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Caught by the Tail: Tail Risk Neutrality and Hedge Fund Returns

Caught by the Tail: Tail Risk Neutrality and Hedge Fund Returns. Stephen J. Brown Jonathan F. Spitzer NYU Stern. Caught by the tail. Historical perspective The myth of market neutrality Robust measure of tail risk neutrality Application to TASS data Conclusion. The History of Hedge Funds.

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Caught by the Tail: Tail Risk Neutrality and Hedge Fund Returns

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  1. Caught by the Tail:Tail Risk Neutrality and Hedge Fund Returns Stephen J. Brown Jonathan F. Spitzer NYU Stern

  2. Caught by the tail • Historical perspective • The myth of market neutrality • Robust measure of tail risk neutrality • Application to TASS data • Conclusion

  3. The History of Hedge Funds • The first hedge fund: Alfred Winslow Jones (1949) • Limited Partnership (exempt from ’40 Act) • Long-short strategy • 20% of profit, no fixed fee • Used short positions and leverage • “Hedge Fund” (Fortune magazine 1966) • Tiger Fund (Institutional Investor 1986) • George Soros $3.2Billion raid on the ERM (1992) • CalPERS (2000)

  4. Institutional concern about risk • Fiduciary guidelines imply concern for risk • Financial risk • Operational risk • Institutional demand • Growing popularity of market neutral styles • Explosive growth of funds of funds • Demand for “market neutral” funds of funds

  5. Operational Risk Hedge fund failure is highly predictable … Source: Tremont TASS (Europe) Limited

  6. FinancialRisk Source: Elton and Gruber 1995. Risk is measured relative to the standard deviation of the average stock

  7. Financial Risk

  8. Caught by the tail • “S&P500 returns at Treasury Bill risk” • Most new funds claim to be “market neutral” • Zero correlation with benchmark • Zero correlation is not a strategy • Zero correlation is an outcome of a strategy • These strategies fail in liquidity crises • Risk is considerably understated • New concept: “tail risk neutrality”

  9. Data • TASS hedge funds – both dead and alive • US funds with at least 10 returns, average of 40 max of 120. • Not a lot of data per fund, but plenty when the universe is combined – nearly 50,000 fund-month observations.

  10. An example of ‘market neutrality’ 1.5% 0.8 1.1% 0.6 Fund Returns 0.8% 0.4 0.4% 0.2 0.2 0.4 0.6 0.8 Market Returns Assuming MVN returns Beta = .28, rho = .24

  11. Market neutrality in the ‘real world’ 2.5% 0.8 1.9% 0.6 Fund Returns 1.3% 0.4 0.6% 0.2 0.2 0.4 0.6 0.8 S&P500 Returns Using TASS data Beta = .28, rho = .24

  12. Market neutrality in the ‘real world’ 2.5% 0.8 1.9% 0.6 Fund Returns 1.3% 0.4 0.6% 0.2 0.2 0.4 0.6 0.8 S&P500 Returns Beta = .28, rho = .24

  13. Long Short Equity Funds 2.9% 0.8 2.2% 0.6 Fund Returns 1.3% 0.4 0.6% 0.2 0.2 0.4 0.6 0.8 S&P500 Returns Beta = .50, rho = .37

  14. Event driven style 3.1% 0.8 2.3% 0.6 Fund Returns 1.5% 0.4 0.8% 0.2 0.2 0.4 0.6 0.8 S&P500 Returns Beta = .20, rho = .23

  15. Dedicated Short Sellers 4.5% 0.8 3.4% 0.6 Fund Returns 2.3% 0.4 1.1% 0.2 0.2 0.4 0.6 0.8 S&P500 Returns Beta = -.91, rho = -.61

  16. Fixed income arbitrage 1.5% 0.8 1.1% 0.6 Fund Returns 0.8% 0.4 0.4% 0.2 0.2 0.4 0.6 0.8 S&P500 Returns Beta = 0.01, rho = 0.02

  17. Funds of Hedge Funds

  18. Funds of Hedge Funds • Provides

  19. Funds of Hedge Funds • Provides • Diversification – lower value at risk

  20. Funds of Hedge Funds • Provides • Diversification – lower value at risk • Smaller unit size of investment

  21. Funds of Hedge Funds • Provides • Diversification – lower value at risk • Smaller unit size of investment • Professional management / Due diligence

  22. Funds of Hedge Funds • Provides • Diversification – lower value at risk • Smaller unit size of investment • Professional management / Due diligence • Access to otherwise closed funds

  23. Institutions love FoF • Spectacular growth of Funds of Funds 2000: 15% of all Hedge funds were FoF 2003: 18% of all Hedge funds were FoF 2005: 27% of all Hedge funds were FoF • Institutional attraction of Funds of Funds • Risk management • Due diligence

  24. Funds of Funds 2.9% 0.8 2.2% 0.6 Fund Returns 1.3% 0.4 0.6% 0.2 0.2 0.4 0.6 0.8 S&P500 Returns Beta = .14, rho = .22

  25. Relationship to LIBOR 1.0% 0.8 0.8% 0.6 Fund Returns 0.5% 0.4 0.3% 0.2 0.2 0.4 0.6 0.8 LIBOR return Beta = 0.0, rho = 0.0

  26. Fixed income arbitrage 2.0% 0.8 1.5% 0.6 Fund Returns 1.0% 0.4 0.5% 0.2 0.2 0.4 0.6 0.8 LIBOR return Beta = -.02, rho = -.05

  27. Simple measures of tail risk exposure • Independence an unrealistic benchmark • Consider • MV Normal with the same sample correlation • MV Student with 3 df

  28. Simple measures of tail risk exposure • Independence an unrealistic benchmark • Consider • MV Normal with the same sample correlation • MV Student with 3 df 0.0188 0.24

  29. An example of ‘market neutrality’ 1.5% 0.8 1.1% 0.6 Fund Returns 0.8% 0.4 0.4% 0.2 0.2 0.4 0.6 0.8 Market Returns Assuming MVN returns Beta = .28, rho = .24

  30. An example of ‘market neutrality’ 1.5% 0.8 1.1% 0.6 LW WW Fund Returns 0.8% 0.4 0.4% 0.2 LL WL 0.2 0.4 0.6 0.8 LL should be 1.88% of sample assuming MVN returns Market Returns Beta = .28, rho = .24

  31. Size and power of tail risk measures Percentage of rejections at 5% level. 100 funds with market beta 3.2. When market is in bottom decile, fund betas all increase by βEXTRA.

  32. Comparison with S&P500 Benchmark

  33. Comparison with LIBOR Benchmark

  34. Logit Specification Boyson, Stahel and Stulz [2006] suggest running logit regressions of whether a fund index crashes in a month upon the market return and a dummy for market crashes. A positive coefficient on the dummy indicates additional dependence during crashes. Lacks power when run on a single index. We run the regressions on the cross-section.

  35. Logit Results

  36. Conclusions Undiversifiable crash risk lurks in hedge fund returns, despite their seemingly light dependence in normal times.

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