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
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
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