1. Hedge Fund Diversification: The good, the bad and the ugly Michelle Learned Banque Syz (3A) François-Serge Lhabitant Edhec et HEC Université de Lausanne Contact: francois@lhabitant.net francois@lhabitant.net

2. 2 Agenda Introduction Our approach of hedge fund diversification Empirical results Conclusion

3. 3 Growth of hedge funds

4. 4

5. 5 Improving the Efficient Frontier

6. 6 Return and Volatility

7. 7 Return and Max Drawdown

8. 8 Riskier than traditional investments? Iraq Crisis (8/90) Asia Crisis (8/97) Russia Crisis (8/98) September 11 (9/01) MSCI World Equity Hedge Event Driven Relative Value

9. 9 How to Invest into Hedge Funds? Diversification seems to be the rule. It reduces the impact of selecting a bad manager. Low correlation between managers supports the idea of diversifying. In practice, There are very few index products. Dedicated hedge fund portfolio. Fund of hedge funds. The new questions: What is the optimal number of hedge funds in a portfolio? What is the maginal impact of adding a new hedge fund in an existing hedge fund portfolio?

10. 10 How many assets/funds? How many assets make a diversified portfolio? Evans and Archer (1968): 8 to 10. Statman (1987): 30 to 40. How about hedge funds? Billingsley and Chance (1996) for managed futures. Henker and Martin (1998) for CTAs. Henker (1998) for hedge funds. Amin and Kat (2000) Ruddick (2002) 8 to 10 at least 20

11. 11 Naive Diversification for Hedge Funds Naive diversification is better for HF than Markowitz optimisation. Non normality of returns is ignored by mean-variance optimisers. Optimisers need good forecasts of expected return and expected risk. Operational difficulties, e.g. lockup clauses, minimum investments, exit notifications, etc. A recent survey by Arthur Andersen (2002) of Swiss hedge fund investors and fund of hedge funds managers confirms our intuition. It appears that most participants do not use a quantitative approach for their asset allocation strategy. Many respondents even admitted to having no asset allocation strategy at all!

12. 12 Formulation of asset allocation strategy by financial intermediaries using hedge funds Many hedge fund services suppliers do not have an asset allocation strategy another approach (qualitative) mean-variance approach no asset allocation strategy quantitative model Banks Advisors no asset allocation strategy another approach (qualitative) quantitative model mean-variance- approach 41% 25% 21% 13% 62% 13% 12% 13%

13. 13 Methodology Database: 6,985 distinct hedge funds, including dead funds. Sources: public databases + data from administrators and managers Monte-Carlo simulation We create equally weighted portfolios of increasing size (N=1, 2, … 50) by randomly selecting hedge funds from our data (no replacement). For each portfolio size, this process is repeated 1,000 times to obtain 1,000 observations of each statistic.

14. 14 Returns, 1998-2001

15. 15 Volatility, 1998-2001

16. 16 Volatility, 1998-2001

17. 17 Skewness, 1998-2001

18. 18 Kurtosis, 1998-2001

19. 19 Worst Monthly Return, 1998-2001

20. 20 VaR (95%, 1M), 1998-2001

21. 21 VaR (95%, 1M), 1998-2001

22. 22 Max. Drawdown, 1998-2001

23. 23 Correlation with S&P 500, 1998-2001

24. 24 Correlation to Tremont Indices, 1998-2001

25. 25 Some Variations We repeated the experiment for the 1990-1993 and 1994-1997 periods. Findings are similar, although the level of risk seems to have increased over the years. We repeated the experiment using only surviving funds. Findings are similar, although the level of risk is lower. It seems that most funds that disappeared did it for performance reasons. We repeated the experiment using a smarter diversification technique, based on the self-attributed classification of the funds.

26. 26 Smart Diversification

27. 27 Smart Diversification

28. 28 Conclusions Diversification (naive or smart) is clearly a protection against ignorance. Diversification brings most of its benefits already with very few funds in a portfolio. Funds of hedge funds seem overdiversified, at least from a market risk perspective. How about time?