intertemporal eq~ilibrium:~ namely, it is claimed thatif all risky assets are held in the same proportions throughout time, then the only waythis is possible is if the ex-post returns on all assets are the same. Of course, thisis nonsense. For this criticism to follow, one must make some rather absurd assumptionsabout the supplies of assets. Namely, it must be assumed that firms cannot raise addi-tional investment capital except through internally-generated profits and that firmsmust reinvest all such profits in their own technology. In other words, a firm cannotdistribute profits through dividends or share repurchase and it cannot invest in thetechnologies of other firms. So, for example, in the early part of this century, buggywhip manufacturers would have had to reinvest all their profits in further production ofbuggy whips, while automobile manufacturers could not have raised new capital to produceautomobiles. Given that a purported major function of the capital markets is the effi-cient allocation of resources to the most productive investments, it is not surprisinqthat strange results would follow from such a set of restrictions.I would point out the positive results that the posited structure of returns in thissimple version of the continuous-time model is consistent with intertemporal equilibriumfor a simple wheat economy where the different risky assets 'correspond to alternative(uncertain) harvest technologies which remain the same through time. Indeed, in thiseconomy, equilibrium is achieved through time by a pure quantity adjustment in the amountof wheat allocated to each technology.I would also point out that the behavior implied by this model is consistent witha changing investment opportunity set if such changes are purely random.That is, evenif the expected returns and covariances among those returns do change over time, thebehavior at each point in time will be as if they are fixed at the current levels pro-vided that such changes are completely random. The proof follows along lines used byFama in his 1970 AER article [6].In a closely related interpretation, the simple version of the model is also con-sistent with an investor who does not know the period-by-period, transitory expectedreturn and covariance structure, but who does know the long-run or steady-state equili-brium structure of returns. For example, an investor may not know the ex-ante expectedreturn on the market for the next six months, but he may know that historically, therisk premium on the market has averaged 7 percent. If he believes that this structureis constant (at least in real terms), then his optimal behavior will be generated byusing this model. Of course, he will still have reason to adjust his portfolio overtime to achieve the appropriate pattern of consumption, to maintain diversification,and to maintain the optimal risk-return mix.This simple version of the continuous-time model forms a point of connection be-tween the models based on the maximization of single-period expected utility of terminalwealth and the more general, multiperiod consumption-portfolio models, and therefore is7See Rosenberg and Ohlson [21].

important. However, I view it more as a beginning rather than a final model.In a recent paper,8 I extended this basic continuous-time model by allowing formultiple sources of uncertainty in addition to end-of-period return uncertainty. Whilethe concrete examples in that paper focus on the impact of a changing investment opportunityset (i.e., the case where the per period expected returns and covariance structureare changing stochastically over time), I also indicated in a general derivation thatsimilar results would obtain for other sources of uncertainty, for example, multiple consumptiongoods with uncertain relative prices or when the investor has uncertain wageincome. The changing opportunity set is a particularly important type of uncertaintybecause it only affects intertemporal investors and therefore, its impact would nevershow itself in a one-period analysis. For example, an investor with a one-period planninghorizon facing a specified one-period rate of return structure which includes aninterest rate of 8 percent will not change his optimal portfolio if informed that nextperiod's return structure might have an interest rate of either 5 percent or 11 percent,instead of the same 8 percent as this period. However, a multiperiod maximizer facingthe same specified one-period rate of return structure will change his current portfolioholdings upon being informed of the changed beliefs about future investment rates. Andthis is so, even though both investors are making an investment decision for one periodat a time.In analyzing this model, it was found that, in contrast to the basic continuous-timemodel, all investors will not hold the same relative proportions of risky assets, andtherefore the standard separation or mutual fund theorem of Markowitz and Tobin will notobtain. However, the first-order conditions are still linear in the demand functionsfor risky assets, and can, therefore, be solved by matrix inversion. Inspection of thesedemand functions reveals a rather interesting structure. Namely, the demand for eachasset can be written as a sum of terms: the first term is identical to the demand derivedin the basic model where the only source of uncertainty is end-of-period returns. Eachother term can be identified with a specific additional source of uncertainty. Moreover,differential demand terms have the interpretation of being "hedges" by the investoragainst these other sources of uncertainty. To'see why "hedge" is an appropriate terminology:consider the following.The actual path of optimal consumption will be a stochastic process because optimalconsumption is a function of wealth and the other state variables (e.g., interest rates,prices, and time) which themselves follow stochastic processes. This consumption stochasticprocess will have an expected time path and a variance around that path. In essence,the derived differential demands for the risky assets are such as to minimize the varianceof consumption for a given expected time path. So, for example, if an unanticipateddecline in interest rates produces an unanticipated decline in consumption for a givenlevel of wealth, then the investor will tend to hold more of those securities that willproduce higher realized returns in the event interest rates do decline. So, in this case,he may hold long maturity bonds. For by doing so, if an unanticipated decline in interestrates does occur, then he will also find himself with an unanticipated higher wealthwhich will tend to offset the'negative impact of the interest rate decline on consumption.

Indeed, this general pattern repeats itself for each additional source of uncer-tainty for which securities can be used to hedqe. Moreover, the two-mutual fund orseparation theorem of the basic model generalizes to a multifund theorem where in addi-tion to the two funds, there is a fund for each additional source of uncertainty. Ofcourse, the term "mutual fund" is used broadly since simple financial instruments likebonds may serve the function of some of the funds.Thus, in this more general modeL securities have, in addition to their manifestfunction of providing an "efficient" risk-return tradeoff for end-of-period wealth, alatent function of allowing consumers to "hedge" against other uncertainties.9These findings suggest what I call a "Consumer Services" model of asset pricingwhich falls somewhere in between a model that considers only the uncertainty associatedwith end-of-period wealth (for example, the Capital Asset Pricing Model) and the completemarkets model of Arrow and Debreu. The model is rich enough to explain the functions offinancial intermediaries and financial instruments while maintaining sufficient specifi-cation to be empirically testable. The basic ideas behind the model go as follows below.If we start with the Arrow-Debreu model with complete markets where there are moresecurities than states of nature n, then Cass and Stiglitz [3] have proven a "mutualfund" or "separation" theorem which states that there can be constructed n mutual fundsor (composite) securities made up of linear combinations of all the securities such that(1) all consumer-investors would be indifferent between having available just these nmutual funds or all the securities; (2) the construction of these composite securitiesrequires no knowledge of consumer preferences, wealth allocations, or their subjectiveprobabilities for each of the states of nature.While the theorem states "indifferent" when there are no transactions costs andinformation is freely available to everyone, it is reasonable to presume strict prefer-ence for the mutual funds if the number of securities greatly exceeds the number ofstates. Economies of scale in transactions costs and information gatherinq and process-ing make it more sensible to have a centralized compilation of the distributions foreach of the primary securities rather than have each investor do it for himself. Forthe same reason, it would make sense for each mutual fund to have the property of payinga positive amount in one state of nature and zero otherwise (i.e., a set of basic con-tingent claims) rather than some other more complicated combination which in theorywould be equivalent.Since the number of possible states of nature, n, is very large, such a completeset of markets is economically infeasible. There are three basic reasons: (1) there arethe direct costs of operation of so many separate mutual funds; (2) that despite the re-duction in the number of securities to be analyzed, the large size of n would make theconsumer's information processing costs very larqe; (3) the occurrence of certain statesmay be controllable by some consumers (i.e., the moral hazard problem). Hence, some"compromise" is obviously required. TO do so, we retain the notion that the mutual fundapproach is preferred when there are large numbers of securities and large numbers ofrelatively small economic units (e.g., consumers), but we restrict the number of funds.Consumers have access to limited amounts of information and have limited abilities toprocess the information that they have. Further, because of the costs of informationhis section was originally presented as a part of "A Reexamination of the CapitalAsset Pricing Model;' (mimeo) July 1973.

gathering and processing, one would expect the consumer to center his attentions on themajor sources of uncertainty which affect his consumption plan. Hence, it is reasonableto assume that these sources of uncertainty can be represented by a finite and not verylarge number of state variables. Further, one would expect the number and type of mutualfunds that would be created would correspond roughly to the number and type of major uncertaintieswhich consumers face. The primary prerequisites for such a fund to becreated are: (1) the source of uncertainty must be important to a sufficient number ofconsumers; (2) it must be possible to have a standardized contract with payoffs in contingencieswhich are easily recognizable; (3) the source of uncertainty must not be controllableby the consumer(s). Thus, for some of the major uncertainties, it is virtuallyimpossible to construct a financial security which would allow the consumer to hedgeagainst them. Broadly, we would expect to find two types of securities traded: (1) "natural"or primary securities, such as common stocks, which are issued by firms to financeproduction of real output; (2) financial securities or financial intermediaries createdto serve the purposes of the "mutual funds" to be derived [namely, to aid the consumerin achieving a higher (expected) consumption level (through a return to capital), abetter intertemporal allocation of resources (by not requiring that savings equals investmentat each point in time), a lower level of risk (by providing hedges against themajor (common) sources of uncertainty faced by the consumer)].The individual consumer's demand for assets can be partitioned as follows: forthose important sources of uncertainty which he faces in common with other consumers, hewill take positions in the mutual funds or financial securities created for that purpose.For those important sources of uncertainty for which no mutual fund exists (either becauseit is specialized to him or there is inherent moral hazard), he will take positionsin those primary securities, if they exist, to hedge. For those sources of uncertaintyfor which no security is a hedge and for those sources which he simply neglects in hisanalysis, no security position can help so his (differential) demand for securities willbe unaffected.As an example, if the consumers are one-period maximizers of the utility of meanand variance of end-of-period wealth, then the well-known separation or two-fund theoremobtains. Namely, each investor will be indifferent between selecting a portfolio fromall the primary securities and from two funds: (1) the market portfolio of risky assetsand (2) a riskless asset. Presumably, such funds or financial instruments would becreated since there is an obvious common demand. However, consider an investor who alsohas (uncertain) labor income which he cannot sell forward to eliminate its risk becauseof the moral hazard problem. Suppose further that it is a very highly-specialized formof labor which can only be used by one company (or a small number of similar companies).Then, from risk-aversion, it would be natural to suppose that this investor would wantto hold less of this company's stock to hedge aqainst unfavorable changes in his laborincome. If, on the other hand, there were no security whose outcome was correlated withthis particular source of uncertainty, he can do nothing to hedge, and his optimal portfoliowould be generated by the two mutual funds alone.Thus, to a reasonable approximation, most of the aggregate demand for the individualprimary securities can be viewed as coming in an "indirect" way through mutual funds,

i.e., individual consumers for the most part only purchase a relatively small number ofcomposite financial securities or mutual funds. Mutual fund managers serve the functionof purchasing the primary securities to form the portfolio necessary to perform theseservices. Therefore, the aggregate demand for a primary security will depend on how itsreturn contributes to the formation of these "service" portfolios.Since the equilibrium expected return on an asset is "determined" in part by theaggregate demand for it, one would expect to find a correspondence between its expectedreturn and the statistical dependence between the asset's return and the various majorsources of uncertainty. All risk-averse consumers would prefer to have less uncertaintyfor the same expected consumption stream, and therefore would "give up" some (expected)return on an asset in return for that asset providing a hedqe against some of these uncertainties.Hence, to the extent that any asset's return contributes to (or aggravates)the consumers' attempts to hedge against these uncertainties, one would expect theequilibrium return on that asset to be affected. If, on average, a particular asset'sreturn contributes to consumers' attempts to hedge against a common source of uncertainty,then one would expect the equilibrium expected return on that asset to be differentiallylower than on a similar asset which does not provide that "service." This negative differentialin expected return can be interpreted as the market "cost" to the consumerfor the hedging service provided by this asset. If, on average, an asset's returnaggravates consumers' attempts to hedqe, than its equilibrium expected return would bedifferentially higher, and this positive differential in expected return can be interpretedas the market "premium" to the consumer in return for bearing the extra riskcaused by holding this asset. A simple illustration of this principle can be found inthe CAPM. Since the only source of uncertainty is end-of-period wealth and all investorsare assumed to be risk-averse, a given investor would view an asset as providing a("diversification") service if it lowers the variance of his end-of-period wealth andhence, would accept a lower expected return on this asset than on one which did not providethis service. However, since all investors' optimal portfolios are perfectly correlated,an asset which aids diversification for one investor does so for all investors,and therefore, all investors would accept a lower expected return on this asset. Inspectionof the Security Market Line, indeed shows this is the case.However, with respect to most sources of uncertainty, such unanimity among investors'views of whether an asset contributes to risk or not will be the exception. Thus, onegroup of consumers may consider a long position in an asset as contributing to a reductionof the risks it perceives, while another group may view a short position as contributingto a reduction in its risks. Thus, whether the equilibrium expected return on theasset reflects a differential cost or premium will depend on the aggregation of investors'demands, and unless there is a systematic "weak side" to the market, the sign of the differentialmay fluctuate through time. One example of this type is the Modigliani-Sutch[I91 Habitat theory of bond pricing. If a consumer has preferences which induce riskaversionwith respect to wealth, then he will view long-term bonds as risky and wouldrequire a market premium over short-term bonds to hold them. However, if a consumerhas preferences which induce risk-aversion with respect to income, then short-term bondsare risky to him, and he would require a market premium over long-term bonds to hold them.

Thus, with respect to the uncertainty about future interest rates, the differential expectedreturn between long- and short-term bonds could be of either sign.To determine the types of securities one would expect to find and the sources ofdifferentials in expected returns, it is necessary to establish what the important uncertaintiesare for a typical consumer in making his plan. Although not a complete listing,thefollowing seven items would seem to cover most of the important common sourcesof uncertainty for a consumer:(S.1) Uncertainty about his own future tastes;(S.2) Uncertainty about the menu of possible consumption goods that will beavailable to the future;(5.3) Uncertainty about relative prices of consumption goods;(S.4) Uncertainty about his labor income;(S.5) Uncertainty about future values of nonhuman assets;(S.6) Uncertainty about the future investment opportunity set; i.e., thefuture rates of return which can be earned on capital;(5.7) Uncertainty about the age of death.While all of these have been considered in one model or another, it is important to notethat those models based on the criterion of maximizing the expected utility of end-ofperiodwealth explicitly take into account only the uncertainty associated with nonhumanwealth. Included in this class of models is the CAPM.Even though all these uncertainties are important to the consumer, not all willdifferentially affect security prices'or returns. It is difficult to imagine a financialsecurity which could reduce the uncertainties associated with one's own future tastes orthe menu of possible consumption goods in the future. While uncertainty about the ageof death is an important problem for all consumers and life insurance was created inresponse to this demand, the event of death is probably reasonably statistically independentacross people, and it is unlikely that the returns on securities (other than lifeinsurance policies) would be statistically dependent on the event of an individual'sdeath. Hence, one would not expect this source of uncertainty to have differential effectson security prices. The risks associated with labor income can be completelyeliminated if the consumer could sell forward his wage income in the same way shares areissued on nonhuman capital. But, because of the moral hazard problem, it is difficultfor the consumer to do so. While some of the individual risk can be eliminated by disabilityand life insurance and by "investing" in education to make his labor more substitutableacross finns, there still will be systemath risk due to (unanticipated)shifts in capital and labor's relative shares (i.e., the wage-rental ratio). This uncertaintycould produce a differential demand for shares in labor-intensive versus capitalintensiveindustries. Similarly, inflation risk may cause differentials in demand betweendifferent maturity "money" securities. Although information costs and the uncertaintiesabout tastes and future products prohibit complete future markets for consumption goods,it is reasonable to expect consumers to differentiate broad classes of consumption (e.g.,housing, food, transportation, clothing, and recreation) and hence, differentials indemand for shares in different industries could occur as the result of uncertainty aboutrelative consumption good prices. The standard end-of-period wealth uncertainty will

induce differential demands for those securities which aid diversification. Finally,if there is uncertainty about the rates of return which will be available in the future,differential demands may occur between long- and short-term bonds and between shares offirms whose returns are sensitive to shifts in capitalization rates versus ones thatare not.If these are the sources of uncertainty common to most investors, then we canidentify a set of mutual funds which would be (approximately) sufficient to span thespace of consumers' optimal portfolios. Specifically, we might identify these funds tobe: (1) the "market" portfolio; (2) a (short-term) riskless asset; hedging portfoliosfor unanticipated; (3) shifts in rates of return; (4) shifts in the wage-rental ratio;(5) changes in prices for basic groups of consumption goods. Further, consumer demandsfor individual securities can be written as if they came indirectly through the demandsfor these mutual funds. Hence, the equilibrium expected return on a security will be afunction of the expected return on each of these funds and the statistical dependencebetween the security's return and the return on each of these funds.Indeed, this model is testable in its continuous-time formulation because, inequilibrium, the expected excess return on an individual security will be equal to aweighted sum of the excess returns on the mutual funds where the weights will equal theinstantaneous multiple regression coefficients between the return on the individualsecurity and the returns on the funds. This result is a natural generalization of thestandard Security Market Line to a Security Market Hyperplane:For my last topic, I turn to the theory for pricing financial instruments and inparticular the pricing of corporate liabilities. It is here where the continuous-timeanalysis has had its greatest impact. In what may be one of the most important contri-10butions to Finance in this decade, Fischer Black and Myron Scholes used the continuous-time analysis to deduce a formula for common stock options. In essence, they were ableto demonstrate that by following a specified dynamic portfolio policy consisting of mix-tures of positions in the underlying common stock and riskless borrowing or lending,they could exactly replicate the payoff structure associated with a call option.Given this demonstration, it is immediately obvious that this portfolio strategyis a perfect substitute for the option, and indeed, any two of the three securities in-volved can be combined in an appropriate portfolio strategy to exactly replicate thepayoff structure of the third. Hence, given the prices of any two of the securities(for example, the stock and riskless bond), the third security's price (in this case theoption) is uniquely determined, i.e., their analysis is clearly a relative pricinq theory.Having solved the call option case, it is straightforward to see that the same tech-nique can be used to price other types of options, and from there, it is not a long stepto recognize that their approach is equally valid when applied to the firm as a whole toprice its entire capital structure. As a result, their analysis has led to a unified10 See Black and Scholes [I]. For further discussion, see Merton [121.

theory for pricing of virtually any financial claim on the firm.'I view the Black-Scholes contribution in three parts. The first and most importantpart is the initial insight in setting up the problem. The second part is the developmentof a quantitative formula based for the most part on observable br reasonably estimatedvariables. In particular, rather surprisingly, consumer preferences and the expectedreturn on the underlying stock do not enter the formula. Moreover, one need noteven assume that the market is in equilibrium. Of course, a quantitative formula is importantbecause it allows for empirical testing and for its direct use in applications.This is one of those rare cases where a piece of analysis conceived entirely in theoryhas had an immediate and important impact on actual operations. Indeed, the Black-Scholesformula is widely used by most firms trading in the option market. The third part isthat the Black-Scholes analysis has led to some important qualitative propositions. Forexample, it is widely held that the Modigliani-Miller irrelevance-of-financing theoremdoes not hold when there is a positive probability of bankruptcy because in such cases,personal borrowing and corporate borrowing are no longer perfect substitutes for oneanother. The Black-Scholes type analysis can be used to demonstrate that this conclusionis false. Namely, while no fixed portfolio strategy can replicate the nonlinear payoffstructure of such corporate debt, a continuous-time, dynamic portfolio strategy can.Also, some earlier studiesL2 attempted to use warrant price and stock price comparisonsto estimate investor's expectations for the stock or investor's risk preferences.But since the Black-Scholes formula requires neither as inputs for pricing warrants, itclearly demonstrates that such attempts are doomed to failure.Since the pricing formula does not depend upon knowledge of the expected return onthe stock, both Bulls and Bears who agree on the other inputs, will agree on the priceof the option relative to the stock, or the prices of the individual elements of thecapital structure relative to the total value of the firm. This demonstrates that theinvestor's decision as to what investment action to take in regard to a specific firmcan be separated into two parts. First, in an evaluation of the firm as a whole, is ita good or bad investment? Second, given this decision, what financial claim on the firmis the best vehicle for either being long or short in the firm? Since the Black-Scholesformula requires an estimate of the variance on the stock, it has created a demand forfurther research into estimation techniques for variances.While much of the research in this area is still in progress,13 I believe that beforelong we will have answers to many of the long outstanding questions about corporate financingpolicy including a rationale for debt targets and debt capacity, and a quantitativeanalysis of the optimal debt structure when interest payments are deductible.Moreover, most of the assumptions required in the original Black-Scholes derivationhave been substantially weakened in more recent research with no significant changes intheir more important conclusions.While time does not permit me to cover all the continuous-time research going on in'seMerton [12, 151 and Ingersoll [a].12See Sprenkle [861.13~nexcellent survey can be found in Smith [25].

Finance, I will simply mention the Solnik [271 analysis in international capital markets,the Richard [201 analysis of the demand for insurance, the Fischer [71 analysis of indexlinkedbonds, and Scheffman [24] analysis of the optimal investment decision by firms.In summary, the continuous-time mode of analysis has proved fruitful in analyzingsome of the basic problems in Finance. The costs associated with getting these resultsare the twin assumptions that markets are open most of the time and that the stochasticprocesses can be described by either diffusion or compound Poisson processes. The benefitsare generally sharper results that are easier to interpret than in the discretetimecase, and an enormous literature on these stochastic processes which allows one toanalyze rather complex models and still get quantitative results.REFERENCES[I] Black, F., and M. Scholes. "The Pricing of Options and Corporate Liabilities."Journal of Political Economy, vol. 81 (1973), pp. 637-659.[21 . "The Valuation of Option Contracts and a Test of Market Efficiency."Journal of Finance,vol. 27 (1972), pp. 399-417.[3] Cass, D., and J. Stiglitz. "The Structure of Investor Preferences and Asset Returns,and Separability in Portfolio Allocation: A Contribution to the Pure Theoryof Mutual Funds." Journal of Economic Theory, vol. 2 (1970), pp. 122-160.[4] Cox, J., and S. Ross. "The Pricing of Options for Jump Processes." Journal ofFinancial Economics, (forthcoming).[51 Farna, E. "Efficient Capital Markets: A Review of Theory and Empirical Work."Journal of Finance, vol. 25 (19701, pp. 383-417.[GI. "Multiperiod Consumption-Investment Decisions." American EconomicReview, vol. 60 (1970), pp. 163-174.[71 Fischer, S. "The Demand for Index Bonds." Journal of Political Economy, vol. 83(1975), pp. 509-534.[81 Ingersoll, J. "A Theoretical and Empirical Investigation of the Dual Purpose Funds:An Application of Contingent Claims Analysis." Journal of Financial Economics,(forthcoming).[91 Magill, M., and G. Constantinides. "Portfolio Selection with Transactions Costs."Journal of Economic Theory, (forthcoming).[lo] Merton, R. C. "Lifetime Portfolio Selection under Uncertainty: The Continuous-TimeCase." Review of Economics and Statistics, vol. 51 (1969), pp. 247-257.[Ill. "Optimum Consumption and Portfolio Rules in a Continuous Time Model."Journal of Economic Theory, vol. 3 (1971), pp. 373-413.[I21 . "Theory of Rational Option Pricing." Bell Journal of Economics andManagement Science, vol. 4 (19731, pp. 141-183.[131 . "An Intertemporal Capital Asset Pricing Model." Econometrica, vol. 41(1973), pp. 867-887.[I41 . "Appendix: Continuous-Time Speculative Processes." In P. A. Samuelson,"Mathematics of Speculative Price," SIAM Review.[I51 . "On the Pricing of Corporate Debt: The Risk Structure of InterestRates." Journal of Finance, vol. 29 (1974) , pp. 449-470.

[161 . "Option Pricing when Underlying Stock Returns Are Discontinuous."Journal of Financial Economics, (forthcoming).[18] Merton, R. C., and P. A. Samuelson. "Fallacy of the Log-Normal ~pproximation toOptimal Portfolio Decision-Making over Many Periods." Journal of Financial Economics,vol. 1 (1974), pp. 67-94.[191 Modigliani, F., and R. Sutch. "Innovations in Interest Rate Policy." AmericanEconomic Review, vol. 56 (1966), pp. 178-197.[20] Richard, S. "Optimal Consumption, Portfolio and Life Insurance Rules for an UncertainLived Individual in a Continuous-Time Model." Journal of Financial Economics,vol 2 (1975), pp. 187-204.[21] Rosenberg, B., and J. Ohlson. "The Stationary Distribution of Returns and PortfolioSeparation in Capital Markets: A Fundamental Contradiction." University ofCalifornia, Berkeley (unpublished, 1973).[221 Rubinstein, M. "The Strong Case for the Generalized Logarithmic Utility Model asthe Premier Model of Financial Markets." W. P. #34, Institute of Business and EconomicResearch, University of California, Berkeley (1975).[23] Samuelson, P. A. "Proof that Properly Anticipated Prices Fluctuate Randomly."Industrial Management Review, vol. 6 (1965), pp. 41-49.[241 Scheffman, D. "'Optimal' Investment under Uncertainty." University of WesternOntario (unpublished, 1975).[25] Smith, C. "Option Pricing: A Review." Journal of Financial Economics,(forthcoming).[26] Sprenkle, C. "Warrant Prices as Indicators of Expectations and Preferences." InThe Random Character of Stock Market Prices, edited by P. Cootner. Cambridge:M.I.T. Press, pp. 412-474.[271 Solnik, B. European Capital Markets. Lexington, Mass: Lexington Books (1973).

The Capital Asset Pricing ModelAndré F. PeroldThe Journal of Economic Perspectives, Vol. 18, No. 3. (Summer, 2004), pp. 3-24.Stable URL:http://links.jstor.org/sici?sici=0895-3309%28200422%2918%3A3%3C3%3ATCAPM%3E2.0.CO%3B2-ZThe Journal of Economic Perspectives is currently published by American Economic Association.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/aea.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgMon Dec 17 05:49:47 2007

Journal of Economic Perspectives-Volume 18, Number 3-Summer 2004 -Pages 3-24The Capital Asset Pricing ModelAndr6 F. Peroldfundamental question in finance is how the risk of an investment shouldaffect its expected return. The Capital Asset Pricing Model (CAPM)provided the first coherent framework for answering this question. TheCAPM was developed in the early 1960s by William Sharpe (1964),Jack Treynor(1962),John Lintner (1965a, b) and Jan Mossin (1966).The CAPM is based on the idea that not all risks should affect asset prices. Inparticular, a risk that can be diversified away when held along with other investmentsin a portfolio is, in a very real way, not a risk at all. The CAPM gives usinsights about what kind of risk is related to return. This paper lays out the key ideasof the Capital Asset Pricing Model, places its development in a historical context,and discusses its applications and enduring importance to the field of finance.Historical BackgroundIn retrospect, it is striking how little we understood about risk as late as the1960s-whether in terms of theory or empirical evidence. After all, stock andoption markets had been in existence at least since 1602 when shares of the EastIndia Company began trading in Amsterdam (de la Vega, 1688); and organizedinsurance markets had become well developed by the 1700s (Bernstein, 1996). By1960, insurance businesses had for centuries been relying on diversification tospread risk. But despite the long history of actual risk-bearing and risk-sharing inorganized financial markets, the Capital Asset Pricing Model was developed at atime when the theoretical foundations of decision making under uncertainty wererelatively new and when basic empirical facts about risk and return in the capitalmarkets were not yet known.Andre' F. Perold is the George Gund Professor of Finance and Banking, Harvard BusinessSchool, Boston, Massachusetts. His e-mail address is (aperoldQhbs.edu).

4 Journal of Economic PerspectivesRigorous theories of investor risk preferences and decision-making underuncertainty emerged only in the 1940s and 1950s, especially in the work of vonNeumann and Morgenstern (1944) and Savage (1954). Portfolio theory, showinghow investors can create portfolios of individual investments to optimally trade offrisk versus return, was not developed until the early 1950s by Harry Markowitz(1952, 1959) and Roy (1952).Equally noteworthy, the empirical measurement of risk and return was in itsinfancy until the 1960s, when sufficient computing power became available so thatresearchers were able to collect, store and process market data for the purposes ofscientific investigation. The first careful study of returns on stocks listed on the NewYork Stock Exchange was that of Fisher and Lorie (1964) in which they note: "It issurprising to realize that there have been no measurements of the rates of returnon investments in common stocks that could be considered accurate and definitive."In that paper, Fisher and Lorie report average stock market returns overdifferent holding periods since 1926, but not the standard deviation of thosereturns. They also do not report any particular estimate of the equity risk premium-thatis, the average amount by which the stock market outperformedrisk-free investments-although they do remark that rates of return on commonstocks were "substantially higher than safer alternatives for which data are available."Measured standard deviations of broad stock market returns did not appearin the academic literature until Fisher and Lorie (1968). Carefully constructedestimates of the equity risk premium did not appear until Ibbotson and Sinquefield(1976) published their findings on long-term rates of return. They found that overthe period 1926 to 1974, the (arithmetic) average return on the Standard andPoor's 500 index was 10.9 percent per annum, and the excess return over U.S.Treasury bills was 8.8 percent per annum.' The first careful study of the historicalequity risk premium for UK stocks appeared in Dimson and Brealey (19'78) with anestimate of 9.2 percent per annum over the period 1919-19'77.In the 1940s and 1950s, prior to the development of the Capital Asset PricingModel, the reigning paradigm for estimating expected returns presupposed thatthe return that investors would require (or the "cost of capital") of an assetdepended primarily on the manner in which that asset was financed (for example,Bierman and Smidt, 1966). There was a "cost of equity capital" and a "cost of debtcapital," and the weighted average of these-based on the relative amounts of debtand equity financing-represented the cost of capital of the asset.The costs of debt and equity capital were inferred from the long-term yields ofthose instruments. The cost of debt capital was typically assumed to be the rate ofinterest owed on the debt, and the cost of equity capital was backed out from thecash flows that investors could expect to receive on their shares in relation to thecurrent price of the shares. A popular method of estimating the cost of equity thisway was the Gordon and Shapiro (1956) model, in which a company's dividends areThese are arithmetic average returns. Ibbotson and Sinquefield (1976) were also the first to report theterm premium on long-term bonds: 1.1 percent per annum average return in excess of Treasury billsover the period 1926-1974.

Andre' F. Perold5assumed to grow in perpetuity at a constant rate g. In this model, if a firm's currentdividend per share is D, and the stock price of the firm is P, then the cost of equitycapital r is the dividend yield plus the dividend growth rate: r = D/P + g.2From the perspective of modern finance, this approach to determining thecost of capital was anchored in the wrong place. At least in a frictionless world, thevalue of a firm or an asset more broadly does not depend on how it is financed, asshown by Modigliani and Miller (1958). This means that the cost of equity capitallikely is determined by the cost of capital of the asset, rather than the other wayaround. Moreover, this process of inferring the cost of equity capital from futuredividend growth rates is highly subjective. There is no simple way to determine themarket's forecast of the growth rate of future cash flows, and companies with highdividend growth rates will be judged by this method to have high costs of equitycapital. Indeed, the Capital Asset Pricing Model will show that there need not beany connection between the cost of capital and future growth rates of cash flows.In the pre-CAPM paradigm, risk did not enter directly into the computation of thecost of capital. The working assumption was often that a firm that can be financedmostly with debt is probably safe and is thus assumed to have a low cost of capital; whilea firm that cannot support much debt is probably risky and is thus assumed tocommand a high cost of capital. These rules-of-thumb for incorporating risk intodiscount rates were ad hoc at best. As Modigliani and Miller (1958) noted: "Nosatisfactory explanation has yet been provided . . . as to what determines the size of therisk [adjustment] and how it varies in response to changes in other variables."In short, before the arrival of the Capital Asset Pricing Model, the question of howexpected returns and risk were related had been posed, but was still awaiting an answer.Why Investors Might Differ in Their Pricing of RiskIntuitively, it would seem that investors should demand high returns forholding high-risk investments. That is, the price of a high-risk asset should be bidsufficiently low so that the future payoffs on the asset are high (relative to theprice). A difficulty with this reasoning arises, however, when the risk of an investmentdepends on the manner in which it is held.To illustrate, consider an entrepreneur who needs to raise $1million for a riskynew venture. There is a 90 percent chance that the venture will fail and end upworthless; and there is a 10 percent chance that the venture will succeed within ayear and be worth $40 million. The expected value of the venture in one year istherefore $4 million, or $4 per share assuming that the venture will have a millionshares outstanding.Case I: If a single risk-averse individual were to fund the full $1 million-where'The cost of equity capital in this model is the "internal rate of return," the discount rate that equates thepresent value of future cash flows to the current stock price. In the GordonShapiro model, the projecteddividend stream is D, D(l + g),D ( l + g)2. . . The present value of these cash flows when discounted at rater is D / ( r - g),which when set equal to the current stock price, P, establishes r = D/P + g.

6 Journal of Economic Perspectivesthe investment would represent a significant portion of the wealth of thatindividual-the venture would have to deliver a very high expected return, say100 percent. To achieve an expected return of 100 percent on an investment of $1million, the entrepreneur would have to sell the investor a 50 percent stake:300,000 shares at a price per share of $2.Case 11: If the funds could be raised from someone who can diversify acrossmany such investments, the required return might be much lower. Consider aninvestor who has $100 million to invest in 100 ventures with the same payoffs andprobabilities as above, except that the outcomes of the ventures are all independentof one another. In this case, the probability of the investor sustaining a largepercentage loss is small-for example, the probability that all 100 ventures fail is aminiscule .003 percent (= 0.9~")-and the diversified investor might consequentlybe satisfied to receive an expected return of only, say, 10 percent. If so, theentrepreneur would need to sell a much smaller stake to raise the same amount ofmoney, here 27.5 percent (= $1.1 million/$4 million); and the investor would paya higher price per share of $3.64 (= $1 million/275,000 shares).Cases I and I1 differ only in the degree to which the investor is diversified; thestand-alone risk and the expected future value of any one venture is the same inboth cases. Diversified investors face less risk per investment than undiversifiedinvestors, and they are therefore willing to receive lower expected returns (and topay higher prices). For the purpose of determining required returns, the risks ofinvestments therefore must be viewed in the context of the other risks to whichinvestors are exposed. The CAPM is a direct outgrowth of this key idea.Diversification, Correlation and RiskThe notion that diversification reduces risk is centuries old. In eighteenth-centuryEnglish language translations of Don Quixote, Sancho Panza advises his master, "It is thepart of a wise man to . . . not venture all his eggs in one basket." According to Herbison(2003), the proverb "Do not keep all your eggs in one basket" actually appeared as farback as Torriano's (1666) Common Place ofItalian Proverbs.However, diversification was typically thought of in terms of spreading your wealthacross many ind@endent risks that would cancel each other if held in sufficient number(as was assumed in the newventures example). Harry Markowitz (1952) had the insightthat, because of broad economic influences, risks across assets were correlated to adegree. As a result, investors could eliminate some but not all risk by holding adiversified portfolio. Markowitz wrote: "This presumption, that the law of large numbersapplies to a portfolio of securities, cannot be accepted. The returns from securitiesare too intercorrelated. Diversification cannot eliminate all variance."Markowitz (1952) went on to show analytically how the benefits of diversificationdepend on correlation. The correlation between the returns of two assetsmeasures the degree to which they fluctuate together. Correlation coefficientsrange between -1.0 and 1.0. When the correlation is 1.0, the two assets areperfectly positively correlated. They move in the same direction and in fixed

The Capital Asset Pricing i\/lodel 7proportions (plus a constant). In this case, the two assets are substitutes for oneanother. When the correlation is -1.0, the returns are perfectly negatively correlatedmeaning that when one asset goes up, the other goes down and in a fixedproportion (plus a constant). In this case, the two assets act to insure one another.When the correlation is zero, knowing the return on one asset does not help youpredict the return on the other.To show how the correlation among individual security returns affects portfoliorisk, consider investing in two risky assets, A and B. Assume that the risk of anasset is measured by its standard deviation of return, which for assets A and B isdenoted by a, and a,, respectively. Let p denote the correlation between thereturns on assets A and B; let x be the fraction invested in Asset A and y (= 1 -x) be the fraction invested in Asset B.When the returns on assets within a portfolio are perfectly positively correlated(p = l),the portfolio risk is the weighted average of the risks of the assets in theportfolio. The risk of the portfolio then can be expressed asap= xa, + yu~.The more interesting case is when the assets are not perfectly correlated (p < 1).Then there is a nonlinear relationship between portfolio risk and the risks of theunderlying assets. In this case, at least some of the risk from one asset will be offsetby the other asset, so the standard deviation of the portfolio upis always less thanthe weighted average of a, and a,.3 Thus, the risk of a portfolio is less than theaverage risk of the underlying assets. Moreover, the benefit of diversification willincrease the farther away that the correlation p is from 1.These are Harry Markowitz's important insights: 1) that diversification does notrely on individual risks being uncorrelated, just that they be imperfectly correlated; and2) that the risk reduction from diversification is limited by the extent to whichindividual asset returns are correlated. If Markowitz were restating Sancho Panza'sadvice, he might say: It is safer to spread your eggs among imperfectly correlatedbaskets than to spread them among perfectly correlated baskets.Table 1 illustrates the benefits of diversifying across international equity markets.The table lists the world's largest stock markets by market capitalization as ofDecember 31, 2003, the combination of which we will call the world equity market"he portfolio standard deviation, up,can be expressed in terms of the standard deviations of assets Aand B and their correlation using the variance formula:This expression can be algebraically manipulated to obtainWhen p = 1,the final term disappears, gibing the formula in the text. When p < 1,then the size of the secondterm will increase as p declines, and so the standard deviation of the portfolio hill fall as p declines.

- -8 Journal of Economic PerspectivesTable 1Market Capitalizations and Historical Risk Estimates for 24 Countries,January 1994-December 2003'MarketCapztalzzatzonBeta($ Bzllzons, Capztalzzatzon S.D. of us. Correlatzon12/31/O?) H'ezght Return TI.IEIMP us 'IIELWU.S. $14,266 47.8%Japan 2,953 9.9%UK 2,426 8.1%France 1,403 4.7%Germany 1,079 3.6%Canada 910 3.0%Switzerland 727 2.4%Spain 726 2.4%Hong Kong 715 2.4%Italy 615 2.1%Australia 586 2.0%China 513 1.7%Taiwan 379 1.3%Netherlands 368 1.2%Sweden 320 1.1%South Korea 298 1.0%India 279 0.9%South Africa 261 0.9%Brazil 235 0.8%Russia 198 0.7%Belgium 174 0.6%Mala! sia 168 0.6%Singapore 149 0.5%Mexico 123 0.4%U'EMP $29,870 100%S.D. of MEMP assuming perfect correlationS.D. of MEMP assuming zero correlation'Ihtes: M'EMP stands for World Equity Market Portfolio. S.D. is standard de~iation expressed on anannualized basis. Calculations are based on historical monthly returns obtained from Global FinancialData Inc.portfolio, labeled in the table as MTMP. The capitalization of the world equitymarket portfolio was about $30 trillion-comprising over 95 percent of all publiclytraded equities-with the United Statese representing by far the largest fraction.Table 1 includes the standard deviation of monthly total returns for each country overthe ten-year period ending December 31, 2003, expressed on an annualized basis.Assuming that the historical standard deviations and correlations of return aregood estimates of future standard deviations and correlations, we can use this datato calculate that the standard deviation of return of the W'EMP-given the capitalizationweights as of December 20034s 15.3 percent per annum. If the countryreturns were all perfectly correlated with each other, then the standard deviation ofthe WEMP would be the capitalization-weighted average of the standard deviations,

Andre' F. Perold9which is 19.9 percent per annum. The difference of 4.6 percent per annumrepresents the diversification benefit-the risk reduction stemming from the factthat the world's equity markets are imperfectly correlated. Also shown in Table 1 isthat the standard deviation of the WEMP would be only 8.4 percent per annum if thecountry returns were uncorrelated with one another. The amount by which this figureis lower than the actual standard deviation of 15.3 percent per annum is a measure ofthe extent to which the world's equity markets share common influences.Portfolio Theory, Riskless Lending and Borrowing and FundSeparationTo arrive at the CAPM, we need to examine how imperfect correlation amongasset returns affects the investor's tradeoff between risk and return. MThile riskscombine nonlinearly (because of the diversification effect), expected returns combinelinearly. That is, the expected return on a portfolio of investments is just theweighted average of the expected returns of the underlying assets. Imagine twoassets with the same expected return and the same standard deviation of return. Byholding both assets in a portfolio, one obtains an expected return on the portfoliothat is the same as either one of them, but a portfolio standard deviation that islower than any one of them individually. Diversification thus leads to a reduction inrisk without any sacrifice in expected return.Generally, there will be many combinations of assets with the same portfolioexpected return but different portfolio risk; and there will be many combinationsof assets with the same portfolio risk but different portfolio expected return. Usingoptimization techniques, we can compute what Markowitz coined the "efficientfrontier." For each level of expected return, we can solve for the portfolio combinationof assets that has the lowest risk. Or for each level of risk, we can solve forthe combination of assets that has the highest expected return. The efficientfrontier consists of the collection of these optimal portfolios, and each investor canchoose which of these best matches their risk tolerance.The initial development of portfolio theory assumed that all assets were risky.James Tobin (1958) showed that when investors can borrow as well as lend at therisk-free rate, the efficient frontier simplifies in an important way. (A "risk-free"instrument pays a fixed real return and is default free. U.S. Treasury bonds thatadjust automatically with inflation-called Treasury inflation-protected instruments,or TIPS-and short-term U.S. Treasury bills are considered close approximationsof risk-free instruments.)To see how riskless borrowing and lending affects investors' decision choices,consider investing in the following three instruments: risky assets M and H, and theriskless asset, where the expected returns and risks of the assets are shown in Table 2.Suppose first that you had the choice of investing all of your wealth in just one ofthese assets. Which would you choose? The answer depends on your risk tolerance.Asset Hhas the highest risk and also the highest expected return. You would choose

10 Journal of Economic PerspectivesTable 2How Riskless Borrowing and Lending AffectInvestors' ChoicesExpected returnRisk (S.D.)Riskless asset 3% (r,) 0%Asset ,Vl 10% ( E M ) 20% (alw)Asset H 12% (E,) 40% (a,)Asset H if you had a high tolerance for risk. The riskless asset has no risk but alsothe lowest expected return. You would choose to lend at the risk-free rate if you hada very low tolerance for risk. Asset M has an intermediate risk and expected return,and you would choose this asset if you had a moderate tolerance for risk.Suppose next that you can borrow and lend at the risk-free rate, that you wishto invest some of your wealth in Asset H and the balance in riskless lending orborrowing. If x is the fraction of wealth invested in Asset H, then 1 - x is thefraction invested in the risk-free asset. When x < 1,you are lending at the risk-freerate; when x > 1, you are borrowing at the risk-free rate. The expected return ofthis portfolio is (1 - x) rf + xE, which equals rf + x(EH - rf) , and the risk of theportfolio is xa,. The risk of the portfolio is proportional to the risk of Asset H,since Asset H i s the only source of risk in the portfolio.Risk and expected return thus both combine linearly, as shown graphically inFigure 1. Each point on the line connecting the risk-free asset to Asset H representsa particular allocation ( x) to Asset Hwith the balance in either risk-free lending orrisk-free borrowing. The slope of this line is called the Sharpe Ratio-the riskpremium of Asset H divided by the risk of Asset H:Sharpe Ratio = (EH- rf)/aH.The Sharpe Ratio of Asset H evaluates to 0.175 (= (12 percent - 5 percent)/40 percent) and all combinations of Asset H with risk-free borrowing or lendinghave this same Sharpe Ratio.Also shown in Figure 1 are the risks and expected returns that can be achievedby combining Asset M with riskless lending and borrowing. The Sharpe Ratio ofAsset M is 0.25, which is higher than that of Asset H, and any level of risk and returnthat can be obtained by investing in Asset H along with riskless lending or borrowingis dominated by some combination of Asset M and riskless lending or borrowing.For example, for the same risk as Asset H, you can obtain a higher expectedreturn by investing in Asset Mwith 2:l leverage. As shown in Figure 1, the expectedreturn of a 2:l leveraged position in Asset M is 15 percent (that is, (2 X 10 percent)- (1 X 5 percent)), which is higher than the 12 percent expected return ofAsset H. If you could hold only one risky asset along with riskless lending orborrowing, it unambiguously would be Asset M.Being able to lend and borrow at the risk-free rate thus dramatically changes

The Capital Asset Pricing ModelI IFigure 1Combining a Risky Asset with Risk-Free Lending and BorrowingCombinations of Combinations ofasset 121 invol~ing asset 121 involving14 risk-free risk-free2:l Leverage-I--+-I ---)Coinbinations of Combinations ofasset H involving asset H invol~ingrisk-freerisk-freelendingborrowing0 5 10 15 20 25 30 35 40 45 50Risk (standard de~lation)our investment choices. The asset of choice-if you could choose only one riskyasset-is the one with the highest Sharpe Ratio. Given this choice of risky asset, youneed to make a second decision, which is how much of it to hold in your portfolio.The answer to the latter question depends on your risk tolerance.Figure 2 illustrates the approach in the case where we can invest in combinationsof two risky assets, M and H, plus riskless lending and borrowing. Thecorrelation between the returns of assets M and H is assumed to be zero. In thefigure, the curve connecting assets M and H represents all expected return/standard deviation pairs that can be attained through combinations of assets M andH. The combination of assets M and H that has the highest Sharpe Ratio is74 percent in Asset M and 26 percent in Asset H (the tangency point). Theexpected return of this combination is 10.52 percent, and the standard deviation is18.09 percent. The Sharpe Ratio evaluates to 0.305, which is considerably higherthan the Sharpe Ratios of assets M and H (0.25 and 0.175, respectively). Investorswho share the same estimates of expected return and risk all will locate theirportfolios on the tangency line connecting the risk-free asset to the frontier. Inparticular, they all will hold assets M and H in the proportions 74/26.The optimal portfolio of many risky assets can be found similarly. Figure 3offers a general illustration. Use Markowitz's algorithm to obtain the efficientfrontier of portfolios of risky assets. Find the portfolio on the efficient frontier thathas the highest Sharpe Ratio, which will be the point where a ray stretching up fromthe risk-free point is just tangent to the efficient frontier. Then, in accordance withyour risk tolerance, allocate your wealth between this highest Sharpe Ratio portfolioand risk-free lending or borrowing.This characterization of the efficient frontier is referred to as "fund separation."Investors with the same beliefs about expected returns, risks and correlationsall will invest in the portfolio or "fund" of risky assets that has the highest Sharpe

12 Journal of Economic PerspectiuesFigure 2Efficient Frontier with Two Risky Assets15I0 3 10 15 20 25 30 35 40 45Risk (standard de~lation)Figure 3Efficient Frontier with Many Risky AssetsHighest SharpemmIImEfficient frontierof risky assets-IndividualassetsRisk (standard deviation)Ratio, but they will differ in their allocations between this fund and risk-freelending or borrowing based on their risk tolerance. Notice in particular that thecomposition of the optimal portfolio of risky assets does not depend on theinvestor's tolerance for risk.Market-Determined Expected Returns and Stand-Alone RiskPortfolio theory prescribes that investors choose their portfolios on the efficientfrontier, given their beliefs about expected returns and risks. The Capital

Asset Pricing Model, on the other hand, is concerned with the pricing of assets inequilibrium. CAPM asks: What are the implications for asset prices if everyoneheeds this advice? In equilibrium, all assets must be held by someone. For themarket to be in equilibrium, the expected return of each asset must be such thatinvestors collectively decide to hold exactly the supply of shares of the asset. TheCapital Asset Pricing Model will tell us how investors determine those expectedreturns-and thereby asset prices-as a function of risk.In thinking about how expected return and risk might be related, let us askwhether, as a rule, the expected return on an investment could possibly be afunction of its stand-alone risk (measured by standard deviation of return). Theanswer turns out to be "no." Consider the shares of two firms with the samestand-alone risk. If the expected return on an investment was determined solely byits stand-alone risk, the shares of these firms would have the same expected return,say 10 percent. Any portfolio combination of the two firms would also have anexpected return of 10 percent (since the expected return of a portfolio of assets isthe weighted average of the expected returns of the assets that comprise theportfolio). However, if the shares of the firms are not perfectly correlated, then aportfolio invested in the shares of the two firms will be less risky than either onestand-alone. Therefore, if expected return is a function solely of stand-alone risk,then the expected return of this portfolio must be less than 10 percent, contradictingthe fact that the expected return of the portfolio is 10 percent. Expectedreturns, therefore, cannot be determined solely by stand-alone risk.Accordingly, any relationship between expected return and risk must be basedon a measure of risk that is not stand-alone risk. As we will soon see, that measureof risk is given by the incremental risk that an asset provides when added to aportfolio, as discussed in the next section.Improving the Sharpe Ratio of a PortfolioSuppose you were trying to decide whether to add a particular stock to yourinvestment portfolio of risky assets. If you could borrow and lend at the risk-freerate, you would add the stock if it improved the portfolio's Sharpe Ratio. It turnsout there is a simple rule to guide the decision-a rule that can be derived byunderstanding the two special cases: 1) when the additional stock is uncorrelatedwith the existing portfolio, and 2) when the additional stock is perfectly correlatedwith the existing portfolio. The rule will lead us directly to the equilibriumrisk-return relationship specified by the Capital Asset Pricing Model.In what follows, it will be helpful to think in terms of "excess return," thereturn of an instrument in excess of the risk-free rate. The expected excess returnis called the risk premium.Adding a Stock that is Uncorrelated with the Existing PortfolioWhen should a portfolio be diversified into an uncorrelated stock? If theexcess returns on the stock and existing portfolio are uncorrelated, adding a small

14 Journal of Economic Perspectivesamount of the stock has almost no effect on the risk of the portfolio.4 At themargin, therefore, the stock is a substitute for investing in the risk-free asset.Including the stock will increase the portfolio's Sharpe Ratio if the stock's expectedreturn Es exceeds the risk-free rate rf. Said another way, the additional stock shouldbe included in the portfolio if its risk premium Es - rf is positive.Adding a Stock that is Perfectly Correlated with the Existing PortfolioIf the stock and portfolio excess returns are perfectly correlated, investing inthe stock becomes a substitute for investing in the portfolio itself. To see this, recallthat a perfect correlation means that the stock and the portfolio excess returnsmove together in a fixed ratio plus a constant. The fixed ratio is called beta,denoted by P, and the constant is called alpha, denoted by a. In other words, theexcess return of the stock is equal to alpha plus beta times the excess return of theportfolio. It also follows that the expected excess return of the stock is alpha plus betatimes the expected excess return on the portfolio-that is, Es - r- = a + P(EP -rf)The constant alpha is therefore given by the difference between the riskpremium of the stock and beta times the risk premium of the portfolio. Since thestock and the portfolio move together in a fixed proportion, beta is given by theratio of stock to portfolio standard deviations of excess return: P = as/a,.Compare now an investment of $1 in the stock with the following "mimicking"strategy: invest $P in the portfolio and the balance $(1 - P) in the risk-free asset,assuming that p < 1. For example, if beta is 0.5, then investing $0.50 in the portfolioand $0.50 in the riskless asset is a strategy that will gain or lose 0.5 percent of excessreturn for every 1 percent gain or loss in the portfolio excess return. The excess returnof the mimicking strategy is beta times the excess return of the portfolio. The mimickingstrategy will behave just like the stock up to the constant difference alpha. Themimicking strategy can be thought of as a "stock" with the given beta but an alpha of zero.Similarly, if P > 1, the mimicking strategy involves investing $P in the portfolioof which $(P - 1) is borrowed at the riskless rate. For example, if beta is 3, themimicking portfolio involves investing $3 in the portfolio of which $2 is borrowedat the risk-free rate. This strategy will gain or lose 3 percent of excess return forevery 1 percent gain or loss in the portfolio excess return. Again, the mimickingstrategy will behave just like the stock up to the constant difference alpha.When should a stock be added to the portfolio if its return is perfectly correlatedwith that of the portfolio? Since, up to the constant alpha, the stock is just a substitutefor the portfolio, adding $1 of the stock to the portfolio amounts to owning $P moreof the portfolio. But owning more of the portfolio by itself does not change its SharpeRatio. Therefore, adding the stock will increase the portfolio's Sharpe Ratio if theAssume that you have $1 ofwealth invested in the portfolio. Then, adding an investment of $x in sharesof the stock increases the portfolio variance to u; + x2uz, where u: is the variance of the portfolio andx2uz is the variance of the additional stock, weighted by the number of dollars invested in the stock.Remember, the variance of a combination of uncorrelated risks equals the sum of the variances of theindi~ldual risks. The increase in portfolio risk (standard deviation as well as variance) is proportional tox2, which implies that the change in portfolio risk is negligible for small x. The $x needed to purchasethe shares can come from holding less of the risk-free asset or by borrowing at the risk-free rate.

The Capital Asset Pricing Model 15stock's expected excess return exceeds that of the mimicking portfolio. This occurs ifa > 0 or equivalently if Es - rf > P(Ep - 9,meaning that the stock's risk premiummust exceed beta times the portfolio risk premium.The General Case: Adding a Stock that is Imperfectly Correlated with theExisting PortfolioSuppose next that the returns on the stock and the portfolio are correlated tosome degree (0 < p < 1). In this case, the stock's return can be separated into a returncomponent that is perfectly correlated with the portfolio and a return component that isuncorrelated with the portfolio. Since the standard deviation of the stock is a,, thestandard deviation of the perfectly correlated component of the stock's return isThus, the beta of the perfectly correlated component of the stock's excess return to theportfolio's excess return is given by the ratio of standard deviations: P = pada,As just discussed, the component of the stock's return that is perfectly correlatedwith the portfolio is a substitute for the portfolio itself and can be mimickedthrough an investment of /3 in the portfolio and (1- P) in the riskless asset. Thecomponent of the stock's excess return that is uncorrelated with the portfolio can,at the margin, be diversified away and will thus have no effect on the risk of theportfolio. This component of return can be mimicked through an investment inthe risk-free asset. We can therefore conclude that adding the stock to the portfoliowill improve the Sharpe Ratio if the stock's risk premium exceeds the sum of therisk premia of the two mimicking portfolios: P (E, - rf) for the perfectly correlatedreturn component and zero for the uncorrelated return component.This insight establishes a rule for improving the portfolio. Adding a marginalshare of stock to a portfolio will increase the portfolio's Sharpe Ratio if the stock'salpha is positive, that is, if its risk premium satisfiesConversely, selling short a marginal share of the stock will increase the portfolio'sSharpe Ratio if the alpha is negative, E, - rf < P (E, - rf) . The portfolio has thehighest attainable Sharpe Ratio if Es - rf = P(Ep - rf) for every stock-that is, ifthe risk premium for each stock is equal to beta times the risk premium for theportfolio as a whole.The Capital Asset Pricing ModelThe rule for improving the Sharpe Ratio of a portfolio allows us to derive theCapital Asset Pricing Model in a straightforward and intuitive way. We begin with fourassumptions. First, investors are risk averse and evaluate their investment portfoliosThe correlation coefficient p is the "R in "R-squared"--the fraction of the stock's variance that isattributable to movements in the portfolio. If p < 0, the standard deviation of the perfectly correlatedcomponent is Ipla,.

16 Journal of Economic Perspectivessolely in terms of expected return and standard deviation of return measured over thesame single holding period. Second, capital markets are perfect in several senses: allassets are infinitely divisible; there are no transactions costs, short selling restrictions ortaxes; information is costless and available to everyone; and all investors can borrowand lend at the risk-free rate. Third, investors all have access to the same investmentopportunities. Fourth, investors all make the same estimates of individual asset expectedreturns, standard deviations of return and the correlations among asset returns.These assumptions represent a highly simplified and idealized world, but areneeded to obtain the W M in its basic form. The model has been extended in manyways to accommodate some of the complexities manifest in the real world. But underthese assumptions, given prevailing prices, investors all will determine the same highestSharpe Ratio portfolio of risky assets. Depending on their risk tolerance, each investorwill allocate a portion of wealth to this optimal portfolio and the remainder to risk-freelending or borrowing. Investors all will hold risky assets in the same relative proportions.For the market to be in equilibrium, the price (that is, the expected return) ofeach asset must be such that investors collectively decide to hold exactly the supply ofthe asset. If investors all hold risky assets in the same proportions, those proportionsmust be the proportions in which risky assets are held in the market portfolio-theportfolio comprised of all available shares of each risky asset. In equilibrium, therefore,the portfolio of risky assets with the highest Sharpe Ratio must be the market portfolio.If the market portfolio has the highest attainable Sharpe Ratio, there is no wayto obtain a higher Sharpe Ratio by holding more or less of any one asset. Applyingthe portfolio improvement rule, it follows that the risk premium of each asset mustsatisfy Es - r- = /3 (ElM- rf) , where E, and E , are the expected return on the assetand the market portfolio, respectively, and /3 is the sensitivity of the asset's returnto the return on the market portfolio.We have just established the Capital Asset Pricing Model: In equilibrium, theexpected return of an asset is given byThis formula is the one that Sharpe, Treynor, Lintner and Mossin successfully setout to find. It is the relationship between expected return and risk that is consistentwith investors behaving according to the prescriptions of portfolio theory. If thisrule does not hold, then investors will be able to outperform the market (in thesense of obtaining a higher Sharpe Ratio) by applying the portfolio improvementrule, and if sufficiently many investors do this, stock prices will adjust to the pointwhere the CAPM becomes true.Another way of expressing the CAPM equation isSharpe Ratio of Asset S = p X Sharpe Ratio of the Market ~ o r t f o l i o . ~Using the fact that that P = pa Ju,, the equation E, = ,rf + P(EM - rf) can be rearranged to give( E , - rf)/u, = p (E, - rf)/uW,which is the expression in the text.

Andre' F. Perold 17In other words, in equilibrium, the Sharpe Ratio of any asset is no higher than theSharpe Ratio of the market portfolio (since p 5 1). Moreover, assets having thesame correlation with the market portfolio will have the same Sharpe Ratio.The Capital Asset Pricing Model tells us that to calculate the expected returnof a stock, investors need know two things: the risk premium of the overall equitymarket EM - rf (assuming that equities are the only risky assets) and the stock'sbeta versus the market. The stock's risk premium is determined by the componentof its return that is perfectly correlated with the market-that is, the extent to whichthe stock is a substitute for investing in the market. The component of the stock'sreturn that is uncorrelated with the market can be diversified away and does notcommand a risk premium.The Capital Asset Pricing Model has a number of important implications. First,perhaps the most striking aspect of the CAPM is what the expected return of anasset does not depend on. In particular, the expected return of a stock does notdepend on its stand-alone risk. It is true that a high beta stock will tend to have ahigh stand-alone risk because a portion of a stock's stand-alone risk is determinedby its beta, but a stock need not have a high beta to have a high stand-alone risk.A stock with high stand-alone risk therefore will only have a high expected returnto the extent that its stand-alone risk is derived from its sensitivity to the broad stockmarket.Second, beta offers a method of measuring the risk of an asset that cannot bediversified away. We saw earlier that any risk measure for determining expectedreturns would have to satisfy the requirement that the risk of a portfolio is theweighted average of the risks of the holdings in the portfolio. Beta satisfies thisrequirement. For example, if two stocks have market betas of 0.8 and 1.4, respectively,then the market beta of a 50/50 portfolio of these stocks is 1.1, the averageof the two stock betas. Moreover, the capitalization weighted average of the marketbetas of all stocks is the beta of the market versus itself. The average stock thereforehas a market beta of 1 .O.On a graph where the risk of an asset as measured by beta is on the horizontalaxis and return is on the vertical axis, all securities lie on a single line-the so-calledSecurities Market Line shown in Figure 4. If the market is in equilibrium, all assetsmust lie on this line. If not, investors will be able to improve upon the marketportfolio and obtain a higher Sharpe Ratio. In contrast, Figure 3 presented earliermeasured risk on the horizontal axis as stand-alone risk, the standard deviation ofeach stock, and so stocks were scattered over the diagram. But remember that notall of the stand-alone risk of an asset is priced into its expected return, just thatportion of its risk, pa,, that is correlated with the market portfolio.Third, in the Capital Asset Pricing Model, a stock's expected return does notdepend on the growth rate of its expected future cash flows. To find the expectedreturn of a company's shares, it is thus not necessary to carry out an extensive financialanalysis of the company and to forecast its future cash flows. According to the CAPM,all we need to know about the specific company is the beta of its shares, a parameterthat is usually much easier to estimate than the expected future cash flows of the firm.

18 Journal of Economic PerspectivesFigure 4The Securities Market Line (SML)ISMLLBeta of market = 1.0BetaIs the CAPM Useful?The Capital Asset Pricing Model is an elegant theory with profound implicationsfor asset pricing and investor behavior. But how useful is the model gven the idealizedworld that underlies its derivation? There are several ways to answer this question. First,we can examine whether real world asset prices and investor portfolios conform to thepredictions of the model, if not always in a strict quantitative sense, and least in a strongqualitative sense. Second, even if the model does not describe our current worldparticularly well, it might predict future investor behavior-for example, as a consequenceof capital market frictions being lessened through financial innovation, improvedregulation and increasing capital market integration. Third, the CAPM canserve as a benchmark for understanding the capital market phenomena that causeasset prices and investor behavior to deviate from the prescriptions of the model.Suboptimal DiversificationConsider the W M prediction that investors all will hold the same (market)portfolio of risky assets. One does not have to look far to realize that investors donot hold identical portfolios, which is not a surprise since taxes alone will causeidiosyncratic investor behavior. For example, optimal management of capital gainstaxes involves early realization of losses and deferral of capital gains, and so taxableinvestors might react very differently to changes in asset values depending on whenthey purchased the asset (Constantinides, 1983).Nevertheless, it will still be a positivesign for the model if most investors hold broadly diversified portfolios. But even herethe evidence is mixed. On one hand, popular index funds make it possible for investorsto obtain diversification at low cost. On the other hand, many workers hold concentratedownership of company stock in employee retirement savings plans and manyexecutives hold concentrated ownership of company stock options.One of the most puzzling examples of suboptimal diversification is the so-

The Capital Asset Pricing Model 19called home bias in international investing. In almost all countries, foreign ownershipof assets is low, meaning that investors tend to hold predominantly homecountry assets. For example, in 2003, foreign ownership accounted for only10 percent of publicly traded U.S. equities and 21 percent of publicly tradedJapanese equities. Japanese investor portfolios therefore deviate significantly fromthe world equity market portfolio: they own the vast majority of their home countryequities, but only a tiny share of U.S. equities. By contrast, and as shown inTable 1, an investor holding the world equity market portfolio would be invested48 percent in U.S. equities and only 10 percent in Japanese equities.Why is suboptimal diversification so pervasive? Common explanations are thatobtaining broad diversification can be costly, in terms of direct expenses and taxes,and that investors are subject to behavioral biases and lack of sophistication. Noneof these reasons, if valid, would mean that the CAPM is not useful. The CAPM tellsus that investors pay a price for being undiversified in that they are taking risks forwhich they are not being compensated. Thus, there exists the potential for portfolioimprovement, which in turn creates opportunities for investor education andfinancial innovation. Indeed, foreign ownership of equities in many countries hasmore than doubled over the last 20 years, most likely due to the increasedavailability of low-cost vehicles to invest globally and greater investor appreciationof the need for diversification. Investors today seem to be much better diversifiedthan in decades past, a trend that appears likely to continue.Performance MeasurementOne of the earliest applications of the Capital Asset Pricing Model was toperformance measurement of fund managers (Treynor, 1965; Sharpe, 1966;Jensen, 1968). Consider two funds, A and B, that are actively managed in the hopeof outperforming the market. Suppose that the funds obtained returns of 12 percentand 18 percent, respectively, during a period when the risk-free rate was5 percent and the overall market returned 15 percent. Assume further that thestandard deviation of funds A and B were 40 percent per annum and 30 percentper annum, respectively. Which fund had the better performance?At first glance, fund A had greater risk and a lower return than fund B, so fundB would appear to have been the better performing fund. However, we know fromthe CAPM that focusing on stand-alone risk is misleading if investors can holddiversified portfolios. To draw a firmer conclusion, we need to know how thesefunds are managed: Suppose that fund A consists of a high-risk but "marketneutral"portfolio that has long positions in some shares and short positions inothers, with a portfolio beta of zero. Fund B, on the other hand, invests in selectedhigh beta stocks, with a portfolio beta of 1.5.Instead of investing in funds A and/or B, investors could have held correspondingmimicking or "benchmark portfolios. For fund A, since its beta is zero,the benchmark portfolio is an investment in the risk-free asset; for fund B, thebenchmark is a position in the market portfolio leveraged 1.5:l with borrowing atthe risk-free rate. The benchmark portfolios respectively would have returned5 percent and 20 percent (= 5 percent + 1.5 X (15 percent - 5 percent)). Fund

20 Journal of Economic PerspectivesTable 3Evaluating Portfolio Managers with the CAPM&turn Rzsk (S.D.) Beta AlphaRiskless asset 5% 0% 0.0 05%Market portfolio 15% 20% 1 .O 05%Fund A 12% 40% 0.0 7%Fund B 18% 30% 1.5 -2%A thus outperformed its benchmark by 7 percent, while fund B underperformed itsbenchmark by 2 percent, as shown in Table 3.In terms of the CAPM framework, funds A and B had alphas of 7 percent and-2 percent, respectively, where alpha is the difference between a fund's performanceand that predicted given the beta of the fund. Appropriately risk adjusted,fund A's performance (alpha = 7 percent) exceeded that of fund B (alpha =-2 percent). An investor who held the market portfolio would, at the margin, haveobtained a higher return for the same risk by allocating money to fund A ratherthan to fund B.'The key idea here is that obtaining high returns by owning high beta stocksdoes not take skill, since investors can passively create a high beta portfolio simplythrough a leveraged position in the market portfolio. Obtaining high returns withlow beta stocks is much harder, however, since such performance cannot bereplicated with a passive strategy. Investors therefore need to assess performancebased on returns that have been appropriately risk adjusted. The CAPM provides aclear framework for thinking about this issue.The CAPM and Discounted Cash Flow AnalysisAccording to the CAPM,the appropriate discount rate for valuing the expectedfuture cash flows of a company or of a new investment project is determinedby the risk-free rate, the market risk premium and the beta versus the market of thecompany or project. Accuracy in estimating these parameters matters greatly forreal world decisionmaking since, for long-dated cash flows, an error in the discountrate is magnified manyfold when calculating the net present value.Beta is usually estimated with use of linear regression analysis applied to historicalstock market returns data. Beta can in many circumstances be accurately measured thisway even over a relatively short period of time, provided that there is sufficienthigh-frequency data. MThen the company or project being valued is not publicly tradedor there is no relevant return history, it is customary to infer beta from comparableentities whose betas can be estimated. But measurement issues can arise even if theavailability of market returns data is not an issue, for example when the covariance with' This assumes that the beta of the overall portfolio is held constant-bv holding more of the marketportfolio if money is allocated to fund A and less of the market portfolio if money is allocated to fund B.

Andre' F. Pprold 21the market is time varying and when local stock market indexes are used as proxies forthe broad market portfolio because the latter is not well specified.The hardest of all parameters to estimate is usually the market risk premium.The historical risk premium is estimated from the average of past returns and,unlike variance-related measures like beta, average returns are very sensitive to thebeginning and ending level of stock prices. The risk premium must therefore bemeasured over long periods of time, and even this may not be sufficient if the riskpremium varies over time.None of these measurement questions poses a problem for the CAPM per se,however. The market risk premium is common to all models of cash flow valuation,and its estimation needs to be performed regardless of the difficulty of the task.Provided that the W M is the "right" model, beta too needs to be estimated,irrespective of difficulty.Extensions of the CAPMThe Capital Asset Pricing Model has been extended in a variety of ways. Some ofthe best-known extensions include allowing heterogenous beliefs (Lintner, 1969; Merton,1987); eliminating the possibility of risk-free lending and borrowing (Black, 1972);having some assets be nonmarketable (Mayers, 1973); allowing for multiple timeperiods and investment opportunities that change from one period to the next(Merton, 1973; Breeden, 1979); extensions to international investing (Solnik, 1974;Stulz, 1981; Adler and Dumas, 1983) ;and employing weaker assumptions by relying onarbitrage pricing (Ross, 1976). In most extensions of the CAPM, no single portfolio ofrisky assets is optimal for everyone. Rather, investors allocate their wealth differentiallyamong several risky portfolios, which across all investors aggregate to the marketportfolio.To illustrate, consider the International Capital Asset Pricing Model. Thismodel takes into account that investors have consumption needs particular to thecountry in which they are resident. Thus, British investors will worry about thepurchasing power of pounds while American investors worry about the purchasingpower of dollars, which means that British and American investors will differentlyassess the incremental contribution that any particular asset makes to portfolio risk.As a result, they will hold somewhat different portfolios.8 In the basic CAPM,investors care about only one risk factor-the overall market. In this internationalversion of the model, they are also concerned about real currency fluctuations. Thisinsight leads to a model of expected returns involving not only the beta of an assetversus the overall market, but also the betas of the asset versus currency movementsand any other risk that is viewed differently by different investor segments.Almost all variants of the CAPM have a multi-beta expression for expected"ritish investors who own American assets will hedge a portion of their real pound/dollar exchangerate exposure by borrowing in dollars and lending in pounds, and American investors who own Britishassets will hedge a portion of their real dollar/pound exchange rate exposure by borrowing in poundsand lending in dollars. British and American investors thus will lend to and borrow from each other, andthey will have opposite exposures to the dollar/pound exchange rate.

22 Journal of Economic Perspectivesreturn. They are derived from the same basic notions: 1) investors will holdportfolios that are optimized given their specific needs, constraints and risk preferences;2) in equilibrium, asset prices reflect these demands; and 3) assets withhigh expected returns are those that are correlated with any risk that a significantgroup of investors has been unable to eliminate from their portfolios.Whether the basic CAPM or one of its multifactor extensions is the "correct"model of asset prices is ultimately an empirical question, one that is discussed indetail by Fama and French in their companion paper in this journal. Initial tests ofthe CAPM by Black, Jensen and Scholes (1972) and Fama and MacBeth (1973)supported the theory in that high beta stocks were found to have had higherreturns than low beta stocks. However, the relationship between beta and averagereturns was not as steep as indicated by the theoretical Securities Market Line.Since this early work, a vast body of research has looked for additional riskfactors that affect expected returns. Most notably, Fama and French (1992) findthat adding a "value" factor and a "size" factor (in addition to the overall market)greatly improves upon the explanatory power of the CAPM. The pervasiveness ofthese findings in follow-up research across time and other countries provides strongevidence that more than one systematic risk factor is at work in determining assetprices. However, the value and size factors are not explicitly about risk; at best, theyare proxies for risk. For example, size per se cannot be a risk factor that affectsexpected returns, since small firms would then simply combine to form large firms.Another criticism of the Fama-French findings is that their value effect is based ongiving equal weight to small and large companies and is much stronger thanobserved in capitalization-weighted value indexes. Until the risks that underlie theFama-French factors are identified, the forecast power of their model will be indoubt and the applications will be limited.ConclusionThe Capital Asset Pricing Model is a fundamental contribution to our understandingof the determinants of asset prices. The CAPM tells us that ownership ofassets by diversified investors lowers their expected returns and raises their prices.Moreover, investors who hold undiversified portfolios are likely to be taking risksfor which they are not being rewarded. As a result of the model, and despite itsmixed empirical performance, we now think differently about the relationshipbetween expected returns and risk; we think differently about how investors shouldallocate their investment portfolios; and we think differently about questions suchas performance measurement and capital budgeting.m I thank Josh Coval, Mihir Desai, Craig French, Ken Froot, Jim Hines, Elon Kohlberg,Adam Perold, Melissa Perold, Andrei Shleifer, Bill Sharpe, Rene' Stulz, Timothy Taylor, LuisViceira and Michael Waldman for he@ful discussions and comments.

The Capital Asset Pricing Model 23ReferencesAdler, Michael and Bernard Dumas. 1983. "InternationalPortfolio Choice and CorporationFinance: A Synthesis." Journal of Fznance. June,38, pp. 92.5-84.Bernoulli, Daniel. 1738 [19.54]. "SpecimenTheoriae Novae de Mensura Sortis (Expositionof a New Theory on the Measurement ofRisk)." Louise Sommer, trans. Econometrica. 22,pp. 23-36.Bernstein, Peter L. 1996. Against the Gods: TheRemarkable Stoy of Risk. New York: John Wiley &Sons, Inc.Bierman, Harold and Seymour Smidt. 1966.The Capital Budgeting Decision-Economic Analysisand Financing of Investment Projects. New York:Macmillan Company.Black, Fischer. 1972. "Capital Market Equilibriumwith Restricted Borrowing." Journal of Business.July, 45:3, pp. 444-55.Black, Fischer, Michael C. Jensen and MyronScholes. 1972. "The Capital Asset Pricing Model:Some Empirical Tests," in Studies in the Theoy ofCapitalLMarkets.Michael C. Jensen, ed. New York:Praeger, pp. 79-121.Breeden, Douglas T. 1979. "An IntertemporalAsset Pricing Model with Stochastic Consumptionand Investment Opportunities." Journal ofFinancial Economics. September, 7, pp. 265-96.Constantinides, George M. 1983. "CapitalMarket Equilibrium with Personal Tax." Econometric~.May,.51:3, pp. 611-36.Dimson, Elroy and R. A. Brealey. 1978. "TheRisk Premium on UK Equities." The InvestmentAnabst. December, 52, pp. 14-18,Fama, Eugene F. and Kenneth R. French.1992. "The Cross-Section of Expected StockReturns." Journal of Finance. June, 47, pp. 427-65.Fama, Eugene F. and James D. MacBeth. 1973."Risk, Return, and Equilibrium: EmpiricalTests." Journal of Political Economy. May/June, 3,pp. 753-55.Fisher, L. and J. H. Lorie. 1964. "Rates ofReturn on Investments in Common Stocks." JournalofBusiness. Januarv, 37, pp. 1-21.Fisher, L. and J. H. Lorie. 1968. "Rates ofReturn on Investments in Common Stock: TheYear-by-Year Record, 1926-1965." Journal of Buszness.July, 41, pp. 291-316.Gordon, Myron J. and Eli Shapiro. 1956. "CapitalEquipment Analysis: The Required Rateof Profit." Management Sczence. October, 3:1,pp. 102-10.Ibbotson, Robert G. and Rex A. Sinquefield.1976. "Stocks, Bonds, Bills, and Inflation: Year-by-Year Historical Returns ( 1926-1974) ."Journalof Business. January, 49, pp. 11-47.Herbison, B. J. 2003. "Notes on the TranslationofDon Quixote."Available at (\nnv.herbison.com/herbison/broken-eggs-quixote.htm1).Jensen, Michael C. 1968. "The Performance ofMutual Funds in the Period 1945-1964." JournalofFinance. May, 23, pp. 389-416.Lintner, John. 196.5a. "The Valuation of RiskAssets and the Selection of Risky Investmentsin Stock Portfolios and Capital Budgets." Reviewof Economics and Statistics. February, 47,pp. 13-37.Lintner, John. 1965b. "Security Prices, Riskand Maximal Gains from Diversification." Journalof Finance. December, 20, pp. 587-615.Lintner, John. 1969. "The Aggregation of InvestorsDiverse Judgments and Preferences inPurely Competitive Security Markets." Journal ofFinancial and Quantitative Analysis. December, 4,pp. 347-400.Markowitz, Harry. 19.52. "Portfolio Selection."Journal of Finance. March, 7, pp. 77-91.Markowitz, Harry. 1959. Portfolio Selection: EfficientDivprsz$cations of Investments. Cowles FoundationMonograph No. 16. New York: JohnWiley & Sons, Inc.Mayers, David. 1973. "Nonmarketable Assetsand the Determination of Capital Asset Prices inthe Absence of a Riskless Asset." Journal of Business.April, 46, pp. 2.58-67.Merton, Robert C. 1973. "An IntertermporalCapital Asset Pricing Model." Econometrica. September,41, pp. 867-87.Merton, Robert C. 1987. "A Simple Model ofCapital Market Equilibrium with Incomplete Information."Journal ofFinance. July, 42, pp. 483-510.Modigliani, Franco and Merton H. Mier.1958. "The Cost of Capital, Corporation Finance,and the Theory of Investment." AmericanEconomic him.June, 48:3, pp. 261-97.Mossin, Jan. 1966. "Equilibrium in a CapitalAsset Market." Econometrica. October, 3.5,pp. 768-83.Ross, Stephen A. 1976. "Arbitrage Theory ofCapital Asset Pricing." Journal of Economic Theov.December, 13, pp. 341-60.Roy, Andrew D. 1952. "Safety First and theHolding of Assets." Econometnca. July, 20,pp. 431-39.Savage, Leonard J. 1954. The Foundations ojStatistics. New York: John Wiley & Sons, Inc.Sharpe,Wiiam F. 1964. "Capital Asset Prices:A Theory of Market Equilibrium Under Condi-

24 Journal of Economic Perspectivesrions of ksk " Journal ofFznance September, 19,pp 425-42Sharpe, Wiiam F. 1966 "Mutual Fund Performance" Journal of Buszness Januarv, 39,pp 119-38Solnik, Bruno H. 1974 ''An Equilibriumhfodcl of the International Capital Market "JournalofEconomlc Theoq kugust, 8, pp 500-24Stulz, Rene M. 1981 "A Model of Internationalhsct Pricing "Jou7rzal ofhnanczal Econom-1c5 Septetnber, 9, pp 383-406Tobin, James. 1958 liquidi it^ Preference asBchalior Towards ksk " Rczlzew ofEconomzc StudlesFcbruan, 25, pp 68-85Treynor, J. L. 1962 "To~\ard a Theorv of hfarkerValue of Rlsk~ Assets " Unpublished mnnuscript.Final version in Asset Pricing and PortfolioPerfo~mance1999, Robert A. Korajczyk, ed., London:Risk Books, pp. 15-22.Treynor, J. L. 1965. "How to Rate the Performanceof Mutual Funds." Haward Business Review.January/February,43, pp. 63-75.de la Vega, Joseph P. 1688 [1957]. Confusionde Confusiones. English translation by H. Kallenbenz,No. 13. Cambridge, Mass.: The KressLibrary Series of Publications, The Kress Libraryof Business and Economics, HarvardUniversity.von Neumann, John L. and Oskar Morgenstern.1944. The09 of Games and Economic Behavior.Princeton, N.J.: Princeton UniversityPress.

http://www.jstor.orgLINKED CITATIONS- Page 1 of 5 -You have printed the following article:The Capital Asset Pricing ModelAndré F. PeroldThe Journal of Economic Perspectives, Vol. 18, No. 3. (Summer, 2004), pp. 3-24.Stable URL:http://links.jstor.org/sici?sici=0895-3309%28200422%2918%3A3%3C3%3ATCAPM%3E2.0.CO%3B2-ZThis article references the following linked citations. If you are trying to access articles from anoff-campus location, you may be required to first logon via your library web site to access JSTOR. Pleasevisit your library's website or contact a librarian to learn about options for remote access to JSTOR.[Footnotes]1 Stocks, Bonds, Bills, and Inflation: Year-by-Year Historical Returns (1926-1974)Roger G. Ibbotson; Rex A. SinquefieldThe Journal of Business, Vol. 49, No. 1. (Jan., 1976), pp. 11-47.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28197601%2949%3A1%3C11%3ASBBAIY%3E2.0.CO%3B2-2ReferencesInternational Portfolio Choice and Corporation Finance: A SynthesisMichael Adler; Bernard DumasThe Journal of Finance, Vol. 38, No. 3. (Jun., 1983), pp. 925-984.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28198306%2938%3A3%3C925%3AIPCACF%3E2.0.CO%3B2-UExposition of a New Theory on the Measurement of RiskDaniel BernoulliEconometrica, Vol. 22, No. 1. (Jan., 1954), pp. 23-36.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28195401%2922%3A1%3C23%3AEOANTO%3E2.0.CO%3B2-XNOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 2 of 5 -Capital Market Equilibrium with Restricted BorrowingFischer BlackThe Journal of Business, Vol. 45, No. 3. (Jul., 1972), pp. 444-455.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28197207%2945%3A3%3C444%3ACMEWRB%3E2.0.CO%3B2-GCapital Market Equilibrium with Personal TaxGeorge M. ConstantinidesEconometrica, Vol. 51, No. 3. (May, 1983), pp. 611-636.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28198305%2951%3A3%3C611%3ACMEWPT%3E2.0.CO%3B2-IThe Cross-Section of Expected Stock ReturnsEugene F. Fama; Kenneth R. FrenchThe Journal of Finance, Vol. 47, No. 2. (Jun., 1992), pp. 427-465.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199206%2947%3A2%3C427%3ATCOESR%3E2.0.CO%3B2-NRisk, Return, and Portfolio Analysis: ReplyEugene F. FamaThe Journal of Political Economy, Vol. 81, No. 3. (May - Jun., 1973), pp. 753-755.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28197305%2F06%2981%3A3%3C753%3ARRAPAR%3E2.0.CO%3B2-LRates of Return on Investments in Common StocksL. Fisher; J. H. LorieThe Journal of Business, Vol. 37, No. 1. (Jan., 1964), pp. 1-21.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28196401%2937%3A1%3C1%3AROROII%3E2.0.CO%3B2-TRates of Return on Investments in Common Stock: The Year-by-Year Record, 1926-65Lawrence Fisher; James H. LorieThe Journal of Business, Vol. 41, No. 3. (Jul., 1968), pp. 291-316.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28196807%2941%3A3%3C291%3AROROII%3E2.0.CO%3B2-8NOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 3 of 5 -Capital Equipment Analysis: The Required Rate of ProfitMyron J. Gordon; Eli ShapiroManagement Science, Vol. 3, No. 1. (Oct., 1956), pp. 102-110.Stable URL:http://links.jstor.org/sici?sici=0025-1909%28195610%293%3A1%3C102%3ACEATRR%3E2.0.CO%3B2-XStocks, Bonds, Bills, and Inflation: Year-by-Year Historical Returns (1926-1974)Roger G. Ibbotson; Rex A. SinquefieldThe Journal of Business, Vol. 49, No. 1. (Jan., 1976), pp. 11-47.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28197601%2949%3A1%3C11%3ASBBAIY%3E2.0.CO%3B2-2The Performance of Mutual Funds in the Period 1945-1964Michael C. JensenThe Journal of Finance, Vol. 23, No. 2, Papers and Proceedings of the Twenty-Sixth AnnualMeeting of the American Finance Association Washington, D.C. December 28-30, 1967. (May,1968), pp. 389-416.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28196805%2923%3A2%3C389%3ATPOMFI%3E2.0.CO%3B2-GThe Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios andCapital BudgetsJohn LintnerThe Review of Economics and Statistics, Vol. 47, No. 1. (Feb., 1965), pp. 13-37.Stable URL:http://links.jstor.org/sici?sici=0034-6535%28196502%2947%3A1%3C13%3ATVORAA%3E2.0.CO%3B2-7Security Prices, Risk, and Maximal Gains From DiversificationJohn LintnerThe Journal of Finance, Vol. 20, No. 4. (Dec., 1965), pp. 587-615.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28196512%2920%3A4%3C587%3ASPRAMG%3E2.0.CO%3B2-UNOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 4 of 5 -The Aggregation of Investor's Diverse Judgments and Preferences in Purely CompetitiveSecurity MarketsJohn LintnerThe Journal of Financial and Quantitative Analysis, Vol. 4, No. 4. (Dec., 1969), pp. 347-400.Stable URL:http://links.jstor.org/sici?sici=0022-1090%28196912%294%3A4%3C347%3ATAOIDJ%3E2.0.CO%3B2-SPortfolio SelectionHarry MarkowitzThe Journal of Finance, Vol. 7, No. 1. (Mar., 1952), pp. 77-91.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28195203%297%3A1%3C77%3APS%3E2.0.CO%3B2-1Nonmarketable Assets and the Determination of Capital Asset Prices in the Absence of aRiskless AssetDavid MayersThe Journal of Business, Vol. 46, No. 2. (Apr., 1973), pp. 258-267.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28197304%2946%3A2%3C258%3ANAATDO%3E2.0.CO%3B2-UAn Intertemporal Capital Asset Pricing ModelRobert C. MertonEconometrica, Vol. 41, No. 5. (Sep., 1973), pp. 867-887.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197309%2941%3A5%3C867%3AAICAPM%3E2.0.CO%3B2-EA Simple Model of Capital Market Equilibrium with Incomplete InformationRobert C. MertonThe Journal of Finance, Vol. 42, No. 3, Papers and Proceedings of the Forty-Fifth Annual Meetingof the American Finance Association, New Orleans, Louisiana, December 28-30, 1986. (Jul., 1987),pp. 483-510.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28198707%2942%3A3%3C483%3AASMOCM%3E2.0.CO%3B2-7NOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 5 of 5 -The Cost of Capital, Corporation Finance and the Theory of InvestmentFranco Modigliani; Merton H. MillerThe American Economic Review, Vol. 48, No. 3. (Jun., 1958), pp. 261-297.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28195806%2948%3A3%3C261%3ATCOCCF%3E2.0.CO%3B2-3Equilibrium in a Capital Asset MarketJan MossinEconometrica, Vol. 34, No. 4. (Oct., 1966), pp. 768-783.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28196610%2934%3A4%3C768%3AEIACAM%3E2.0.CO%3B2-3Safety First and the Holding of AssetsA. D. RoyEconometrica, Vol. 20, No. 3. (Jul., 1952), pp. 431-449.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28195207%2920%3A3%3C431%3ASFATHO%3E2.0.CO%3B2-SCapital Asset Prices: A Theory of Market Equilibrium under Conditions of RiskWilliam F. SharpeThe Journal of Finance, Vol. 19, No. 3. (Sep., 1964), pp. 425-442.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28196409%2919%3A3%3C425%3ACAPATO%3E2.0.CO%3B2-OMutual Fund PerformanceWilliam F. SharpeThe Journal of Business, Vol. 39, No. 1, Part 2: Supplement on Security Prices. (Jan., 1966), pp.119-138.Stable URL:http://links.jstor.org/sici?sici=0021-9398%28196601%2939%3A1%3C119%3AMFP%3E2.0.CO%3B2-6Liquidity Preference as Behavior Towards RiskJ. TobinThe Review of Economic Studies, Vol. 25, No. 2. (Feb., 1958), pp. 65-86.Stable URL:http://links.jstor.org/sici?sici=0034-6527%28195802%2925%3A2%3C65%3ALPABTR%3E2.0.CO%3B2-8NOTE: The reference numbering from the original has been maintained in this citation list.

Capital Asset Prices: A Theory of Market Equilibrium under Conditions of RiskWilliam F. SharpeThe Journal of Finance, Vol. 19, No. 3. (Sep., 1964), pp. 425-442.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28196409%2919%3A3%3C425%3ACAPATO%3E2.0.CO%3B2-OThe Journal of Finance is currently published by American Finance Association.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/afina.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgThu Dec 20 06:47:48 2007

Tlze Journal of FINANCEVOL.XIX SEPTEMBER1964 No. 3CAPITAL ASSET PRICES: A THEORY OF MARKETEQUILIBRIUM UNDER CONDITIONS OF RISK*ONEOF THE PROBLEMS which has plagued those attempting to predict thebehavior of capital markets is the absence of a body of positive microeconomictheory dealing with conditions of risk. Although many usefulinsights can be obtained from the traditional models of investment underconditions of certainty, the pervasive influence of risk in financial transactionshas forced those working in this area to adopt models of pricebehavior which are little more than assertions. A typical classroom explanationof the determination of capital asset prices, for example,usually begins with a careful and relatively rigorous description of theprocess through which individual preferences and physical relationshipsinteract to determine an equilibrium pure interest rate. This is generallyfollowed by the assertion that somehow a market risk-premium is alsodetermined, with the prices of assets adjusting accordingly to account fordifferences in their risk.A useful representation of the view of the capital market implied insuch discussions is illustrated in Figure 1. In equilibrium, capital assetprices have adjusted so that the investor, if he follows rational procedures(primarily diversification), is able to attain any desired point along acapital market line.l He may obtain a higher expected rate of return onhis holdings only by incurring additional risk. In effect, the marketpresents him with two prices: the price of time, or the pure interest rate(shown by the intersection of the line with the horizontal axis) and theMe of risk, the additional expected return per unit of risk borne (thereciprocal of the slope of the line).* A great many people provided comments on early versions of this paper which ledto major improvements in the exposition. In addition to the referees, who were mosthelpful, the author wishes to express his appreciation to Dr. Harry Markowitz of theRAND Corporation, Professor Jack Hirshleifer of the University of California at LosAngeles, and to Professors Yoram Barzel, George Brabb, Bruce Johnson, Walter Oi andR. Haney Scott of the University of Washington.t Associate Professor of Operations Research, University of Washington.1. Although some discussions are also consistent with a non-linear (but monotonic) curve.425

426 The Journal of FinanceAt present there is no theory describing the manner in which the priceof risk results from the basic influences of investor preferences, the physicalattributes of capital assets, etc. Moreover, lacking such a theory, it isdifficult to give any real meaning to the relationship between the priceof a single asset and its risk. Through diversification, some of the riskinherent in an asset can be avoided so that its total risk is obviously notthe relevant influence on its price; unfortunately little has been saidconcerning the particular risk component which is relevant.O- Expected Rate of Returnpure Interest'RateFIGURE1In the last ten years a number of economists have developed normativemodels dealing with asset choice under conditions of risk. Markowitz?following Von Neumann and Morgenstern, developed an analysis basedon the expected utility maxim and proposed a general solution for theportfolio selection problem. Tobin3 showed that under certain conditionsMarkowitz's model implies that the process of investment choice can bebroken down into two phases: first, the choice of a unique optimumcombination of risky assets; and second, a separate choice concerning theallocation of funds between such a combination and a single riskless2. Harry M. Markowitz, Portfolio Selection, Eficient Diversification of Investments(New York: John Wiley and Sons, Inc., 1959). The major elements of the theory firstappeared in his article "Portfolio Selection," The Journal of Finance, XI1 (March 1952),77-91.3. James Tobin, "Liquidity Preference as Behavior Towards Risk," The Review ofEconomic Studies, XXV (February, 1958), 65-86.

Capital Asset Prices427asset. Recently, Hicks4 has used a model similar to that proposed byTobin to derive corresponding conclusions about individual investorbehavior, dealing somewhat more explicitly with the nature of the conditionsunder which the process of investment choice can be dichotomized.An even more detailed discussion of this process, including a rigorousproof in the context of a choice among lotteries has been presented byGordon and Gang~lli.~Although all the authors cited use virtually the same model of investorbeha~ior,~ none has yet attempted to extend it to construct a marketequilibrium theory of asset prices under conditions of risk.7 We will showthat such an extension provides a theory with implications consistent withthe assertions of traditional financial theory described above. Moreover,it sheds considerable light on the relationship between the price of anasset and the various components of its overall risk. For these reasonsit warrants consideration as a model of the determination of capital assetprices.Part I1 provides the model of individual investor behavior under conditionsof risk. In Part I11 the equilibrium conditions for the capitalmarket are considered and the capital market line derived. The implicationsfor the relationship between the prices of individual capital assetsand the various components of risk are described in Part IV.The Investor's Preference FunctionAssume that an individual views the outcome of any investment inprobabilistic terms; that is, he thinks of the possible results in terms ofsome probability distribution. In assessing the desirability of a particularinvestment, however, he is willing to act on the basis of only two para-4. John R. Hicks, "Liquidity," The Economic Journal, LXXII (December, 1962), 787-802.5. M. J. Gordon and Ramesh Gangolli, "Choice Among and Scale of Play on LotteryType Alternatives," College of Business Administration, University of Rochester, 1962.For another discussion of this relationship see W. F. Sharpe, "A Simplified Model forPortfolio Analysis," Management Science, Vol. 9, No. 2 (January 1963), 277-293. Arelated discussion can be found in F. Modigliani and M. H. Miller, "The Cost of Capital,Corporation Finance, and the Theory of Investment," The American Economic Review,XLVIII (June 1958), 261-297.6. Recently Hirshleifer has suggested that the mean-variance approach used in thearticles cited is best regarded as a special case of a more general formulation due toArrow. See Hirshleifer's "Investment Decision Under Uncertainty," Papers and Proceedingsof the Seventy-Sixth Annual Meeting of the American Economic Association, Dec. 1963,or Arrow's lLLe Role des Valeurs Boursieres pour la Repartition la Meilleure des Risques,"Inter~tational Colloquium on Econometrics, 1952.7. After preparing this paper the author learned that Mr. Jack L. Treynor, of ArthurD. Little, Inc., had independently developed a model similar in many respects to the onedescribed here. Unfortunately Mr. Treynor's excellent work on this subject is, at present,unpublished.

428 The Journal of Financemeters of this distribution-its expected value and standard deviation.'This can be represented by a total utility function of the form:U = f(Ew, ow)where Ew indicates expected future wealth and ow the predicted standarddeviation of the possible divergence of actual future wealth from Ew.Investors are assumed to prefer a higher expected future wealth to alower value, ceteris paribus (dU/dEw > 0). Moreover, they exhibitrisk-aversion, choosing an investment offering a lower value of ow toone with a greater level, given the level of Ew (dU/do, < 0). These assumptionsimply that indifference curves relating Ew and OW will beupward-sloping?To simplify the analysis, we assume that an investor has decided tocommit a given amount (Wi) of his present wealth to investment. LettingWt be his terminal wealth and R the rate of return on his investment:we haveWt = R Wi $. Wi.This relationship makes it possible to express the investor's utility interms of R, since terminal wealth is directly related to the rate of return:U = ~ (ER,CR).Figure 2 summarizes the model of investor preferences in a family ofindifference curves; successive curves indicate higher levels of utility asone moves down and/or to the right.1°8. Under certain conditions the mean-variance approach can be shown to lead tounsatisfactory predictions of behavior. Markowitz suggests that a model based on thesemi-variance (the average of the squared deviations below the mean) would be preferable;in light of the formidable computational problems, however, he bases his analysis on thevariance and standard deviation.9. While only these characteristics are required for the analysis, it is generally assumedthat the curves have the property of diminishing marginal rates of substitution betweenE, and a,, as do those in our diagrams.10. Such indifference curves can also be derived by assuming that the investor wishesto maximize expected utility and that his total utility can be represented by a quadraticfunction of R with decreasing marginal utility. Both Markowitz and Tobin present sucha derivation. A similar approach is used by Donald E. Farrar in The Investment DecisionUnder Uncertainty (Prentice-Hall, 1962). Unfortunately Farrar makes an error in hisderivation; he appeals to the Von-Neumann-Morgenstern cardinal utility axioms to transforma function of the form:E(U) = a+ bER - cER2 - coR2into one of the form:E (U) =klER -k2aR2.That such a transformation is not consistent with the axioms can readily be seen in thisform, since the first equation implies non-linear indifference curves in the ER, aR2 planewhile the second implies a linear relationship. Obviously no three (different) points canlie on both a line and a non-linear curve (with a monotonic derivative). Thus the twofunctions must imply different orderings among alternative choices in at least someinstance.

Capital Asset PricesThe Investment Opportunity CurveThe model of investor behavior considers the investor as choosing froma set of investment opportunities that one which maximizes his utility.Every investment plan available to him may be represented by a point inthe En, OR plane. If all such plans involve some risk, the area composedof such points will have an appearance similar to that shown in Figure 2.The investor will choose from among all possible plans the one placinghim on the indifference curve representing the highest level of utility(point F). The decision can be made in two stages: first, find the set ofefficient investment plans and, second choose one from among this set.A plan is said to be efficient if (and only if) there is no alternative witheither (1) the same ERand a lower on, (2) the same OR and a higher EBor (3) a higher En and a lower on. Thus investment Z is inefficient sinceinvestments B, C, and D (among others) dominate it. The only planswhich would be chosen must lie along the lower right-hand boundary(AFBDCX)-the investment opportunity curve.To understand the nature of this curve, consider two investment plans-A and B, each including one or more assets. Their predicted expectedvalues and standard deviations of rate of return are shown in Figure 3.

430 The Journal of FinanceIf the proportion a of the individual's wealth is placed in plan A and theremainder (1-a) in B, the expected rate of return of the combination willlie between the expected returns of the two plans:The predicted standard deviation of return of the combination is:Note that this relationship includes Tab, the correlation coefficient betweenthe predicted rates of return of the two investment plans. A value of f 1would indicate an investor's belief that there is a precise positive relationshipbetween the outcomes of the two investments. A zero value wouldindicate a belief that the outcomes of the two investments are completelyindependent and -1 that the investor feels that there is a precise inverserelationship between them. In the usual case r,b will have a value between0 and +l.Figure 3 shows the possible values of ER~and OR, obtainable withdifferent combinations of A and B under two different assumptions about

Capital Asset Prices 431the value of Tab. If the two investments are perfectly correlated, thecombinations will lie along a straight line between the two points, sincein this case both ER~and OR, will be linearly related to the proportionsinvested in the two plans.ll If they are less than perfectly positively correlated,the standard deviation of any combination must be less than thatobtained with perfect correlation (since lab will be less) ; thus the combinationsmust lie along a curve below the line AB.12 AZB shows such acurve for the case of complete independence (r,b = 0); with negativecorrelation the locus is even more U-shaped.13The manner in which the investment opportunity curve is formed isrelatively simple conceptually, although exact solutions are usually quitedifficult.14 One first traces curves indicating ER, OR values available withsimple combinations of individual assets, then considers combinations ofcombinations of assets. The lower right-hand boundary must be eitherlinear or increasing at an increasing rate (d2O R/~E~R > 0). AS suggestedearlier, the complexity of the relationship between the characteristics ofindividual assets and the location of the investment opportunity curvemakes it difficult to provide a simple rule for assessing the desirabilityof individual assets, since the effect of an asset on an investor's over-allinvestment opportunity curve depends not only on its expected rate ofreturn (ER~) and risk (ORi), but also on its correlations with the otheravailable opportunities (ril, ri2, ... . ,ri,). However, such a rule is impliedby the equilibrium conditions for the model, as we will show in part IV.The Pure Rate of InterestWe have not yet dealt with riskless assets. Let P be such an asset; itsrisk is zero ( a = ~ 0) ~ and its expected rate of return, ER*, is equal (bydefinition) to the pure interest rate. If an investor places a of his wealthbut rab = 1, therefore the expression under the square root sign can be factored:bRc= dEabRa+ (1 - a) oRbI2= a bRa+ (1 - a) bRb= oRb+ (bRa-bRb)a12. This curvature is, in essence, the rationale for diversification.'Ra13. When rab = 0, the slope of the curve at point A is - , at point B it isE ~ b-E ~ abRb. When r,,=-1, -- the curve degenerates to two straight lines to a pointE ~ b-E ~ aon the horizontal axis.14. Markowitz has shown that this is a problem in parametric quadratic programming.An efficient solution technique is described in his article, "The Optimization of a QuadraticFunction Subject to Linear Constraints," Naval Research Logistics Quarterly, Vol. 3(March and June, 1956), 111-133. A solution method for a special case is given in theauthor's iiA Simplified Model for Portfolio Analysis," op. cit.

432 The Journal of Financein P and the remainder in some risky asset A, he would obtain an expectedrate of return:ERe =aE~p+ ( 1 -a) ER~The standard deviation of such a combination would be:but since a~,= 0, this reduces to:This implies that all combinations involving any risky asset or combinationof assets plus the riskless asset must have values of ER~ and URCwhich lie along a straight line between the points representing the twocomponents. Thus in Figure 4 all combinations of ERand OR lying alongthe line PA are attainable if some money is loaned at the pure rate andsome placed in A. Similarly, by lending at the pure rate and investing inB, combinations along PB can be attained. Of all such possibilities, however,one will dominate: that investment plan lying at the point of theoriginal investment opportunity curve where a ray from point P is tangentto the curve. In Figure 4 all investments lying along the original curve

Capital Asset Prices433from X to + are dominated by some combination of investment in 9 andlending at the pure interest rate.Consider next the possibility of borrowing. If the investor can borrowat the pure rate of interest, this is equivalent to disinvesting in P. Theeffect of borrowing to purchase more of any given investment than ispossible with the given amount of wealth can be found simply by lettinga take on negative values in the equations derived for the case of lending.This will obviously give points lying along the extension of line PA ifborrowing is used to purchase more of A; points lying along the extensionof PB if the funds are used to purchase B, etc.As in the case of lending, however, one investment plan will dominateall others when borrowing is possible. When the rate at which funds canbe borrowed equals the lending rate, this plan will be the same one whichis dominant if lending is to take place. Under these conditions, the investmentopportunity curve becomes a line (P+Z in Figure 4). Moreover,if the original investment opportunity curve is not linear at point +,theprocess of investment choice can be dichotomized as follows: first selectthe (unique) optimum combination of risky assets (point +), and secondborrow or lend to obtain the particular point on PZ at which an indifferencecurve is tangent to the line.16Before proceeding with the analysis, it may be useful to consider alternativeassumptions under which only a combination of assets lying at thepoint of tangency between the original investment opportunity curve anda ray from P can be efficient. Even if borrowing is impossible, the investorwill choose + (and lending) if his risk-aversion leads him to a pointbelow + on the line P+. Since a large number of investors choose to placesome of their funds in relatively risk-free investments, this is not an unlikelypossibility. Alternatively, if borrowing is possible but only up tosome limit, the choice of + would be made by all but those investorswilling to undertake considerable risk. These alternative paths lead to themain conclusion, thus making the assumption of borrowing or lendingat the pure interest rate less onerous than it might initially appear to be.In order to derive conditions for equilibrium in the capital market weinvoke two assumptions. First, we assume a common pure rate of interest,with all investors able to borrow or lend funds on equal terms. Second,we assume homogeneity of investor expectation^:'^ investors are assumed15. This proof was first presented by Tobin for the case in which the pure rate ofinterest is zero (cash). Hicks considers the lending situation under comparable conditionsbut does not allow borrowing. Both authors present their analysis using maximizationsubject to constraints expressed as equalities. Hicks' analysis assumes independence andthus insures that the solution will include no negative holdings of risky assets; Tobin'scovers the general case, thus his solution would generally include negative holdings ofsome assets. The discussion in this paper is based on Markowitz' formulation, whichincludes non-negativity constraints on the holdings of all assets.16. A term suggested by one of the referees.

434 The Journal of Financeto agree on the prospects of various investrnents-the expected values,standard deviations and correlation coefficients described in Part 11.Needless to say, these are highly restrictive and undoubtedly unrealisticassumptions. However, since the proper test of a theory is not the realismof its assumptions but the acceptability of its implications, and since theseassumptions imply equilibrium conditions which form a major partof classical financial doctrine, it is far from clear that this formulationshould be rejected--especially in view of the dearth of alternative modelsleading to similar results.Under these assumptions, given some set of capital asset prices, eachinvestor will view his alternatives in the same manner. For one set ofprices the alternatives might appear as shown in Figure 5. In this situa-tion, an investor with the preferences indicated by indifference curves A1through A4 would seek to lend some of his funds at the pure interest rateand to invest the remainder in the combination of assets shown by point+,since this would give him the preferred over-all position A*. An investorwith the preferences indicated by curves B1 through B4 would seek to investall his funds in combination +, while an investor with indifferencecurves C1 through C4 would invest all his funds plus additional (borrowed)

Capital Asset Prices 435funds in combination 9 in order to reach his preferred position (C*). Inany event, all would attempt to purchase only those risky assets whichenter combination 9.The attempts by investors to purchase the assets in combination 9 andtheir lack of interest in holding assets not in combination 9 would, ofcourse, lead to a revision of prices. The prices of assets in 9 will rise and,since an asset's expected return relates future income to present price,their expected returns will fall. This will reduce the attractiveness of combinationswhich include such assets; thus point 9 (among others) willmove to the left of its initial position.17 On the other hand, the prices ofassets not in 9 will fall, causing an increase in their expected returns anda rightward movement of points representing combinations which includethem. Such price changes will lead to a revision of investors' actions; somenew combination or combinations will become attractive, leading to differentdemands and thus to further revisions in prices. As the process continues,the investment opportunity curve will tend to become more linear,with points such as 9 moving to the left and formerly inefficient points(such as F and G) moving to the right.Capital asset prices must, of course, continue to change until a set ofprices is attained for which every asset enters at least one combinationlying on the capital market line. Figure 6 illustrates such an equilibriumcondition.'' All possibilities in the shaded area can be attained with combinationsof risky assets, while points lying along the line PZ can be attainedby borrowing or lending at the pure rate plus an investment insome combination of risky assets. Certain possibilities (those lying alongPZ from point A to point B) can be obtained in either manner. For example,the ER, OR values shown by point A can be obtained solely by somecombination of risky assets; alternatively, the point can be reached by acombination of lending and investing in combination C of risky assets.It is important to recognize that in the situation shown in Figure 6many alternative combinations of risky assets are efficient (i.e., lie alongline PZ), and thus the theory does not imply that all investors will holdthe same combination.lQ On the other hand, all such combinations mustbe perfectly (positively) correlated, since they lie along a linear border of17. If investors consider the variability of future dollar returns unrelated to presentprice, both E, and a, will fall; under these conditions the point representing an assetwould move along a ray through the origin as its price changes.18. The area in Figure 6 representing ER, uR values attained with only risky assetshas been drawn at some distance from the horizontal axis for emphasis. It is likely thata more accurate representation would place it very close to the axis.19. This statement contradicts Tobin's conclusion that there will be a unique optimalcombination of risky assets. Tobin's proof of a unique optimum can be shown to beincorrect for the case of perfect correlation of efficient risky investment plans if theline connecting their ER, aR points would pass through point P. In the graph on page 83of this article (09. cit.) the constant-risk locus would, in this case, degenerate from afamily of ellipses into one of straight lines parallel to the constant-return loci, thus givingmultiple optima.

436 The Journal of Financethe ER, OR region.20 This provides a key to the relationship between theprices of capital assets and different types of risk.IV. THEPRICESOF CAPITALASSETSWe have argued that in equilibrium there will be a simple linear relationshipbetween the expected return and standard deviation of return forefficient combinations of risky assets. Thus far nothing has been saidabout such a relationship for individual assets. Typically the ER,OR valuesassociated with single assets will lie above the capital market line, reflectingthe inefficiency of undiversified holdings. Moreover, such points maybe scattered throughout the feasible region, with no consistent relationshipbetween their expected return and total risk (OR). However, therewill be a consistent relationship between their expected returns and whatmight best be called systematic risk, as we will now show.Figure 7 illustrates the typical relationship between a single capital20. ER, bR values given by combinations of any two combinations must lie withinthe region and cannot plot above a straight line joining the points. In this case they cannotplot below such a straight line. But since only in the case of perfect correlation will theyplot along a straight line, the two combinations must be perfectly correlated. As shownin Part IV, this does not necessarily imply that the individual securities they containare perfectly correlated.

Capita2 Asset Prices 437asset (point i) and an efficient combination of assets (point g) of whichit is a part. The curve igg' indicates all ER,an values which can be obtainedwith feasible combinations of asset i and combination g. As before, wedenote such a combination in terms of a proportion a of asset i and(1 -a) of combination g. A value of a = 1 would indicate pure invest-ment in asset i while a = 0 would imply investment in combination g.Note, however, that a = .5 implies a total investment of more than halfthe funds in asset i, since half would be invested in i itself and the otherhalf used to purchase combination g, which also includes some of asset i.This means that a combination in which asset i does not appear at all mustbe represented by some negative value of a. Point g' indicates such acombination.In Figure 7 the curve igg' has been drawn tangent to the capital marketline (PZ) at point g. This is no accident. All such curves must be tangentto the capital market line in equilibrium, since (1) they must touch it atthe point representing the efficient combination and (2) they are continuousat that point.21 Under these conditions a lack of tangency would21. Only if rig=-1 will the curve be discontinuous over the range in question.

438 The Journal of Financeimply that the curve intersects PZ. But then some feasible combination ofassets would lie to the right of the capital market line, an obvious impossibilitysince the capital market line represents the efficient boundary offeasible values of En and OR.The requirement that curves such as igg' be tangent to the capitalmarket line can be shown to lead to a relatively simple formula whichrelates the expected rate of return to various elements of risk for all assetswhich are included in combination g.22Its economic meaning can bestbe seen if the relationship between the return of asset i and that of combinationg is viewed in a manner similar to that used in regression analy-~ i s Imagine . ~ ~ that we were given a number of (ex post) observations ofthe return of the two investments. The points might plot as shown in Fig.8. The scatter of the Ri observations around their mean (which will approximateERI)is, of course, evidence of the total risk of the asset -o ~i.But part of the scatter is due to an underlying relationship with the returnon combination g, shown by Big, the slope of the regression line. The responseof Ri to changes in R, (and variations in Rg itself) account for22. The standard deviation of a combination of g and i will be:= dh20Ri2+ (1 - a12 bRg2 + Prig a(l - a) aRiaRg4but a = aRg at a = 0. Thus:The expected return of a combination will be:E = aE,, $ (1- a) ERgThus, at all values of a:and, at a = 0:do a, -rigb~i-=dE ER, -ERiLet the equation of the capital market line be:aR = s(ER - P)where P is the pure interest rate. Since igg' is tangent to the line when u = 0, and since(ERg, oRg) lies on the line:~ R P-rigo~i '=R,_- -ER~-ERI E R ~-Por:[-I [-I'igb~i P 1-~ R P= - + E ~ ~ .23. This model has been called the diagonal model since its portfolio analysis solutioncan be facilitated by re-arranging the data so that the variance-covariance matrix becomesdiagonal. The method is described in the author's article, cited earlier.

Capital Asset PricesReturn on Asset i (Ri)Return on Combination g (R )gmuch of the variation in Ri. It is this component of the asset's total riskwhich we term the systematic risk. The remainder? being uncorrelatedwith R,, is the unsystematic component. This formulation of the relationshipbetween Ri and Rg can be employed ex ante as a predictive model. Bigbecomes the predicted response of Ri to changes in Rg. Then, given OR,(the predicted risk of Rg), the systematic portion of the predicted riskof each asset can be determined.This interpretation allows us to state the relationship derived fromthe tangency of curves such as igg' with the capital market line in theform shown in Figure 9. All assets entering efficient combination g musthave (predicted) Big and ER~values lying on the line PQ.26 Prices will24. ex post, the standard error.25.and:The expression on the right is the expression on the left-hand side of the last equation infootnote 22. ~ hus:P 1

A440 The Journal of Financeadjust so that assets which are more responsive to changes in R, will havehigher expected returns than those which are less responsive. This accordswith common sense. Obviously the part of an asset's risk which is due toits correlation with the return on a combination cannot be diversified awaywhen the asset is added to the combination. Since Big indicates the magnitudeof this type of risk it should be directly related to expected return.The relationship illustrated in Figure 9 provides a partial answer to thequestion posed earlier concerning the relationship between an asset's riskPure Rate of InterestFIGURE9and its expected return. But thus far we have argued only that the relationshipholds for the assets which enter some particular efficient combination(g). Had another combination been selected, a different linearrelationship would have been derived. Fortunately this limitation is easilyovercome. As shown in thewe may arbitrarily select any one26. Consider the two assets i and i*, the former included in efficient combination gand the latter in combination g*. As shown above:P 1and:[-I = - + [-] E ~ g I?E ~ i

Capital Asset Prices 441of the efficient combinations, then measure the predicted responsivenessof every asset's rate of return to that of the combination selected; andthese coefficients will be related to the expected rates of return of theassets in exactly the manner pictured in Figure 9.The fact that rates of return from all efficient combinations will beperfectly correlated provides the justification for arbitrarily selecting anyone of them. Alternatively we may choose instead any variable perfectlycorrelated with the rate of return of such combinations. The vertical axisin Figure 9 would then indicate alternative levels of a coefficient measuringthe sensitivity of the rate of return of a capital asset to changes in thevariable chosen.This possibility suggests both a plausible explanation for the implicationthat all efficient combinations will be perfectly correlated and a usefulinterpretation of the relationship between an individual asset's expectedreturn and its risk. Although the theory itself implies only thatrates of return from efficient combinations will be perfectly correlated,we might expect that this would be due to their common dependence onthe over-all level of economic activity. If so, diversification enables theinvestor to escape all but the risk resulting from swings in economic activity-thistype of risk remains even in efficient combinations. And, sinceall other types can be avoided by diversification, only the responsivenessof an asset's rate of return to the level of economic activity is relevant inBi*g* = -[ P ] + [ 1 ] ERi*.ER,* - ER,* -Since Rgand Rgr are perfectly correlated:- riagThus:Since both g and g* lie on a line which intercepts the E-axis at P:and:ER, -PBi*.* = Bi*, [ ]ER,* -PThus:P 1 ER, -P- [ ERg*-P] + [ ] 'Ri* = 'i*g 1ER,* -P ,ER,*- ]from which we have the desired relationship between K,and g:P 1Bi,,ER, -Pmust therefore plot on the same line as does Big.

442 The Journal of Financeassessing its risk. Prices will adjust until there is a linear relationshipbetween the magnitude of such responsiveness and expected return. Assetswhich are unaffected by changes in economic activity will return thepure interest rate; those which move with economic activity will promiseappropriately higher expected rates of return.This discussion provides an answer to the second of the two questionsposed in this paper. In Part 111 it was shown that with respect to equilibriumconditions in the capital market as a whole, the theory leads toresults consistent with classical doctrine (i.e., the capital market line).We have now shown that with regard to capital assets considered individually,it also yields implications consistent with traditional concepts:it is common practice for investment counselors to accept a lower expectedreturn from defensive securities (those which respond little to changes inthe economy) than they require from aggressive securities (which exhibitsignificant response). As suggested earlier, the familiarity of the implicationsneed not be considered a drawback. The provision of a logical frameworkfor producing some of the major elements of traditional financialtheory should be a useful contribution in its own right.

http://www.jstor.orgLINKED CITATIONS- Page 1 of 2 -You have printed the following article:Capital Asset Prices: A Theory of Market Equilibrium under Conditions of RiskWilliam F. SharpeThe Journal of Finance, Vol. 19, No. 3. (Sep., 1964), pp. 425-442.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28196409%2919%3A3%3C425%3ACAPATO%3E2.0.CO%3B2-OThis article references the following linked citations. If you are trying to access articles from anoff-campus location, you may be required to first logon via your library web site to access JSTOR. Pleasevisit your library's website or contact a librarian to learn about options for remote access to JSTOR.[Footnotes]3 Liquidity Preference as Behavior Towards RiskJ. TobinThe Review of Economic Studies, Vol. 25, No. 2. (Feb., 1958), pp. 65-86.Stable URL:http://links.jstor.org/sici?sici=0034-6527%28195802%2925%3A2%3C65%3ALPABTR%3E2.0.CO%3B2-84 LiquidityJ. R. HicksThe Economic Journal, Vol. 72, No. 288. (Dec., 1962), pp. 787-802.Stable URL:http://links.jstor.org/sici?sici=0013-0133%28196212%2972%3A288%3C787%3AL%3E2.0.CO%3B2-P5 A Simplified Model for Portfolio AnalysisWilliam F. SharpeManagement Science, Vol. 9, No. 2. (Jan., 1963), pp. 277-293.Stable URL:http://links.jstor.org/sici?sici=0025-1909%28196301%299%3A2%3C277%3AASMFPA%3E2.0.CO%3B2-75 The Cost of Capital, Corporation Finance and the Theory of InvestmentFranco Modigliani; Merton H. MillerThe American Economic Review, Vol. 48, No. 3. (Jun., 1958), pp. 261-297.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28195806%2948%3A3%3C261%3ATCOCCF%3E2.0.CO%3B2-3NOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 2 of 2 -14 A Simplified Model for Portfolio AnalysisWilliam F. SharpeManagement Science, Vol. 9, No. 2. (Jan., 1963), pp. 277-293.Stable URL:http://links.jstor.org/sici?sici=0025-1909%28196301%299%3A2%3C277%3AASMFPA%3E2.0.CO%3B2-719 Liquidity Preference as Behavior Towards RiskJ. TobinThe Review of Economic Studies, Vol. 25, No. 2. (Feb., 1958), pp. 65-86.Stable URL:http://links.jstor.org/sici?sici=0034-6527%28195802%2925%3A2%3C65%3ALPABTR%3E2.0.CO%3B2-8NOTE: The reference numbering from the original has been maintained in this citation list.

From Efficient Markets Theory to Behavioral FinanceRobert J. ShillerThe Journal of Economic Perspectives, Vol. 17, No. 1. (Winter, 2003), pp. 83-104.Stable URL:http://links.jstor.org/sici?sici=0895-3309%28200324%2917%3A1%3C83%3AFEMTTB%3E2.0.CO%3B2-JThe Journal of Economic Perspectives is currently published by American Economic Association.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/aea.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgTue Jan 15 08:07:41 2008

Journal of Economic Perspectives-Volume 17, Number 1-Winter 2003-Pages 83-1 04From Efficient Markets Theory toBehavioral FinanceRobert J. Shillercademic finance has evolved a long way from the days when the efficientmarkets theory was widely considered to be proved beyond doubt. Behavioralfinance-that is, finance from a broader social science perspectiveincluding psychology and sociology-is now one of the most vital research programs,and it stands in sharp contradiction to much of efficient markets theory.The efficient markets theory reached its height of dominance in academiccircles around the 1970s. At that time, the rational expectations revolution ineconomic theory was in its first blush of enthusiasm, a fresh new idea that occupiedthe center of attention. The idea that speculative asset prices such as stock pricesalways incorporate the best information about fundamental values and that priceschange only because of good, sensible information meshed very well with theoreticaltrends of the time. Prominent finance models of the 1970s related speculativeasset prices to economic fundamentals, using rational expectations to tie togetherfinance and the entire economy in one elegant theory. For example, RobertMerton published "An Intertemporal Capital Asset Pricing Model" in 1973, whichshowed how to generalize the capital asset pricing model to a comprehensiveintertemporal general equilibrium model. Robert Lucas published "Asset Prices inan Exchange Economy" in 1978, which showed that in a rational expectationsgeneral equilibrium, rational asset prices may have a forecastable element that isrelated to the forecastability of consumption. Douglas Breeden published histheory of "consumption betas" in 1979, where a stock's beta (which measures thesensitivityof its return compared to some index) was determined by the correlationRobertJ. Shiller is the Stanley B. Resor Professor of Economics and also afJiliated with theCowles Foundation and the International Centerfor Finance, Yale C'niuersitj, N m Haven,Connecticut. He is a Research Associate at the National Bureau of Economic Research,Cambridge, Massachusetts. His e-mail address is (robert.shiller@jale.edu).

84 Journal of Economic Perspectivesof the stock's return with per capita consumption. These were exciting theoreticaladvances at the time. In 1973, the first edition of Burton Malkiel's acclaimed book,A Random Walk Down Wall Street, appeared, which conveyed this excitement to awider audience.In the decade of the 1970s, I was a graduate student writing a Ph.D. dissertationon rational expectations models and an assistant and associate professor, and I wasmostly caught up in the excitement of the time. One could easily wish that thesemodels were true descriptions of the world around us, for it would then be awonderful advance for our profession. We would have powerful tools to study andto quantiQ the financial world around us.Wishful thinking can dominate much of the work of a profession for a decade,but not indefinitely. The 1970s already saw the beginnings of some disquiet overthese models and a tendency to push them somewhat aside in favor of a moreeclectic way of thinking about financial markets and the economy. Browsing todayagain through finance journals from the 1970s, one sees some beginnings ofreports of anomalies that didn't seem likely to square with the efficient marketstheory, even if they were not presented as significant evidence against the theory.For example, Eugene Fama's 1970 article, "Efficient Capital Markets: A Review ofEmpirical M'ork," while highly enthusiastic in its conclusions for market efficiency,did report some anomalies like slight serial dependencies in stock market returns,though with the tone of pointing out how small the anomalies were.The 1980s and Excess VolatilityFrom my perspective, the 1980s were a time of important academic discussionof the consistency of the efficient markets model for the aggregate stock marketwith econometric evidence about the time series properties of prices, dividends andearnings. Of particular concern was whether these stocks show excess volatilityrelative to what would be predicted by the efficient markets model.The anomalies that had been discovered might be considered at worst smalldepartures from the fundamental truth of market efficiency, but if most of thevolatility in the stock market was unexplained, it would call into question the basicunderpinnings of the entire efficient markets theory. The anomaly represented bythe notion of excess volatility seems to be much more troubling for efficiencymarkets theory than some other financial anomalies, such as the January effect orthe day-of-the-week effect.' The volatility anomaly is much deeper than thoserepresented by price stickiness or tatonnement or even by exchange-rate overshooting.The evidence regarding excess volatility seems, to some observers at least, toimply that changes in prices occur for no fundamental reason at all, that they occurbecause of such things as "sunspots" or "animal spirits" or just mass psychology.The efficient markets model can be stated as asserting that the price P, of a'A good discussion of the major anomalies, and the evidence for them, is in Siege1 (2002)

Robert J. Shiller 85share (or of a portfolio of shares representing an index) equals the mathematicalexpectation, conditional on all information available at the time, of the presentvalue eof actual subsequent dividends accruing to that share (or portfolio ofshares). Eis not known at time t and has to be forecasted. Efficient markets say thatprice equals the optimal forecast of it.Different forms of the efficient markets model differ in the choice of thediscount rate in the present value, but the general efficient markets model can bewritten just as P, = E,P"I; where E, refers to mathematical expectation conditionalon public information available at time t. This equation asserts that any surprisingmovements in the stock market must have at their origin some new informationabout the fundamental value e.It follows from the efficient markets model that E = P, + C;, where C; is aforecast error. The forecast error U, must be uncorrelated with any informationvariable available at time t, otherwise the forecast would not be optimal; it wouldnot be taking into account all information. Since the price P, itself is informationat time t, P, and C; must be uncorrelated with each other. Since the variance of thesum of two uncorrelated variables is the sum of their variances, it follows that thevariance of emust equal the variance of P, plus the variance of C;, and hence,since the variance of U,cannot be negative, that the variance of emust be greaterthan or equal to that of P,.Thus, the fundamental principle of optimal forecasting is that the forecastmust be less variable than the variable forecasted. Any forecaster whose forecastconsistently varies through time more than the variable forecasted is making aserious error, because then high forecasts would themselves tend to indicateforecast positive errors, and low forecasts indicate negative errors. The maximumpossible variance of the forecast is the variance of the variable forecasted, and thiscan occur only if the forecaster has perfect foresight and the forecasts correlateperfectly with the variable forecasted.If one computes for each year since 1871 the present value subsequent to thatyear of the real dividends paid on the Standard & Poor's Composite Stock PriceIndex, discounted by a constant real discount rate equal to the geometric averagereal return 1871-2002 on the same Standard & Poor Index, one finds that thepresent value, if plotted through time, behaves remarkably like a stable trend.2 Incontrast, the Standard & Poor's Composite Stock Price Index gyrates wildly up anddown around this trend. Figure 1 illustrates these patterns.How, then, can we take it as received doctrine that, according to the simplestefficient markets theory, the stock price represents the optimal forecast of thispresent value, the price responding only to objective information about it? I arguedin Shiller (1981), as did also Stephen LeRoy and Richard Porter (1981), that thestability of the present value through time suggests that there is excess volatility in'The present ralue, constant discount rate, is computed for each year t as PT,,,,,~,~ = ELI+, p"llD,,where p is a constant discount factor, and D, is the real dividend at time t. .kn assumption was madeabout real di~ldends after 2002. See note to Figure 1.

86 Journal of Economic PerspectivesFig-ure 1Real Stock Prices and Present Values of Subsequent Real Dividends(annual data)Real Stock Price (S&P 500)1000 -PD\: Interest Rates..-u ic'PDV, Constant Discount Rate100 -PD\: ConsumptionAVotes:The heaviest line is the Standard & Poor 500 Index for Januan of year shown. The less-heayline is the present value for each year of subsequent real didends accruing to the index discountedby the geometric-average real return for the entire sample, 6.61 percent. Di~idends after 2002 wereassumed equal to the 2002 dividend times 1.25 (to correct for recent lower dividend payout) andgrowing at the geometric-average historical growth rate for di~idends, 1.11 percent. The thin line isthe present value for each year of subsequent real di~idends discounted by one-year interest ratesplus a risk premium equal to the geometric average real return on the market minus the geometricaverage real one-year interest rate. The dashed line is the present value for each year of subsequentreal di~idends discounted by marginal rates of substitution in consumption for a representativeindi~idualwith a coefficient of relative risk aversion of 3 who consumes the real per capitanondurable and senice consumption from the U. S. National Income and Product Accounts.Real values were computed from nominal values by dividing by the consumer price index (CPI-LTsince 1913, linked to the Warren and Pearson producer price index before 1913) and rescaling toJanuan 2003 = 100. Some of the ven latest obsen~ations of underlying series were estimated basedon data available as of this writing; for example, the consumer price index forJanwan 2003 wasestimated based on data from previous months. Source data are available on (http://x\uw.econ.yale.edu/-shiller), and the further descriptions of some of the data are in Shiller (1989). See alsofootnotes 1, 5 and 6.the aggregate stock market, relative to the present value implied by the efficientmarkets model. Our work launched a remarkable amount of controversy, fromwhich I will recall here just a few highlights.The principal issue regarding our original work on excess volatility was inregard to thinking about the stationarity of dividends and stock prices. My ownwork in the early 1980s had followed a tradition in the finance literature of

From Eficient 1Tfarkets Theory to Behavioral Finance 87assuming that dividends fluctuated around a known trend.' However, one mightalso argue, as do Marsh and Merton (1986), that dividends need not stay close toa trend and that even if earnings followed a trend, share issuance or repurchasecould make dividends depart from a trend indefinitely. In addition, if businessmanagers use dividends to provide a smoothed flow of payouts from their businesses,then the stock prices might be expected to shift more rapidly than dividends.Marsh and Merton argued that such dividend smoothing could make stockprices unstationary in such a way that in finite samples prices appear more volatilethan the present values.Thus, the challenge became how to construct a test for expected volatility thatmodeled dividends and stock prices in a more general way. ill., such tests weredeveloped, they tended to confirm the overall hypothesis that stock prices hadmore volatility than an efficient markets hypothesis could explain. For example,West (1988) derived an inequality that the variance of innovations (that is, surprises)in stock prices must be less than or equal to the variance of the innovations in theforecasted present value of dividends based on a subset of information available tothe market. This inequality is quite general: it holds even when dividends and stockprices have infinite variances so long as the variance of the innovation (theunexpected change) in these is finite. Using long-term annual data on stock prices,MTest found that the variance of innovations in stock prices was four to 20 times itstheoretical upper bound.4 ~ ohn Campbell and I (1988) recast the time series modelin terms of a cointegrated model of real prices and real dividends, while alsorelaxing other assumptions about the time series, and again found evidence ofexcess volatility." Campbell (1991) provided a variance decomposition for stockreturns that indicated that most of the variability of the aggregate stock marketconveyed information about future returns, rather than about future dividends.Another contested issue regarding the early work on excess volatility questionedthe assumption of the early work that the efficient markets model was bestconveyed through an expected present value model in which the real discount rateis constant through time. The assumption of a constant discount rate over time canonly be considered a first step, for the theory suggests more complex relationships.'It should be pointed out that dividend payouts as a fraction of earnings have shown a gradualdowntrend over the period since 1871 and that di~idend payouts have increasingly been substituted byshare repurchases. Set share repurchases reached approximately 1percent of shares outstanding by thelate 1990s. However, share repurchases do not invalidate the theoretical model that stock prices shouldequal the present ralue of dividends. See Cole, Helwege and Laster (1996).'In more technical terms, this argument is over whether dividends could be viewed as a stationan series.The discussion was often phrased in terms of the "unit root" properh of the time series, tvhere a unitroot refers to notion that when a variable is regressed on its otvn lags, the characteristic equation of thedifference equation has a root on the unit circle. \Vest (1988) can be vietved as a \cay of addressing theunit root issue. In our 1988 paper, Campbell and I handled nonstationarity by using a vector autoregressivemodel including the log dividend-price ratio and the change in log di~idends as elements.Barsky and De Long (1993), hotvever, later shotved that if one assumes that real dividends must be twicedifferenced to induce stationarity (so that dividends are even more unstationan in the sense thatdi~idendgroruth rates, not just levels, are unstationan), then the efficient markets model looks rathermore consistent with the data.

88 Journal of Economic PerspectiuesOne such efficient markets model makes the discount rate correspond tointerest rates. The line in Figure 1 labeled "PDV, Interest Rates" illustrates thisconcept.%owever, allowing time-varying interest rates in the present value formuladoes little to support the efficient markets model. The actual price is stillmore volatile than the present value, especially for the latest half century. Moreover,what changes through time there are in the present value bear little resemblanceto the changes through time in the stock prices, Note for example that thepresent value is extremely high throughout the depression years of the 1930s, notlow as was the actual stock market. The present value is high then because realinterest rates were at extreme lows after 1933, into the early 195Os, and since realdividends really did not fall much after 1929. After 1929, real Standard & Poor'sdividends fell to around 1925 levels for just a few years, 1933-1935 and 1938, but,contrary to popular impressions, were generally higher in the 1930s than they werein the 1920s.'An alternative approach to the possibility of varying real discount rates looks atthe intertemporal marginal rate of substitution for consumption, which is shown inFigure 1 with the line labeled "PDV, ~onsum~tion."~he models of efficientfinancial markets from the 1970s like Merton (1973), Lucas (1978) and Breeden(1979) concluded that stock prices are the expected present value of futuredividends discounted using marginal rates of substitution of consumption, and inthese models the equations for stock returns were derived in the context of a modelmaximizing the utility of consumption. Grossman and Shiller (1981) produced aplot of that present value since 1881, using Standard & Poor dividend data andusing aggregate consumption data to compute the marginal rates of substitution asdiscount factors, and this plot is updated here, and this is what is shown in Figure 1. We"hepresent value, discounted by interest rates, is a plot for each year t ofSee note to Figure 1.' Campbell and I (1989) recast the argument in terms of a vector autoregressive model of real stockprices, real interest rates and real dividends, in tshich each of these variables tsas regressed on lags ofitself and lags of the other variables. TVe found that the di~idend-price ratio not only shows excessvolatilit!, but shows ven little correlation with the dividend divided by the forecast of the present valueof future dividends."he present value, consumption discounted, is a plot for each year t ofwhere C, is real per cafiita real consumption at time t. This expression is inspired by Lucas (1978) andderived in &ossman and Shiller (1981) assuming a coefficient of relative risk aversion of 3. See note toFigure 1.

RobertJ. Shiller 89found, as can also be seen here in Figure 1, that the present value of dividends asdiscounted in this model had only a tenuous relation to actual stock prices, and didnot appear volatile enough to justify the price movements unless we pushed thecoefficient of relative risk aversion to ridiculously high levels, higher than the valueof three that was used for the plot.Grossman and Shiller (1981) stressed that there were some similarities betweenthe present value and the actual real price, notably the present value peaksin 1929 and bottoms out in 1933, close to the actual peak and trough of the market.But the present value does this because consumption peaked in 1929 and thendropped very sharply, bottoming out in 1933, and the present value takes accountof this, as if people had perfect foresight of the coming depression. But in fact itappears very unlikely that people saw this outcome in 1929, and if they did not, thenthe efficient model does not predict that the actual real price should have trackedthe present value over this period.Actually, the consumption discount model, while it may show some comovementsat times with actual stock prices, does not work well because it does notjustifythe volatility of stock prices. I showed (1982) that the theoretical model implies alower bound on the volatility of the marginal rate of substitution, a bound which iswith the U.S. data much higher than could be observed unless risk aversion wereimplausibly high. Hansen and Jagannathan later generalized this lower bound andelaborated on its implications, and today the apparent violation of this "Hansen-Jagannathan lower bound" is regarded as an important anomaly in finance."Some very recent research has emphasized that, even though the aggregatestock market appears to be wildly inefficient, individual stock prices do show somecorrespondence to efficient markets theory. That is, while the present value modelfor the aggregate stock market seems unsupported by the data, there is someevidence that cross-sectionalvariations in stock prices relative to accounting measuresshow some relation to the present value model. Paul Samuelson some years agoposited that the stock market is "micro efficient but macro inefficient," since thereis considerable predictable variation across firms in their predictable future pathsof dividends but little predictable variation in aggregate dividends. Hence, Samuelsonasserted, movements among individual stocks make more sense than domovements in the market as a whole. There is now evidence to back up thisassertion.Vuolteenaho (2002) showed, using vector-autoregressive methods, that theratio of book-to-market-value of U.S. firms explains a substantial fraction of changesin future firms' earnings. Cohen, Polk and Vuolteenaho (2002) concluded that 75to 80 percent of the variation across firms in their book-to-market ratios can beexplained in terms of future variation in profits. Jung and Shiller (2002) show that,cross-sectionally, for U.S. stocks that have been continually traded since 1926, theprice-dividend ratio is a strong forecaster of the present value of future dividend"ee, for example, John Cochrane's (2001)book As.rrt Pnczng tvhich sun.eys this literature. Much of theolder literature is summarized in my 1989 book 114nrkrt 1701ntilitj.

90 Journal of Economic Perspectiveschanges. So, dividend-price ratios on individual stocks do serve as forecasts oflong-term future changes in their future dividends, as efficient markets assert.This does not mean that there are not substantial bubbles in individual stockprices, but that the predictable variation across firms in dividends has often been solarge as to largely swamp out the effect of the bubbles. A lot of this predictablevariation across firms takes the form of firms' paying zero dividends for many yearsand investors correctly perceiving that eventually dividends will be coming, and offirms in very bad shape with investors correctly perceiving they will not be payingsubstantial dividends much longer. Wen it comes to individual stocks, suchpredictable variations, and their effects on price, are often far larger than thebubble component of stock prices.There is a clear sense that the level of volatility of the overall stock marketcannot be well explained with any variant of the efficient markets model in whichstock prices are formed by looking at the present discounted value of futurereturns. There are many ways to tinker with the discount rates in the present valueformulas, and someday someone may find some definition of discount rates thatproduces a present value series that "fits" the actual price better than any of theseries shown in Figure 1.loBut it is unlikely that they will do so convincingly, giventhe failure of our efforts to date to capture the volatility of stock prices. To justifythe volatility in terms of such changes in the discount rates, one will have to arguethat investors also had a great deal of information about changes in the factorsinfluencing these future discount rates.After all the efforts to defend the efficient markets theory, there is still everyreason to think that, while markets are not totally crazy, they contain quite substantialnoise, so substantial that it dominates the movements in the aggregatemarket. The efficient markets model, for the aggregate stock market, has still neverbeen supported by any study effectively linking stock market fluctuations withsubsequent fundamentals. By the end of the 1980s, the restless minds of manyacademic researchers had turned to other theories.The Blossoming of Behavioral FinanceIn the 1990s, a lot of the focus of academic discussion shifted away from theseeconometric analyses of time series on prices, dividends and earnings towarddeveloping models of human psychology as it relates to financial markets. The fieldof behavioral finance developed. Researchers had seen too many anomalies, toolo Other factors are considered by hlcGrattan and Prescott (2001),who emphasize tax rate changes, andSiege1 (2002),who considers not only tax rate changes hut also changes in the volatility of the economy,changes in the inflation rate, and changes in transactions costs. Neither of these studies sho~vs a "fit"between present due and prices over the long sample, however. Notably, the factors they use do notgo through sudden changes at the time of the stock market booms and crashes surrounding 1929 and2000.

From Efficient 1Varkets The09 to Behavioral Finance 91little inspiration that our theoretical models captured important fluctuations. Anextensive body of empirical work, summarized in Campbell, Lo and MacKinlay's1996 book The Econometm'cs ofFznanczal lVarkets, laid the foundation for a revolutionin finance.Richard Thaler and I started our National Bureau of Economic Researchconference series on behavioral finance in 1991, extending workshops that Thalerhad organized at the Russell Sage Foundation a few years earlier.'' Many otherworkshops and seminars on behavioral finance followed. There is so much goingon in the field that it is impossible to summarize in a short space. Here, I willillustrate the progress of behaxioral finance with two salient examples from recentresearch: feedback models and obstacles to smart money. For overall surveys of thefield of behavioral finance, the interested reader might begin with Hersh Shefrin'sByond Greed and Fear: Understanding Behavzoral Finance and the Psycholog?: of Investing(2000) or Andrei Shleifer's InefJiczent Markets (2000). There are also some newbooks of collected papers in behavioral finance, including a three-volume set,Behavzoral Fznance, edited by Hersh Shefrin (2001), and Advances zn BehavzoralFznance 11, edited by Richard H. Thaler (2003).Feedback ModelsOne of the oldest theories about financial markets, expressed long ago innewspapers and magazines rather than scholarly journals, is, if translated intoacademic words, a price-to-price feedback theory. Maen speculative prices go up,creating successes for some investors, this may attract public attention, promoteword-of-mouth enthusiasm, and heighten expectations for further price increases.The talk attracts attention to "new era" theories and "popular models" that justifythe price increases.12 This process in turn increases investor demand and thusgenerates another round of price increases. If the feedback is not interrupted, itmay produce after many rounds a speculative "bubble," in which high expectationsfor further price increases support very high current prices. The high prices areultimately not sustainable, since they are high only because of expectations offurther price increases, and so the bubble eventually bursts, and prices come fallingdown. The feedback that propelled the bubble carries the seeds of its own destruction,and so the end of the bubble may be unrelated to news stories aboutfundamentals. The same feedback may also produce a negative bubble, downwardprice movements propelling further downward price movements, promoting wordof-mouthpessimism, until the market reaches an unsustainably low level.Such a feedback theory is very old. As long ago as 1841, Charles MacKay in his" For a list of our programs since 1991, with links to authors' websites, see (http://colrles.eco~yale.edu/hel~fin).l2 Descriptions of nen. era theories attending mrious speculative bubhles are described in my book(2000). Popular models that acconlpanied the stock market crash of 1987, the real estate buhblespeaking around 1990 and various initial public offering booms are discussed in my paper in this journal(1990).

92 ~Joz~rnal of Economic Perspectivesinfluential book Memoirs of Extraordina~ Popular Delusions described the famoustulipmania in Holland in the 1630s, a speculative bubble in tulip flower bulbs, withwords that suggest feedback and the ultimate results of the feedback (pp. 118-119):Many individuals grew suddenly rich. A golden bait hung temptingly outbefore the people, and one after another, they rushed to the tulip marts, likeflies around a honey-pot . . . .At last, however, the more prudent began to seethat this folly could not last forever. Rich people no longer bought the flowersto keep them in their gardens, but to sell them again at cent per cent profit.It was seen that somebody must lose fearfully in the end. As this convictionspread, prices fell, and never rose again.13The feedback theory seems to be even much older than this. Note of such feedback,and the role of word-of-mouth communications in promoting it, was in fact madeat the time of the tulipmania itself. One anonymous observer publishing in 1637(the year of the peak of the tulipmania) gives a fictional account of a conversationbetween two people, Gaergoedt and Waermondt, that illustrates this author'simpression of the word-of-mouth communications of that time:Gaergoedt: "You can hardly make a return of 10% with the money that youinvest in your occupation [as a weaver], but with the tulip trade, you can makereturns of lo%, loo%, yes, even 1000%.Waerrnondt: " . . . . But tell me, should I believe you?"Gaergoedt: "I hill tell you again, what I just said."Waermondt: "But I fear that, since I would only start now, it's too late, becausenow the tulips are very expensive, and I fear that I'll be hit uith the spit rod,before tasting the roast."Gaergoedt: "It's never too late to make a profit, you make money whilesleeping. I've been away from home for four or five days, and I came homejust last night, but now I know that the tulips I have have increased in valueby three or four thousand guilder; where do you have profits like that fromother goods?"Waermondt: "I am perplexed when I hear you talking like that, I don't knowwhat to do; has anybody become rich with this trade?"Gaergoedt: "What kind of question is this? Look at all the gardeners that usedto wear white-gray outfits, and now they're wearing new clothes. Many weavers,that used to wear patched up clothes, that they had a hard time putting"' Garher questions hlacIiay's facts about the tulipmania in his 1990 article in this journal and in hisbook Famous Erst Bubbles. For example, the crash was not absolutely final; Garber documents very hightulip prices in 1643. The actual course of the bubble is ambiguous, as all contracts were suspended bythe states of Holland in 1637just after the peak, and no price data are available from that date.

on, now wear the glitteriest clothes. Yes, many who trade in tulips are ridinga horse, have a carriage or a wagon, and during winter, an ice carriage, . . . ."I4Casual observations over the years since then are plentiful evidence that such talk,provoking a sense of relative futility of one's day-to-day work and envy of thefinancial successes of others, and including some vacuous answer to doubts that theprice rise may be over, is effective in overcoming rational doubts among somesubstantial number of people and tends to bring successive rounds of them into themarket.In my book Irrational Exuberanre, published (with some luck) at the ver) peakof the stock market bubble in March 2000, I argued that very much the samefeedback, transmitted by word-of-mouth as well as the media, was at work inproducing the bubble we were seeing then. I further argued that the naturalself-limiting behavior of bubbles, and the possibility of downward feedback after thebubble was over, suggested a dangerous outlook for stocks in the future.One might well also presume that such simple feedback, if it operates sodramatically in events like the tulip bubble or the stock market boom until 2000,ought often to recur at a smaller scale and to play an important if lesser role inmore normal day-to-day movements in speculative prices. Feedback models, in theform of difference equations, can of course produce complicated dynamics. Thefeedback may be an essential source of much of the apparently inexplicable"randomness" that we see in financial market prices.But the feedback theory is very hard to find expressed in finance or economicstextbooks, even today. Since the theor) has appeared mostly in popular discourse,and not in the textbooks, one might well infer that it has long been discredited bysolid academic research. In fact, academic research has until recently hardlyaddressed the feedback model.The presence of such feedback is supported by some experimental evidence.Psychologists Andreassen and Kraus (1988) found that when people are shown realhistorical stock prices in sequence (and which they knew were real stock prices) andinvited to trade in a simulated market that displays these prices, they tended tobehave as if they extrapolate past price changes when the prices appear to exhibita trend relative to period-to-period variability. Smith, Suchanek and Williams(1988) were able to create experimental markets that generated bubbles that areconsistent with feedback trading. Marimon, Spear and Sunder (1993) showedexperiments in which repeating bubbles were generated if subjects were preconditionedby past experience to form expectations of bubbles.The presence of such feedback is also supported by research in cognitivepsychology, which shows that human judgments of the probability of future eventsshow systematic biases. For example, psychologists Tversky and Kahneman haveshown that judgments tend to be made using a representativeness heuristic,"Anommous (1637) Bjorn Tuypens translated this passage

94 journal of Economic Perspectiveswhereby people try to predict by seeking the closest match to past patterns, withoutattention to the obsesved probability of matching the pattern. For example, whenasked to guess the occupations of people whose personality and interests aredescribed to them, subjects tended to guess the occupation that seemed to matchthe description as closely as possible, without regard to the rarity of the occupation.Rational subjects would have chosen humdrum and unexceptional occupationsmore because more people are in these occupations. (Kahneman and Tversky,1974). By the same principle, people may tend to match stock price patterns intosalient categories such as dramatic and persistent price trends, thus leading tofeedback dynamics, even if these categories may be rarely seen in fundamentalunderlying factors.Daniel, Hirschleifer and Subramanyam (1999) have shown that the psychologicalprinciple of "biased self-attribution" can also promote feedback. Biasedself-attribution, identified by psychologist Daryl Bem (1965), is a pattern of humanbehavior whereby individuals attribute events that confirm the validity of theiractions to their own high ability and attribute events that disconfirm their actionsto bad luck or sabotage. Upon reading the above passage from the time of thetulipmania, one easily imagines that Gaergoedt is basking in self-esteem andrelishing the telling of the story. Many readers today can probably easily recallsimilar conversations, and similar ego-involvement by the spreaders of the word, inthe 1990s. Such human interactions, the essential cause of speculative bubbles,appear to recur across centuries and across countries: they reflect fundamentalparameters of human behavior.There is also evidence supportive of feedback from natural experiments, whichmay be more convincing than the lab experiments when they occur in real time,with real money, with real social networks and associated interpersonal support andemotions, with real and visceral envy of friends' investment successes, and withcommunications-media presence. Ponzi schemes may be thought of as representingsuch natural experiments. A Ponzi scheme (or pyramid scheme or moneycirculation scheme) involves a superficially plausible but unverifiable stor) abouthow money is made for investors and the fraudulent creation of high returns forinitial investors by giving them the money invested by subsequent investors. Initialinvestor response to the scheme tends to be weak, but as the rounds of high returnsgenerates excitement, the stor) becomes increasingly believable and enticing toinvestors. These schemes are often ver) successful in generating extraordinar)enthusiasms among some investors. We have seen some spectacular Ponzi schemesrecently in countries that do not have effective regulation and surveillance toprevent them. A number of Ponzi schemes in Albania 1996-1997 were so large thattotal liabilities reached half a year's GDP; their collapse brought on a period ofanarchy and civil war in which 2000 people were killed (Janis, 1999). Real worldstock-market speculative bubbles, I argued in my 2000 book Iwational Exuberance,resemble Ponzi schemes in the sense that some "new era" story becomes attachedto the bubble and acquires increasing plausibility and investor enthusiasm as themarket continues to achieve high returns. Given the obvious success of Ponzi

From Effirient Markets The09 to Behavioral Finanre 95schemes when they are not stopped by the law, we would need a good reason tothink that analogous phenomena of speculative bubbles are not also likely.The stock market boom that ended in early 2000 is another relevant episode.According to my survey data, now expressed in the form of stock market confidenceindexes produced by the Yale School of Management and available at (http:,l/icf.som.yale.edu/confidence.index),the confidence of individual investors that thestock market will go up in the next year, and will rebound from any drop, rosedramatically 1989-2000. As in the tulipmania centuries before, there was a focusingof public attention and talk on the speculative market and a proliferation ofwishful-thinking theories about a "new era" that would propel the stock market ona course that, while uneven, is relentlessly upward, theories that were spread byword of mouth as well as the media.It is widely thought that there is a problem with the feedback theories: thetheories would seem to imply that speculative price changes are strongly seriallycorrelated through time, that prices show strong momentum, continuing uniformlyin one direction day after day. This seems inconsistent with the evidence that stockprices are approximately a random walk.But simple feedback models do not imply strong serial correlation, as I stressedin Shiller (1990). There, I presented a model of the demand for a speculative assetas equaling a distributed lag with exponentially declining weights on past pricechanges through time (the distributed lag representing feedback distributed overtime), plus other factors that affect demand. The model asserts that people reactgradually to price changes over months or years, not just to yesterday's pricechange. A history of price increases over the last year may encourage buying todayeven if yesterday's price change was down. Also, the model recognizes that there areother shocks, besides feedback, influencing price.In such a model, a disturbance in some demand factor other than feedbackcan in certain cases be amplified, at least for a time, because it changes the priceand thus affects future prices through the distributed lag.15 However, unless weknow something about the other factors that drive demand, such a distributed lagmodel does not imply anything at all about the serial correlation properties ofspeculative price changes. The feedback model does not imply that there is muchserial correlation in day-to-day stock price changes, since the noise in the otherfactors feeds directly into short-run changes, and the effect on today's price oflagged other factors operates at a low frequency that is essentially unrelated today-to-day changes and has effects that can be observed only from its cumulativeeffect after a long period of time.Thus, the approximate random walk character of stock prices is not evidence"The feedback model is p, = c J"', eCY('-" dp, + T,, 0 < c < 1, 0 < y. Here, p, is price at timet, and r,is the combined effect of other factors on demand. It follo~vs that p, = r,+ (c/(l - c))(r,-is a ~veighted average of lagged T. See Shiller(1990, p. 60). Such a model does not imply that price behaves smoothly through time: price can lookmuch like a random walk if, for example, T, is a random walk.- -T~),where T, = (y/(1- c)) 51, eC(? '('-'""-"T,~T

96 journal of Economic Perspectivesagainst feedback. Moreover, even if feedback did imply some momentum, we canalso note that the random walk character of stock prices is really not fully supportedby the evidence anyway, and that in fact there has been more than a little momentumto stock prices. Jegadeesh and Titman (1993) found that winning stocks, stocksthat showed exceptionally high six-month returns, beat losing stocks, stocks thatshowed exceptionally low six-month returns, by 12 percent over the following year.In contrast, over longer periods of time this momentum seems to reverse itself. DeBondt and Thaler (1985) find that over the period 1926 to 1982, stocks representedon the Center for Research in Security Prices data set of the University of Chicagowhose returns had been in the top decile across firms over three years (thus,"winner" stocks) tended to show negative cumulative returns in the succeedingthree years. They also found that "loser" stocks whose returns had been in thebottom decile over the prior three years tended to show positive returns over thesucceeding three years. Thus, there is a tendency for stock prices to continue in thesame direction over intesvals of six months to a year, but to reverse themselves overlonger intemals. Campbell, Lo and Mackinlav (1996) document this fact care full^.'^A pattern like this is certainly consistent with some combination of feedback effectsand other demand factors driving the stock market largely independently offundamentals.Smart Money vs. Ordinary InvestorsTheoretical models of efficient financial markets that represent everyone asrational optimizers can be no more than metaphors for the world around us.Nothing could be more absurd than to claim that everyone knows how to solvecomplex stochastic optimization models. For these theoretical models to have anyrelevance to the stock market, it must somehow be the case that a smaller elementof "smart money" or the "marginal trader" can offset the foolishness of manyinvestors and make the markets efficient.The efficient markets theory, as it is commonly expressed, asserts that whenirrational optimists buy a stock, smart money sells, and when irrational pessimistssell a stock, smart money buys, thereby eliminating the effect of the irrationaltraders on market price. But finance theory does not necessarily imply that smartmoney succeeds in fully offsetting the impact of ordinary investors. In recent years,research in behavioral finance has shed some important light on the implicationsof the presence of these two classes of investors for theor) and also on somecharacteristics of the people in the two classes.From a theoretical point of view, it is far from clear that smart money has thepower to drive market prices to fundamental values. For example, in one modelwith both feedback traders and smart money, the smart money tended to amplzjj,rather than diminish, the effect of feedback traders, by buying in ahead of the'"rinblatt and Han (2001) have argued that this tendency of stock prices to sho~\. nlomentunl for awhile and then reverse themselves might be related to the phenomenon that investors tend to hold onto losers and sell winners (Statman and Shefrin, 1985; Odean, 1998).

feedback traders in anticipation of the price increases they will cause (De Long,Shleifer, Summers and Waldman, 1990b). In a related model, rational, expectedutility-maximizingsmart money never chooses to offset all of the effects of irrationalinvestors because they are rationally concerned about the risk generated by theirrational investors and do not want to assume the risk that their completelyoffsetting these other investors would entail (De Long, Shleifer, Summers andWaldman, 1990b) .IiOften, speculative bubbles appear to be common to investments of a certain"style," and the bubbles may not include many other investments. For example, thestock market bubble that peaked in the year 2000 was strongest in tech stocks orNasdaq stocks. Barberis and Shleifer (2002) present a model in which feedbacktraders' demand for investments within a particular style is related to a distributedlag on past returns of that style class. By their budget constraint, when feedbacktraders are enticed by one style, they must move out of competing styles. The smartmoney are rational utility maximizers. Barberis and Shleifer present a numericalimplementation of their model and find that smart money did not fully offset theeffects of the feedback traders. Style classes go through periods of boom and bustamplified by the feedback.Goetzmann and Massa (1999) provided some direct evidence that it is reasonableto suppose that there are c\vo distinct classes of investors: feedback traders whofollow trends and the smart money who move the other way. Fidelity Investmentsprovided them with two years of daily account information for 91,000 investors ina Standard and Poor's 500 index fund. Goetzmann and Massa were able to sortthese investors into two groups based on how they react to daily price changes.There were both momentum investors, who habitually bought more after priceswere rising, and contrarian investors, or smart money, who habitually sold afterprices were rising. Individual investors tended to stay as one or the other, rarelyshifted between the two categories.Recent research has focused on an important obstacle to smart money'soffsetting the effects of irrational investors. The smart money can always buy thestock, but if the smart money no longer owns the stock and finds it difficult to shortthe stock, then the smart money may be unable to sell the stock. Some stocks couldbe in a situation where zealots have bought into a stock so much that only zealotsown shares, and trade is only among zealots, and so the zealots alone determine theprice of the stock. The smart money who know that the stock is priced ridiculouslyhigh may well use up all the easily available shortable shares and then will bestanding on the sidelines, unable to short more shares and profit from theirknowledge. Miller (1977) pointed out this flaw in the argument for market efficiency,and his paper has been discussed ever since.It seems incontrovertible that in some cases stocks have been held primarily byzealots and that short sellers have found it very difficult to short. One example is the"Shleifer and Summers (1990) present a nice summary of these themes in this journal

98 Journal of Economic Perspectives3Com sale of Palm near the peak of the stock market bubble (Lamont and Thaler,2001). In March 2000, Scorn, a profitable provider of network systems and senices,sold to the general public via an initial public offering 5 percent of its subsidiaryPalm, a maker of handheld computers. 3Com announced at the same time that therest of Palm would follow later. The price that these first Palm shares obtained inthe market was so high, when compared with the price of the 3Com shares, that ifone subtracts the implied value of the remaining 95 percent of Palm from the3Com market value, one finds that the non-Palm part of 3Com had a negativevalue.Since the worst possible price for 3Com after the Palm sale was completed wouldbe zero, there was thus a strong incentive for investors to short Palm and buy Scorn.But, the interest cost of borrowing Palm shares reached 35 percent by July 2000,putting a damper on the advantage to exploiting the mispricing." Even an investorwho knew for certain that the Palm shares would fall substantially may have beenunable to make a profit from this knowledge. The zealots had won with Palm andhad control over its price, for the time being.The Palm example is an unusual anomaly. Shorting stocks only rarely becomesso costly. But the example proves the principle. The question is: How important areobstacles to smart money's selling in causing stocks to deviate from fundamentalvalue?Of course, in reality, the distinction between zealots and smart money is notalways sharp. Instead, there are sometimes all gradations in between, especiallysince the objective evidence about the fundamental value of individual stocks isalways somewhat ambiguous. If selling short is difficult, a number of individualstocks could become overpriced. It would also appear possible that major segmentsof the stock market, say the Nasdaq in 1999, or even the entire stock market, couldwind up owned by, if not zealots, at least relatively optimistic people. Short-saleconstraints could be a fatal flaw in the basic efficient markets theory.The problem with evaluating Miller's (1977) theory that a lack of short sellingcan cause financial anomalies like overpricing and bubbles is that there has beenlittle or no data on which stocks are difficult to short. There are long time seriesdata series on "short interest," which is the total number of shares that are shorted.Figlewski (1981) found that high levels of short interest for individual stockspredicts low subsequent returns for them, a direction that would be predicted byMiller's theory. But the predictability was weak. On the other hand, differences inshort interest across stocks do not have an unambiguous connection with difficultyof shorting. Stocks differ from each other in terms of the fraction of shares that arein accounts that are shortable. Differences across stocks in short interest can alsoreflect different demand for shorting for hedging needs. Thus, there is a significantl8 Put option prices on Palm also hegan to reflect the negative opinions and became so experlsive thatthe usual relation between options prices and stock price, the so-called "put-call parih," failed to hold.One must remember that options markets are derivative markets that clear separately from stockmarkets, and overpriced puts have no direct impact on the supply and demand for stock unlessarhitrageurs can exploit the overpricing hy shorting the stock.

From EfJicient 1Varkets The09 to Behauioral Finance 99errors-in-variables problem when using short interest as an indicator of the cost ofshorting.Some recent papers have sought to detect the presence of barriers that mightlimit short sales indirectly by obsening the differences of opinion that can have animpact on price if there is a difficulty shorting stocks. Without obsening barriers toshorting stocks directly, we can still infer that when differences of opinion are highabout a stock, it is more likely that short-sale restrictions will be binding for thatstock, and thus that the more pessimistic investors hill not prevent the stock frombecoming overpriced and hence subject to lower subsequent returns.Scherbina (2000) measured differences of opinion by calculating the dispersionof analysts' earnings forecasts. She found that stocks with a high dispersion ofanalysts' forecasts had lower subsequent returns, and she linked the low returns tothe resolution of the uncertainty. Chen, Hong and Stein (2000) measured differenceof opinion by a breadth of ownership measure derived from a database onmutual fund portfolios. The breadth variable for each quarter is the ratio of thenumber of mutual funds that hold a long position in the stock to the total numberof mutual funds for that quarter. They find that firms in the top decile by breadthof ownership outperformed those in the bottom decile by 4.95 percent per annumafter adjusting for various other factors.What we would really like to have to test the importance of short salesrestrictions on stock pricing is some evidence on the cost of shorting. If those stocksthat have become very costly to short tend to have poor subsequent returns, thenwe will have more direct confirmation of Miller's (1977) theory. There is surprisinglylittle available information about the cost of shorting individual stocks. Suchdata have not been available for economic research until recently. A number ofrecent unpublished papers have assembled data on the cost of shorting individualstocks, but these papers have assembled data for no more than a year around 2000.Recently, Jones and Lamont (2001) discovered an old source of data on thecost of shorting stocks. In the 1920s and 1930s in the United States, there used tobe a "loan crowd" on the floor of the New York Stock Exchange, where one couldlend or borrow shares, and the interest rates at which shares were loaned werereported in the Wall Street Journal. Jones and Lamont assembled time series of theinterest rates charged on loans of stocks from 1926 to 1933, eight years of data onan average of 80 actively-traded stocks. They found that, after controlling for size,over this period the stocks that were more expensive to short tended to be morehighly priced (in terms of market-to-book ratios), consistent with the Miller (1977)theory. Moreover, they found that the more expensive-to-short stocks had lowersubsequent returns on average, again consistent with the Miller theory. Of course,their data span only eight years from a remote period in history, and so theirrelevance to today's markets might be questioned.Why has there not been more data on the cost of shorting? Why did the loancrowd on the New York Stock Exchange disappear and the loan rates in the WallStreetJournalwith it? Perhaps after the crash of 1929 the widespread hostility to shortsellers (who were widely held responsible for the crash) forced the market to go

100 Journal of Eronomir Perspectivesunderground. Jones and Lamont (2001) document a consistent pattern of politicalopposition to short sellers after 1929 and point out thatJ. Edgar Hoover, the headof the Federal Bureau of Investigation, was quoted as saying that he would investigatea conspiracy to keep stock prices low. By 1933, the rates shown on the loanlist become all zeros, and the Wall Street Journal stopped publishing the loan list in1934.Fortunately, this long drought of data on the cost of shorting stocks may beover, and stocks should become easier to short. In 2002, a consortium of financialinstitutions established an electronic market for borrowing and lending stocksonline via a new firm, EquiLend, LLC. The new securities lending platform at(http://uww.equilend.corn)exceeded $11 billion in transactions in its first twoweeks, and daily availability posting exceed $1 trillion.But the true cost of shorting stocks is probably much higher than the explicitinterest cost of borrowing the shares, because of the psychological cost that inhibitsshort selling. Most investors, even some very smart investors, have probably nevereven considered shorting shares. Shorting shares is widely reputed to involve somesubstantial risks and nuisances. For example, the short-seller always stands the riskthat the ultimate owner of the shares will want to sell the shares, at which time theshort-seller is forced to return the shares. This detail may be little more than anuisance, for the short seller can likely borrow them again from another lender, butit may figure largely in potential short-sellers' minds.A more important consideration that may weigh on short sellers' minds is theunlimited loss potential that short sales entail. When an investor buys a stock, thepotential loss is no greater than the original investment. But when an investorshorts a stock, the potential losses can greatly exceed the original investment. Aninvestor can always terminate these losses by covering the shorts, but this actiontypically brings considerable psychological anguish. Deciding to cover one's shortsand get out of a short position after losses is psychologically difficult, given theevidence on the pain of regret. Kahneman and Tversky's prospect theory (1979)suggests that individuals are far more upset by losses than they are pleased byequivalent gains; in fact, individuals are so upset by losses that they will even takegreat risks with the hope of avoiding any losses at all. The effects of this pain ofregret have been shown to result in a tendency of investors in stocks to avoid sellinglosers, but the same pain of regret ought to cause short sellers to want to avoidcovering their shorts in a losing situation. People prefer to avoid putting themselvesin situations that might confront them with psychologically difficult decisions in thefuture.The stock market that we have today always limits the liability of investors. AsMoss (2002) has documented, the idea that all publicly traded stocks should havelimited liability for their investors was the result of experimenting with differentkinds of stockholder liability in the United States in the early nineteenth centuryand the discovery of the psychological attractiveness of limited liability stocks. Thedebates in the early nineteenth century were concerned with the balancing of theagency costs of limited liability, which encourages businesses to take greater risks,

Rob&,J Shiller 101against the benefits in terms of peace of mind to investors. Various alternatives wereconsidered or experimented with, including unlimited liability, unlimited proportionalliability (where individual investors in a company are limited to their proportionateshare of the company's losses according to their share in the company),and double liability (where individual investors are accountable for the capitalsubscribed once again). By around 1830, it was apparent from experiments in NewYork and surrounding states that investors found it very appealing that they couldput money down to buy a stock today, and from that day forward face no furtherlosses beyond what they already put down. It allowed them, once having purchaseda stock, to concentrate their emotions on the small probability of the stock doingextremely well, rather on the small probability that someone would come afterthem for more money. People have always been very attracted to lottery tickets, andthe invention of limited liability, Moss concludes, turned stock investments psychologicallyinto something a lot like lottery tickets. By the same theory, then, investorswill not find short~ng stocks very attractive.Remarkably few shares are in fact sold short. According to New York StockExchange data, from 1977 to 2000 year-end short interest ranged from 0.14 percentto 1.91 percent of all shares. According to Dechow, Hutton, Muelbroek and Stone(2001), less than 2 percent of all stocks had short interest greater than 5 percent ofshares outstanding 1976-1983. Given the obviously large difference of opinionabout and difference of public attention to different stocks, it is hard to see howsuch a small amount of short selling could offset the effect on stock price of theextra demand of investors who develop an irrational fixation on certain stocks.ConclusionThe collaboration between finance and other social sciences that has becomeknown as behavioral finance has led to a profound deepening of our knowledge offinancial markets. In judging the impact of behavioral finance to date, it is importantto apply the right standards. Of course, we do not expect such research toprovide a method to make a lot of money off of financial market inefficiency veryfast and reliably. We should not expect market efficiency to be so egregiously wrongthat immediate profits should be continually available. But market efficiency can beegregiously wrong in other senses. For example, efficient markets theory may leadto drastically incorrect interpretations of events such as major stock marketbubbles.In his review of the literature on behavioral finance, Eugene Fama (1998)found fault for two basic reasons. The first was that the anomalies that werediscovered tended to appear to be as often underreaction by investors as overreaction.The second was that the anomalies tended to disappear, either as timepassed or as methodology of the studies improved. His first criticism reflects anincorrect view of the psychological underpinnings of behavioral finance. Sincethere is no fundamental psychological principle that people tend always to over-

102 Journal of Economic Perspectivesreact or always to underreact, it is no surprise that research on financial anomaliesdoes not reveal such a principle either. His second criticism is also weak. It is thenature of scholarly research, at the frontier, in all disciplines, that initial claims ofimportant discoveries are often knocked down by later research. The most basicanomaly, of excess volatility, seems hardly to have been knocked down, and it is infact graphically reinforced by the experience of the past few years in the stockmarkets of the world. Moreover, the mere fact that anomalies sometimes disappearor switch signs with time is no evidence that the markets are fully rational. That isalso what we would expect to see happen even in highly irrational markets. (Itwould seem peculiar to argue that irrational markets should display regular andlasting patterns!) Even the basic relation suggested by market inefficiency, thatstocks whose price is bid up by investors will tend to go back down later, and stocksthat are underpriced by investors will tend to go up later, is not a relation that canbe easily tested or that should hold in all time periods. The fundamental value ofstocks is hard to measure, and, moreover, if speculative bubbles (either positivebubbles or negative bubbles) last a long time, then even this fundamental relationmay not be observed except in very long sample periods.In further research, it is important to bear in mind the demonstrated weaknessesof efficient markets theory and maintain an eclectic approach. While theoreticalmodels of efficient markets have their place as illustrations or characterizationsof an ideal world, we cannot maintain them in their pure form as accuratedescriptors of actual markets.Indeed, we have to distance ourselves from the presumption that financialmarkets always work well and that price changes always reflect genuine information.Evidence from behavioral finance helps us to understand, for example, thatthe recent worldwide stock market boom, and then crash after 2000, had its originsin human foibles and arbitrary feedback relations and must have generated a realand substantial misallocation of resources. The challenge for economists is to makethis reality a better part of their models.ReferencesAndreassen, Paul and Stephen Kraus. 1988. "Style Investing." NBER Working Paper No.'Yudgmental Prediction by Extrapolation." Un- w8039.published paper, Department of Psycholoa, Barsky, Robert and J. Bradford De Long.Ha1.i-ard University.1993. "Why Does the Stock Market Fluctuate?"Anonymous. 1637. Samen-spraeck tusschen Wnw- Qunterb Journal of Economics. May, 108, pp. 291-mondt ende Gawgoedt nopende de opkomste ende on- 311.dergangh van flora. Haerlem: Adriaen Roman, Bern, Daryl J. 1965. "An Experimental Analysisreprinted in Economisch Histon'sch Janrboek. 1926, of Self-Persuasion." Journal of Experimental Social12:20-43, pp. 28-29. psycho lo^. 1, pp.199-218.Barberis, Nicholas and Andrei Shleifer. 2000. Breeden, Douglas T. 1979. "AnIntertemporal

From Efficient Markets Theoly to Behavioral Finance 103Asset Pricing Model with Stochastic Consumptionand Investment Opportunities." Journal ofFinancial Economics. 7:2, pp. 265-96.Campbell, John Y. 1991. "A Variance Decompositionfor Stock Returns." Economic Journal.March, 101:405, pp. 157-79.Campbell, John Y. and Robert J. Shiller. 1988."Stock Prices, Earnings, and Expected Dividends."Journal ofFinance. July, 43:3, pp. 661-76.Campbell, John Y. and Robert J. Shiller. 1989."The Dividend-Price Ratio and Expectations ofFuture Dibldends and Discount Factors." RevimofFinancia1 Studies. 1:3, pp. 195-228.Campbell, John Y., Andrew W. Lo and A.Craig MacKinlay. 1996. The Econometrics of FinancialiWarkets. Princeton: Princeton UniversityPress.Qlen, Joseph, Harrison Hong and Jeremy C.Stein. 2000. "Breadth of Ownership and Stock Returns."Unpublished paper, stanford University.Cochrane, John H. 2001. Asset Pricing. Princeton:Princeton University Press.Cohen, Randolph, Christopher Polk andTuomo Vuolteenaho. 2002. "The Value Spread."Unpublished paper, Harvard Business School.Forthcoming,Journal of Finance.Cole, Kevin, Jean Helwege and David Laster.1996. "Stock Market Valuation Indicators: IsThis Time Different?" Financial Analysts Journal.May/June, pp. 56-64.Daniel, Kent, David Hihleifer and AvanidharSubramanyam. 1998. "Investor Psychology andSecurity Market Under- and Overreactions."Journal of Finance. December, 53:6, pp. 1839-885.De Bondt, Werner F. M. and Richard H. Thaler.1985."Does the Stock Market Overreact?"Journal of Finance. July, 40:3, pp. 793-805.De Long, J. Bradford, Andrei Shleifer, LawrenceH. Summers and Robert J. Waldmann.1990a. "Noise Trader Risk in Financial Markets."Journal of Political Economy. August, 98:4, pp.703-38.De Long, J. Bradford, Andrei Shleifer, LawrenceH. Summers and Robert J. Waldmann.1990b. "Positive Feedback Investment Strategiesand Destabilizing Rational Speculation." Jouhalof Finance. June, 45:2, pp. 379-95.Dechow, Patricia M., Amy P. Hutton, LisaMuelbroek and Richard G. Stone. 2001. "Short-Selling, Fundamental Analysis and Stock Returns."Journal ofFinancia1 Economics. Forthcoming.Fama, Eugene F. 1970. "Efficient Capital Markets:A Review of Empirical Work." Journal ofFinance. May, 25:2, pp. 383-417.Fama, Eugene F. 1991. "Efficient Capital Mar-kets: 11." Journal of Finance. December, 46:5,pp. 1575-617.Fama, Eugene F. 1998. "Market Efficiency,Long-Term Returns, and Behavioral Finance."Journal of Financial Economics. September, 49:3,pp. 283-306.Figlewski, Stephen. 1981. "The InformationalEffects of Restrictions on Short Sales: Some EmpiricalEvidence." Journal of Financial and QuantitativeAnalysis. November, 16:4, pp. 463-76.Figlewski, Stephen and Gwendolyn P. Webb.1993. "Options, Short Sales, and Market Completeness."Journal of Finance. June, 48:2, pp.761-77.Garber, Peter M. 1990. "Famous First Bubbles."Journal ofEconomic Pwspectives. Spring, 4:2,pp. 35-54.Garber, Peter M. 2000. Famous First Bubbles.Cambridge: MIT Press.Goetzmann, William N. and Massimo Massa.1999. "Daily Momentum and Contrarian Behaviorof Index Fund Investors." Unpublished paper,Yale University.Grinblatt, Mark and Bing Han. 2001. "TheDisposition Effect and Momentum." Unpublished paper, Anderson School, UCLA.Grossman, Sanford J. and Robert J. Shiller.1981. "The Determinants of the Variability ofStock Market Prices." American Economic him.May, 71:2, pp. 222-27.Hansen, Lars P. and Ravi Jagannathan. 1991."Implications of Security Market Data for Modelsof Dynamic Economies." Journal of PoliticalEconomy. April, 99:2, pp. 225-62.Jarvis, Chris. 1999. "The Rise and Fall of thePyramid Schemes in Albania." InternationalMonetary Fund Working Paper No. 99-98.Jegadeesh, Narasimhan and Sheridan Titman.1993. "Returns to Buying Winners and SellingLosers: Implications for Stock Market Efficiency."Journal of Finance. March, 48:1, pp.65-91.Jones, Charles M. and Owen A. Lamont.2001."Short-Sale Constraints and Stock Returns."NBER Working Paper No. 8494.Jung, Jeeman and Robert J. Shiller. 2002."One Simple Test of Samuelson's Dictum for theStock Market." NBER Working Paper No.w9348.Kahneman, Daniel and Amos Tversky. 1979."Prospect Theory: An Analysis of Decision UnderRisk." Econometrica. March, 47:2, pp. 263-92.Lamont, Owen A. and Richard H. Thaler.2001. "Can the Market Add and Subtract? Mispricingin Stock Market Ca1.i-e-Outs." NationalBureau of Economic Research Working Paper

104 Journal of Economzc PerspectivesNo. 8302, 2000. Forthcoming, Journal of PoliticalEconomy.LeRoy, Stephen F. and Richard D. Porter.1981. "The Present-Value Relation: Tests Basedon Implied L'ariance Bounds." Econometn'ca. May,49:3, p p 97-113.Lucas, Robert E. 1978. "Asset Prices in anExchange Economy." Econometn'ca. November,465, pp. 1429-445.MacKay, Charles. 1996. "Memoirs of ExtraordinaryPopular Delusions," 1841, in ExtraordinaqPopular Delusions and the ,C3ndness of Crowds andConfusidn de Confusiones. Martin Fridson, ed. NewYork: John Wiley.Malkiel, Burton G. 1973. A Random Jt'alk DownMrall Street. New York: W. W. Norton.Marimon, Ramon, Stephen E. Spear andShyam Sunder. 1993. "Expectationally DrivenMarket L'olatility: An Experimental Study." JournalofEconomic Theo?. October, 61:l, pp. 74-103.Marsh, Teny A. and Robert C. Merton. 1986."Dividend Variability and Variance Bounds Testsfor the Rationality of Stock Market Prices." AmericanEconomic Revim. June, 763, pp. 483-98.McGrattan, Wen R. and Edward C. Prescott.2001. "Taxes, Regulation, and Asset Prices." Unpublishedpaper, Federal Reserve Bank of Minneapolis.Merton, Robert C. 1973. "An IntertemporalCapital Asset Pricing Model." Econometn'ca. September,41:5, pp. 867-87.Miller, Edward M. 1977. "Risk, Uncertaintyand Divergence of Opinion." Journal of Finance.September, 32:4, pp. 1151-168.Moss, David A. 2002. When All Else Fails: Governmentas the LJltimate Risk iknager. Cambridge,Mass.: Harvard University Press.Odean, Terrance. 1998. "Are Investors Reluctantto Realize their Losses?" Journal of Finance.October, 53:5, pp. 1775-798.Samuelson, Paul A. 1998. "Summing Up onBusiness Cycles: Opening Address," in BeyondShocks: T.l'hat Causes Business Cycles. Jeffrey C. Fuhrerand Scott Schuh, eds. Boston: Federal ReserveBank of Boston, pp. 33-36.Scherbina, Anna. 2000. "Stock Prices and Differencesin Opinion: Empirical Evidence thatPrices Reflect Optimism." Unpublished paper,Northwestern University.Shefrin, Hersh. 2000. Beyond Greed and Fear:Lkderstanding Behavioral Finance and the Psycholog?'oflnvesting. Boston, Mass.: Harvard BusinessSchool Press.Shefrin, Hersh. 2001. Behavioral Finance (TheInternational Libra? of Critical M'ritings in FinancialEconomics), Volumes I through lV Cheltenham,U.K.: Edward Elgar.Shiller, Robert J. 1982. "Consumption, AssetMarkets and Macroeconomic Fluctuations."Carnegze-Rochester Confprence Series on Public Policy.Autumn, 17, pp. 203-38.Shiller, Robert J. 1989. Market Volatility. Cambridge,Mass.: MIT Press.Shiller, Robert J. 1990a. "Speculative Pricesand Popular Models." Journal ofEconomic Perspectives.Spring, 4:2, pp. 55-65.Shiller, Robert J. 1990b. "Market Volatilityand Investor Behavior." Amm'can Economic Revim.May, 80:2, pp. 58-62.Shiller, Robert J. 2000a. In-ational Exuberance.Princeton, N.J.: Princeton University Press.Shiller, Robert J. 2000b. "Measuring BubbleExpectations and Investor Confidence." Journalof psycho lo^ and Financial Markets. 1: 1, pp.49-60.Shiller, Robert J. 2002. "Bubbles, HumanJudgment, and Expert Opinion." Financial AnalystsJournal. 58, pp. 18-26.Shleifer, Andrei. 2000. InefJicient ,C3nrkets. Oxford:Oxford University Press.Shielfer, Andrei and Lawrence Summers.1990. "The Noise-Trader Approach to Finance."Journal of Economic Perspectzves. Spring, 4:2 pp.19-33.Siegel, Jeremy J. 2002. Stocks for the Long Run.Third Edition. New York: McGraw-Hill.Smith, Vernon, Geny Suchanek and ArlingtonWilliams. 1988. "Bubbles, Crashes, and EndogenousExpectations in Experimental Spot AssetMarkets." Econometn'ca. September, 565, pp.1119-153.Statman, Meir and Hersh Shefrin. 1985. "TheDisposition to Sell Winners Too Early and RideLosers Too Long: Theory and Evidence." Journalof Finance. July, 40:3, pp. 777-90.Thaler, Richard. 2003. Advances in BehavioralFinance II. New York: Russell Sage.Tversky, Amos and Daniel Kahneman. 1974."Judgment under Uncertainty: Heuristics andBiases." Science. 185:4157, pp. 1124-31.Vuolteenaho, Tuomo. "What Drives Firm-Level Stock Returns?" Journal of Finance. February,57:1, pp. 233-64.West, Kenneth D. 1988. "Dividend Innovationsand Stock Price Volatility." Econometrica.January, 561, pp. 36-71.

http://www.jstor.orgLINKED CITATIONS- Page 1 of 7 -You have printed the following article:From Efficient Markets Theory to Behavioral FinanceRobert J. ShillerThe Journal of Economic Perspectives, Vol. 17, No. 1. (Winter, 2003), pp. 83-104.Stable URL:http://links.jstor.org/sici?sici=0895-3309%28200324%2917%3A1%3C83%3AFEMTTB%3E2.0.CO%3B2-JThis article references the following linked citations. If you are trying to access articles from anoff-campus location, you may be required to first logon via your library web site to access JSTOR. Pleasevisit your library's website or contact a librarian to learn about options for remote access to JSTOR.[Footnotes]4 Dividend Innovations and Stock Price VolatilityKenneth D. WestEconometrica, Vol. 56, No. 1. (Jan., 1988), pp. 37-61.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28198801%2956%3A1%3C37%3ADIASPV%3E2.0.CO%3B2-M5 Why Does the Stock Market Fluctuate?Robert B. Barsky; J. Bradford De LongThe Quarterly Journal of Economics, Vol. 108, No. 2. (May, 1993), pp. 291-311.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28199305%29108%3A2%3C291%3AWDTSMF%3E2.0.CO%3B2-I7 The Dividend-Price Ratio and Expectations of Future Dividends and Discount FactorsJohn Y. Campbell; Robert J. ShillerThe Review of Financial Studies, Vol. 1, No. 3. (Autumn, 1988), pp. 195-228.Stable URL:http://links.jstor.org/sici?sici=0893-9454%28198823%291%3A3%3C195%3ATDRAEO%3E2.0.CO%3B2-O8 Asset Prices in an Exchange EconomyRobert E. Lucas, Jr.Econometrica, Vol. 46, No. 6. (Nov., 1978), pp. 1429-1445.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197811%2946%3A6%3C1429%3AAPIAEE%3E2.0.CO%3B2-INOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 2 of 7 -8 The Determinants of the Variability of Stock Market PricesSanford J. Grossman; Robert J. ShillerThe American Economic Review, Vol. 71, No. 2, Papers and Proceedings of the Ninety-ThirdAnnual Meeting of the American Economic Association. (May, 1981), pp. 222-227.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28198105%2971%3A2%3C222%3ATDOTVO%3E2.0.CO%3B2-815 Market Volatility and Investor BehaviorRobert J. ShillerThe American Economic Review, Vol. 80, No. 2, Papers and Proceedings of the Hundred andSecond Annual Meeting of the American Economic Association. (May, 1990), pp. 58-62.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28199005%2980%3A2%3C58%3AMVAIB%3E2.0.CO%3B2-H16 A Theoretical Analysis of Real Estate Returns: DiscussionMeir StatmanThe Journal of Finance, Vol. 40, No. 3, Papers and Proceedings of the Forty-Third Annual MeetingAmerican Finance Association, Dallas, Texas, December 28-30, 1984. (Jul., 1985), pp. 719-721.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28198507%2940%3A3%3C719%3AATAORE%3E2.0.CO%3B2-816 Are Investors Reluctant to Realize Their Losses?Terrance OdeanThe Journal of Finance, Vol. 53, No. 5. (Oct., 1998), pp. 1775-1798.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199810%2953%3A5%3C1775%3AAIRTRT%3E2.0.CO%3B2-4ReferencesWhy Does the Stock Market Fluctuate?Robert B. Barsky; J. Bradford De LongThe Quarterly Journal of Economics, Vol. 108, No. 2. (May, 1993), pp. 291-311.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28199305%29108%3A2%3C291%3AWDTSMF%3E2.0.CO%3B2-INOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 3 of 7 -A Variance Decomposition for Stock ReturnsJohn Y. CampbellThe Economic Journal, Vol. 101, No. 405. (Mar., 1991), pp. 157-179.Stable URL:http://links.jstor.org/sici?sici=0013-0133%28199103%29101%3A405%3C157%3AAVDFSR%3E2.0.CO%3B2-XStock Prices, Earnings, and Expected DividendsJohn Y. Campbell; Robert J. ShillerThe Journal of Finance, Vol. 43, No. 3, Papers and Proceedings of the Forty-Seventh AnnualMeeting of the American Finance Association, Chicago, Illinois, December 28-30, 1987. (Jul.,1988), pp. 661-676.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28198807%2943%3A3%3C661%3ASPEAED%3E2.0.CO%3B2-1The Dividend-Price Ratio and Expectations of Future Dividends and Discount FactorsJohn Y. Campbell; Robert J. ShillerThe Review of Financial Studies, Vol. 1, No. 3. (Autumn, 1988), pp. 195-228.Stable URL:http://links.jstor.org/sici?sici=0893-9454%28198823%291%3A3%3C195%3ATDRAEO%3E2.0.CO%3B2-OInvestor Psychology and Security Market under- and OverreactionsKent Daniel; David Hirshleifer; Avanidhar SubrahmanyamThe Journal of Finance, Vol. 53, No. 6. (Dec., 1998), pp. 1839-1885.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199812%2953%3A6%3C1839%3AIPASMU%3E2.0.CO%3B2-%23Does the Stock Market Overreact?Werner F. M. De Bondt; Richard ThalerThe Journal of Finance, Vol. 40, No. 3, Papers and Proceedings of the Forty-Third Annual MeetingAmerican Finance Association, Dallas, Texas, December 28-30, 1984. (Jul., 1985), pp. 793-805.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28198507%2940%3A3%3C793%3ADTSMO%3E2.0.CO%3B2-QNoise Trader Risk in Financial MarketsJ. Bradford De Long; Andrei Shleifer; Lawrence H. Summers; Robert J. WaldmannThe Journal of Political Economy, Vol. 98, No. 4. (Aug., 1990), pp. 703-738.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28199008%2998%3A4%3C703%3ANTRIFM%3E2.0.CO%3B2-LNOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 4 of 7 -Positive Feedback Investment Strategies and Destabilizing Rational SpeculationJ. Bradford de Long; Andrei Shleifer; Lawrence H. Summers; Robert J. WaldmannThe Journal of Finance, Vol. 45, No. 2. (Jun., 1990), pp. 379-395.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199006%2945%3A2%3C379%3APFISAD%3E2.0.CO%3B2-YEfficient Capital Markets: A Review of Theory and Empirical WorkEugene F. FamaThe Journal of Finance, Vol. 25, No. 2, Papers and Proceedings of the Twenty-Eighth AnnualMeeting of the American Finance Association New York, N.Y. December, 28-30, 1969. (May,1970), pp. 383-417.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28197005%2925%3A2%3C383%3AECMARO%3E2.0.CO%3B2-VEfficient Capital Markets: IIEugene F. FamaThe Journal of Finance, Vol. 46, No. 5. (Dec., 1991), pp. 1575-1617.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199112%2946%3A5%3C1575%3AECMI%3E2.0.CO%3B2-LThe Informational Effects of Restrictions on Short Sales: Some Empirical EvidenceStephen FiglewskiThe Journal of Financial and Quantitative Analysis, Vol. 16, No. 4, Proceedings of 16th AnnualConference of the Western Finance Association, June 18-20, 1981, Jackson Hole, Wyoming. (Nov.,1981), pp. 463-476.Stable URL:http://links.jstor.org/sici?sici=0022-1090%28198111%2916%3A4%3C463%3ATIEORO%3E2.0.CO%3B2-COptions, Short Sales, and Market CompletenessStephen Figlewski; Gwendolyn P. WebbThe Journal of Finance, Vol. 48, No. 2. (Jun., 1993), pp. 761-777.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199306%2948%3A2%3C761%3AOSSAMC%3E2.0.CO%3B2-QNOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 5 of 7 -Famous First BubblesPeter M. GarberThe Journal of Economic Perspectives, Vol. 4, No. 2. (Spring, 1990), pp. 35-54.Stable URL:http://links.jstor.org/sici?sici=0895-3309%28199021%294%3A2%3C35%3AFFB%3E2.0.CO%3B2-9The Determinants of the Variability of Stock Market PricesSanford J. Grossman; Robert J. ShillerThe American Economic Review, Vol. 71, No. 2, Papers and Proceedings of the Ninety-ThirdAnnual Meeting of the American Economic Association. (May, 1981), pp. 222-227.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28198105%2971%3A2%3C222%3ATDOTVO%3E2.0.CO%3B2-8Implications of Security Market Data for Models of Dynamic EconomiesLars Peter Hansen; Ravi JagannathanThe Journal of Political Economy, Vol. 99, No. 2. (Apr., 1991), pp. 225-262.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28199104%2999%3A2%3C225%3AIOSMDF%3E2.0.CO%3B2-LReturns to Buying Winners and Selling Losers: Implications for Stock Market EfficiencyNarasimhan Jegadeesh; Sheridan TitmanThe Journal of Finance, Vol. 48, No. 1. (Mar., 1993), pp. 65-91.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199303%2948%3A1%3C65%3ARTBWAS%3E2.0.CO%3B2-YProspect Theory: An Analysis of Decision under RiskDaniel Kahneman; Amos TverskyEconometrica, Vol. 47, No. 2. (Mar., 1979), pp. 263-292.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197903%2947%3A2%3C263%3APTAAOD%3E2.0.CO%3B2-3The Present-Value Relation: Tests Based on Implied Variance BoundsStephen F. LeRoy; Richard D. PorterEconometrica, Vol. 49, No. 3. (May, 1981), pp. 555-574.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28198105%2949%3A3%3C555%3ATPRTBO%3E2.0.CO%3B2-3NOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 6 of 7 -Asset Prices in an Exchange EconomyRobert E. Lucas, Jr.Econometrica, Vol. 46, No. 6. (Nov., 1978), pp. 1429-1445.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197811%2946%3A6%3C1429%3AAPIAEE%3E2.0.CO%3B2-IDividend Variability and Variance Bounds Tests for the Rationality of Stock Market PricesTerry A. Marsh; Robert C. MertonThe American Economic Review, Vol. 76, No. 3. (Jun., 1986), pp. 483-498.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28198606%2976%3A3%3C483%3ADVAVBT%3E2.0.CO%3B2-CAn Intertemporal Capital Asset Pricing ModelRobert C. MertonEconometrica, Vol. 41, No. 5. (Sep., 1973), pp. 867-887.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28197309%2941%3A5%3C867%3AAICAPM%3E2.0.CO%3B2-ERisk, Uncertainty, and Divergence of OpinionEdward M. MillerThe Journal of Finance, Vol. 32, No. 4. (Sep., 1977), pp. 1151-1168.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28197709%2932%3A4%3C1151%3ARUADOO%3E2.0.CO%3B2-MAre Investors Reluctant to Realize Their Losses?Terrance OdeanThe Journal of Finance, Vol. 53, No. 5. (Oct., 1998), pp. 1775-1798.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28199810%2953%3A5%3C1775%3AAIRTRT%3E2.0.CO%3B2-4Speculative Prices and Popular ModelsRobert J. ShillerThe Journal of Economic Perspectives, Vol. 4, No. 2. (Spring, 1990), pp. 55-65.Stable URL:http://links.jstor.org/sici?sici=0895-3309%28199021%294%3A2%3C55%3ASPAPM%3E2.0.CO%3B2-INOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 7 of 7 -Market Volatility and Investor BehaviorRobert J. ShillerThe American Economic Review, Vol. 80, No. 2, Papers and Proceedings of the Hundred andSecond Annual Meeting of the American Economic Association. (May, 1990), pp. 58-62.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28199005%2980%3A2%3C58%3AMVAIB%3E2.0.CO%3B2-HBubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset MarketsVernon L. Smith; Gerry L. Suchanek; Arlington W. WilliamsEconometrica, Vol. 56, No. 5. (Sep., 1988), pp. 1119-1151.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28198809%2956%3A5%3C1119%3ABCAEEI%3E2.0.CO%3B2-3A Theoretical Analysis of Real Estate Returns: DiscussionMeir StatmanThe Journal of Finance, Vol. 40, No. 3, Papers and Proceedings of the Forty-Third Annual MeetingAmerican Finance Association, Dallas, Texas, December 28-30, 1984. (Jul., 1985), pp. 719-721.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28198507%2940%3A3%3C719%3AATAORE%3E2.0.CO%3B2-8Judgment under Uncertainty: Heuristics and BiasesAmos Tversky; Daniel KahnemanScience, New Series, Vol. 185, No. 4157. (Sep. 27, 1974), pp. 1124-1131.Stable URL:http://links.jstor.org/sici?sici=0036-8075%2819740927%293%3A185%3A4157%3C1124%3AJUUHAB%3E2.0.CO%3B2-MWhat Drives Firm-Level Stock Returns?Tuomo VuolteenahoThe Journal of Finance, Vol. 57, No. 1. (Feb., 2002), pp. 233-264.Stable URL:http://links.jstor.org/sici?sici=0022-1082%28200202%2957%3A1%3C233%3AWDFSR%3E2.0.CO%3B2-FDividend Innovations and Stock Price VolatilityKenneth D. WestEconometrica, Vol. 56, No. 1. (Jan., 1988), pp. 37-61.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28198801%2956%3A1%3C37%3ADIASPV%3E2.0.CO%3B2-MNOTE: The reference numbering from the original has been maintained in this citation list.

Rationality as Process and as Product of ThoughtHerbert A. SimonThe American Economic Review, Vol. 68, No. 2, Papers and Proceedings of the Ninetieth AnnualMeeting of the American Economic Association. (May, 1978), pp. 1-16.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28197805%2968%3A2%3C1%3ARAPAAP%3E2.0.CO%3B2-4The American Economic Review is currently published by American Economic Association.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/aea.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgTue Jan 15 08:09:07 2008

RICHARD T. ELY LECTURERationality as Process and as Product of ThoughtThis opportunity to deliver the RichardT. Ely Lecture affords me some very personalsatisfactions. Ely. unbeknownst tohim, bore a great responsibility for my economiceducation, and even for my choice ofprofession. The example of my uncle,Harold Merkel, who was a student of Commonsand Ely at Wisconsin before WorldWar I, taught me that human behavior wasa fit subject for scientific study, anddirected me to economics and politicalscience instead of high energy physics ormolecular biology. Some would refer to thisas satisficing, for I had never heard of highenergy physics or molecular biology. andhence was spared an agonizing weighing ofalternative utiles. I simply picked the firstprofession that sounded fascinating.Ely's influence went much further thanthat. My older brother's copy of his Oirtlinesof Er.ono~?~ic.c -the 1930 edition-wason our bookshelves when I prepared forhigh school debates on tariffs versus freetrade, and on the Single Tax of HenryGeorge. It provided me with a sufficientlygood grounding in principles that I was laterable to take Henry Simons' intermediatetheory course at the University of Chicago.and the graduate courses of Frank Knightand Henry Schultz without additionalpreparation.The Ely textbook. in its generation, heldthe place of Samuelson or Bach in ours. If itwould not sound as though I were denyingany progress in economics over the pasthalf century, I might suggest that Ely'stextbook could be substituted for any of ourcurrent ones at a substantial reduction inweight. and without students or teacher beingmore than dimly aware of the replacement.Of course they would not hear fromEly about marginal propensities to do thisCarnegie-Mellon Universityor that, nor about the late lamented Phillipscurve. But monetarists could rejoice inEly's uncompromising statement of thequantity theory (p. 298, italics). and in hisassertion that "the solution of the problemof unemployment depends largely upon indirectmeasures, such as monetary andbanking reform"-Ely does go on to say,however. that "we shall recognize that societymust offer a willing and able man anopportunity to work" (p. 528).I. Rationalit! in and out of EconomicsI have more than personal reasons for directingyour attention to Ely's textbook.On page 4. we find a definition of economicsthat is, I think, wholly characteristicof books contemporary with his."Economics," he says, "is the sciencewhich treats of those social phenomena thatare due to the wealth-getting and wealthusingactivities of man." Economics. that isto say. concerns itself with a particularsubset of man's behaviors-those having todo with the production, exchange, andconsumption of goods and services.Many, perhaps most. economists todaywould regard that view as too limiting.They would prefer the definition proposedin the Internationnl Encyt lopedia of tlzeSociril Sciences: "Economics . . . is thestudy of the allocation of scarce resourcesamong unlimited and competing uses" (vol.4. p. 472). If beefsteak is scarce. they wouldsay. so are votes, and the tools of economicanalysis can be used as readily to analyzethe allocation of the one as of the other.This point of view has launched economicsinto many excursions and incursions intopolitical science and her other sister socialsciences, and has generated a certainamount of hubris in the profession withrespect to its broader civilizing mission. I

) MIC ASSOCIA TI0 V MAY 1978would suppose that the program of thismeeting. hith its emphasis upon the relationsbetween economics and the othersocial sciences. is at least partly a reflectionof that hubris.The topic of allocating scarce resourcescan be approached from either its normativeor its positive sicie. Fundamental to theapproach from either side are assumptionsabout the adaetation of means to ends. ofactions to goals and situations. Economics.whether normative or positive, has notsimply been the study of the allocation ofscarce resources. it has been the study ofthe rrrtional allocation of scarce resources.Moreover, the term "rational" has loneuhad in economics a much more specificmeaning than its general dictionarysignification of "agreeable to reason; notabsurd. preposterous. extravagant. foolish,fanciful. or the like; intelligent. sensible."4s is \bell known. the rational man of economic.,is a maximizer. who will \ettle fornothing less than the best. Even his expectations,we have learned in the past fewyears, are rational (see John Muth, 1961).'And his rationality extends as far as thebedroom for. as Gary Becker tells us, "hewould read in bed at night only if the valueof reading exceeded the value (to him) ofthe loss in sleep suffered by his wife"(1974, p. 1078).It is this concept of rationality that is economics'main export commodity in its tradewith the other social sciences. It is nonovelty in those sciences to propose thatpeople behave rationally-if that term istahen in its broader dictionary sense.Assumptions of rationality are essentialcomponents of virtually all the sociological.psychological, political. and ~tnthropologicaltheories with which I am familiar.What economics has to export, then, is not'The term is ill-chown. for rational expectations inthe sense of Muth are profit-maximizing expectationsonly under very special circumstances (see belo\+).Perhaps we would mislead o~irselves and others less ifwe called then1 by the less alluring phrase. "consistentexpectations.''rationality, but a very particular and specialform of it-the rationality of the utilitymaximizer, and a pretty smart one at that.But international flows have to bebalanced. If the program of this meetingaims at more active intercourse betweeneconomics and her sister social sciences,then we must ask not only what economicswill export. but also what she will receive inpayment. An economist might well betempted to murmur the lines of thetentmaker: "I wonder often what theVintners buy-One half as precious as thestuff they sell."My paper will be much concerned withthat question, and before I proceed, it maybe well to sketch in outline the path Ipropose to follow in answering it. The argumenthas three major steps.First. I would like to expand on thetheme that almost all human behavior has alarge rational component, but only in termsof the broader everyday sense of rationality,not the economists' more specializedsense of maximization.Second, I should like to show that economicsitself has not by any means limiteditself to the nar-rower definition of rationality.Much economic literature (forexample. the literature of comparative institutionalanalysis) uses weaker definitionsof rationality extensively; and that literaturewould not be greatly. if at all,improved by substituting the strongerdefinition for the weaker one.' To theextent that the weaker definition is adeqyatefor purposes of analysis. economicswill find that there is indeed much that isimportable from the other social sciences.Third, economics has largely been preoccupiedwith the resulrs of rational choicerather than the proc,c1s.s of choice. Yet aseconomic analysis acquires a broaderconcern with the dynamics of choice underuncertainty. it will become more and Inoreessential to consider choice processes. Inthe past twenty years, there have been irn-*For an interesting argument in s~ipport of thisproposition from a surprising source. see Becker(1962). What Becker calls "irrationality" in his articleuould be called "hounded rationality'' here.

VOL 68 YO 2RICHARD T. EL-Y LtCTURE3portant advances in our understanding ofprocedural rationality. particularly as aresult of research in artificial intelligenceand cognitive psychology. The importationof these theories of the processes of choiceinto economics could provide immensehelp in deepening our understanding of thedynamics of rationality. and of theinfluences upon choice of the institutionalstructure uithin which it takes place.We begin. then. by looking at the broaderconcept of rationality to which I have referred.and its social xience applications.Let me provide some examples how rationalitytypically enters into social sciencetheories. Consider first so-called "socialexchange" theories (see, for example.George Homans). The central idea here isthat uhen two or more people interact,each expects to get something from theinteraction that is valuable to him. and isthereby motivated to give something upthat is valuable to the others. Social exchange,in the form of the "inducementscontr-ibutionsbalance" of Chester I. Barnardand the author (1947). has played animportant role in organization theory. andin even earlier times (see. for example.George Sirnmel) was a central ingredient insociological theories. Much of the theorizingand empirical work on the topic hasbeen concerned with determining whatconstitutes a significant inducement orcontribution in particular classes of exchangesituations-that ih, with the actualshape and substance of the "utility function."Clearly. the man of social exchangetheory is a rational man, even if he is neverasked to equate things at the margin.It is perhaps more surprising to discoverhow pervasive assumptions of rationalityare in psychoanalytic theory-confil-mingthe suhpicion that ther-e is indeed method inmadness. In his Fir*c~ 1,c~r.tui.c~~ SigmundFreud has this to say about neurotic illnesses:We see that human beings fall illwhen. as a result of external obstaclesor of an internal lack of adaptation. thesatisfaction of their erotic needs ittt~jrrlityis frustratect. We see that theythen take flight into illilcss in order thatby its help they may find a satisfactionto take the place of what has beenfrustrated . . . We suspect that ourpatients' resistance to recovery is nosimple one. but compounded of severalmotives. Not only does the patient'sego rebel against giving up therepressions by means of which it hasrisen above its original disposition. butthe sexual instincts are unwilling torenounce their substitutive satisfactionso long as it is uncertain whetherreality will offer them anything better.Almost all explanattons of pathological behaviorin the psychoanalytic literature taketh~sform: they explain the patient's illnessin terms of the functions it performs forhim.The auotation from Freud is illustrativeof a kind of functional reasoning that goesfar beyond psychoan:~lysis and is uidelyused throughout the social sciences. andespecially anthropology and sociology. Behaviorsare functional if they contribute tocertain goals, where these goals may be theple;lsur-e or satisfaction of an individual orthe guarantee of food or shelter for themembers of a society. Functional analysisin this sense is concerned with explaininghow "major social patterns operate tomaintain the integration or adaptation ofthe larger system" (see Frank Cancian). Institutionsare functional if reasonable menmight create and maintain them in order tomeet social needs or achieve social goals.It is not necessary or implled that theadaptation of institutions or behavior patternsto goals be conscious or ~ntended.When awareness and intention are present.the function is usually called intrn(fest.otherwise it is a ltrtolt function. The function,whether it be manifest or latent.provides the grounds for the reasonablenessor rationalitv of the institution or behaviorpattern. As in economics, evolutionaryarguments are often adduced toexplain the persistence and survival of

4 A llLRlC A 1' CCOVO MIC ASSOCIATIOY \IAk I978functional patterns. and to avoid assumptionsof deliberate calculation in explainingthem.In practice, it is very rarely that theexistence or character of institutions aretictlirc,c~tlfrom the functions that must beperformed for system survival. In almost allcases it is the other way round: it is empiricalobservation of the behavior patternthat raises the question of why it persistswhatfunction it performs. Perhaps, in anappropriate axiomatic formulation. it wouldbe possible to tt~~t1lrc.rthat every societymust have food-gathering institutions. Inpoint of fact, such institutions can be ob-.xer~.e~tl in every society. and their existenceis then rationalized by the argument thatobtaining food is a functional requisite forall societies. This kind of argument maydemonstrate the sufficiency of a particularpattern for performing an essential function,but cannot demonstrate itsnecessity-cannot show that there may notbe alternative, functionally equivalent, behaviorpatterns that would satisfy the sameneed.The point may be stated more formally.Functional arguments are arguments aboutthe movements of systems toward stableself-maintaining equilibria. But withoutfurther specification, there is no reason tosuppose that the attained equilibria that arereached will be global maxima or minima ofsome function rather than local. relativemaxima or minima. In fact. we know thatthe conditions that every local maximum ofa system be a global maximum are verystrong (usually some kind of "convexity"conditions).Further. when the system is complex andits environment continually changing (thatis. in the conditions under which biologicaland social evolution actually take place).there is no assurance that the system's momentaryposition will lie anywhere near apoint of equilibrium, whether local orglobal. Hence, all that can be concludedfrom a functional argument is that certaincharacteristics (the satisfaction of certainfunctional requirements in a particular way)are consistent with the survival and furtherdevelopment of the system. not that thesesame requirements could not be satisfied insome other way. Thus. for example.societies can satisfy their functional needsfor food by hunting or fishing activities. byagriculture. or by predatory exploitation ofother societies.Functional analysis of exactly this kind.though with a different vocabulary, is commonlyemployed by economists, especiallywhen they seek to use economic tools to"explain" institutions and behaviors thatlie outside the traditional domains ofproduction and distribution. Moreover. itoccurs within those domains. As anexample. the fact is observed that individualsfrequently insure against certainkinds of contingencies. Attitudes are thenpostulated (for example. risk aversion) forwhich buying insurance is a functional andreasonable action. If some people are observedto insure. and others not. then thisdifference in behavior can be explained bya difference between them in risk aversion.To take a second example. GeorgeStigler and Becker wish to explain the fact(if it is a fact-their empiricism is verycasual) that as people hear more music.they want to hear still more. They invent acommodity, "music appreciation" (not tobe confused with time spent in listening tomusic). and suggest that listening to musicmight produce not only immediate enjoymentbut also an investment in c,c~pac,ityforappreciating music (i.e.. in amount of enjoymentproduced per listening hour). Oncethese assumptions are granted. variousconclusions can be drawn about the demandfor music appreciation. However.only weak conclusions follow about listeningtime unless additional strong postulatesare introduced about the elasticity of demandfor appreciation.A rough "sociological" translation of theStigler-Becker argument would be thatlistening to music is functional both in producingpleasure and in enhancing thepleasure of subsequent listening-a typicalfunctional argument. It is quite unclearwhat is gained by dressing it in the garb of

VOL. 68 .VO. 2RICHARD T. EL-Y LECTURE5marginalism. We might be willing togrant that people would be inclined to investmore in musical appreciation early inlife than later in life (because they wouldhave a longer time in which to amortize theinvestment) without insisting that costs andreturns were being equated at the margin.and without gaining any new insights intothe situation from making the latterassumption.A sense of fairness compels me to take athird example from my own work. In my1951 paper. I defined the characteristics ofan employment contract that distinguish itfrom an ordinary sales contract. and thenshowed why reasonable men might preferthe former to the latter as the basis for establishingan employment relation. Myargument requires a theorem and fifteennumbered equations. and assumes thatboth employer and employee maximizetheir utilities. Actually, the underlyingfunctional argument is very simple. An employeewho didn't care very much which ofseveral alternative tasks he performedwould not require a large inducement to acceptthe authority of an employer-that is,to permit the employer to make the choiceamong them. The employer in turn wouldbe willing to provide the necessary inducementin order to acquire the right topostpone his decisions about the employee'sagenda, and in this way topostpone some of his decisions whose outcomesare contingent on future uncertainevents.' The rigorous economic argument.involving the idea of maximizing behaviorby employer and employee. is readily translatableinto a simple qualitative argumentthat an employment contract may be afunctional ("reasonable") way of dealingwith certain kinds of uncertainty. The argu-'Recently. Oliver Williamson has pointed out that Iwould have to introduce slightly stronger assumptionsto justify the employment contract as rational if one ofthe alternatives to it were what he calls a "contingentclaims" contract, but the point of my example is notaffected. To exclude the contingent claims contract asa viable alternative, we need merely take account ofthe large transaction costs it aould entail under realworld conditions.~nent then explains why employment relationsare so widely used in our society.The translation of these examples of economicreasoning into the language of functionalanalysis could be paralleled by examplesof translation scholarship which run inthe opposite direction. Political scientists.for example. long ago observed that undercertain circumstances institutions ofrepresentative democracy spawned a multiplicityof political parties. while under othercircumstances. the votes were divided inequilibrium between two major parties.These contrasting equilibria could readilybe shown by functional arguments to resultfrom rational voting decisions under differentrules of the electoral game. as wasobserved by Maurice Duverger, in hisclassic work on political parties. as well asby a number of political scientists who precededhim. In recent years. these sameresults have been rederived morerigorously by economists and gametheorists. employing much strongerassumptions of utility maximization by thevoters: it was hard to see that themaximization assumptions have producedany new predictions of b e h a ~ i o r . ~Perhaps these examples suffice to showthat there is no such gap as is commonlysupposed between the view of manespoused by economics and the view foundin the other social sciences. The view ofman as rational is not peculiar to economics.but is endemic, and even ubiquitous,throughout the social sciences. Economicstends to emphasize a particular4For an introduction to this literature. see WilliamH. Riker and Peter C. Ordeshook. and Riker. AnthonyDowns' book belongs to an intermediate genre. Whileit employs the language of economics, it limits itself toverbal. nonrigorous reasoning which certainly doesnot make any essential use of maximizing assumptions(as contra\ted with rationality assumptions in thebroader sense). and which largely translates into theeconomic vocabulary generalizations that were ;:Ireadypart of the science and folklore of politics. In thcnext section, other examples of this kind of informaluse of rationality principles are examined to analyzein\titutions and their behavior.

form of rationality-maximizing behavior-asits preferred engine of explanation.but the differences are often differencesin vocabulary more than insubstance. We shall see in a moment that inmuch economic discussion the notion ofmaximization is used in a loose sense that isvery close to the common sense notions ofrationality used elsewhere in the socialsciences.One conclusion we may draw is thateconomists might well exercise a certainamolint of circumspection in theirendeavors to export economic analysis tothe other social sciences. 'They may discoverthat they are sometimes offeringcommodities that are already in generoussupply, and which can therefore be disposedof only at a ruinously low price. Onthe other side of the trade. they may findthat there is more of interest in the modesand results of inquiry of their fellow socialscientists than they have generally beenaware.11. On ippljing the Principle of Rationalit!What is characteristic of the examples offunctional analysis cited in the last section.whether thev be dra\vn from economics orfrom the other socinl sciences, i5 that theyare not focu5ed on. or eken muchconcerned with. h o variable\ ~ are eau'itedat the margin. or how equilibrium is alteredby marginal shifts in conditions (forexample, shifts in a supply or demandschedule). Rather, they are focused onqualitative and structural questions. typically.on the choice among a small numberof discrete institutional alternatives:Not "how much flood insurance will aman buy?" but "what are the structuralconditions that make buying insurance rationalor attractive?"Not "at what levels will wages befixed'?" but "when will work be performed~~nder an employment contract rather thana sales contract?"If we M ant a natural science analogy tothis kind of theorizing, we can find it ingeology. A geologist notice5 deep scrntchesin rock; he notices that certain hills ofgravel are elongated along a north-southaxis. and that the boulders embedded inthem are not as smooth as those usuallyfound on beaches. To explain these facts,he evokes a structural. and not at all quantitative.hypothesis: that these phenomenawere produced by the process of glaciation.In the first instance, he does not try toexplain the depth of the glacial till, or estimatethe weight of the ice that procluced it.but simply to identify the basic causativeprocess. He wants to explain the role ofglaciation. of erosion. of vulcanization, ofsedimentation in producing the land formsthat he observes. His explanations.niorever. are after-the-fact, and not predictive.As economics expands beyond its centralcore of price theory, and its central concernwith quantities of commodities and money.we observe in it this same shift from ahighly quantitative analysis. in whichequilibration at the margin plays a centralrole, to a much more q~lalitative institutionalanalysis, in which discrete structuralalternatives are compared.In these analyses aimed at explaining institutionalstructure, maximizing assumptionsplay a much less significant role thanthey typically do in the analysis of marketequilibria. The rational man who sometimesprefers an employment contract to asales contract need not be a maximizer.Even a satisficer will exhibit such apreference whenever the difference inrewards between the two arrangements issufficiently large and evident.For this same reason. such analyses canoften be carried out without elaboratemathematical apparatus or marginal calculation.In general, much cruder andsimpler arguments will suffice todemonstrate an inequality between t n oquantities than are required to show theconditions under which these quantities areequated at the margin. Thus. in the recentworks of Janos Kornai. Williamson. andJohn Montias on economic organization.we find only rather modest and simple ap-

VOL. 68 .VO. 2RICHARD T. ELY LECTURE7plications of mathematical analysis. In theways in which they involve principles of rationality.the arguments of these authors resembleJames March and the author's Orgtrnizntioilsmore closely than PaulSamuelson's Folrntlr~rio/~s.~What is the predominant form of reasoningthat we encounter in these theoreticaltreatments of social institutions? Do theycontain arguments based on maximizingassumptions? Basically. they rest upon avery simple form of causal analysis.Particular institutional structures orpractices are seen to entail certain undesirable(for example, costly) 01- desirable(for example. value-producing) consequences.Cctc1ri.s plit'ihlr.~,situations andpractices will be preferred when importantfavorable conseq~lences are associated withthem. and avoided when important unfavorableconsequences are associated withthem. A shift in the balance of consequences.or in awareness of them. may motivatea change in institutional arrangements.Consider the following argument fromMontias typical of this genre of analysis.which relates to the balance in organizationsbetween centralization anddecentralization.Decentralizing measures are generallyaimed at remedying two shortcom-'A notable exception to this generalization about theeconomic literature on organizations is the aork ofJacob Marschak and Roy Radner on the theory ofteams. These authors chow the strategy of detailed.precise analysis of the implications of maximizingassumptions for the transmi\\ion of information in organization\.The price they paid for this rigor b%as tofind them\elves limited to the highly simplified situationsahere wlutions could be found for themathematical problems they posed. We need not. ofcourse. make an either-or choice betaeen these taomodes of inquiry. While it may be difficult or impossibleto extend the formal analysis of the theor) of teamsto problems of real world complexity. the rigorousmicrotheory may illuminate the workings of importantcomponent mechanisms in the complex macrosituations.The methodological i\\ues in choo\ing betweenanalytic tractability and realism are quite parallel tothme involved in the choice between laboratory andfield methods for gathering empirical informationabout social phenomena. Neither one by itself marksthe exclusive path tob%ard truth.ings of an 'overcentralized' systemstructure. (1) Superordinates areoverburdened with responsibility forthe detailed direction and coordinationof their subordinates' activities. (3)This 'petty tutelage' deprives subordinatesof the opportunity to make decisionsthat might increase the payoffof the organization of which they are apart. . . . Why not loosen controls. . . ? . . . When controls areloosened, unless the incentive systemis modified to bring about greaterharmony between the goals of supervisorsand supervisees. it may induceproducers to shift their input andoutput mix in directions that . . . vitiateany benefits that might be reapedby the organization as a whole from theexercise of greater initiative at lowertiers. [p. 3151Here two costs or disadvantages ofcentralization (burden on supervisors.restriction of choice-set of subordinates)are set off against a disadvantage ofdecentralization (goals of subordinates divergentfrorn organization goals).What can we learn about organizationfrom an at-gument like this'? Certainly littleor nothing about the optirnal balance pointbetween centralization and decentralizationin any particular organization. Rather, wemight derive conclusions of these kinds:1. That increasing awareness of one ofthe predicted consequences may cause anorganization to move in the direction ofcentralization 01- decentralization. (Forexample. an egregious case of "suboptimizing"by a subordinate may cause additionalcentralized controls to be instituted.)2. That new technical devices may tiltthe balance between centralization anddecentralization. For example, inventionand adoption of divisionalized profit andloss statements led toward decentralizationof many large America11 business firms inthe 1950's: while reduction in informationcosts through computerization led at alater date to centralization of inventorycontrol decisions in those same firms.Of course Montias' conclusions couldalso be derived from a more formaloptimization analysis-in fact he presents

such an analysis on the t~vo pages follo~vingthe passage quoted above. But it is notclear that anything new is added by the formalization.since the parameters imputed tothe system are largely unmeiisured and unmeasurable.There is something to be said for anOckham's Razor that. escheu ing assumptionsof optimization. provictes an explanationof behavior that is consistent withoitl~(~t. optimizing or satisficing procedureson the part of the human agents. Parsimonyrecommends that bve prefer the postulatethat rnen are reasonable to the postulatethat they are supremely rational wheneither one of the tc\o assumptions \ \ i l l doour work of inference as uell as theThe kind of qualitative analysis I havebeen describing has another virtue. In complexsituations there is likely to be aconsiderable gap bet~been the real environmentof u decision (the world as God orsome other omniscient observer sees it) andthe environment as the actors perceive it.The analysis can then address itself eitherto normative questions-the whole rangeof consequences that .shoi~ltlenter into decisionsin such situations-or descriptivequestions. including the q~~estions of whichcomponents of the situation are likely to betaken into account by the actors, and howthe actors are likely to represent the situationas a w hole.In the precomputer era. for example. itwas very difficult for managers in businessorganizations to pay attention to all themajor variables affected by their decisions.Company treasurers frequently rnade deci-"Ockharn is usu:~ll) invoked on behalf of the parsimonyof optimizing a\\urnption\. and against the additional[rtl I~oc.postulates that \ati\ticing mvdel., arethought to require in order- to guariintee ~~niquene\\ ofsolution\. Rut that :lrgument only :~pplies\+hen\\e aretrying to deduce unique equilibl-ia. a ta\k quite differentfr-om the one rnost institution:il \triter\ \et forthernselves. Ho~te~er. I h;i\e no urge to enlar-ge onthi\ point. kly intent here i\ not polemical. on bchalf ofsatisficing po\tulates, but rather to \ho\\ ho\+ large aplot of comnion gro~~nd i\ shzired b! optirniring nilsati\ficing analy sis. Again. compare Beckel- ( 1962).sions about ~vot:king capital with little 01.noattention to their irnpact on inventorylevels. while production and marketingexecutives rnade decisions about inventorywithout taking into account impacts onliquidity. The introduction of computerschanged the hays in which executives bvereable to reach decisions: they could nowview them in terms of a much hider set ofinterrelated consequences than before. Theperception of the environment of a decisionis a function of-among other things-theinformation sources and computational capabilitiesof the executives ~ v h o make it.[,earning phenomena are also readilyhandled within this frarneuork. A numberof the changes introduced into planning andcontrol procedu~.es in eastern Europeancountries during the 1960's were instituteduhen the governments in question learnedby experience of some of the dysfunctionalconsequences of trying to control productionby means of crude aggregates ofphysical quantities. An initial distrust ofprices and market mechanisms bvasgradually and partially overcome afterdirect experience of the disadvantages ofsome of the alternative mechanisms. Theselearning experiences could be paralleledwith experiences of American steel companies.for example. that experimentedwith tonnage incentives for mill departmentsuperintendents.'4 general proposition that rnight beasserted about organizations is that thenumber of considerations that arepotentially relevant to the effectiveness of:in organization design is so large that onlya few of the more salient of these lie uithitithe circle of awareness at any given time.that the rnembership of this subset changescontinually 21s new situations (produced byexternal or internal events) arise, and that"learning" in the form of reaction toperceived consequences is the dominantc\ay in uhich rationality exhibits itself.In a world where these kinds of adjustmentsare prominent. a theory of rationalbehavior must be quite as much concernedwith the characteristics of the rational actors-themeans they use to cope with uncertaintyand cognitive complexity-as

POL 68 \O 2 RICH4RD TELY LE( TUREYwith the characteristics of the objective environmentin which they make their decisions.In such a world. ue must give an accountnot only of .rril?.~tcit~tit.cl rnfiotltrlitytheextent to c\ hich appropriate courses ofaction are chosen-but also proc.c~clllrct1 rrrtionrrlity-theeffectiveness, in light ofhuman cognitive po\+,ers and limitations, ofthe proc.rt1rri.c.v used to choose actions. Aseconomics moves out toward situations ofincreasing cognitive complexity, it becomesincreasingly concerned with theability of actors to cope ~vith the complexity.and hence ~vith the proceduralaspects of rationality. In the remainder ofmy talk. I \zould like to develop this conceptof procedul-al rationality, and its implicationsfor economic analysis.111. \lincl as the Scarce ResourceUntil rather recently. such limited attentionas was paid by economists to pl-ocedural.us distinct from substantive. rationality\\,as mainly motivated by the problemsof uncertainty and expectations. Thesimple notion of maximizing utility or profitcould not be applied to situations uhere theoptitnurn action depended on uncertain environmentalevents. or upon the actions ofother rational agents (for example, imperfectcompetition).The former difficulty was l.emoved tosome degree by replacing utility rnaxirnizationwith the maximization of subjective expectedutility (SEU)as the criterion of rationality.In spite of its conceptualelegance. however, the SEU solution hassome grave defects us either a normative or21 descriptive formulation. In general. theoptimal solution depends upon all of themoments of the frequency distributions ofuncertain events. The exceptions are asmall but ilnportant class of cases uherethe utility or pt.ofit function is quadratic andall constraints are in the form of equationsrather than inequalities.' The empirical-In thi\ caw the expccteci v;tlues of the en\ironmentalv;ir~able\ xrve as certainty equivalent\. so thatSEU maximiration recluires onl! I-eplacing the unkno\\ntr-ue \due\ by the\e expected balue\. See theauthor ( l9i7).defect of the SEU formulation is that whenit has been subjected to test in the laboratoryor the real \\,orld. even in relativelysimple situations. the behavior of humansubjects has generally departed ~videlyfrom it.Some of the evidence has been surveyedby Ward Ed\vnrds. and more recently byDaniel Kahneman and Amos Tversky.They describe experilnental situations in\\,hich estimates formed on the basis ofinitial information are not revised nearly asmuch by subsequent information as ~vouldhe required by Bayes' Theorem. In othersituations. suhjects respond largely to theinformation received most recently. andtake inadequate account of prior informatlon.Beha~ior that is rad~cally inconsistentuith the SEU frame\\ol-k occurs also innaturalistic settings. Ho\rard Kunreuther etal. have recently carried out extensivestudies of behavior and attitudes relating tothe purchase of flood insurance by personso\+ning property in lob-lying areas Theyfound that kno\+ledge of the ubailability ofinsurance. or rates. and of objective risksuas very imperfect. and that the actual deci5ionswhether or not to insure \+ere relatedmuch more to personul experienceuith floods than to an! objective factsabout the situation-or even to personalsubjective beliefs about those facts. In theface of this evidence. kt is hard to tahe Stbseriously as a theory of actual human behatior in the face of uncertainty .XFor situations u here the rationality of anaction depends upon hat others (uho arealso striving to be ration'll) do again. noconsensus has been reached as to \\hatconstitutes optimal behavior. This is one ofthe reasons I have else~bhere called imperfectcornpetltion "the permanent andineradicable scandal of economic theory"(I976b. p. 140). The most ~maginatike andXKunreuther et al. point out that thc theory cannothe "saved" by ass~~rning utility to be radically non-linear in money. In the Hood in\urance case. that interpretationof the data mould uork only if ue werenilling to as\ume that money has strongly itlc.retrsitlr:marginal utility. not a Ler) plausible e\cape route forthe theory.

ambitious attempt to resolve the difficulty\\as the von Neurnanti-Morgenstern theoryof garnes, \+,hich is embarrassing in thewealth of alternative solutions it offers.While the theory of garnes reveals thepotential richness of behavior uhen rationalindividuals are faced ~vith conflict ofinterest. the capability of reacting to eachother's actions (or expected actions). andpossibilities for coalition. it has provided nounique ancl universally accepted criterionof rationality to generalize the SEU criterionand extend it to this broader range ofsituations.The so-called "rational expectations"models, currently so popular (and due originallyto hluth). pass over these problemsrather than solving thern. They ignorepotential coalitions and attempted mutualoutguessing behavior. and correspond tooptitnal solutions only ~vhen the losses arequadratic functions of the errors of estimate.9Hence they do not correspond toany classical criterion of rationality. and labelingthem with that term. rather than themore neutral "consistent expectations."provides them ~vith a rather unwarrantedlegitimation.Finally. it should be retnarkerl that thernain motivation in economics for developingtheories of uncertainty and mutual expectationshas not been to replace substantivecriteria of rationality with pt-oceduralcriteria. but rather to find substantive criteriabroad enough to extend the concept ofrationality beyond the boundaries of staticoptirnizatioti under certainty. As M ithclassical decision theory. the interest liesnot in 11011. tiecisions are made but in n

C'OL. 68 .YO. 2 RIC'HARD T. EL Y LECTURE 1IThe theory of teams, as developed byMarschak and Radner. goes a step fartherin specifying the procedure of decision.That theory, as is hell known. is concernedwith the in~proven~ent that may be realizedin a team's decisions by interchange of informationamong the team members. Buthere the theory does not limit itself to determiningthe aggregate amount of informationthat should be transmitted, but seeks to calculateuhat messages should be exchanged,under bvhat conditions. and at what cost.The content of the communication as hellas the total amount of information becomesrelevant to the theory.In its attitude toward rationality. thetheory of teams is as "classical." houever.as is search theory. The bounds on the rationalityof the team members are"externalized" and represented as costs ofcommunication. so that they can be foldedinto the economic calculation along uiththe costs and benefits of outcomes.To find theories that compare the meritsof alternative search procedures. we mustlook largely outside the domain of economics.A number of such theories havebeen developed in the past thirty years.mainly by management scientists and researchersin the field of artificial intelligence.An important example is thebody of uork that has been done on integerprogramming.Integer programming problen~s resemblelinear programming problems (to maximizesome quantity, subject to constraints in theform of linear equations and inequalities).uith the added condition that certain variablescan only take whole numbers as theirvalues. The integer constraint makes inapplicablemost of the powerful computationalmethods available for solving linearprogramming problems. uith the result thatinteger programming problems are far lesstractable. computationally. than linearprogramming problen~s having comparablenumbers of variables.Solution methods for integer program-mlng problems use various forms of hlghlyselective search-for example branch-andboundmethods that establish successivelynarrobler limits for the value of the optimum.and hence permit a correspondingnarrow Ing of search to promising regions ofthe space. It becomes a matter ofconsiderable practical and theoreticalinterest to evaluate the relative computationalefficiency of competing searchprocedures. and also to estimate hob+ thecost of search u ill grou I+ith the size of theproblem posed. Until recently. mostevaluation of search algorithms has beenempirical: they have been tested on sampleproblems. Recently. however, a body oftheory-called theory of computationalcomplexity-has grown up that begins toanswer some of these questions in a moresystematic way.I cannot give here an account of thetheory of computational con~plexity. or allof its implications for procedural rationality.A good introduction I+i l l be foundin Alfred Aho et al. One important set ofresults that comes out of the theory does requireat least brief mention. These resultshave to do hith the way In ~hich theamount of computation requlred to solveproblems of a given class grous wlth thesize of the problems-wlth the number ofvariables. say . I0In a domain where computational requirementsgrow rapidly with problem slze,be will be able to solve only small problems;in domains uhere the requirementsgrou slowly. b+e ill be able to solve muchlarger problems. The problems that the realworld presents to us are generallyenormous compared 1+1th the problems thatwe can solve on even our largest computersHence. our computational modelsare al~bays rough approximations to thereality. and be must hope that the approximatlonb+ill not be too Inexact to be useful."'Most of the theorems in computational complexityhave to do uith the "worst case." that is. with themaximum amount of computation required to solventl? problem of the given class. Very feu results areavailable for the expected cost. averaged over all problemsof the class.

I2 A 1IERIC 4 \ LC0 VO MIC A5SOC14710 "L \lAl 1978We hill be particularly concerned that computationalcosts not increase rapidly ivithprobletn size.It is customary in the theory of computationalcomplexity to regard problems of agiven size as "tractable" if comp~~tationsdo not grow faster than at some fixed pouerof problem size. Such classes of problemsare known as "polynomial complex."Problems that grow exponentially in cornplexitywith size are not polynomial complex.since the rate of grouth of computationcomes to exceed any fixed pobver oftheir size.A large and important class of probletns~vhich includes the general integer programmingproblem. as well as standard schedulingproblems. all have been sho~vn to havethe same level of complexity-if one ispolynomial complex, then all are; if one isnot polynomial complex. then none are.These probletns have been labeled ",YPcomplete."It is conjectured. but not yetproven. that the class of IYP-completeprobletns is not polynotnially complex. butprobably exponentially complex.The significance of these findings andconjectures is in sho~ving that computationaldifficulties. and the need to approximate.are not just a minor annoying featureof our ~vorld to be dealt with by rnanufacturinglarger computers or breedingsmarter people. Cornplexity is deep in thenature of things. and discovering tolerableapproximation procedures and heuristicsthat pertnit huge spaces to be searched veryselectively lies at the heart of intelligence,uhether hurnan or artificial. A theory of rationalitythat does not give an account ofprobletn solving in the face of cotnplexity issadly incomplete. It is horse than incomplete:it can be seriously misleading by providing"solutions" to econornic questionsthat are w i t h o ~ operational ~ t significance.One interesting and important directionof research in cotnp~~tational co~nplexitylies in sho~ving how the complexity of problemsmight be decreased by lveakening therequirements for solution-by requiring solutionsonly to approximate the optimum.or by replacing an optitnality criterion by asatisficing criterion. Results are still frag-mentary. but it is already known that thereare some cases where such modificationsreduce exponential or NP-complete problernclasses to polynomial-completeclasses.The theory of heuristic search. cultivatedin artificial intelligence and informationprocessing psychology, is concerned withdevising or identifying search proceduresthat hill permit systems of limited computationalcapacity to make complex decisionsand solve difficult problems. (For ageneral survey of the theory. see NilsNilsson.) When a task environment has patternedstructure. so that solutions to asearch probletn are not scattered randornlythroughout it. but are located in bays relatedto the structure. then an intelligentsystem capable of detecting the pattern canexploit it in order to search for solutions ina highly selective h a y .One form. for example. of selectiveheuristic search. called best-first search.assigns to each node in the search space anestimate of the distance of that node frorn asolution. At each stage, the next incrementof effort is expended in searching frotn thenode. among those already reached, thathas the smallest distance estimate (see. forexample. the author and J.B. Kadane). Asanother example. when the task is to find agood or best solution, it may be possible toassign upper and lo~ver bounds on thevalues of the solutions that can be obtainedby searching a particular part of the space.If the upper bound on region A is lowerthan the lower bound on some other region.then region A does not need to be searchedat all.I hill leave the topics of computationalcotnplexity and heuristic search ~vith thesesketchy remarks. What implications thesedevelopments in the theory of proceduralrationality will have for econotnics definedas "the science ~vhich treats of the uealthgettingand wealth-using activities of man"remain to be seen. That they are an integralpart of economics defined as "the sciencewhich treats of the allocation of scarceresources" is obvious. The scarce resourceis cotnputational capacity-the mind. Theability of tnan to solve cotnplex problems,

and the m,ignitude of the resources thathave to be alloc'ited to solving them,depend on the efficiency \\ith \\hich thisresource. mind. is deployed.Finally. I uould like to turn from therather highly developed approaches toprocedural rationality that I have been discussingback to the more qualitative kindsof institutional issues that were consideredin the previous section of this paper. Manyof the central issues of our time are questionsof hou we use limited information andlimited computation~il capacity to deal c\ ithenormous problems whose shape we barelygrasp.For many purposes. a modern governmentcan be regarded as a parallel computingdevice. While one part of its capabilityfor rational problem solving is directed tofire protection. another is directed to pavinghigh~vays. ancl another to collectingrefi~se. For other important purposes. ugovernment. like a human being. is a serialprocessing system. capable of attending toonly one thing at u time. When importantnew policies must be formulated. publicand official attention must be focused onone or a few matters. Other concerns. nomatter how pressing. must wait their turnon the agenda. When the agenda becomescrowded. public life begins to appeal moreand more as a succession of crises. Whenproblems become interrelated. as energyand pollution problems have become. thereis the constant danger that attentiondirected to a single facet of the c\eb \\illspaun solutions that disregard vital consequencesfor the other t"icets. When oil isscarce, bve return to coal. but forget that wemust then deal with vastly increased quantitiesof sulfur oxides in our urban ail.. Orwe outlaw nuclear pouer stations becauseof radiation hazards, but fail to make alternativeprovi4ion to meet our energyneeds. It is futile to talk of substantive rationalityin public affairs without considering\\,hat p~ucedural means are available toorder issues on the public agenda in :t rationaluay. and to in5i11-e attention to the in-direct consequences of actions taken toreach specific goals or solve specific problems.In a uot.ld uhere information is relativelyscarce. and where p~.oblems for decisionare few and simple. information is almostal~vaysa positive good. In a cjorld whereattention is a major scarce resource. informationmay be an expensive luxury, forit may turn our attention frorn c\ hat is importantto uhat is unimportant. We cannotafford to attend to inforrnation simply becauseit is there. I am not aware that therehas been any systematic development of atheory of inforrnation and communicationthat treats attention rather than information21s the scarce resource." Some of thepractical consequences of attentionscarcity have already been noticed in businessand government. where early designsof so-called "management informationsystems" flooded executives with trivialdata and. until they learned to ignore them.dist~.itcted their attention from more irnportantmatters. It is probably true ofcontemporary organizations that an automatedinformation system that does notconsume and digest vastly more informationthan it produces and distributes harmsthe performance of the organization incjhich it is incorporated.The management of attention and tracingindirect consequences of action are two ofthe basic issues of procedural rationalitythat confront a modern society. There areothers of comparable importance: what decision-makingprocedure is rational whenthe basic quantities for making marginalcomparisons are simply not known? A fewyears ago. I served as chairman of a NationalAcademy of Sciences (,YAS) committeewhose job it Ivas to advise the Congresson the control of automobile emissions (see,YAS, Coordinating Committee on Ail-Quality Stuclies). It is easy to formulate anSEU model to conceptualize the problem.There is a production function for automobilesthat associates different costs with differentlevels of emissions. The laws govern-"Somc un\)\tc'matic ~-e~nnrk\ on the subject \rill br.found in the ;i~tho~.( 107hu. chs. 13. 1.1).

ing the chemistry of the atmosphere determinethe concentrations of pollutingsubstances in the air as a function of thelevels of emissions. Biomedical sciencetells us uhat effects on life and health canbe expected from various concentrations ofpollutants. ,411 we need do is to attach aprice tag to life and health. and ue can calculatethe optimum level of pollution control.There is only one hitch-which will beapparent to all of you. None of the relevantparameters of the various "productionfunctions" are knoun-except. within halfan order of magnitude, the cost of reducingthe emissions themselves. The physics andchemistry of the atmosphere presents aseries of unsolved problems-particularlyrelating to the photochemical reactions affectingthe oxides of nitrogen and ozone.Medical science is barely able to detect thatthere trr~health effects from pollutants,much less measure hou large these effectsare. The committee's deliberations led immediatelyto one conclusion-one thatcongressmen are 'tccustomed to hearingfrom such committees: We need more research.But uhile the I-esearch is beingdone. uh'tt provisions should be incorpor-utedin the Clean Air Act of 1977 (or theActs of 1978 through 2000. for that matter)''For- research won't give us clear answersthen either. What constitirtes procedural rationalityin such cir-cumstances?"Reasonable men" reach "reasonable"conclusions in circumstances uher-e theyhave no prospect of applying classicalmodels of s~rbstnntive rationality. We knowonly imper-fectly hou they do it. We knoueven less uhether- the ~rocedures thev usein place of the inapplicable models haveany merit-although most of us wouldchoose them in preference to drauing lots.The st~rdy of procedural r-ationality in circumstancesuhere attention is scarce.uher-e problems are immensely complex.and where crucial information is absentpresents a host of challenging and fundamentalresearch problems to anyone uho isinter-ested in the rational allocution ofscar-ce resources.IV. ConclusionIn histories of human civilization, theinvention of writing and the invention ofprinting are always treated as key events.Perhaps in future histories the invention ofelectrical communication and the inventionof the computer will receive comparableemphasis. What all of these developmentshave in common, and what makes them soimportant, is that they represent basicchanges in man's equipment for making rationalchoices-in his computational capabilities.Problems that are impossible tohandle with the head alone (multiplyinglarge numbers together. for example) becometrivial when they can be written downon paper. Interactions of energy and environmentthat almost defy conceptualizationlend themselves to at least approximatemodeling with modern computers.The advances in man's capacity forprocedural rationality are not limited tothese obvious examples. The invention ofalgebra. of analytic geometry, of the calculuswere such advances. So was theinvention. if we may call it that. of themodern organization, which greatlyincreased man's capacity for coordinatedparallel activity. Changes in the productionfunction for information and decisions arecentral to any account of changes over thecenturies of the human condition.In the past, econornics has largelyignored the processes that rational manuses in reaching his resource allocation decisions.This was possibly an acceptablestrategy for explaining rational decision instatic. relatively simple problem situationsuhere it might be assumed that additionalcomputational time or pouer could notchange the outcome. The strategy does notuosk. however. uhen ue are seeking toexplain the decision maker's behavior incomplex. dynamic circumstances that involvea great deal of uncertainty. and thatmake severe demands upon his attention.As economics acquires aspirations toexplain behavior under these typical conditionsof modern organizational and publiclife, it will have to devote major energy to

VOL. 68 NO. 2RICHARD 7. ELY LECTURE15building a theory of procedural rationalityto complement existing theories of substantiverationality. Some elements of such atheory can be borrowed from the neighboringdisciplines of operations research.artificial intelligence, and cognitivepsychology; but an enormous job remainsto be done to extend this work and to applyit to specifically economic problems.Jacob Marschak, throughout his longcareer, had a deep belief in and commitmentto the interdependencies and complementarityof the several social sciences. Ihave shared that belief and commitment,without always agreeing with him in detailas to the precise route for exploiting it. Thedevelopments I have been describingstrengthen greatly, it seems to me, the rationalgrounds for both belief and commitment.Whether ue accept the morerestricted definition of economics that Iquoted from Ely's textbook, or the uiderdefinition that is widely accepted today. Liehave every reason to try to communicatewith the other social sciences. both to findout what we have to 4ay that may be ofinterest to them. and to discover what theycan teach us about the nature of proceduralrationality.REFERENCESAlfred V. Aho et al., The Design and Analj,.si.soj'Compurer AIgorithm.s, Reading 1974.Chester I. Barnard, Thr Functions of' theExecutive, Cambridge 1938.G. S. Becker, "Irrational Behavior and EconomicTheory," J. Polir. Econ., Feb.1962, 70, 1-13.. "A Theory of Social Interations,"J. Polit. Econ., Nov./Dec. 1974, (92,1063-93.F. M. Cancian, "Functional Analysis," inInternational Ency~clopedia of' the SocialSciences, 1968.6, 29-42.R. M. Cyert and M. H. Degrott, "SequentialStrategies in Dual Control," Theor!,Decn., Apr. 1977,8, 173-92.Anthony Downs, An Econonzic Throrj. ofDemocracj,, New Y ork 1957.Maurice Duverger, Political Parties, rev. ed.,New York 1959, (Les Partis Politiques,Paris 1951).W. Edwards, "Conservation in Human InformationProcessing," in BenjaminKleinmuntz, ed., Forr~al Representationof'Human Thought, New York 1968.Richard T. Ely, Outlines of' Econonzics, rev.ed., New York 1930.S. Freud, "Five Lectures on Psychoanalysis"(originally "The Origin and Developmentof Psychoanalysis" 1910) in The ConzpletePsychological Works of SigrnundFreud, Vol. 11, London 1957.George Homans, Social Behavior: Its Elemmtar),Fornzs, New York 1961.D. Kahneman and A. Tversky, "On the Psychologyof Prediction," Psj.cho1. Rrv.,July 1973,80, 237-5 1.Janos Kornai, Anti-Eyuilihriunz, Amsterdam1971.Howard Kunreuther et al., Protecting AgainstHigh-Risk Hazards: Public Polic!. Lrssons,New York 1978.James G. March and Herbert A. Simon, Organizations,New York 1958.Jacob Marschak and Roy Radner, EcononzicTheor, of' Team.s, New Haven 1972.John M. Montias, The Structure of EcononlicSj>.stem.s,New Haven 1976.J. F. Muth, "Rational Expectations and theTheory of Price Movements," Econometrica,July 1961, ZY, 315-35.Nils Nilsson, Prohlerrl-Solving Methods inArtificial Intelligmce, New York 1971.A. Rees, "Econon~ics," in IntrrnationalEncj,cloprdiu qf the Social Sciences, 1968,4,472.William H. Riker, Thr Throrj oj' PoliticalCoalitions, New Haven 1962.and Peter C. Ordeshook, An Introductionto Positit~e Poliric*al Tlleorj,, NewJersey 1973.Paul Samuelson, Foundations of EconomicAnalj,.sis, Cambridge 1947.George Simmel, Soziologir, Berlin 1908.Herbert A. Simon, "A Formal Theory of theEmployment Relation," Encononzrrrica,July 1951, lY, 293305., "A Behavioral Model of Rational

115 A.MtRIC.AN tC'ONO.ZfIC ASSOC IA7lOl' MAY 1978Choice," Quart. J. Econ., Feb. 1955, 69,99-1 18,, "Dynamic Programming UnderUncertainty with a Quadratic CriterionFunction," Econot~lrtric,a,Jan. 1956, 24,74- 8 1 .,(1976a) Adn~inistrarivr Bcha~*ior, 3ded., New York 1976., (1976b) "From Substantive toProcedural Rationality," in Spiro J.Latsis, ed., Mcthod and Appraisal inEconomics, Cambridge 1976.a n d J. B. Kadane, "Optit~iai Problem-Solving Search: All-or-None Solutions,"Artificial Intel., Fall 1975,6, 23548.G. J. Stigler, "The Economics of Information,"J. Polit. Econ., June 1961, 69,213-15.a n d G. S. Becker, "De Gustibus nonest Disputandum," Anlrr. Econ. Rev.,Mar. 1977.67. 76-90.Oliver E. Williamson, Markets and Hierarchies,New York 1975.National Academy of Sciences, (hr,4S ) CoordinatingCommittee on Air QualityStudies, '4ir Qualitj! and Autot~~ohileEttlission Cot?trol, Vol. 1 summary rep.,Washington 1974.

http://www.jstor.orgLINKED CITATIONS- Page 1 of 2 -You have printed the following article:Rationality as Process and as Product of ThoughtHerbert A. SimonThe American Economic Review, Vol. 68, No. 2, Papers and Proceedings of the Ninetieth AnnualMeeting of the American Economic Association. (May, 1978), pp. 1-16.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28197805%2968%3A2%3C1%3ARAPAAP%3E2.0.CO%3B2-4This article references the following linked citations. If you are trying to access articles from anoff-campus location, you may be required to first logon via your library web site to access JSTOR. Pleasevisit your library's website or contact a librarian to learn about options for remote access to JSTOR.[Footnotes]2 Irrational Behavior and Economic TheoryGary S. BeckerThe Journal of Political Economy, Vol. 70, No. 1. (Feb., 1962), pp. 1-13.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28196202%2970%3A1%3C1%3AIBAET%3E2.0.CO%3B2-J6 Irrational Behavior and Economic TheoryGary S. BeckerThe Journal of Political Economy, Vol. 70, No. 1. (Feb., 1962), pp. 1-13.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28196202%2970%3A1%3C1%3AIBAET%3E2.0.CO%3B2-JReferencesIrrational Behavior and Economic TheoryGary S. BeckerThe Journal of Political Economy, Vol. 70, No. 1. (Feb., 1962), pp. 1-13.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28196202%2970%3A1%3C1%3AIBAET%3E2.0.CO%3B2-JNOTE: The reference numbering from the original has been maintained in this citation list.

http://www.jstor.orgLINKED CITATIONS- Page 2 of 2 -A Theory of Social InteractionsGary S. BeckerThe Journal of Political Economy, Vol. 82, No. 6. (Nov. - Dec., 1974), pp. 1063-1093.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28197411%2F12%2982%3A6%3C1063%3AATOSI%3E2.0.CO%3B2-WRational Expectations and the Theory of Price MovementsJohn F. MuthEconometrica, Vol. 29, No. 3. (Jul., 1961), pp. 315-335.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28196107%2929%3A3%3C315%3AREATTO%3E2.0.CO%3B2-GDynamic Programming Under Uncertainty with a Quadratic Criterion FunctionHerbert A. SimonEconometrica, Vol. 24, No. 1. (Jan., 1956), pp. 74-81.Stable URL:http://links.jstor.org/sici?sici=0012-9682%28195601%2924%3A1%3C74%3ADPUUWA%3E2.0.CO%3B2-5The Economics of InformationGeorge J. StiglerThe Journal of Political Economy, Vol. 69, No. 3. (Jun., 1961), pp. 213-225.Stable URL:http://links.jstor.org/sici?sici=0022-3808%28196106%2969%3A3%3C213%3ATEOI%3E2.0.CO%3B2-DDe Gustibus Non Est DisputandumGeorge J. Stigler; Gary S. BeckerThe American Economic Review, Vol. 67, No. 2. (Mar., 1977), pp. 76-90.Stable URL:http://links.jstor.org/sici?sici=0002-8282%28197703%2967%3A2%3C76%3ADGNED%3E2.0.CO%3B2-8NOTE: The reference numbering from the original has been maintained in this citation list.

Why We Have Never Used the Black-Scholes-Merton Option Pricing FormulaEspen Gaarder Haug & Nassim Nicholas TalebJanuary 2008- Fourth VersionAbstract: Options traders use a pricing formula which they adapt by fudgingand changing the tails and skewness by varying one parameter, the standarddeviation of a Gaussian. Such formula is popularly called “Black-Scholes-Merton”owing to an attributed eponymous discovery (though changing the standarddeviation parameter is in contradiction with it). However we have historicalevidence that 1) Black, Scholes and Merton did not invent any formula, justfound an argument to make a well known (and used) formula compatible withthe economics establishment, by removing the “risk” parameter through“dynamic hedging”, 2) Option traders use (and evidently have used since 1902)heuristics and tricks more compatible with the previous versions of the formulaof Louis Bachelier and Edward O. Thorp (that allow a broad choice of probabilitydistributions) and removed the risk parameter by using put-call parity. 3) Optiontraders did not use formulas after 1973 but continued their bottom-up heuristics.The Bachelier-Thorp approach is more robust (among other things) to the highimpact rare event. The paper draws on historical trading methods and 19 th andearly 20 th century references ignored by the finance literature. It is time to stopcalling the formula by the wrong name.BREAKING THE CHAIN OF TRANSMISSIONFor us, practitioners, theories should arise frompractice 1 . This explains our concern with the “scientific”notion that practice should fit theory. Option hedging,pricing, and trading is neither philosophy normathematics. It is a rich craft with traders learningfrom traders (or traders copying other traders) andtricks developing under evolution pressures, in abottom-up manner. It is technë, not ëpistemë. Had itbeen a science it would not have survived – for theempirical and scientific fitness of the pricing andhedging theories offered are, we will see, at best,defective and unscientific (and, at the worst, thehedging methods create more risks than they reduce).Our approach in this paper is to ferret out historicalevidence of technë showing how option traders wentabout their business in the past.Options, we will show, have been extremely active inthe pre-modern finance world. Tricks and heuristicallyderived methodologies in option trading and riskmanagement of derivatives books have been developedover the past century, and used quite effectively byoperators. In parallel, many derivations were producedby mathematical researchers. The economics literature,1 For us, in this discussion, a practitioner is deemed to besomeone involved in repeated decisions about option hedging,not a support quant who writes pricing software or anacademic who provides “consulting” advice.however, did not recognize these contributions,substituting the rediscoveries or subsequentreformulations done by (some) economists. There isevidence of an attribution problem with Black-Scholes-Merton option “formula”, which was developed, used,and adapted in a robust way by a long tradition ofresearchers and used heuristically by option bookrunners. Furthermore, in a case of scientific puzzle, theexact formula called “Black-Sholes-Merton” was writtendown (and used) by Edward Thorp which,paradoxically, while being robust and realistic, has beenconsidered unrigorous. This raises the following: 1) TheBlack Scholes Merton was just a neoclassical financeargument, no more than a thought experiment 2 , 2) Weare not aware of traders using their argument or theirversion of the formula.It is high time to give credit where it belongs.THE BLACK-SCHOLES-MERTON “FORMULA” WAS ANARGUMENTOption traders call the formula they use the “Black-Scholes-Merton” formula without being aware that by2 Here we question the notion of confusing thoughtexperiments in a hypothetical world, of no predictive power,with either science or practice. The fact that the Black-Scholes-Merton argument works in a Platonic world and appears to be“elegant” does not mean anything since one can alwaysproduce a Platonic world in which a certain equation works, orin which a “rigorous” proof can be provided, a process calledreverse-engineering.

some irony, of all the possible options formulas thathave been produced in the past century, what is calledthe Black-Scholes-Merton “formula” (after Black andScholes, 1973, and Merton, 1973) is the one thefurthest away from what they are using. In fact of theformulas written down in a long history it is the onlyformula that is fragile to jumps and tail events.First, something seems to have been lost in translation:Black and Scholes (1973) and Merton (1973) actuallynever came up with a new option formula, but only antheoretical economic argument built on a new way of“deriving”, rather rederiving, an already existing –andwell known –formula. The argument, we will see, isextremely fragile to assumptions. The foundations ofoption hedging and pricing were already far more firmlylaid down before them. The Black-Scholes-Mertonargument, simply, is that an option can be hedgedusing a certain methodology called “dynamic hedging”and then turned into a risk-free instrument, as theportfolio would no longer be stochastic. Indeed whatBlack, Scholes and Merton did was “marketing”, findinga way to make a well-known formula palatable to theeconomics establishment of the time, little else, and infact distorting its essence.Such argument requires strange far-fetchedassumptions: some liquidity at the level of transactions,knowledge of the probabilities of future events (in aneoclassical Arrow-Debreu style) 3 , and, more critically,a certain mathematical structure that requires “thintails”,or mild randomness, on which, later. The entireargument is indeed, quite strange and ratherinapplicable for someone clinically and observationdrivenstanding outside conventional neoclassicaleconomics. Simply, the dynamic hedging argument isdangerous in practice as it subjects you to blowups; itmakes no sense unless you are concerned withneoclassical economic theory. The Black-Scholes-Merton argument and equation flow a top-downgeneral equilibrium theory, built upon the assumptionsof operators working in full knowledge of the probabilitydistribution of future outcomes –in addition to acollection of assumptions that, we will see, are highlyinvalid mathematically, the main one being the ability tocut the risks using continuous trading which only worksin the very narrowly special case of thin-taileddistributions. But it is not just these flaws that make itinapplicable: option traders do not “buy theories”,particularly speculative general equilibrium ones, whichthey find too risky for them and extremely lacking in3 Of all the misplaced assumptions of Black Scholes thatcause it to be a mere thought experiment, though an extremelyelegant one, a flaw shared with modern portfolio theory, is thecertain knowledge of future delivered variance for the randomvariable (or, equivalently, all the future probabilities). This iswhat makes it clash with practice –the rectification by themarket fattening the tails is a negation of the Black-Scholesthought experiment.standards of reliability. A normative theory is, simply,not good for decision-making under uncertainty(particularly if it is in chronic disagreement withempirical evidence). People may take decisions basedon speculative theories, but avoid the fragility oftheories in running their risks.Yet professional traders, including the authors (and,alas, the Swedish Academy of Science) have operatedunder the illusion that it was the Black-Scholes-Merton“formula” they actually used –we were told so. Thismyth has been progressively reinforced in the literatureand in business schools, as the original sources havebeen lost or frowned upon as “anecdotal” (Merton,1992).Figure 1 The typical "risk reduction" performedby the Black-Scholes-Merton argument. Theseare the variations of a dynamically hedgedportfolio. BSM indeed "smoothes" out risks butexposes the operator to massive tail events –reminiscent of such blowups as LTCM. Otheroption formulas are robust to the rare event andmake no such claims.This discussion will present our real-world, ecologicalunderstanding of option pricing and hedging based onwhat option traders actually do and did for more than ahundred years.This is a very general problem. As we said, optiontraders develop a chain of transmission of technë, likemany professions. But the problem is that the “chain” isoften broken as universities do not store the acquiredskills by operators. Effectively plenty of robustheuristically derived implementations have beendeveloped over the years, but the economicsestablishment has refused to quote them oracknowledge them. This makes traders need to relearnmatters periodically. Failure of dynamic hedging in1987, by such firm as Leland O’Brien Rubinstein, forinstance, does not seem to appear in the academicliterature published after the event 4 (Merton, 1992,4 For instance –how mistakes never resurface into theconsciousness, Mark Rubinstein was awarded in 1995 the2© Copyright 2007 by N. N. Taleb.

Rubinstein, 1998, Ross, 2005); to the contrary dynamichedging is held to be a standard operation 5 .There are central elements of the real world that canescape them –academic research without feedbackfrom practice (in a practical and applied field) can causethe diversions we witness between laboratory andecological frameworks. This explains why some manyfinance academics have had the tendency to makesmooth returns, then blow up using their own theories 6 .We started the other way around, first by years ofoption trading doing million of hedges and thousands ofoption trades. This in combination with investigatingthe forgotten and ignored ancient knowledge in optionpricing and trading we will explain some commonmyths about option pricing and hedging.There are indeed two myths:• That we had to wait for the Black-Scholes-Merton options formula to trade the product,price options, and manage option books. Infact the introduction of the Black, Scholes andMerton argument increased our risks and setus back in risk management. More generally, itis a myth that traders rely on theories, evenless a general equilibrium theory, to priceoptions.• That we “use” the Black-Scholes-Mertonoptions “pricing formula”. We, simply don’t.In our discussion of these myth we will focus on thebottom-up literature on option theory that has beenhidden in the dark recesses of libraries. And thataddresses only recorded matters –not the actualpractice of option trading that has been lost.MYTH 1: PEOPLE DID NOT PROPERLY “PRICE” OPTIONSBEFORE THE BLACK-SCHOLES-MERTON THEORYIt is assumed that the Black-Scholes-Merton theory iswhat made it possible for option traders to calculatetheir delta hedge (against the underlying) and to priceoptions. This argument is highly debatable, bothhistorically and analytically.Options were actively trading at least already in the1600 as described by Joseph De La Vega –implyingsome form of technë, a heuristic method to price themFinancial Engineer of the Year award by the InternationalAssociation of Financial Engineers. There was no mention ofportfolio insurance and the failure of dynamic hedging.6 For a standard reaction to a rare event, see the following:"Wednesday is the type of day people will remember in quantlandfor a very long time," said Mr. Rothman, a University ofChicago Ph.D. who ran a quantitative fund before joiningLehman Brothers. "Events that models only predicted wouldhappen once in 10,000 years happened every day for threedays." One 'Quant' Sees Shakeout For the Ages -- '10,000Years' By Kaja Whitehouse, August 11, 2007; Page B3.and deal with their exposure. De La Vega describesoption trading in the Netherlands, indicating thatoperators had some expertise in option pricing andhedging. He diffusely points to the put-call parity, andhis book was not even meant to teach people about thetechnicalities in option trading. Our insistence on theuse of Put-Call parity is critical for the following reason:The Black-Scholes-Merton’s claim to fame is removingthe necessity of a risk-based drift from the underlyingsecurity –to make the trade “risk-neutral”. But one doesnot need dynamic hedging for that: simple put callparity can suffice (Derman and Taleb, 2005), as we willdiscuss later. And it is this central removal of the “riskpremium”that apparently was behind the decision bythe Nobel committee to grant Merton and Scholes the(then called) Bank of Sweden Prize in Honor of AlfredNobel: “Black, Merton and Scholes made a vitalcontribution by showing that it is in fact not necessaryto use any risk premium when valuing an option. Thisdoes not mean that the risk premium disappears;instead it is already included in the stock price.” 7 It isfor having removed the effect of the drift on the valueof the option, using a thought experiment, that theirwork was originally cited, something that wasmechanically present by any form of trading andconverting using far simpler techniques.Options have a much richer history than shown in theconventional literature. Forward contracts seems todate all the way back to Mesopotamian clay tabletsdating all the way back to 1750 B.C. Gelderblom andJonker (2003) show that Amsterdam grain dealers hadused options and forwards already in 1550.In the late 1800 and the early 1900 there were activeoption markets in London and New York as well as inParis and several other European exchanges. Markets itseems, were active and extremely sophisticated optionmarkets in 1870. Kairys and Valerio (1997) discuss themarket for equity options in USA in the 1870s, indirectlyshowing that traders were sophisticated enough toprice for tail events 8 .7 see www.Nobel.se8 The historical description of the market is informativeuntil Kairys and Valerio try to gauge whether options in the1870s were underpriced or overpriced (using Black-Scholes-Merton style methods). There was one tail-event in this period,the great panic of September 1873. Kairys and Valerio find thatholding puts was profitable, but deem that the market panicwas just a one-time event :“However, the put contracts benefit from the “financialpanic” that hit the market in September, 1873. Viewingthis as a “one-time” event, we repeat the analysis for putsexcluding any unexpired contracts written before the stockmarket panic.”Using references to the economic literature that also concludethat options in general were overpriced in the 1950s 1960s and1970s they conclude: "Our analysis shows that optioncontracts were generally overpriced and were unattractive forretail investors to purchase”. They add: ”Empirically we findthat both put and call options were regularly overpricedrelative to a theoretical valuation model."3© Copyright 2007 by N. N. Taleb.

There was even active option arbitrage trading takingplace between some of these markets. There is a longlist of missing treatises on option trading: we traced atleast ten German treatises on options written betweenthe late 1800s and the hyperinflation episode 9 .One informative extant source, Nelson (1904), speaksvolumes: An option trader and arbitrageur, S.A. Nelsonpublished a book “The A B C of Options and Arbitrage”based on his observations around the turn o thetwentieth century. According to Nelson (1904) up to500 messages per hour and typically 2000 to 3000messages per day where sent between the London andthe New York market through the cable companies.Each message was transmitted over the wire system inless than a minute. In a heuristic method that wasrepeated in Dynamic Hedging by one of the authors,(Taleb,1997), Nelson, describe in a theory-free waymany rigorously clinical aspects of his arbitragebusiness: the cost of shipping shares, the cost ofinsuring shares, interest expenses, the possibilities toswitch shares directly between someone being longsecurities in New York and short in London and in thisway saving shipping and insurance costs, as well asmany more tricks etc.The formal financial economics canon does not includehistorical sources from outside economics, a mechanismdiscussed in Taleb (2007a). The put-call parity wasaccording to the formal option literature first fullydescribed by Stoll (1969), but neither he not others inthe field even mention Nelson. Not only was the putcallparity argument fully understood and described indetail by Nelson (1904), but he, in turn, makes frequentreference to Higgins (1902). Just as an example Nelson(1904) referring to Higgins (1902) writes:“It may be worthy of remark that ‘calls’ are moreoften dealt than ‘puts’ the reason probably beingthat the majority of ‘punters’ in stocks and sharesare more inclined to look at the bright side of things,These results are contradicted by the practitioner Nelson(1904): “…the majority of the great option dealers who havefound by experience that it is the givers, and not the takers, ofoption money who have gained the advantage in the long run”.9 Here is a partial list:Bielschowsky, R (1892): Ueber die rechtliche Natur derPrämiengeschäfte, Bresl. Genoss.-BuchdrGranichstaedten-Czerva, R (1917): Die Prämiengeschäftean der Wiener Börse, Frankfurt am MainHolz, L. (1905) Die Prämiengeschäfte, Thesis (doctoral)--Universität RostockKitzing, C. (1925): Prämiengeschäfte : Vorprämien-,Rückprämien-, Stellagen- u. Nochgeschäfte ; Die solidestenSpekulationsgeschäfte mit Versicherg auf Kursverlust, BerlinLeser, E, (1875): Zur Geschichte der PrämiengeschäfteSzkolny, I. (1883): Theorie und praxis derprämiengeschäfte nach einer originalen methode dargestellt.,Frankfurt am MainAuthor Unknown (1925): Das Wesen derPrämiengeschäfte, Berlin : Eugen Bab & Co., Bankgeschäftand therefore more often ‘see’ a rise than a fall inprices.This special inclination to buy ‘calls’ and to leave the‘puts’ severely alone does not, however, tend tomake ‘calls’ dear and ‘puts’ cheap, for it can beshown that the adroit dealer in options can converta ‘put’ into a ‘call,’ a ‘call’ into a ‘put’, a ‘call o’ more’into a ‘put- and-call,’ in fact any option into another,by dealing against it in the stock. We may thereforeassume, with tolerable accuracy, that the ‘call’ of astock at any moment costs the same as the ‘put’ ofthat stock, and half as much as the Put-and-Call.”The Put-and-Call was simply a put plus a call with thesame strike and maturity, what we today would call astraddle. Nelson describes the put-call parity over manypages in full detail. Static market neutral delta hedgingwas also known at that time, in his book Nelson forexample writes:“Sellers of options in London as a result of longexperience, if they sell a Call, straightway buy halfthe stock against which the Call is sold; or if a Put issold; they sell half the stock immediately.”We must interpret the value of this statement in thelight that standard options in London at that time wereissued at-the-money (as explicitly pointed out byNelson); furthermore, all standard options in Londonwere European style. In London in- or out-of-themoneyoptions where only traded occasionally andwhere known as “fancy options”. It is quite clear fromthis and the rest of Nelson’s book that that the optiondealers where well aware of the delta for at-the-moneyoptions was approximately 50%. As a matter of fact atthe-moneyoptions trading in London at that time wereadjusted to be struck to be at-the-money forward, inorder to make puts and calls of the same price. Weknow today know that options that are at-the-moneyforward and not have very long time to maturity have adelta very close to 50% (naturally minus 50% for puts).The options in London at that time typically had onemonth to maturity when issued.Nelson also diffusely points to dynamic delta hedging,and that it worked better in theory than practice (seeHaug, 2007). It is clearly from all the details describedby Nelson that options in the early 1900 traded activelyand that option traders at that time in no way felthelpless in either pricing or in hedging them.Herbert Filer was another option trader that wasinvolved in option trading from 1919 to the 1960s.Filler(1959) describes what must be consider areasonable active option market in New York andEurope in the early 1920s and 1930s. Filer mentionhowever that due to World War II there was no tradingon the European Exchanges, for they were closed.Further, he mentions that London option trading did notresume before 1958. In the early 1900, option tradersin London were considered to be the mostsophisticated, according to Nelson. It could well be thatWorld War II and the subsequent shutdown of option4© Copyright 2007 by N. N. Taleb.

trading for many years was the reason known robustarbitrage principles about options were forgotten andalmost lost, to be partly re-discovered by financeprofessors such as Stoll (1969).Earlier, in 1908, Vinzenz Bronzin published a bookderiving several option pricing formulas, and a formulavery similar to what today is known as the Black-Scholes-Merton formula. Bronzin based his risk-neutraloption valuation on robust arbitrage principles such asthe put-call parity and the link between the forwardprice and call and put options –in a way that wasrediscovered by Derman and Taleb (2005) 10 . Indeed,the put-call parity restriction is sufficient to remove theneed to incorporate a future return in the underlyingsecurity –it forces the lining up of options to theforward price 11 .Again, 1910 Henry Deutsch describes put-call parity butin less detail than Higgins and Nelson. In 1961 Reinachagain described the put-call parity in quite some detail(another text typically ignored by academics). Tradersat New York stock exchange specializing in using theput-call parity to convert puts into calls or calls intoputs was at that time known as Converters. Reinach(1961):“Although I have no figures to substantiate myclaim, I estimate that over 60 per cent of allCalls are made possible by the existence ofConverters.”In other words the converters (dealers) who basicallyoperated as market makers were able to operate andhedge most of their risk by “statically” hedging optionswith options. Reinach wrote that he was an optiontrader (Converter) and gave examples on how he andhis colleagues tended to hedge and arbitrage optionsagainst options by taking advantage of optionsembedded in convertible bonds:“Writers and traders have figured out otherprocedures for making profits writing Puts &10 The argument Derman Taleb(2005) was present inTaleb (1997) but remained unnoticed.11 Ruffino and Treussard (2006) accept that one couldhave solved the risk-premium by happenstance, not realizingthat put-call parity was so extensively used in history. But theyfind it insufficient. Indeed the argument may not be sufficientfor someone who subsequently complicated the representationof the world with some implements of modern finance such as“stochastic discount rates” –while simplifying it at the sametime to make it limited to the Gaussian and allowing dynamichedging. They write that “the use of a non-stochastic discountrate common to both the call and the put options isinconsistent with modern equilibrium capital asset pricingtheory.” Given that we have never seen a practitioner use“stochastic discount rate”, we, like our option tradingpredecessors, feel that put-call parity is sufficient & does thejob.The situation is akin to that of scientists lecturing birds onhow to fly, and taking credit for their subsequent performance–except that here it would be lecturing them the wrong way.Calls. Most are too specialized for all but theseasoned professional. One such procedure isthe ownership of a convertible bonds and thenwriting of Calls against the stock into which thebonds are convertible. If the stock is calledconverted and the stock is delivered.”Higgins, Nelson and Reinach all describe the greatimportance of the put-call parity and to hedge optionswith options. Option traders where in no way helplessin hedging or pricing before the Black-Scholes-Mertonformula. Based on simple arbitrage principles theywhere able to hedge options more robustly than withBlack- Scholes-Merton. As already mentioned staticmarket-neutral delta hedging was described by Higginsand Nelson in 1902 and 1904. Also, W. D. Gann (1937)discusses market neutral delta hedging for at-themoneyoptions, but in much less details than Nelson(1904). Gann also indicates some forms of auxiliarydynamic hedging.Mills (1927) illustrates how jumps and fat tails werepresent in the literature in the pre-Modern PortfolioTheory days. He writes: ”A distribution may departwidely from the Gaussian type because the influence ofone or two extreme price change.”Option Formulas and Delta HedgingWhich brings us to option pricing formulas. The firstidentifiable one was Bachelier (1900). Sprenkle (1962)extended Bacheliers work to assume lognormal ratherthan normal distributed asset price. It also avoidsdiscounting (to no significant effect since manymarkets, particularly the U.S., option premia were paidat expiration).James Boness (1964) also assumed a lognormal assetprice. He derives a formula for the price of a calloption that is actually identical to the Black-Scholes-Merton 1973 formula, but the way Black, Scholes andMerton derived their formula based on continuousdynamic delta hedging or alternatively based on CAPMthey were able to get independent of the expected rateof return. It is in other words not the formula itself thatis considered the great discovery done by Black,Scholes and Merton, but how they derived it. This isamong several others also pointed out by Rubinstein(2006):“The real significance of the formula to thefinancial theory of investment lies not in itself,but rather in how it was derived. Ten yearsearlier the same formula had been derived byCase M. Sprenkle (1962) and A. James Boness(1964).”Samuelson (1969) and Thorp (1969) publishedsomewhat similar option pricing formulas to Boness andSprenkle. Thorp (2007) claims that he actually had anidentical formula to the Black-Scholes-Merton formula5© Copyright 2007 by N. N. Taleb.

programmed into his computer years before Black,Scholes and Merton published their theory.Now, delta hedging. As already mentioned staticmarket-neutral delta hedging was clearly described byHiggins and Nelson 1902 and 1904. Thorp and Kassouf(1967) presented market neutral static delta hedging inmore details, not only for at-the-money options, but foroptions with any delta. In his 1969 paper Thorp isshortly describing market neutral static delta hedging,also briefly pointed in the direction of some dynamicdelta hedging, not as a central pricing device, but arisk-management tool. Filer also points to dynamichedging of options, but without showing muchknowledge about how to calculate the delta. Another“ignored” and “forgotten” text is a book/bookletpublished in 1970 by Arnold Bernhard & Co. Theauthors are clearly aware of market neutral static deltahedging or what they name “balanced hedge” for anylevel in the strike or asset price. This book has multipleexamples of how to buy warrants or convertible bondsand construct a market neutral delta hedge by shortingthe right amount of common shares. Arnold Bernhard &Co also published deltas for a large number of warrantsand convertible bonds that they distributed to investorson Wall Street.Referring to Thorp and Kassouf (1967), Black, Scholesand Merton took the idea of delta hedging one stepfurther, Black and Scholes (1973):“If the hedge is maintained continuously, then theapproximations mentioned above become exact, andthe return on the hedged position is completelyindependent of the change in the value of the stock. Infact, the return on the hedged position becomescertain. This was pointed out to us by Robert Merton.”This may be a brilliant mathematical idea, but optiontrading is not mathematical theory. It is not enough tohave a theoretical idea so far removed from reality thatis far from robust in practice. What is surprising is thatthe only principle option traders do not use and cannotuse is the approach named after the formula, which is apoint we discuss next.MYTH 2: OPTION TRADERS TODAY “USE” THE BLACK-SCHOLES-MERTON FORMULATraders don’t do “Valuation”First, operationally, a price is not quite “valuation”.Valuation requires a strong theoretical framework withits corresponding fragility to both assumptions and thestructure of a model. For traders, a “price” produced tobuy an option when one has no knowledge of theprobability distribution of the future is not “valuation”,but an expedient. Such price could change. Theirbeliefs do not enter such price. It can also bedetermined by his inventory.This distinction is critical: traders are engineers,whether boundedly rational (or even non interested inany form of probabilistic rationality), they are not privyto informational transparency about the future states ofthe world and their probabilities. So they do not need ageneral theory to produce a price –merely theavoidance of Dutch-book style arbitrages against them,and the compatibility with some standard restriction: Inaddition to put-call parity, a call of a certain strike Kcannot trade at a lower price than a call K+!K(avoidance of negative call and put spreads), a callstruck at K and a call struck at K+2 !K cannot be moreexpensive that twice the price of a call struck at K+!K(negative butterflies), horizontal calendar spreadscannot be negative (when interest rates are low), andso forth. The degrees of freedom for traders are thusreduced: they need to abide by put-call parity andcompatibility with other options in the market.In that sense, traders do not perform “valuation” withsome “pricing kernel” until the expiration of thesecurity, but, rather, produce a price of an optioncompatible with other instruments in the markets, witha holding time that is stochastic. They do not need topdown“science”.When do we value?If you find traders operated solo, in a desert island,having for some to produce an option price and hold itto expiration, in a market in which the forward isabsent, then some valuation would be necessary –butthen their book would be minuscule. And this thoughtexperiment is a distortion: people would not tradeoptions unless they are in the business of tradingoptions, in which case they would need to have a bookwith offsetting trades. For without offsetting trades, wedoubt traders would be able to produce a positionbeyond a minimum (and negligible) size as dynamichedging not possible. (Again we are not aware of manynon-blownup option traders and institutions who havemanaged to operate in the vacuum of the BlackScholes-Merton argument). It is to the impossibility ofsuch hedging that we turn next.On the Mathematical Impossibility ofDynamic HedgingFinally, we discuss the severe flaw in the dynamichedging concept. It assumes, nay, requires all momentsof the probability distribution to exist 12 .12 Merton (1992) seemed to accept the inapplicability ofdynamic hedging but he perhaps thought that these ills wouldbe cured thanks to his prediction of the financial world“spiraling towards dynamic completeness”. Fifteen years later,we have, if anything, spiraled away from it.6© Copyright 2007 by N. N. Taleb.

Assume that the distribution of returns has a scale-freeor fractal property that we can simplify as follows: for xlarge enough, (i.e. “in the tails”), P[X>n x]/P[X>x]depends on n, not on x. In financial securities, say,where X is a daily return, there is no reason forP[X>20%]/P[X>10%] to be different fromP[X>15%]/P[X>7.5%]. This self-similarity at all scalesgenerates power-law, or Paretian, tails, i.e., above acrossover point, P[X>x]=K x -! . It happens, looking atmillions of pieces of data, that such property holds inmarkets –all markets, baring sample error. Foroverwhelming empirical evidence, see Mandelbrot(1963), which predates Black-Scholes-Merton (1973)and the jump-diffusion of Merton (1976); see alsoStanley et al. (2000), and Gabaix et al. (2003). Theargument to assume the scale-free is as follows: thedistribution might have thin tails at some point (sayabove some value of X). But we do not know wheresuch point is –we are epistemologically in the dark as towhere to put the boundary, which forces us to useinfinity.Some criticism of these “true fat-tails” accept that suchproperty might apply for daily returns, but, owing to theCentral Limit Theorem, the distribution is held tobecome Gaussian under aggregation for cases in which! is deemed higher than 2. Such argument does nothold owing to the preasymptotics of scalabledistributions: Bouchaud and Potters (2003) andMandelbrot and Taleb (2007) argue that thepresasymptotics of fractal distributions are such thatthe effect of the Central Limit Theorem are exceedinglyslow in the tails –in fact irrelevant. Furthermore, thereis sampling error as we have less data for longerperiods, hence fewer tail episodes, which give an insampleillusion of thinner tails. In addition, the pointthat aggregation thins out the tails does not hold fordynamic hedging –in which the operator dependsnecessarily on high frequency data and their statisticalproperties. So long as it is scale-free at the time periodof dynamic hedge, higher moments become explosive,“infinite” to disallow the formation of a dynamicallyhedge portfolio. Simply a Taylor expansion is impossibleas moments of higher order that 2 matter critically –one of the moments is going to be infinite.The mechanics of dynamic hedging are as follows.Assume the risk-free interest rate of 0 with no loss ofgenerality. The canonical Black-Scholes-Merton packageconsists in selling a call and purchasing shares of stockthat provide a hedge against instantaneous moves inthe security. Thus the portfolio " locally "hedged"against exposure to the first moment of the distributionis the following:Take the discrete time change in the values of theportfolioBy expanding around the initial values of S, we havethe changes in the portfolio in discrete time.Conventional option theory applies to the Gaussian inwhich all orders higher than !S 2 and disappears rapidly.Taking expectations on both sides, we can see herevery strict requirements on moment finiteness: allmoments need to converge. If we include another term,of order !S 3 , such term may be of significance in aprobability distribution with significant cubic or quarticterms. Indeed, although the n th derivative with respectto S can decline very sharply, for options that have astrike K away from the center of the distribution, itremains that the delivered higher orders of !S arerising disproportionately fast for that to carry amitigating effect on the hedges.So here we mean all moments--no approximation. Thelogic of the Black-Scholes-Merton so-called solutionthanks to Ito's lemma was that the portfolio collapsesinto a deterministic payoff. But let us see how quicklyor effectively this works in practice.The Actual Replication process is as follows: The payoffof a call should be replicated with the following streamof dynamic hedges, the limit of which can be seen here,between t and TSuch policy does not match the call value: thedifference remains stochastic (while according to BlackScholes it should shrink). Unless one lives in a fantasyworld in which such risk reduction is possible 13 .Further, there is an inconsistency in the works ofMerton making us confused as to what theory findsacceptable: in Merton (1976) he agrees that we canuse Bachelier-style option derivation in the presence ofjumps and discontinuities –no dynamic hedging– butonly when the underlying stock price is uncorrelated towhere C is the call price, and S the underlying security.13 We often hear the misplaced comparison to Newtonianmechanics. It supposedly provided a good approximation untilwe had relativity. The problem with the comparison is that thethin-tailed distributions are not approximations for fat-tailedones: there is a deep qualitative difference.7© Copyright 2007 by N. N. Taleb.

the market. This seems to be an admission thatdynamic hedging argument applies only to somesecurities: those that do not jump and are correlated tothe market.Figure 2 A 25% Gap in Ericsson, one of the MostLiquid Stocks in the World. Such move candominate hundreds of weeks of dynamichedging.The Robustness of the GaussianThe success of the “formula” last developed by Thorp,and called “Black-Scholes-Merton” was due to a simpleattribute of the Gaussian: you can express anyprobability distribution in terms of Gaussian, even if ithas fat tails, by varying the standard deviation # at thelevel of the density of the random variable. It does notmean that you are using a Gaussian, nor does it meanthat the Gaussian is particularly parsimonious (sinceyou have to attach a # for every level of the price). Itsimply mean that the Gaussian can express anythingyou want if you add a function for the parameter #,making it function of strike price and time to expiration.This “volatility smile”, i.e., varying one parameter toproduce #(K), or “volatility surface”, varying twoparameter, #(S,t) is effectively what was done indifferent ways by Dupire(1994, 2005) and Derman(1994,1998), see Gatheral(2006). They assume avolatility process not because there is necessarily sucha thing –only as a method of fitting option prices to aGaussian. Furthermore, although the Gaussian hasfinite second moment (and finite all higher moments aswell), you can express a scalable with infinite varianceusing Gaussian “volatility surface”. One strong constrainon the # parameter is that it must be the same for aput and call with same strike (if both are Europeanstyle),and the drift should be that of the forward 14 .Indeed, ironically, the volatility smile is inconsistentwith the Black-Scholes-Merton theory. This has lead tohundreds if not thousands of papers trying extend(what was perceived to be) the Black-Scholes-Mertonmodel to incorporate stochastic volatility and jumpdiffusion.Several of these researchers have beensurprised that so few traders actually use stochastic14 See Breeden and Litzenberberger (1978), Gatheral(2006). See also Bouchaud and Potters (2001) for hedgingerrors in the real world.volatility models. It is not a model that says how thevolatility smile should look like, or evolves over time; itis a hedging method that is robust and consistent withan arbitrage free volatility surface that evolves overtime.In other words, you can use a volatility surface as amap, not a territory. However it is foolish to justifyBlack-Scholes-Merton on grounds of its use: we repeatthat the Gaussian bans the use of probabilitydistributions that are not Gaussian –whereas nondynamichedging derivations (Bachelier, Thorp) are notgrounded in the Gaussian.Order Flow and OptionsIt is clear that option traders are not necessarilyinterested in probability distribution at expiration time –given that this is abstract, even metaphysical for them.In addition to the put-call parity constrains thataccording to evidence was fully developed already in1904, we can hedge away inventory risk in options withother options. One very important implication of thismethod is that if you hedge options with options thenoption pricing will be largely demand and supplybased 15 . This in strong contrast to the Black-Scholes-Merton (1973) theory that based on the idealized worldof geometric Brownian motion with continuous-timedelta hedging then demand and supply for optionssimply not should affect the price of options. Ifsomeone wants to buy more options the market makerscan simply manufacture them by dynamic delta hedgingthat will be a perfect substitute for the option itself.This raises a critical point: option traders do not“estimate” the odds of rare events by pricing out-ofthe-moneyoptions. They just respond to supply anddemand. The notion of “implied probability distribution”is merely a Dutch-book compatibility type ofproposition.Bachelier-ThorpThe argument often casually propounded attributingthe success of option volume to the quality of the BlackScholes formula is rather weak. It is particularlyweakened by the fact that options had been sosuccessful at different time periods and places.Furthermore, there is evidence that while both theChicago Board Options Exchange and the Black-Scholes-Merton formula came about in 1973, the modelwas "rarely used by traders" before the 1980s(O'Connell, 2001). When one of the authors (Taleb)became a pit trader in 1992, almost two decades afterBlack-Scholes-Merton, he was surprised to find thatmany traders still priced options “sheets free”, “pricing15See Gârleanu, Pedersen, and Poteshman (2006).8© Copyright 2007 by N. N. Taleb.

off the butterfly”, and “off the conversion”, withoutrecourse to any formula.Even a book written in 1975 by a finance academicappears to credit Thorpe and Kassouf (1967) -- ratherthan Black-Scholes (1973), although the latter waspresent in its bibliography. Auster (1975):Sidney Fried wrote on warrant hedges before 1950,but it was not until 1967 that the book Beat theMarket by Edward O. Thorp and Sheen T. Kassoufrigorously, but simply, explained the “shortwarrant/long common” hedge to a wide audience.We conclude with the following remark. Sadly, all theequations, from the first (Bachelier), to the last pre-Black-Scholes-Merton (Thorp) accommodate a scalefreedistribution. The notion of explicitly removing theexpectation from the forward was present in Keynes(1924) and later by Blau (1944) –and long a Call shorta put of the same strike equals a forward. Thesearbitrage relationships appeared to be well known in1904.One could easily attribute the explosion in optionvolume to the computer age and the ease of processingtransactions, added to the long stretch of peacefuleconomic growth and absence of hyperinflation. Fromthe evidence (once one removes the propaganda), thedevelopment of scholastic finance appears to be anepiphenomenon rather than a cause of option trading.Once again, lecturing birds how to fly does not allowone to take subsequent credit.This is why we call the equation Bachelier-Thorp. Wewere using it all along and gave it the wrong name,after the wrong method and with attribution to thewrong persons. It does not mean that dynamic hedgingis out of the question; it is just not a central part of thepricing paradigm. It led to the writing down of a certainstochastic process that may have its uses, some day,should markets “spiral towards dynamic completeness”.But not in the present.ReferencesBachelier, L. (1900): Theory of speculation in: P.Cootner, ed., 1964, The random character of stockmarket prices, MIT Press, Cambridge, Mass.Bernhard, A. (1970): More Profit and Less Risk:Convertible Securities and Warrants. Written and Editedby the Publisher and Editors of The Value LineConvertible Survey, Arnold Bernhard & Co., IncBlack, F., and M. Scholes (1973): “The Pricing ofOptions and Corporate Liabilities,” Journal of PoliticalEconomy, 81, 637–654.Blau, G. (1944-1945): “Some Aspects of The Theory ofFutures Trading,” The Review of Economic Studies,12(1).Boness, A. (1964): “Elements of a Theory of Stock-Option Value,” Journal of Political Economy, 72, 163–175.Bouchaud J.-P. and M. Potters (2003): Theory ofFinancial Risks and Derivatives Pricing, From StatisticalPhysics to Risk Management, 2 nd Ed., CambridgeUniversity Press.Bouchaud J.-P. and M. Potters (2001): “Welcome to anon-Black-Scholes world”, Quantitative Finance, Volume1, Number 5, May 01, 2001 , pp. 482-483(2)Breeden, D., and R. Litzenberger (1978): Prices ofstate-contingent claims implicit in option prices, Journalof Business 51, 621–651.Bronzin, V. (1908): Theorie der Prämiengeschäfte.Leipzig und Wien: Verlag Franz Deticke.Cootner, P. H. (1964): The Random Character of StockMarket Prices. Cambridge, Massachusetts, The M.I.T.Press.De La Vega, J. (1688): Confusión de Confusiones. Reprintedin the book: ‘Extraordinary Popular Delusionsand the Madness of Crowds & Confusión deConfusiones’ edited by Martin S. Fridson, 1996, NewYork: Wiley Publishing.Derman, Emanuel, and Iraj Kani (1994) “Riding on asmile”, Risk 7, 32–39.Derman, Emanuel (1998), Stochastic implied trees:Arbitrage pricing with stochastic term and strikestructure of volatility, International Journal ofTheoretical and Applied Finance 1, 61–110.Derman, E., and N. Taleb (2005): “The Illusion ofDynamic Delta Replication,” Quantitative Finance, 5(4),323–326.Dupire, Bruno (1994): Pricing with a smile, Risk 7, 18–20.Dupire, Bruno (1998): A new approach forunderstanding the. impact of volatility on option prices,Discussion paper Nikko Financial Products.Dupire, Bruno (2005): Volatility derivatives modeling,www.math.nyu.edu/ carrp/mfseminar/bruno.ppt.Filer, H. 1959: Understanding Put and Call Option’s,New York: Popular Library.Gabaix, X. , P. Gopikrishnan, V.Plerou & H.E.Stanley,2003, A theory of power-law distributions infinancial market fluctuations, Nature, 423, 267-270.Gann, W. D. (1937) How to Make Profits in Puts andCalls.Gârleanu, N., L. H. Pedersen, and Poteshman (2006):“Demand-Based Option Pricing”. Working Paper: New9© Copyright 2007 by N. N. Taleb.

York University - Leonard N. Stern School of Business.Gatheral, Jim (2006), The volatility Surface, WileyGelderblom, O. and Jonker, J. (2003) ” Amsterdam asthe cradle of modern futures and options trading, 1550-1650” , Working PaperHaug E. G. (1996): The Complete Guide to OptionPricing Formulas, New York: McGraw-HillHaug, E. G. (2007): Derivatives Models on Models, NewYork, John Wiley & SonsHiggins, L. R. (1902): The Put-and-Call. London: E. WQ ilson.Kairys and Valerio (1997) “The Market for EquityOptions in the 1870s” Journal of Finance, Vol LII, NO.4., Pp 1707 – 1723Keynes, J. M. (1924): A Tract on Monetary Reform. Reprinted2000, Amherst New York: Prometheus Books.Mandelbrot, Benoit 1997, Fractals and Scaling inFinance, Springer-Verlag.Mandelbrot, Benoit (2001a):Quantitative Finance, 1,113-123Mandelbrot, Benoit (2001b): Quantitative Finance, 1,124-130Mandelbrot, Benoit (1963): The variation of certainspeculative prices. The Journal of Business, 36(4):394–419.Mandelbrot, B. and N. N. Taleb (2007): “Mild vs. WildRandomness: Focusing on Risks that Matter.”Forthcoming in Frank Diebold, Neil Doherty, andRichard Herring, eds., The Known, the Unknown andthe Unknowable in Financial Institutions. Princeton,N.J.: Princeton University Press.Merton R. C. (1973): “Theory of Rational OptionPricing,” Bell Journal of Economics and ManagementScience, 4, 141–183.Merton R. C. (1976): ‘‘Option Pricing When UnderlyingStock Returns are Discontinuous,’’ Journal of FinancialEconomics, 3, 125–144.Merton, RC (1992): Continuous-Time Finance, revisededition, BlackwellMills F. (1927) The Behaviour of Prices, National Bureauof Economic ResearchNelson, S. A. (1904): The A B C of Options andArbitrage. New York: The Wall Street Library.O'Connell, Martin, P. (2001): The Business of Options ,New York: John Wiley & Sons.Reinach, A. M. (1961): The Nature of Puts & Calls. NewYork: The Book-mailer.Review of the International Statistics Institute, 37(3).Rubinstein M. (1998): Derivatives. www.in-themoney.comRubinstein M. (2006): A History of The Theory ofInvestments. New York: John Wiley & Sons.Ruffino and Treussard (2006) "Derman and Taleb's`The Ilusion of Dynamic Replication': a comment",Quantitative Finance, 6, 5, pp 365-367Samuelson, P. (1965): “Rational Theory of WarrantPricing,” Industrial Management Review, 6, 13–31.Sprenkle, C. (1961): “Warrant Prices as Indicators ofExpectations and Preferences,” Yale Economics Essays,1(2), 178–231.Stanley, H.E. , L.A.N. Amaral, P. Gopikrishnan, and V.Plerou, 2000, Scale invariance and universality ofeconomic fluctuations”, Physica A, 283,31-41Stoll, H. (1969): “The Relationship Between Put AndCall Prices,” Journal of Finance, 24(5), 801–824.Taleb, N. (1997): Dynamic Hedging. New York: JohnWiley & Sons.Taleb, N. (2007a): The Black Swan. New York:Random House.Taleb. N. (2007b): “Scale-Invariance in Practice: SomeQuestions and Workable Patches”, working paperThorp, E. O. (1969): “Optimal Gambling Systems forFavorable Games”,Thorp, E. O., and S. T. Kassouf (1967): Beat theMarket. New York: Random HouseThorp, E. O. (2002): “What I Knew and When I KnewIt – Part 1, Part 2, Part 3,” Wilmott Magazine, Sep-02,Dec-02, Jan-03Thorp, E. O. (2007): “Edward Thorp on Gambling andTrading,” in Haug (2007)Thorp, E. O., and S. T. Kassouf (1967): Beat theMarket. New York: Random House10© Copyright 2007 by N. N. Taleb.