Characterizing Hedge Fund Risks

1
Characterizing Hedge Fund Risks
FMRC Conference, 2002 Innovation in
Finance Vanderbilt University

• April 11, 2002

Vikas Agarwal Georgia State University vagarwal_at_gs
u.edu
Narayan Y. Naik London Business
School nnaik_at_london.edu
2
Background

• Rapid growth in the hedge fund industry
• Significant investment by institutional investors
  including Endowments, Pension funds, Foundations
  and Charities etc.

3
Risk-Return Characteristics

• Low correlation with standard asset classes
• Dynamic nature of trading strategies and
  option-like payoffs
• There are many factor risk premia
• Mutual funds (or buy-and-hold type strategies)
  provide exposure to market, credit and liquidity
  risk premia.
• Dynamic trading or Option-based trading
  strategies can provide exposure to volatility
  risk premia (compensation for stochastic
  volatility risk, price-jump risk etc. see Jun
  Pan (JFE 2001))

4
Evidence on non-linearities

• Trend-following strategies employed by CTAs
  exhibit lookback straddle-like payoff (Fung and
  Hsieh (RFS 2001))
• Event or Risk Arbitrage strategies exhibit
  payoff similar to writing an uncovered put option
  on the market index (Mitchell and Pulvino (JF
  2001))

5
An Example of Non-Linearities Case of Event
Driven Strategy
Event Driven Index Exposure to Russell 3000 Index
6
4
2
0
-15
-10
-5
0
5
10
Event Driven Index Returns
-2
-4
-6
-8
Russell 3000 Index Returns
6
Behavior of Residuals without Options
7
Behavior of Residuals with Options
8
Our Generic Approach

• Augment the traditional linear factor model with
  option-based strategies
• Option-based factors proxy for
• Dynamic trading strategies
• State-contingent bets

9
Research Questions

• What are the systematic risk components of hedge
  fund returns? Do other hedge fund strategies
  show non-linear risk-return tradeoffs as well?
• Can we passively replicate hedge fund payoffs
  buy-and- hold and option-based strategies?
• What implications do non-linearities have in
  portfolio decisions?

10
Our Study -main findings

• A wide range of hedge fund strategies
  especially the non-directional ones - show
  non-linear risk-return payoffs
• Findings for Event Arbitrage are similar to that
  of Mitchell and Pulvino (JF 2001) results
  independent corroboration
• Replicating portfolios explain out-of-sample
  variation
• Findings are robust to Choice of database,
  Options on broader index and alternative
  non-linear specifications

11
Sample Data

• Hedge Fund Research (HFR) Database
• Index Performance Jan 90 to Jun 00
• Individual Fund Performance Jan 90 to Aug 99
• CSFB/Tremont (CSFB) Database
• Index and Individual Fund Performance Jan 94
  to Jun 00

12
Equity-Oriented Hedge Funds

• Event Driven
• Relative Value Arbitrage
• Equity Hedge (Long-Short Equity)
• Equity Non-Hedge
• Short Selling (Dedicated Short-Bias)

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Classification

• Non-directional Strategies
• Event Driven
• Relative Value Arbitrage
• Equity Hedge (Long-Short Equity)
• Directional Strategies
• Equity Non-Hedge
• Short Selling (Dedicated Short-Bias)

14
Multifactor Model

• HFt Hedge Fund Return at time t
• BHt Buy-and-Hold Strategy Return at time t
• OSt Option-Based Strategy Return at time t

15
Buy-and-Hold Strategies

• Market Risk Factors
• Equities U.S. and Non-U.S.
• Fama-French Size and Book-to-Market Factors
• Carharts Momentum Factor
• Bonds Government and Corporate
• Currencies
• Commodities
• Default Risk
• Change in Default Spread
• High Yield Bond

16
Option-Based Strategies

• CME-traded SP 500 Composite index options
  (European)
• At-the-money options
• S / PV(X) 1.0
• Out-of-the-money options
• S / PV(X) 1.0 0.01

17
Results
Sample Period Jan 90 to Dec 99
18
Robustness Checks

• Choice of database
• Sub-period Analysis
• Use of lagged Russell 3000 index
• Options on a broader equity index (Russell 2000)
• Use of deeper out-of-the-money options
• Use of American-style options on SP 500 futures
• Alternative non-linear specifications

19
Implications of non-linearities

• Underestimation of expected loss using M-V
  analysis
• Fung and Hsieh (1999)
• Mean-Variance Analysis Limited applicability
• Alternative framework for portfolio optimization
  and asset allocation
• Mean-Value-at-Risk approach
• Conditional Value-at-Risk
• Conditional Drawdown Risk
• Smoothed Value-at-Risk

20
Concluding Remarks

• Option-based strategies capture non-linear risks
• Number of hedge fund strategies writing deep
  out-of-the-money options (similar to selling
  portfolio insurance or catastrophic insurance)

21
Concluding Remarks (contd.)

• Potentially useful in
• Asset allocation
• Construction of fund of hedge funds
• Risk management
• Design of benchmark and managerial compensation
  contract

22
Research Paper URLs

• http//papers.ssrn.com/paper.taf?Abstract_id15308
  8
• http//papers.ssrn.com/paper.taf?Abstract_id19038
  9
• http//papers.ssrn.com/paper.taf?Abstract_id23870
  8
• Or
• http//www.hedgeworld.com/research/reports/top_dl.
  cgi
• Most requested research reports number 2, 7 and
  8.
• Or
• http//www.gsu.edu/fncvaa/research.htm
• Or
• http//www.london.edu/faculty_research/working_pap
  ers/working_papers.html (Search under author
  Naik NY)
• IFA working paper numbers 289, 298, 300 and 305