Three Risks of Risk Management Enterprise Risk Management Conference April 2004

1. Three Risks of Risk ManagementEnterprise Risk Management ConferenceApril 2004 Kenneth Yip, Ph.D. Chief Investment Officer THUNDERBAYCAPITAL

2. Fundamentals of Finance • Time • Uncertainty • Risk and Reward

3. Example of Investment Risk • Suppose you invest $ 10M in SPY • What is the risk of your investment? • Time = • Reward = • Risk =

4. VaRα Value at Risk (VaR)Statistics on Loss Distribution Frequency Profit/Loss Expected Shortfall

5. Optimized VaR Portfolio • Treasury Bond • Monthly return 0.5%, volatility 1.9% • Corporate Bond • Monthly return 0.6%, volatility 1.6% • 3-month T-bill • Monthly return 0.45% • Correlation • 0.96 • Positions to put on • What is the 1-month VaR?

6. Notable 10-Sigma Events • Stock market crash on October 19, 1987 • Major indices down by over 20% in one day • No major adverse news • LTCM collapse in Autumn 1998 • Daily VaR = $ 45m • Single day loss on August 31, 1998 = $ 550m • Monthly VaR = $ 206m • Portfolio lost $ 1.7B in August • Russian debt default on August 17

7. Three Risks of Risk Management • Estimation Risk • Extrapolate past history to future • Estimate rare events • Model Risk • Dynamics of assets are not simple Brownian motion • Causality • Preference Risk • Mis-specify preferences

8. Preference Risk

9. Trading with static VaR constraints • Unconstrained trader B • Portfolio Insurer PI • VaR-constrained trader

10. Static VaR-constrained Trader

11. Static VaR-constrained trader can take large risk

12. Trading with dynamic VaR constraints • Dynamically VaR-constrained trader

13. Dynamic VaR-constrained Traderfixed VaR limit

14. Dynamic VaR-constrained Traderproportional VaR limit

15. (Debunking) Myths about VaR • VaR-constrained traders do not necessarily hold more risky positions • VaR requirement does not necessarily increase market volatility • Coherent risk measures (e.g. expected shortfall) may not be any better

16. Information And Events Order Flow Prices Multiple Markets Equities Fixed Income Currency Derivatives Credit Multiple Trader Types Informed Hedging/Liquidity Noise Market Microstructure Trader Behavior Preferences Biases Trading Rules Wealth Market Makers

17. Conclusion • Traditional statistical analysis (e.g., VaR and expected shortfall) can be quite ineffective in assessing true financial risks • A proper risk analysis must be economic-based • Microstructure models • Dynamically-consistent preferences • Portfolio Choice • Challenge • Feedback between risk management and market dynamics • Microstructure models to predict onset of crashes

18. Model Risk

19. Empirical observations about Crashes • Large price movements need not be triggered by any significant news • Meltdown is much more likely than “meltup” • Large price drops are not extreme tail events • Large price drops are contagious

20. Causal Mechanism for Crashes • Differential information • Informed versus uninformed traders • Reverse price/demand relation • Stop-loss sale, distressed sale • Increased uncertainty in signals • Prices become less informative • Grossman, Gennotte & Leland, Jacklin et. al., Kyle & Xiong, Barlevy & Veronesi, Yuan

21. Hedging and October 87 Crash • Information • Prices • Fundamental signals • Order flow • Investors • Supply-informed traders (market makers) • Price-informed traders (active fund managers) • Uninformed traders • Uninformed hedgers (portfolio insurers)

22. Rational Expectation Equilibrium • Conditional expectations • Investor demands • Informed • Uninformed • Market clearing • Supply = Demand • Solve for equilibrium price

23. Rational Confusion • Initial price drop • Hedgers sell • Investors misread the supply shock as bad news • Liquidity providers fear adverse selection • Price drop amplified

24. Model Calibration for October 1987 • Trader composition • Supply informed traders = 0.5% • Price informed traders = 2% • Uninformed traders = 97.5% • Portfolio insured assets = 2 to 5% • Hedging strategy • Dynamically replicating puts • Price • Price level normalized to 1 • Return = 6%, Volatility = 20% • Observability of hedging strategy • Traders are not aware of the extent of dynamic hedging

25. 1% Pessimistic, 2% Asset Hedged 1.1 1.05 - 0.8% 1 .95 .9 .85 .8 .75 .7 .65 .6 4 -4 -2 0 2

26. 1% Pessimistic, 4% Asset Hedged 1.1 1.05 -1.6% 1 .95 .9 .85 .8 .75 .7 .65 .6 4 -4 -2 0 2

27. 1% Pessimistic, 5% Asset Hedged 1.1 1.05 1 .95 .9 .85 -27.5% .8 .75 .7 .65 .6 4 -4 -2 0 2

28. Key insight • October 1987 Crash is almost inevitable as the amount of insured assets grows while the informational differences remain

29. Extensions of the model • Multi-period • Learning through multiple rounds of trading • Capital constrained • Uncertainty in trading motives • Rational panics • Multi-assets • Contagion

30. Hedge Fund Investing • Information Asymmetry Capital Uninformed Investors Hedge fund managers Opportunity Set Performance

31. LTCM • Convergence trade • Normally liquidity providers • Wealth had grown significantly • Opportunity diminished • Return of capital • Increased leverage • Russian default triggered price decline • Margin constrained • Reduced positions • Misread as deterioration of fundamentals • Further price decline

32. Microstructure models for hedge fund risks • Traditional statistical analysis (e.g., VaR) can be quite ineffective in assessing true risks of hedge funds • A proper risk analysis must be economic-based • Degree of information asymmetry • Aggregate wealth positions • Margin constraints • Relative proportion of informed, uninformed, and passive investors • Challenge • Microstructure models to predict onset of crashes