Download - Hedge Fund Portfolios

Hedge Fund Portfolios

Ezra Zask

Yale University

September 26, 2005

Benefits of Hedge Funds

Riskier than traditional investments?

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Iraq Crisis (8/90)

Asia Crisis (8/97)

Russia Crisis (8/98)

September 11 (9/01)

MSCI World

-9.55%

-3.60%-2.00%

1.00%

-7.05%

0.62%

-0.26%

0.55%

-14.45%

-11.43% -11.77%

1.49%

-9.34%

-1.57% -1.54%

0.29%

MSCI World Equity Hedge Event Driven Relative Value

Hedge Fund Returns

Assets Risk Return Profile

Hedge Fund Style Beta and Alpha

Portfolio Optimization

• Requirements for Mean Variance Optimization– Returns

• Normally Distributed• Accurate Data• Time Frame

– Standard Deviation• Constant over time

– Correlations• Lower is better

Survivorship and Backfill Bias

Tremont Style Statistics

Summary Statistics - Factors.fld 1/1994-6/2005

N Periods

Geometric

Mean (%)

Arithmetic Mean (%)

Standard Deviation

(%)Sharpe Ratio

Skewness

Kurtosis Alpha Beta

Distressed Index 137 13.08 13.33 7.35 0.5541 -2.8986 18.4301 0.0084 0.2388

Emerging Markets Index 137 6.87 8.35 17.87 0.1407 -0.6758 4.6968 0.0015 0.5272

Equity Market Neutral Index 137 10.07 10.11 3.26 0.9371 0.3328 0.3286 0.0076 0.078

Event Driven Index 137 11.22 11.4 6.3 0.5489 -3.5662 25.1946 0.0072 0.211

Event Driven Multi-Strategy Index 137 10.2 10.4 6.64 0.4735 -2.6838 17.9901 0.0066 0.193

Fixed Income Arbitrage Index 137 6.33 6.41 4.05 0.4695 -3.0921 16.0501 0.0054 0.0073

Global Macro Index 137 13.66 14.38 12.92 0.3425 0.0192 2.5641 0.0099 0.1776

Hedge Fund Index 137 10.58 10.93 8.85 0.3742 0.133 2.1422 0.0065 0.256

Managed Futures Index 137 6.6 7.39 13.12 0.1686 0.0214 0.3497 0.0077 -0.1526

Fund of Funds Universe Average 137 7.21 7.38 6.14 0.3589 -0.1383 2.2125 0.0044 0.1967

CS F B/T re m on t Em e rg in g M a rke ts In de x : F e b rua ry 1994 - Ju ne 2005Returns Histogram

Return

NumberCS F B/T re m on t Em e rg in g M a rke ts In de x : F e b rua ry 1994 - Ju ne 2005

Returns Histogram

-24.0% 18.0%-22.0% -20.0% -18.0% -16.0% -14.0% -12.0% -10.0% -8.0% -6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%

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Normal Distribution?

Hedge Funds in Portfolios

Efficient Frontier

Hedge Fund Styles

Background Information:Why Invest in Alternatives?

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

Historical Risk and Returns(1)(2)

January 1994 to December 2003

Hedge Fund Weighted Composite Index

S&P 500

90 day US T-Bill

LehmanAggregate Bond Index

Russell 2000 Small-Cap

EquityLehman High Yield Credit Bond Index

Distressed Debt Index

Private Equity Index

Venture Capital Index

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

0.0% 5.0% 10.0% 15.0% 20.0% 25.0%

Annualized Volatility

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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

0.06

0.37 0.35

0.17

0.29

0.01

-0.14-0.19

0.58

0.49

-0.4

-0.2

0

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0.4

0.6

Hedge FundMarket Neutral

Hedge FundMacro

Distressed Debt Private Equity Venture Capital

S&P 500 Lehman Aggregate Bond Index

Alternative Asset Correlations(1)(2)

January 1994 to December 2003

Alternatives enhance traditionalinvestment 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)

Risk/Return Tradeoff(1)

5.0%

6.5%

8.0%

9.5%

6.0% 8.0% 10.0% 12.0% 14.0%

Portfolio Volatility

An

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Fund of Funds Portfolios

Risk Exposure by Strategy

Market

Up

Market Down Volatility Volatility

Credit Spread

sCredit

Spreads Liquidity

Increases Decreases Widen Contract Crunch

Convertible Bond Arbitrage Flat Flat Up Down Down Up Down

Distressed Securities Up Down Down Up Down Up Down

Equity Hedge Fund Up Down Flat Flat Down Up Down

Equity Market Neutral Flat Flat Flat Flat Flat Flat Flat

Event Driven Up Down Down Up Down Up Down

Managed Futures Up Up Up Down Up Flat Up

Merger Arbitrage Up Down Down Up Down Up Down

Fixed Income Arbitrate Flat Flat Down Up Down Up Down

Style Risk Return

Ris k (STD)

Return (A M)Ja nu a ry 1990 - Jun e 2005Risk vs. Return

2.0% 19.0%3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 16.0% 17.0% 18.0%

-2.0%

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-1.0%

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CSFB/Tremont Convertible A rbitrage Index

CSFB/Tremont Dedicated Short Bias Index

CSFB/Tremont Emerging Markets Index

CSFB/Tremont Equity Market Neutral Index

CSFB/Tremont Event Driven Index

CSFB/Tremont Fix ed Income A rbitrage Index

CSFB/Tremont Global Macro Index

CSFB/Tremont Long/Short Equity Index

CSFB/Tremont Managed Futures Index

CSFB/Tremont Hedge Fund Index

TA SS Fund of Funds Universe A verage

Style Correlations 1/1994-6/2005

Style Correlations

Distressed EmergingMarkets

EquityMarketneutral

Event Driven Multi Fixed Income Macro HF Index Futures FoF

Distressed Index 1 0.5823 0.363 0.9357 0.7509 0.3117 0.3161 0.5796 -0.1267 0.661

Emerging Markets Index 0.5823 1 0.2464 0.6653 0.6665 0.2751 0.419 0.6535 -0.0991 0.7399

Equity Market Neutral Index 0.363 0.2464 1 0.3918 0.3658 0.1133 0.2098 0.3364 0.1231 0.4441

Event Driven Index 0.9357 0.6653 0.3918 1 0.9317 0.3881 0.3824 0.6691 -0.1741 0.7577

Multi-Strategy Index 0.7509 0.6665 0.3658 0.9317 1 0.4289 0.4279 0.6878 -0.1948 0.7616

Fixed Income Arbitrage Index 0.3117 0.2751 0.1133 0.3881 0.4289 1 0.4541 0.4476 -0.0685 0.426

Global Macro Index 0.3161 0.419 0.2098 0.3824 0.4279 0.4541 1 0.8587 0.2445 0.6453

Hedge Fund Index 0.5796 0.6535 0.3364 0.6691 0.6878 0.4476 0.8587 1 0.1264 0.9082

Managed Futures Index -0.1267 -0.0991 0.1231 -0.1741 -0.1948 -0.0685 0.2445 0.1264 1 0.1171

Fund of Funds 0.661 0.7399 0.4441 0.7577 0.7616 0.426 0.6453 0.9082 0.1171 1

Problems with Portfolio Optimization1990-2005

Optimal Allocation

Convertible Arbitrage Index 0.00

Dedicated Short Bias Index 0.00

Emerging Markets Index 0.00

Equity Market Neutral Index 8.23%

Event Driven Index 45.57%

Fixed Income Arbitrage Index 0.00

Global Macro Index 46.20%

Long/Short Equity Index 0.00

Managed Futures Index 0.00

TASS Fund of Funds Universe Average

0.00

Summary Statistics

Expected Return 1.00

Standard Deviation 1.96

Sharpe Ratio 0.51

Standard Deviation (Risk)

Expected Return

0.0 6.00.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6

-0.2

1.2

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CSFB/Tremont Convertible Arbitrage Index


CSFB/Tremont Emerging Markets IndexCSFB/Tremont Equity Market Neutral Index


CSFB/Tremont Fixed Income Arbitrage Index

CSFB/Tremont Global Macro IndexCSFB/Tremont Long/Short Equity Index




Unconstrained Optimization 1990-1995

5%-20% Optimization1990-2005

CSFB/Tremont Convertible Arbitrage Index 9.09

CSFB/Tremont Dedicated Short Bias Index 5.00

CSFB/Tremont Emerging Markets Index 5.00

CSFB/Tremont Equity Market Neutral Index 20.00

CSFB/Tremont Event Driven Index 20.00

CSFB/Tremont Fixed Income Arbitrage Index 5.00

CSFB/Tremont Global Macro Index 15.17

CSFB/Tremont Long/Short Equity Index 5.74

CSFB/Tremont Managed Futures Index 5.00

CSFB/Tremont Hedge Fund Index 5.00

TASS Fund of Funds Universe Average 5.00

Expected Return 0.80

Standard Deviation 1.25

Sharpe Ratio 0.64

Position 50

CSFB/Tremont Convertible Arbitrage Index (9.09%)

CSFB/Tremont Dedicated Short Bias Index (5.00%)

CSFB/Tremont Emerging Markets Index (5.00%)CSFB/Tremont Equity Market Neutral Index (20.00%)

CSFB/Tremont Event Driven Index (20.00%)

CSFB/Tremont Fixed Income Arbitrage Index (5.00%)

CSFB/Tremont Global Macro Index (15.17%)CSFB/Tremont Long/Short Equity Index (5.74%)

CSFB/Tremont Managed Futures Index (5.00%)

CSFB/Tremont Hedge Fund Index (5.00%)

TASS Fund of Funds Universe Average (5.00%)

5%=20% Optimization1990-2005

Standard Deviation (Risk)

Expected Return

0.0 6.00.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6

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CSFB/Tremont Convertible Arbitrage Index


CSFB/Tremont Emerging Markets IndexCSFB/Tremont Equity Market Neutral Index


CSFB/Tremont Fixed Income Arbitrage Index

CSFB/Tremont Global Macro IndexCSFB/Tremont Long/Short Equity Index




5%=20% Optimization1990-2005