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
B A R C L A Y S G L O B A L I N V E S T O R S2
Overview
The Raw Data: Issues
Skewness, Kurtosis and Autocorrelation
Communality in Hedge Fund Returns
Systematic and Residual Factors
B A R C L A Y S G L O B A L I N V E S T O R S3
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
B A R C L A Y S G L O B A L I N V E S T O R S4
HFR Database : Fund inception date, Reporting start and end date
0
100
200
300
400
500
600N
um
ber
of
Hed
ge
Fu
nd
s la
un
ched
<199
0
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Inception Year First on HFR Last Year on HFR
B A R C L A Y S G L O B A L I N V E S T O R S5
Short histories
0
100
200
300
400
500
600
700
800
900
Nu
mb
er o
f H
edg
e F
un
ds
<20 20-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 101-120
121-150
150+
Number of months with HFR Performance Data
Number of monthly observations
B A R C L A Y S G L O B A L I N V E S T O R S6
Histogram of Hedge Fund AUM (Sept 2004): Not all funds are equally
important
0
100
200
300
400
500
600
5 10 15 20 30 40 50 60 70 80 90 100
150
200
250
500
Mor
e
Fund Assets (Million US$)
Fre
qu
ency
B A R C L A Y S G L O B A L I N V E S T O R S7
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
B A R C L A Y S G L O B A L I N V E S T O R S8
Skewness and Kurtosis
Frequency Distribution Fixed Income Hedge Fund Index Returns
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-3.5
-3.2
-2.9
-2.6 -2
.3 -2 -1.7
-1.4
-1.1
-0.8
-0.5
-0.2 0.
10.
4 0.7 1
1.3
1.6
1.9
2.2
2.5
2.8
3.1
3.4
Standard Deviations
B A R C L A Y S G L O B A L I N V E S T O R S9
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
B A R C L A Y S G L O B A L I N V E S T O R S10
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
B A R C L A Y S G L O B A L I N V E S T O R S11
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
B A R C L A Y S G L O B A L I N V E S T O R S12
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
B A R C L A Y S G L O B A L I N V E S T O R S13
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
B A R C L A Y S G L O B A L I N V E S T O R S14
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
B A R C L A Y S G L O B A L I N V E S T O R S15
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
B A R C L A Y S G L O B A L I N V E S T O R S16
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.
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30 35 40 45 50
Number of Clusters
Pse
ud
o T
-Sta
t
B A R C L A Y S G L O B A L I N V E S T O R S17
Defining the Number of Hedge Fund Styles:
Average Return Correlation with Peers
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
EM
: A
sia
EM
: E
urop
e
EM
: G
loba
l
EM
: La
tin A
mer
ica
EM
Equ
ity H
edge
Equ
ity M
N
Equ
ity N
on H
edge
EQ
UIT
Y
Con
vert
ible
Arb
Eve
nt D
riven
Mer
ger
Arb
itrag
e
Rel
ativ
e V
alue
Arb
RE
L. V
ALU
E
Dis
tres
sed
Sec
.
FI:
Arb
itrag
e
FI:
Con
vert
ible
Bon
d
FI:
Div
ersi
fied
FI:
Hig
h Y
ield
FI:
Mor
tgag
e B
.
FIX
ED
INC
OM
E
For
eign
Exc
hang
e
Mac
ro
Mar
ket T
imin
g
MA
CR
O
Man
aged
Fut
ures
Ave
rag
e C
orr
elat
ion
B A R C L A Y S G L O B A L I N V E S T O R S18
Defining the Number of Hedge Fund Styles: Explanatory Power of first Principal
Component
0%
10%
20%
30%
40%
50%
60%
EM
: Asi
a
EM
: Eur
ope
EM
: Glo
bal
EM
: Lat
in
EM
EQ
Hed
ge
EQ
MN
EQ
Non
-Hed
ge
EQ
UIT
Y
Con
vArb
Eve
nt-D
riven
Mer
ger
Arb
Rel
ativ
e V
alue
Arb
RE
L. V
ALU
E
Dis
tres
sed
FI:
Arb
FI:
Con
vert
ible
s
FI:
Div
ersi
fied
FI:
HY
FI:
Mor
tgag
es
FIX
ED
INC
OM
E
FX
Mac
ro
Mar
ket T
imin
g
MA
CR
O
Man
aged
Fut
ures
Var
ian
ce e
xpla
ined
B A R C L A Y S G L O B A L I N V E S T O R S19
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)
B A R C L A Y S G L O B A L I N V E S T O R S20
Equity Styles
0
10
20
30
40
50
60
70
80
0
0.05 0.1
0.15 0.2
0.25 0.3
0.35 0.4
0.45 0.5
Mor
e
Fre
qu
ency
In-Style
Out-of-Style
Fixed Income Styles
0
5
10
15
20
25
0
0.05 0.1
0.15 0.2
0.25 0.3
0.35 0.4
0.45 0.5
Mor
e
Fre
qu
ency
In-Style
Out-of-Style
Relative Value Styles
0
5
10
15
20
25
30
35
40
45
0
0.05 0.1
0.15 0.2
0.25 0.3
0.35 0.4
0.45 0.5
Mor
e
Fre
qu
ency
In-Style
Out-of-Style
Macro Style
0
5
10
15
20
0
0.05 0.1
0.15 0.2
0.25 0.3
0.35 0.4
0.45 0.5
Mor
e
Fre
qu
ency
In-Style
Out-of-Style
Managed Futures Style
0
5
10
15
20
25
30
35
40
0
0.05 0.1
0.15 0.2
0.25 0.3
0.35 0.4
0.45 0.5
Mor
e
Fre
qu
ency
In-Style
Out-of-Style
Histograms of average correlation with peers (same hedge fund style) versus non-peers
Correlation Structure with Peers and Non-Peers
B A R C L A Y S G L O B A L I N V E S T O R S21
Cluster Analysis within Broadly Defined Styles
0
20
40
60
80
100
120
140
160
Fu
nd
s
Equity Non-Hedge Equity Hedge Equity Market Neutral
Cluster #3
Cluster #2
Cluster #1
0
5
10
15
20
Fu
nd
s
DistressedSecurities
Arbitrage ConvertibleBond
Diversif ied High Yield Mortgage-Backed
Cluster #1 Cluster #2 Cluster #3
Cluster #4 Cluster #5 Cluster #6
0
5
10
15
20
25
30
35
40
45
Fu
nd
s
ConvertibleArbitrage
Event-Driven MergerArbitrage
Relative ValueArbitrage
Cluster #1 Cluster #2
Cluster #3 Cluster #4
0
5
10
15
20
25
30
35
Fu
nd
s
Foreign Exchange Macro Market Timing
Cluster #3
Cluster #2
Cluster #1
B A R C L A Y S G L O B A L I N V E S T O R S22
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?
B A R C L A Y S G L O B A L I N V E S T O R S23
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
B A R C L A Y S G L O B A L I N V E S T O R S24
Factor Model Selection Criteria
Academically Sound?
Best Fit?
Economic Interpretation?
Out of sample explanatory power?
Tradeable?
B A R C L A Y S G L O B A L I N V E S T O R S25
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
B A R C L A Y S G L O B A L I N V E S T O R S26
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)
B A R C L A Y S G L O B A L I N V E S T O R S27
Mean/Median Forecast Error at successive steps Equity Hedge Funds
0
10
20
30
40
50
60
ST
P1
ST
P2
ST
P3
ST
P4
ST
P5
ST
P6
ST
P7
ST
P8
ST
P9
ST
P10
ST
P11
ST
P12
ST
P13
ST
P14
ST
P15
ST
P16
ST
P17
ST
P18
ST
P19
Fo
reca
st E
rro
rMean
Median
B A R C L A Y S G L O B A L I N V E S T O R S28
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
0%
3%
6%
9%
12%
15%
0% 5% 10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
Mor
e
Adjusted Fit
Fre
quen
cyOut-of-Sample
In-Sample
B A R C L A Y S G L O B A L I N V E S T O R S29
Equity Hedge Fund In-Sample Alpha
-5%
0%
5%
10%
15%
20%
25%
30%
1997
01
1997
07
1998
01
1998
07
1999
01
1999
07
2000
01
2000
07
2001
01
2001
07
2002
01
2002
07
2003
01
2003
07
2004
01
Alp
ha
p.a
. (3
6m r
oll
ing
est
imat
ion
)
Median Top Quartile Bottom Quartile
B A R C L A Y S G L O B A L I N V E S T O R S30
Mean/Median Forecast Error at successive steps Fixed Income Hedge Funds
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Median
Mean
B A R C L A Y S G L O B A L I N V E S T O R S31
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%).
0%
5%
10%
15%
20%
25%
0
0.05 0.1
0.15 0.2
0.25 0.3
0.35 0.4
0.45 0.5
0.55 0.6
0.65 0.7
0.75
Mor
e
Adjusted Fit
Fre
qu
en
cy
Out-of-Sample
In-Sample
Median Median*in-sample 21.97% 31.19%out-of-sample 10.26% 30.48%
B A R C L A Y S G L O B A L I N V E S T O R S32
Fixed Income Fund In Sample Alpha
Fund-level rolling 36m estimation
0%
5%
10%
15%
20%
25%
1997
01
1997
07
1998
01
1998
07
1999
01
1999
07
2000
01
2000
07
2001
01
2001
07
2002
01
2002
07
2003
01
2003
07
2004
01
Alp
ha p
.a.
Median Q3 Q1
B A R C L A Y S G L O B A L I N V E S T O R S33
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
B A R C L A Y S G L O B A L I N V E S T O R S34
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