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Dynamic Investment Opportunities and the Cross-Section of Hedge Fund Returns: Implications of Higher-Moment Risks for Pe

18 th Annual Derivative Securities and Risk Management Conference. Dynamic Investment Opportunities and the Cross-Section of Hedge Fund Returns: Implications of Higher-Moment Risks for Performance. Vikas Agarwal Georgia State University Gurdip Bakshi University of Maryland Joop Huij

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Dynamic Investment Opportunities and the Cross-Section of Hedge Fund Returns: Implications of Higher-Moment Risks for Pe

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  1. 18th Annual Derivative Securities and Risk Management Conference Dynamic Investment Opportunities and the Cross-Section of Hedge Fund Returns: Implications of Higher-Moment Risks for Performance Vikas Agarwal Georgia State University Gurdip Bakshi University of Maryland Joop Huij Erasmus University April 11, 2008

  2. Overview and Main Themes • Investors require premiums for bearing higher-moment risks: hate volatility, negative skewness and large moves Rubinstein (1973); Merton ICAPM (1973); Kraus and Litzenberger (1976); Vanden (2006); among others • Higher moment risks are priced in option returns – vast literature EQ[VOL]>EP[VOL] for S&P 500 index

  3. Overview and Main Themes (contd.) • Hedge funds have the capability and flexibility to extract risk premiums • Hedge funds have nonlinear option-like return structure • Hedge funds trade dynamically and take state-contingent bets in response to changes in macroeconomic conditions and arbitrage opportunities [Fung and Hsieh (2001); Mitchell and Pulvino (2001); Agarwal and Naik (2004)] • Hedge funds should exhibit exposures to higher moments of market returns

  4. Research Questions • To what extent are hedge funds exposed to higher-moment market risks? • How much is the premium for the higher moments and how much of the hedge fund performance may be attributable to the higher moment risks? • What are the implications for excluding higher moment risk factors while evaluating hedge fund performance? • What about funds of hedge funds, which are less vulnerable to biases? (other issues: diversification and compensation) • How large are the exposures in case of mutual funds?

  5. Hedge fund and mutual fund data • Monthly net-of-fee returns of 3,771 hedge funds and 1,062 funds of hedge funds from Lipper (previously TASS) database from Jan 1994 to Dec 2004 • Exclude funds that do not report on monthly basis and those that do not have 12 consecutive returns over the sample period • Survivorship-bias free due to inclusion of funds that have disappeared from the database • Monthly net-of-fee returns of about 9,769 mutual funds from CRSP mutual fund database from Jan 1994 to Dec 2004

  6. Measures of higher-moments of market risk • Precise estimation of higher moments require long time-series data • Need forward-looking measures • Estimate the intrinsic values of the second, third, and fourth moments of equity returns from S&P 100 index options traded on CBOE by spanning and valuing the relevant payoffs as shown in Bakshi, Kapadia, and Madan (RFS 2003) • Higher moments of other markets (fixed income, commodities, etc.) may also be relevant but matching high-quality option data unavailable

  7. Time-Series of the Value of Claims to Higher Moments

  8. Time-Series of the Value of Claims to Higher Moments (contd.)

  9. Time-Series of the Value of Claims to Higher Moments (contd.)

  10. Measures of risk-adjusted performance • Fung and Hsieh (2004) seven-factor model –market, size, bond, credit, and three option factors on bonds, currencies, and commodities – FH-7 MODEL • Carhart (1997) four-factor model – market, size, book-to-market, and momentum – CARHART-4 MODEL

  11. Methodology (I) • Standard asset pricing tests using pooled time-series cross-sectional data • First construct a set of base assets that have significant dispersion in the sensitivity to higher-moment risks • Form decile portfolios of hedge funds sorted based on their exposures to innovations in higher moments - VOL, SKEW, and KURT

  12. Methodology (II) • Rolling window regressions over the past 12 months • Short estimation window – compromise between estimating coefficients with precision and allowing for time-varying factor loadings (Bollen and Whaley 2007) – for robustness, perform Bayesian analysis • Keep number of factors minimum in constructing the portfolios but control for all possible factors in the post-formation period (similar to Ang et al. (JF 2006)) • Wait for three months for the post-formation period to allow for lockups and redemption period

  13. Rank Portfolios Wait Investment Period Ranking Period Out-of-sample equally-weighted returns for sorted portfolios (I) Three-month wait (I) Portfolio formation period (I) May ‘95 Jan ‘95 Feb ‘95 Mar ‘95 Apr ‘95 Jan ‘94 Dec ‘04 Feb ‘94 Portfolio formation period (II) Three-month wait (II) Out-of-sample equally-weighted returns for sorted portfolios (II)

  14. Independent sorts on higher moments LARGE AND SIGNIFICANT SPREADS IN ALPHAS

  15. Three-way sorts on higher moments SPREADS IN ALPHAS CONTINUE TO BE LARGE AND SIGNIFICANT

  16. Bootstrapping Results BOOTSTRAPPED ALPHAS BETWEEN EXTREME PORTFOLIOS AT THE 95% CONFIDENCE LEVEL ARE BETWEEN -8.5% AND 8.5% P.A. HISTOGRAM SHOWS HOW BIG A SPREAD IN ALPHAS IS OBTAINED BY CHANCE IF ZERO ALPHA IS IMPOSED IN THE FH-7 MODEL SPECIFICATION

  17. Higher moment risk factors based on hedge fund returns LARGE AND SIGNIFICANT PREMIUMS EXISTING MODELS CAN’T EXPLAIN

  18. Post-Ranking Regressions and Risk Story STRONG PATTERNS IN POST-RANKING LOADINGS RISK-BASED EXPLANATION IMPROVEMENT IN EXPLANATORY POWER SPREADS IN ALPHAS BECOME SMALL

  19. Augmented FH-7 with higher moment factors NEW MODEL CAN CONSIDERABLY ALTER HEDGE FUNDS’ ALPHA-BASED RANKINGS BARS ON THE DIAGONAL INDICATE THE % OF FUNDS THAT ARE RANKED IN THE SAME DECILE USING THE TWO MODELS. OFF-DIAGONAL BARS REPRESENT INCONSISTENT DECILE RANKINGS.

  20. Robustness tests • Liquidity • Fung and Hsieh 9-factor model • Out-of-the-money put option factor • Bayesian estimates • Backfilling bias

  21. Hedge Fund Strategies with extreme exposures

  22. Higher moment exposures for FOFs • FOFs popular among institutional investors; less susceptible to data biases • Three possibilities regarding higher moment exposures • Effective risk management policy would imply neutralizing of higher moment risks • Improving performance to increase compensation would suggest taking on higher moment risks • Unintentional diversification due to investment in disparate strategies

  23. Substantial Reduction in Exposure for FOFs (1) MAGNITUDE OF EXPOSURES ARE 40% OF THOSE FOR THE COMBINED SAMPLE (2) REDUCTION IN THE X-SECTIONAL DISPERSION OF BETAS

  24. Summary of results for FOFs • Sensitivities of FOFs to higher moment risks ameliorated across the board • FOFs may be natural vehicles to offset higher moment exposures • Hitherto unidentified additional benefit accruing to FOF investors

  25. Higher moments not priced in mutual funds • No discernible pattern in alphas • Given the higher dispersion in exposures for hedge funds, our test design on hedge funds is crucial for recovering the risk premiums LOWER DISPERSION IN BETAS COMPARED TO HEDGE FUNDS LOWER SPREAD IN ALPHAS

  26. Summary • Striking patterns in alphas when hedge funds are sorted on exposures to higher moment risks • Significant and large risk premiums for the three higher moments Volatility : ─6.55% Skewness: 3.40% Kurtosis: ─ 2.39% • Far lower dispersion for funds of hedge funds

  27. Summary (contd.) • No patterns in mutual funds — differences in trading strategies compared to hedge funds • Including higher moment risk factors flattens alphas and improves explanatory power • Hedge funds earn a substantial portion of their returns for bearing higher moment risks

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