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

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.