Quantitative Finance - Art or Science?

Quantitative Finance – Art orScience?November 2009Manfred PlankManaging Director, Credit Risk Management,Analytics&Instruments+41-44-333 86 24manfred.plank@credit-suisse.com

Characteristics of Quantitative Science• Quantitative Science is always concerned with the measurement ofquantities and the discovery of the exact relationship betweendifferent quantities• Relationships between different quantities are described bymathematical equations where each variable or constant has a realworld interpretation and relationships, variables and constants arem && x =1Gm m1 22rmeasurable• The mathematical formulation must correctly describe all knownphenomena for which it was designed and predict new phenomenawhich are not yet knownUransus1

Characteristics of Quantitative Science"One can sum up all this by saying that the criterion of thescientific status ofa theory is its falsifiability, or refutability, or testability"(Karl Popper, 1963)2

Fundamental Principles and First ApplicationsClassical Mechanics• Newton's second law: the force on an objectis equal to the mass of the object multiplied by itsaccelerationFinancial Economics• No Arbitrage: the existence of an equivalentmartingale measure for a stochastic process ( S t) isessentially equivalent to the absence of arbitrage• Application – law of inertia:If there acts no force on an object it moves with• Application - pricing of linear derivatives:For a no income asset the relationship between theconstant velocity along a straight line; i.e.m &1x= 0forward F 0and the spot price S 0isF0 = S0erT• Testability:• Testability:An object's velocity & trajectory are observableand measurable and observations & experimentsconfirm the predictionRisk free rate, forward and spot price are observableand measurable and observations & experimentsconfirm the prediction3

Science and ArtUniversal Law of Gravitation Geometric Brownian Motionm m& tt1 21xG2G= (6.67428 +/- 0.00067) x 10-11 m3 kg-1 s-2 dB B rdtt=tm =rdS= S μdt+ S σdWtt⇒ f 0= e−rTEQ[ f ( S )]T• All variables and constants are measurable &therefore their functional relationship can betested• All variables and constants are measurable &therefore their functional relationship can betested• Known empirical phenomena, like Kepler's laws,can be deducted from the mathematical model• Known empirical phenomena like fat tailed equityreturn distributions or non-constant volatilitiescannot be deduced from this model• New predictions, like the existence of newunknown planets, are made & verified throughobservations or experiments• The model does not make any new predictions &predicted derivative prices are in contradictionwith observed prices• Findings do not change if we replace above models by more sophisticated versions4

Implications for Financial Risk Management• How it is• ... and how it should be• Mathematical models are used to quantify risks– the math is right; the problem is that it does notdescribe the real world in a quantitative way• Mathematical models should help to understand risks– the math is right & it should help us to describe the realworld in a qualitative way• Risk management decisions are delegated tomathematical models & judgment cast aside• Risk management decisions should be based onjudgment & mathematical model insights5

Implications for Financial Risk Management cont'd• How it is•... and how it should be• The principle of "No free lunch" is repeatedlyignored resulting in significant losses– Amplified Mortgage Portfolio Super Senior trades– Negative Basis Trades• As a risk manager never accept trades generating"risk free" profits– End of 2007 AMPS contributed 67% and NBT10% of UBS total Super Senior losses• Dig into details before the big picture isunderstood• Understand the big picture before you dig into thedetails6

Implications for Financial Risk Managementcont'd• How it is• Facts are ignored– over the last 24 months Risk Management toolshave blown up repeatedly• Some risk managers act as if there would existgod given laws for financial economics– Human being have a choice• Countries can close their exchange• Central banks can reduce rates• Governments can bail out banks or allow them to fail• Regulators change the rules of the game (short selling)• ... and how it should be• Make sure that models work under extreme scenarios& use tailor made stress scenarios to understand tailrisk• Understand why people do the trades they do– VaR and stress loss frameworks are often arbitraged• Never assume that certain scenarios cannot happen– the fact that we are still alive does not make us immortal• Make sure that you understand in detail the business& the people doing it• It is all about people & their behavior & not so muchabout modeling7

Key Benefits of Financial Models• Financial Models allow us to understand and analysis potential risks in a structured,objective & consistent way across the organization• Implementation of Risk Management tools always leads to tremendous improvements ininformation systems & make deficiencies transparent• Incorrectly booked trades & sometimes (but not always) risk accumulations acrossdesks are made transparent• If I take models seriously they tell us when we should not apply them; i.e. do not includeilliquid securities in the trading book8

How does the big picture look like: Historic Credit CrunchesData as of September 2009600500400300Rise in global credit spreads 1Looking at past experiences, financial marketstabilization could be still far away• 1930• 1979• 1990• Current crisis 22001000SOURCE: Moody’s0 10 20 30 40 50 60 70 801 Shocks classified based on trough to peak rise in spreads and duration2 European market only; indexed to 100 at spread level of October 2007, which marks the starting point of thecurrent crisisDuration of credit shockMonths9

How does the big picture look like: US - On the Real SideFed’s Unemployment Rate Forecast1110Unemployment Rate (%)SepFOMC Central TendenciesQ4 avg20092010201198765LongerRun6Time To Recovery(Number of quarters it takes the level of real GDPto get back to previous cycle peak, startingfrom last quarter of the recession)4Jan 2008 Jan 20095Sources: Federal Reserve, Credit Suisse. 2009 central tendency is9.8% to 10.1%, 2010 is 9.5% to 9.8%, 2011 is 8.4% to 8.8%, andlonger run 4.8% to 5.0% on a Q4 average basis.432101960-61 1970 1973-75 1980 1981-82 1990-91 2001 CurrentForecastSources: Bureau of Economic Analysis, Credit Suisse. End-quarter ofcurrent recession expected to be Q2 2009.10

Visible Risks1. The reach for yield continues to support existing rise of asset prices. They almost surely won’t goup as they have in the last six months, but it’s hard for them to go down against the backdrop ofunrenumerative cash. This is great for PMs, but it’s a misery for CIOs and CEOs and businessmodels where asset yields get too low to cover liability costs. Watch out for pension funds &insurance companies2. Risk management models have blown up as thoroughly in the last six months when correlationsamong asset classes went towards 1 (as everything rallied) as was the case before whencorrelations were near 1 (with all assets selling off). The difference, of course, is that peoplearen’t as sensitive to failures in the risk management models when prices are going up as whenthey’re going down. Black swans have fat tails; so do white swans3. We move into a time of over-regulation where decision makers still believe that financial risks canbe controlled & managed by mathematical models. Sound risk management cannot bedelegated to a model4. FED balance sheet management is complicated/compromised by the Treasury’s debt ceilingproblem leading potentially to some money market accidents5. A lot of senior executives were fired in the financial industry over the last two years, but no seniorregulator had to resign12