stan beckers simon weinberger

B A R C L A Y S G L O B A L I N V E S T O R S1

Stan Beckers

Simon Weinberger

Barclays Global Investors

Fundamental Factors in Hedge Fund Returns

Spitalfields Day

Cambridge 10 March 2005


Overview

The Raw Data: Issues

Skewness, Kurtosis and Autocorrelation

Communality in Hedge Fund Returns

Systematic and Residual Factors


1. Hedge Fund Returns : Data Issues

Return data only (no transparency)

Bias in Pricing/ Returns

• Survivorship Bias

• Instant History Bias

• Self-Reporting Bias

Short histories, low frequency data

Fund size ignored


HFR Database : Fund inception date, Reporting start and end date

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Short histories

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Number of months with HFR Performance Data

Number of monthly observations


Histogram of Hedge Fund AUM (Sept 2004): Not all funds are equally

important

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2. More data issues : these things aren’t normal !?

Skewness and Kurtosis

• Downside Protection

• Use of derivatives

• Non-Linear Factors

Autocorrelation in return series

• Data Smoothing


Skewness and Kurtosis

Frequency Distribution Fixed Income Hedge Fund Index Returns

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Standard Deviations


Non-Linearity in Factors

Period: January 1997- May 2004

Correlation SignificanceDifference down -up market

CONVERTIBLE ARBITRAGE 0.23 ** 0.14CTA -0.22 ** -0.32

DISTRESSED 0.47 ** 0.58

EMERGING MARKETS 0.59 ** 0.42

EQUITY NEUTRAL 0.32 ** 0.02

EVENT DRIVEN 0.66 ** 0.54

FIXED INCOME -0.05 0.6

MACRO 0.4 ** 0.3

LONG/SHORT 0.7 ** 0.22

MERGER ARB 0.53 ** 0.41

RELATIVE VALUE 0.58 ** 0.46

SHORT SELLING -0.79 ** -0.19FUND OF FUNDS 0.54 ** 0.43AVERAGE 0.3 0.28

Correlation HFR Hedge Fund Index - S&P 500


A Broad Cross Section of Funds

Daily data

All Available History

Daily Data

Historical Annual Alpha

Annual Alpha

Volatility

Information ratio

Skewness KurtosisNumber of

ObsJarque Bera

% negative

days

Max Drawdown

Recovery Period (days)

Autocorrel

A 3.85% 3.36% 1.15 0.00 3.86 815 507.14 44% -2.76% 52 -0.10B -0.29% 4.65% -0.06 -0.42 4.90 796 820.61 46% -10.85% NR 0.03C -3.20% 4.35% -0.74 0.00 2.00 402 67.18 40% -10.63% NR -0.12D 5.55% 8.24% 0.67 0.09 1.87 413 60.54 46% -11.40% NR -0.03E 4.42% 5.22% 0.85 -0.22 4.90 770 777.52 44% -9.68% NR -0.03F 2.03% 1.89% 1.08 -0.61 16.28 553 6141.98 43% -1.30% 60 -0.14G 2.09% 3.23% 0.65 2.51 35.10 261 13671.27 44% -2.25% 89 0.00H 15.45% 10.01% 1.54 -0.44 4.19 787 602.16 41% -17.10% 198 0.00I 4.10% 4.24% 0.97 -0.08 0.90 815 28.74 44% -6.20% 68 0.00J 4.43% 4.50% 0.99 -0.63 8.33 815 2408.30 40% -5.11% 72 -0.26K 4.99% 3.59% 1.39 -0.62 6.10 794 1283.61 40% -4.48% 69 -0.17L 18.84% 6.73% 2.80 0.43 10.23 787 3452.73 38% -9.76% 101 -0.10M 5.09% 4.95% 1.03 -0.06 2.91 608 215.28 41% -5.00% 23 0.02N -5.40% 4.80% -1.12 0.20 2.49 533 141.06 49% -14.24% NR 0.01O -12.62% 9.50% -1.33 0.16 1.04 463 23.09 52% -22.19% NR 0.08S&P 500 5.40% 19.92% 0.27 0.99 8.23 794 2367.51 47% -33.75% 477 -0.04Eq Weight 3.97% 1.83% 2.17 -0.39 2.85 815 295.88 41% -3.97% 81 0.06FUND 3.14% 1.69% 1.86 -0.37 3.66 856 496.72 40% -4.29% 65 0.09


A Broad Cross Section of Funds

Monthly data

All Available History Monthly

Data

Historical Annual Alpha

Annual Alpha

Volatility

Information ratio

Skewness KurtosisNumber of

ObsJarque Bera

% negative months

Max Drawdown

Recovery Period

(months)Autocorrel

A 3.05% 2.37% 1.29 1.09 1.67 39 12.28 38% -1.84% 3 -0.09B -0.85% 3.52% -0.24 -0.97 1.57 38 9.86 42% -9.48% NR 0.10C -3.72% 3.29% -1.13 -0.96 0.34 19 3.02 42% -8.71% NR 0.46D 7.54% 6.24% 1.21 1.87 3.45 19 20.50 42% -10.27% NR -0.02E 6.28% 4.54% 1.38 0.87 1.12 36 6.46 36% -8.37% NR 0.30F 2.28% 1.50% 1.52 -0.64 0.54 26 2.06 27% -0.83% NR 0.03G 0.80% 0.69% 1.15 0.94 1.32 13 2.85 38% -1.89% 3 0.27H 12.21% 10.41% 1.17 -0.49 3.01 37 15.41 38% -13.03% 9 0.25I 4.06% 3.33% 1.22 -0.21 1.93 39 6.35 38% -5.49% 4 0.06J 4.84% 4.07% 1.19 -0.88 4.16 39 33.22 23% -3.95% 4 0.07K 5.19% 3.05% 1.70 -0.11 0.46 37 0.40 24% -2.34% 3 0.08L 16.47% 9.21% 1.79 0.49 0.76 37 2.34 22% -8.25% 6 0.28M 3.87% 4.02% 0.96 -0.56 0.79 29 2.30 28% -2.67% 4 0.22N -3.55% 3.41% -1.04 -0.04 1.95 25 3.96 68% -13.90% NR 0.25O -12.35% 6.53% -1.89 -1.09 0.79 22 4.94 73% -21.54% NR 0.07S&P 500 4.29% 15.26% 0.28 -0.16 0.89 38 1.44 39% -28.99% 14 0.09Eq Weight 0.98% 0.35% 2.83 0.50 -0.76 39 2.57 23% -3.13% 5 0.15Fund 3.39% 2.82% 1.20 -0.43 0.66 37 1.81 32% -3.35% 4 0.33


Characteristics Return Distribution Fund X

June 2002 – December 2004

Monthly DailyMean 1.37% 0.05%Stdev 2.21% 0.33%Skewness 0.689 0.047Stand err Skewness 0.44 0.098Significance Skewness 1.566 0.482Kurtosis 1.165 1.142Stand err Kurtosis 0.88 0.196Significance Kurtosis 1.324 5.834Number of Observations 31 626Jarque Bera 4.203 34.263Jarque Bera Significance 0.122 0Autocorrelation 0.358 0.056Significance Autocorrel 1.994 1.396


Characteristics Return Distribution Fund XJanuary 1994 – June 2004

Fund Factor 1 Factor 2 Residualnobs 126 126 126 126mean 2.60% -0.05% 0.11% 0.00%stdev 2.23% 3.71% 2.14% 1.93%skew -0.77 -0.72 0.14 -0.3kurtosis 3.38 8.73 0.7 0.64std error skew 0.22 0.22 0.22 0.22significance skew -3.54 -3.28 0.64 -1.38std error kurt 0.44 0.44 0.44 0.44significance kurt 7.74 20.01 1.61 1.46Jarque Bera 72.47 411.08 3.01 4.06significance Jarque Bera 0 0 0.22 0.13Autocorrelation 0.23 -0.19 0.04 0.15Significance Autocorrelation 2.61 -2.14 0.49 1.71


3. Looking for Communality in Hedge Fund Returns

Hedge Fund Styles as defined by the Index Providers

• Self-Declared

• Opportunistic

Statistical Approaches

• Cluster Analysis

• Principal Component Analysis


The HFR Hedge Fund Style Classification

HFRI Convertible Arbitrage IndexHFRI Distressed Securities IndexHFRI Emerging Markets (Total)HFRI Equity Hedge IndexHFRI Equity Market Neutral IndexHFRI Equity Non-Hedge IndexHFRI Event-Driven IndexHFRI Fixed Income (Total)

HFRI Fixed Income: Arbitrage IndexHFRI Fixed Income: Convertible Bonds IndexHFRI Fixed Income: Diversified IndexHFRI Fixed Income: High Yield IndexHFRI Fixed Income: Mortgage-Backed Index

HFRI Macro IndexHFRI Market Timing IndexHFRI Merger Arbitrage IndexHFRI Relative Value Arbitrage IndexHFRI Short Selling Index


Defining the Number of Hedge Fund Styles: Cluster Analysis[1]

[1] We require 60 months of data (199907-200406), which leaves us with 676 funds for this analysis.

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Defining the Number of Hedge Fund Styles:

Average Return Correlation with Peers

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Defining the Number of Hedge Fund Styles: Explanatory Power of first Principal

Component

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HFR Hedge Fund Style Classification

H E D G E(5 19)

N O N -H E D G E

(70)

M A R K E T -N E UT R A L

(1 50)

E Q UIT Y(7 39)

E V E NTD R IV E N

(1 09)

C O NV E R T IB LEA RB(96)

M E R G E RA RB(46)

R E LA T IV EV A L UE(3 16)

E M E RG INGM A R K E T S

(1 33)

D IS T R E S S E DS E CU R IT IE S

(62)

C O NV E R T IB L E S(12)

D IV E R S IF IE D(44)

H IG HY IE LD

(25)

M O R T G A G E(31)

F I A RB(53)

O T H E RF I

(1 65)

F IX E DIN C O M E

(2 27)

M A RK E TT IM ING

(35)

F O R E IG NE X C HA N G E

(42)

G L O B A LM A C RO

(2 78)

M A NA G E DF U T U R E S

(1 76)

H E G E F U N DS(18 69)


Equity Styles

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Fixed Income Styles

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Relative Value Styles

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Histograms of average correlation with peers (same hedge fund style) versus non-peers

Correlation Structure with Peers and Non-Peers


Cluster Analysis within Broadly Defined Styles

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4. Dissecting Within-Style Hedge Fund Returns: Systematic and Residual factors

A Primer on Multiple Factor Models

• Differentiating between Alpha and Beta

Identifying systematic factors

• Principal Component analysis

• Fundamental Factors

Where is the hedge?


The Academic Background on Multiple Factor Models

The CAPM

• Single Factor : The Market Portfolio

APT : Multiple Factors

• Factors Undefined but the academic world would probably agree that – for equities - they include— Small versus Large— Value Versus Growth— Momentum

• Broad Approaches for Factor Indentification— Macro-Economic Models— Fundamental Models— Statistical Models

Virtually all models are Linear


Factor Model Selection Criteria

Academically Sound?

Best Fit?

Economic Interpretation?

Out of sample explanatory power?

Tradeable?


A First Cut at Identifying Factors within each Style:

Principal Component Analysis

Principal Comp.

Equity Emerging Markets

Fixed Income

Macro Relative Value

Managed Futures

1 23.18% 24.17% 32.85% 19.48% 41.93% 19.34% 2 8.30% 19.27% 15.52% 11.52% 11.27% 12.21% 3 6.79% 8.02% 10.68% 9.43% 8.54% 8.53% 4 4.83% 6.46% 9.59% 8.32% 6.26% 6.69% 5 4.04% 6.40% 6.64% 5.42% 3.86% 5.38% 6 3.61% 5.24% 4.81% 4.63% 3.30% 4.81% 7 3.24% 3.65% 3.60% 3.96% 2.74% 4.36% 8 3.09% 3.11% 2.77% 3.55% 2.26% 4.08% 9 2.85% 2.49% 1.88% 3.27% 2.01% 3.27% 10 2.58% 2.21% 1.66% 3.01% 1.92% 3.17%

(1-3) 38.27% 51.46% 59.05% 40.43% 61.74% 40.08% >5% 3 6 5 5 4 5


Selected Findings from the Hedge Fund Literature

Equity Strategies tend to have market exposure and exposure to Fama/French Factors SMB and HML (among others Fung and Hsieh, 2003)

30% of market-neutral funds have market risk exposure (Patton, 2004)

Option Strategies have explanatory power for non-directional strategies (Agarwal and Naik, 2000)

Trend Following Strategy exhibits payoff similar to by lookback straddle (Fung and Hsieh, 2001)

Merger Arbitrage exhibits payoff like uncovered put on Equity Index (Mitchell and Pulvino, 2000)


Mean/Median Forecast Error at successive steps Equity Hedge Funds

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Explanatory power of a factor risk model (Equity Funds)

Median : 35% in sample, 23% out of sample

Truncated Median: 41% in sample, 34% out of sample

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Mean/Median Forecast Error at successive steps Fixed Income Hedge Funds

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Explanatory power of a factor risk model (Fixed Income Funds)

Histogram of in-sample (199401-200406) and out-of-sample fit (regression of fund returns on return explained by risk model (product sum of prevailing exposure estimate and realised factor return)Median* disregards observations with extreme fit (<10% or >70%).

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Median Median*in-sample 21.97% 31.19%out-of-sample 10.26% 30.48%


Fixed Income Fund In Sample Alpha

Fund-level rolling 36m estimation

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HFR Hedge Fund Index Returns: Where is the Hedge?

T-Stat of Systematic Factors

LONG/SHORT

RELATIVE VALUE

FIXED INCOME

GLOBAL MACRO

FUND OF FUNDS

Adjusted R Squared 0.85 0.63 0.53 0.32 0.64Intercept 2.29 1.54 2.91 2.77 2.02Inflation % change 0.29 1.42 0.88 0.23 1.21Inflation level -0.19 0.23 0.81 -0.45 0.39VIX % change -0.19 -1.9 -0.62 0.35 -0.52Vix level -0.73 0.74 -2.8 -2.13 -1.46S&P 500 return 11.92 4.73 -1.32 3.44 5.1Credit spread % change -0.47 -4.03 -2.9 -0.92 -2US small - large return 9.43 2.8 0.19 3.36 4.9US Value-growth return 6.22 -0.56 0.49 1.92 3.74Slope of yield curve % Change 0.8 -2.5 -6.01 -0.41 -0.03Slope of yield curve -3.78 -3.49 0.07 -0.62 -1.56Risk appetite 1.97 2.99 -0.5 -0.97 1.54


Summary

Given the Quality of the Data, all Hedge Fund Empirical Research has to be taken with a pinch of salt

Skewness, Kurtosis and Autocorrelation are less of an issue than some people would lead you to believe

Hedge Fund Styles are not clearly delineated and somewhat arbitrary

Even so, Common factors can be identified within broad hedge fund style classifications

Significant systematic factors are present in most hedge fund returns

Alpha does remain after taking systematic factors into account

Hedge Fund is somewhat of a misnomer

stan beckers simon weinberger

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