1. Hedge Fund Portfolios Ezra Zask Yale University September 26, 2005

2. Benefits of Hedge Funds

3. 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

4. Hedge Fund Returns

5. Assets Risk Return Profile

6. Hedge Fund Style Beta and Alpha

7. Portfolio Optimization Requirements for Mean Variance Optimization –Returns Normally Distributed Accurate Data Time Frame –Standard Deviation Constant over time –Correlations Lower is better

8. Survivorship and Backfill Bias

9. Tremont Style Statistics Summary Statistics - Factors.fld 1/1994-6/2005 N Periods Geomet ric Mean (%) Arith metic Mean (%) Standard Deviation (%) Sharpe Ratio Skewnes s Kurtosi sAlphaBeta Distressed Index13713.0813.337.350.5541-2.898618.43010.00840.2388 Emerging Markets Index1376.878.3517.870.1407-0.67584.69680.00150.5272 Equity Market Neutral Index13710.0710.113.260.93710.33280.32860.00760.078 Event Driven Index13711.2211.46.30.5489-3.566225.19460.00720.211 Event Driven Multi-Strategy Index13710.210.46.640.4735-2.683817.99010.00660.193 Fixed Income Arbitrage Index1376.336.414.050.4695-3.092116.05010.00540.0073 Global Macro Index13713.6614.3812.920.34250.01922.56410.00990.1776 Hedge Fund Index13710.5810.938.850.37420.1332.14220.00650.256 Managed Futures Index1376.67.3913.120.16860.02140.34970.0077 - 0.1526 Fund of Funds Universe Average1377.217.386.140.3589-0.13832.21250.00440.1967

10. Normal Distribution?

11. Hedge Funds in Portfolios

13. Efficient Frontier

15. Hedge Fund Styles

18. Background Information: Why Invest in Alternatives?

19. Alternative assets offer attractive risk adjusted returns. Notes: (1) Sources as follows: private equity and venture capital data from Venture Economics, hedge fund composite and distressed data from Hedge Fund Research (HFR) and all other data from Pertrac database (2) Annualized volatilities computed from monthly and quarterly series under the assumption of independent returns

20. Alternatives’ returns are not highly correlated with traditional investments. Notes: (1) Sources as follows: hedge fund data from Hedge Fund Research (HFR); private equity and venture capital data from Venture Economics and all other data from Pertrac database (2) The correlation between S&P 500 and Lehman Aggregate Bond Index over the same time period is 0.02 Alternative Asset Correlations (1)(2) January 1994 to December 2003

21. Alternatives enhance traditional investment portfolios. Notes: (1) For illustrative purposes only (2) These portfolios include US Equity (S&P 500), Int’l Equity (MSCI EAFE), US Fixed Income (Lehman Aggregate Bond Index), HedgeFund Composite (Hedge Fund Research (HFR)), Distressed Debt (third party provider), Private Equity (Venture Economics) and Venture Capital (Venture Economics) (3) This portfolio includes US Equity (S&P 500), Int’l Equity (MSCI EAFE) and US Fixed Income (Lehman Aggregate Bond Index) No alternatives (3) 10% alternatives (2) 25% alternatives (2)

22. Fund of Funds Portfolios

23. Risk Exposure by Strategy Market Up Market Do wnVolatility Credit Spread s Liquidity Increase sDecreasesWidenContractCrunch Convertible Bond ArbitrageFlat UpDown UpDown Distressed SecuritiesUpDown UpDownUpDown Equity Hedge FundUpDownFlat DownUpDown Equity Market NeutralFlat Event DrivenUpDown UpDownUpDown Managed FuturesUp DownUpFlatUp Merger ArbitrageUpDown UpDownUpDown Fixed Income ArbitrateFlat DownUpDownUpDown

24. Style Risk Return

25. Style Correlations 1/1994-6/2005 Style Correlations Distressed Emerging Markets Equity Market neutral Event Dri venMultiFixed Income MacroHF IndexFuturesFoF Distressed Index10.58230.3630.93570.75090.31170.31610.5796-0.12670.661 Emerging Markets Index0.582310.24640.66530.66650.27510.4190.6535-0.09910.7399 Equity Market Neutral Index0.3630.246410.39180.36580.11330.20980.33640.12310.4441 Event Driven Index0.93570.66530.391810.93170.38810.38240.6691-0.17410.7577 Multi-Strategy Index0.75090.66650.36580.931710.42890.42790.6878-0.19480.7616 Fixed Income Arbitrage Index0.31170.27510.11330.38810.428910.45410.4476-0.06850.426 Global Macro Index0.31610.4190.20980.38240.42790.454110.85870.24450.6453 Hedge Fund Index0.57960.65350.33640.66910.68780.44760.858710.12640.9082 Managed Futures Index-0.1267-0.09910.1231-0.1741-0.1948-0.06850.24450.126410.1171 Fund of Funds0.6610.73990.44410.75770.76160.4260.64530.90820.11711

26. Problems with Portfolio Optimization 1990-2005 Optimal Allocation Convertible Arbitrage Index0.00 Dedicated Short Bias Index0.00 Emerging Markets Index0.00 Equity Market Neutral Index8.23% Event Driven Index45.57% Fixed Income Arbitrage Index0.00 Global Macro Index46.20% Long/Short Equity Index0.00 Managed Futures Index0.00 TASS Fund of Funds Universe Average 0.00 Summary Statistics Expected Return1.00 Standard Deviation1.96 Sharpe Ratio0.51

27. Unconstrained Optimization 1990-1995

28. 5%-20% Optimization 1990-2005 CSFB/Tremont Convertible Arbitrage Index9.09 CSFB/Tremont Dedicated Short Bias Index5.00 CSFB/Tremont Emerging Markets Index5.00 CSFB/Tremont Equity Market Neutral Index20.00 CSFB/Tremont Event Driven Index20.00 CSFB/Tremont Fixed Income Arbitrage Index5.00 CSFB/Tremont Global Macro Index15.17 CSFB/Tremont Long/Short Equity Index5.74 CSFB/Tremont Managed Futures Index5.00 CSFB/Tremont Hedge Fund Index5.00 TASS Fund of Funds Universe Average5.00 Expected Return0.80 Standard Deviation1.25 Sharpe Ratio0.64

29. 5%=20% Optimization 1990-2005