Daniel l. Rubinfeld

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170 Part:2 Producers, Consumers, and Competitive Markets price of risk Extra risk that an investor must incur to enjoy a higher expected returno NOIV, from equation (502) we see that b a p / a llll so that (5.31 1 This equation is a budget line because it describes the trade-off between risk (a p ) and expected return (R;J Note thatit is the equation for a straight lin.e: Because R1I/! R f , and a lll are constants, the slope (Rill - R f )jam is a constant, as is the intercept Rto The equation says that the expected retul'll on the portfolio Rp increases as the stalliiard deviatioll of tl:at retltr!l a p increase~. We call the slope of this budget line, (RIll - Rt)/a lll , the pnce of ~lsk because It tells us how much extra risk an investor must incur to enjoy a hIgher expected return. The budget line is drawn in Figure 5.6. If our investor wants no risk, she can invest all her funds in Treasury bills (b = 0) and earn an expected rehlrn R f · To receive a higher expected return, she must incur some risk. For example, she could invest all her funds in stocks (b = 1), earning an expected return Rill but Expected Return, Rp . urrina a standard deviation all/' Or she might invest some fraction of her 1l1C 0 funds in each type of asset, earning an expected return somewhere between R f d R and facing a standard deviation less than alii an but greater than zero. III Figure 5.6 also shows the solution to the inrestor's problem. Three indifference curves are drawn in the figure. Each curve ~escribes combinations of risk and return that leave the investor equally satisfied. The curves are up-ward-sloping because risk is undesirable. Thus with a greater amount of risk, it takes a greater expected return to make the investor equally well-off. The curve Ll3 yields the greatest amount of satisfaction and Ll1 the least amount: For a given amount of risk, the investor earns a higher expected return on U 3 than on Ll2' and a higher expected rehlrn on Ll2 than on Ll j • Of the three indifference curves, the investor °would prefer to be on Ll30 This position, however, is not feasible, because Ll3 does not touch the budget line. Curve U j is feasible, but the investor can do better. Like the consumer choosing quantities of food and clothing: our investo~' d~s best by cho~sing. a combin~tion of risk and return at the pomt ,,,rhere an mdifterence curve (m this case Ll 2 ) IS tangent to the budget line. At that point, the investor's return has an expected value R* and a standard deviation a*o Naturally, people differ in their attitudes toward risk This fact is illustrated in Fia-me 5.7, which shows how two different investors choose their portfolios. o 5 Choice Under Uncertainty ¥ RUI ------------------------------ Expected Return, Rp Budget Line R* ---------- RB ---------------- Budget Line R:\ 0
1172 Part 2 Producers, Consumers, and Competitive Markets Investor A is quite risk averse, Because his indifference curve U,\ is tangent to the budget line at a point of lovv risk, he 'will invest almost all his funds in Treasury bills and earn an expected return R,\ just slightly larger than the riskfree return R , I Investor B is less risk averse, She will invest most of her funds in stocks, and \vhile the return on her portfolio vvill have a higher expected value R , B it will also have a higher standard deviation (TB' 1£ Investor B has a sufficiently low level of risk aversion, she might buy stocks on lllllrgill: that is, she would borrow money from a brokerage firm in order to invest more than she achlally owns in the stock market In effect, a person who buys stocks on maro-in hold; a portfolio with more than 100 percent of the port- , 0 folio's value invested in stocks, This situation is illustrated in Figure 5,8, which sho\'vs indifference curves for two investors, Investor A, who is relatively riskaverse, invests about half of his funds in stocks. Investor B, however, has an indifference curve that is relatively nat and tangent with the budget line at a point where the expected return on the portfolio exceeds the expected return on the stock market In order to hold this portfolio, the investor must borrow money because she wants to invest lllorc than 100 percent of her \'\'ealth in the stock market Buying stocks on margin in this vvay is a form of lcvcrngc: the investor increases her expected return above that for the overall stock market, but at the cost of increased risk. Md Budget Line In Chapters 3 and 4, we simplified the problem of consumer choice by assuminO' that the consumer had only two goods from which to choose-food and c1;thing. In the same spirit, we have simplified the investor's choice by limiting it to Treasury bills and stocks. The basic principles, howe\'er, would be the same if we had more assets (e,g" corporate bonds, land, and different types of stocks), Every il1\'estor faces a trade-off between risk and return F The degree of extra risk that each is willing to bear in order to earn a higher expected return depends on hoW risk a\'erse he or she is, Less risk-averse im'estors tend to include a larger fraction of risky assets in their portfolios. During the 1990s, we witnessed a shift in the investing behavior of Americans, First, manv _ Americans started investirw 0 in the stock market for the first time, In 1989, about 32 percent of families in the United States had part of their wealth im'ested in the stock market, either directly (by owning individual stocks) or indirectly (through mutual funds or pension plans invested in stocks). By 1995, that traction had risen to above ,n percent In addition, the share of wealth invested in stocks increased from about 26 percent to about 40 percent during this period,18 Much of this shift is attributable to younger ilwestors, For those under the age of 35, participation in the stock market increased from about 23 percent in 1989 to about 39 percent in 1995. For those older than 35, participation also increased, though by much less, Wlw have more people, and especially vourwer neople started investino- in p • w b rIb the stock market One reason is the ad,'ent of on-line tradino- over the Internet o ' which has made investing much easier. Another reason may be the considerable increase in stock prices that occurred during the late 1990s. These increases may ha\'e convinced some investors that prices could only continue to rise in the fuhue, As one analyst has put it, "The market's relentl~ss se\'en-year climb, the popularity of mutual funds, the shift by employers to self-dire~ted retirement plans, and the avalanche of do-it-yourself investment publications all have combined to create a nation of financial know-it-alls,"l" The run-up in the stock market during the 1990s has indeed surprised many people. Although the American economy has been very strong over this period, by 1999 prices reached almost unprecedented levels relative to earninas and dividends. Figure 5.9 shmvs the dividend vield and price/earnino-s ratio for the ~ 0 S&P 500 (an index of the stocks of 500 large corporations) OWl' the period 1980- 1999, Observe that the dividend yield (the annual dividend di"ided by the stock price) fell from about 5 percent in 1980 to about 15 percent in 1999~ The 5 Choice Under Uncertainty 173 Because Investor A is risk averse, his portfolio contains a mixture of stocks and riskfree Treasury bills. Investor B, however, has a very low degree of risk aversion. Her indifference curve, UB' is tangent to the budget line at a point where the expected return and standard deviation for her portfolio exceed those for the stock market overall. TIus implies that she would like to invest marc than 100 percent of her wealth in the stock market. She does so buying stocks all IlIllrgin-i.e., by borrowing from . As mentioned earlier, what matters is nondi\'ersifiable risk, because im'estors can eliminate di\'erslhable risk by holding many different stocks (eg, \'ia mutual funds) We discuss di\'ersifiable \'er ~~s nondi\'ersifiable risk in Chapter IS . Data are tram the Fcdewi Rcscn'c Blilletill. Januan' 1997 l~ "v i ' . \e r.e :\Il Bulls Here: Strong :Vlarket :V'lakes E\'er\'C'od\' an Exnert " WillI Street JOllnllli September 12,1997 c •• r' '
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PART 1 Introduction: Marl
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Daniel l. Rubinfeld

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