Fundamental Factors in Hedge
Fund Returns
Stan Beckers
Simon Weinberger
Barclays Global Investors
Spitalfields Day
Cambridge 10 March 2005
0
BARCLAYS GLOBAL INVESTORS
Overview
 The Raw Data: Issues
 Skewness, Kurtosis and Autocorrelation
 Communality in Hedge Fund Returns
 Systematic and Residual Factors
1
BARCLAYS GLOBAL INVESTORS
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
2
BARCLAYS GLOBAL INVESTORS
HFR Database : Fund inception date,
Reporting start and end date
500
400
300
200
Inception Year
3
First on HFR
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
0
1990
100
<1990
Number of Hedge Funds launched
600
Last Year on HFR
BARCLAYS GLOBAL INVESTORS
Short histories
Number of monthly observations
900
Number of Hedge Funds
800
700
600
500
400
300
200
100
0
<20
20-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 101120
121150
150+
Number of months with HFR Performance Data
4
BARCLAYS GLOBAL INVESTORS
Histogram of Hedge Fund AUM (Sept 2004):
Not all funds are equally important
600
500
Frequency
400
300
200
100
More
500
250
200
150
100
90
80
70
60
50
40
30
20
15
10
5
0
Fund Assets (Million US$)
5
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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
6
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Skewness and Kurtosis
Frequency Distribution Fixed Income Hedge Fund Index Returns
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Standard Deviations
7
BARCLAYS GLOBAL INVESTORS
Non-Linearity in Factors
Correlation HFR Hedge Fund Index - S&P 500
Difference
Correlation Significance down -up
market
CONVERTIBLE ARBITRAGE
CTA
0.23
-0.22
**
**
0.14
-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
FUND OF FUNDS
AVERAGE
-0.79
0.54
0.3
**
**
-0.19
0.43
0.28
Period: January 1997- May 2004
8
BARCLAYS GLOBAL INVESTORS
A Broad Cross Section of Funds
Daily data
All
Available
History
Daily Data
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
S&P 500
Eq Weight
FUND
9
Historical
Annual
Alpha
3.85%
-0.29%
-3.20%
5.55%
4.42%
2.03%
2.09%
15.45%
4.10%
4.43%
4.99%
18.84%
5.09%
-5.40%
-12.62%
5.40%
3.97%
3.14%
Annual
Information
Alpha
Skewness
ratio
Volatility
3.36%
4.65%
4.35%
8.24%
5.22%
1.89%
3.23%
10.01%
4.24%
4.50%
3.59%
6.73%
4.95%
4.80%
9.50%
19.92%
1.83%
1.69%
1.15
-0.06
-0.74
0.67
0.85
1.08
0.65
1.54
0.97
0.99
1.39
2.80
1.03
-1.12
-1.33
0.27
2.17
1.86
0.00
-0.42
0.00
0.09
-0.22
-0.61
2.51
-0.44
-0.08
-0.63
-0.62
0.43
-0.06
0.20
0.16
0.99
-0.39
-0.37
Kurtosis
3.86
4.90
2.00
1.87
4.90
16.28
35.10
4.19
0.90
8.33
6.10
10.23
2.91
2.49
1.04
8.23
2.85
3.66
Number of
Obs
Jarque
Bera
815
507.14
796
820.61
402
67.18
413
60.54
770
777.52
553 6141.98
261 13671.27
787
602.16
815
28.74
815 2408.30
794 1283.61
787 3452.73
608
215.28
533
141.06
463
23.09
794 2367.51
815
295.88
856
496.72
%
Recovery
Max
negative
Period Autocorrel
Drawdown
days
(days)
44%
46%
40%
46%
44%
43%
44%
41%
44%
40%
40%
38%
41%
49%
52%
47%
41%
40%
-2.76%
-10.85%
-10.63%
-11.40%
-9.68%
-1.30%
-2.25%
-17.10%
-6.20%
-5.11%
-4.48%
-9.76%
-5.00%
-14.24%
-22.19%
-33.75%
-3.97%
-4.29%
52
NR
NR
NR
NR
60
89
198
68
72
69
101
23
NR
NR
477
81
65
-0.10
0.03
-0.12
-0.03
-0.03
-0.14
0.00
0.00
0.00
-0.26
-0.17
-0.10
0.02
0.01
0.08
-0.04
0.06
0.09
BARCLAYS GLOBAL INVESTORS
A Broad Cross Section of Funds
Monthly data
All
Available
History
Monthly
Data
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
S&P 500
Eq Weight
Fund
10
Historical
Annual
Alpha
3.05%
-0.85%
-3.72%
7.54%
6.28%
2.28%
0.80%
12.21%
4.06%
4.84%
5.19%
16.47%
3.87%
-3.55%
-12.35%
4.29%
0.98%
3.39%
Annual
Alpha
Volatility
2.37%
3.52%
3.29%
6.24%
4.54%
1.50%
0.69%
10.41%
3.33%
4.07%
3.05%
9.21%
4.02%
3.41%
6.53%
15.26%
0.35%
2.82%
Information
Skewness
ratio
1.29
-0.24
-1.13
1.21
1.38
1.52
1.15
1.17
1.22
1.19
1.70
1.79
0.96
-1.04
-1.89
0.28
2.83
1.20
1.09
-0.97
-0.96
1.87
0.87
-0.64
0.94
-0.49
-0.21
-0.88
-0.11
0.49
-0.56
-0.04
-1.09
-0.16
0.50
-0.43
Kurtosis
1.67
1.57
0.34
3.45
1.12
0.54
1.32
3.01
1.93
4.16
0.46
0.76
0.79
1.95
0.79
0.89
-0.76
0.66
Number of
Obs
39
38
19
19
36
26
13
37
39
39
37
37
29
25
22
38
39
37
Jarque
Bera
12.28
9.86
3.02
20.50
6.46
2.06
2.85
15.41
6.35
33.22
0.40
2.34
2.30
3.96
4.94
1.44
2.57
1.81
%
Recovery
Max
negative
Period Autocorrel
Drawdown
months
(months)
38%
42%
42%
42%
36%
27%
38%
38%
38%
23%
24%
22%
28%
68%
73%
39%
23%
32%
-1.84%
-9.48%
-8.71%
-10.27%
-8.37%
-0.83%
-1.89%
-13.03%
-5.49%
-3.95%
-2.34%
-8.25%
-2.67%
-13.90%
-21.54%
-28.99%
-3.13%
-3.35%
3
NR
NR
NR
NR
NR
3
9
4
4
3
6
4
NR
NR
14
5
4
-0.09
0.10
0.46
-0.02
0.30
0.03
0.27
0.25
0.06
0.07
0.08
0.28
0.22
0.25
0.07
0.09
0.15
0.33
BARCLAYS GLOBAL INVESTORS
Characteristics Return Distribution Fund X
June 2002 – December 2004
Mean
Stdev
Skewness
Stand err Skewness
Significance Skewness
Kurtosis
Stand err Kurtosis
Significance Kurtosis
Number of Observations
Jarque Bera
Jarque Bera Significance
Autocorrelation
Significance Autocorrel
11
Monthly
1.37%
2.21%
0.689
0.44
1.566
1.165
0.88
1.324
31
4.203
0.122
0.358
1.994
Daily
0.05%
0.33%
0.047
0.098
0.482
1.142
0.196
5.834
626
34.263
0
0.056
1.396
BARCLAYS GLOBAL INVESTORS
Characteristics Return Distribution Fund X
January 1994 – June 2004
nobs
mean
stdev
skew
kurtosis
std error skew
significance skew
std error kurt
significance kurt
Jarque Bera
significance Jarque Bera
Autocorrelation
Significance Autocorrelation
12
Fund
126
2.60%
2.23%
-0.77
3.38
0.22
-3.54
0.44
7.74
72.47
0
0.23
2.61
Factor 1
126
-0.05%
3.71%
-0.72
8.73
0.22
-3.28
0.44
20.01
411.08
0
-0.19
-2.14
Factor 2
126
0.11%
2.14%
0.14
0.7
0.22
0.64
0.44
1.61
3.01
0.22
0.04
0.49
Residual
126
0.00%
1.93%
-0.3
0.64
0.22
-1.38
0.44
1.46
4.06
0.13
0.15
1.71
BARCLAYS GLOBAL INVESTORS
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
13
BARCLAYS GLOBAL INVESTORS
The HFR Hedge Fund Style Classification
HFRI Convertible Arbitrage Index
HFRI Distressed Securities Index
HFRI Emerging Markets (Total)
HFRI Equity Hedge Index
HFRI Equity Market Neutral Index
HFRI Equity Non-Hedge Index
HFRI Event-Driven Index
HFRI Fixed Income (Total)
HFRI Fixed Income: Arbitrage Index
HFRI Fixed Income: Convertible Bonds Index
HFRI Fixed Income: Diversified Index
HFRI Fixed Income: High Yield Index
HFRI Fixed Income: Mortgage-Backed Index
HFRI Macro Index
HFRI Market Timing Index
HFRI Merger Arbitrage Index
HFRI Relative Value Arbitrage Index
HFRI Short Selling Index
14
BARCLAYS GLOBAL INVESTORS
Defining the Number of Hedge Fund Styles:
Cluster Analysis[1]
100
90
80
Pseudo T-Stat
70
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
40
45
50
Num ber of Clusters
15
[1] We require 60 months of data (199907-200406), which leaves us with 676 funds for this analysis.
BARCLAYS GLOBAL INVESTORS
0.00
16
Managed Futures
MACRO
Market Timing
Macro
Foreign Exchange
FIXED INCOME
FI: Mortgage B.
FI: High Yield
FI: Diversified
FI: Convertible Bond
FI: Arbitrage
Distressed Sec.
REL. VALUE
Relative Value Arb
Merger Arbitrage
Event Driven
Convertible Arb
EQUITY
Equity Non Hedge
Equity MN
Equity Hedge
EM
EM: Latin America
EM: Global
EM: Europe
EM: Asia
Average Correlation
Defining the Number of Hedge Fund Styles:
Average Return Correlation with Peers
0.70
0.60
0.50
0.40
0.30
0.20
0.10
BARCLAYS GLOBAL INVESTORS
0%
17
Managed Futures
MACRO
Market Timing
Macro
FX
FIXED INCOME
FI: Mortgages
FI: HY
FI: Diversified
FI: Convertibles
FI: Arb
Distressed
REL. VALUE
Relative Value Arb
Merger Arb
Event-Driven
ConvArb
EQUITY
EQ Non-Hedge
EQ MN
EQ Hedge
EM
EM: Latin
EM: Global
EM: Europe
EM: Asia
Variance explained
Defining the Number of Hedge Fund Styles:
Explanatory Power of first Principal Component
60%
50%
40%
30%
20%
10%
BARCLAYS GLOBAL INVESTORS
HFR Hedge Fund Style Classification
HEGE FUNDS
(1869)
EQUITY
(739)
HEDGE
(519)
18
NONHEDGE
(70)
MARKETNEUTRAL
(150)
EVENT
DRIVEN
(109)
RELATIVE
VALUE
(316)
EMERGING
MARKETS
(133)
FIXED
INCOME
(227)
GLOBAL
MACRO
(278)
MANAGED
FUTURES
(176)
CONVERTIBLE
ARB
(96)
MERGER
ARB
(46)
DISTRESSED
SECURITIES
(62)
OTHER
FI
(165)
MARKET
TIMING
(35)
FOREIGN
EXCHANGE
(42)
CONVERTIBLES
(12)
DIVERSIFIED
(44)
HIGH
YIELD
(25)
MORTGAGE
(31)
FI ARB
(53)
BARCLAYS GLOBAL INVESTORS
Correlation Structure with Peers and Non-Peers
Histograms of average correlation with peers (same hedge fund style) versus non-peers
Fixed Income Styles
Equity Styles
80
70
60
In-Style
Out-of-Style
Out-of-Style
20
40
30
20
Frequency
Frequency
50
15
10
40
In-Style
35
Out-of-Style
30
25
20
15
10
5
In-Style
Out-of-Style
Frequency
10
35
In-Style
30
Out-of-Style
25
20
15
10
5
5
More
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
More
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
19
0
0
0
BARCLAYS GLOBAL INVESTORS
More
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0
More
0.5
0.45
0.4
0.35
0.3
Managed Futures Style
40
15
Frequency
0.25
0.2
0.15
0.1
0.05
0
Macro Style
20
0.1
0
0
More
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
5
0.05
10
0
Frequency
25
In-Style
Relative Value Styles
45
Cluster Analysis within Broadly Defined Styles
20
Cluster #3
160
Cluster #2
140
Cluster #1
Cluster #2
Cluster #3
Cluster #4
Cluster #5
Cluster #6
15
Cluster #1
Funds
120
Funds
100
80
10
60
5
40
20
0
0
Equity Non-Hedge
Equity Hedge
Distressed Arbitrage Convertible Diversified High Yield MortgageSecurities
Bond
Backed
Equity Market Neutral
45
Cluster #1
Cluster #2
40
Cluster #3
Cluster #4
Cluster #2
30
35
30
Cluster #1
25
25
Funds
Funds
Cluster #3
35
20
15
20
15
10
10
5
5
0
Convertible
Arbitrage
20
Event-Driven
Merger
Arbitrage
Relative Value
Arbitrage
0
Foreign Exchange
Macro
Market Timing
BARCLAYS GLOBAL INVESTORS
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?
21
BARCLAYS GLOBAL INVESTORS
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
22
BARCLAYS GLOBAL INVESTORS
Factor Model Selection Criteria
 Academically Sound?
 Best Fit?
 Economic Interpretation?
 Out of sample explanatory power?
 Tradeable?
23
BARCLAYS GLOBAL INVESTORS
A First Cut at Identifying Factors within each Style:
Principal Component Analysis
Principal
Comp.
1
2
3
4
5
6
7
8
9
10
(1-3)
>5%
24
Equity
23.18%
8.30%
6.79%
4.83%
4.04%
3.61%
3.24%
3.09%
2.85%
2.58%
38.27%
3
Emerging
Fixed
Markets
Income
24.17%
32.85%
19.27%
15.52%
8.02%
10.68%
6.46%
9.59%
6.40%
6.64%
5.24%
4.81%
3.65%
3.60%
3.11%
2.77%
2.49%
1.88%
2.21%
1.66%
51.46%
59.05%
6
5
Macro
19.48%
11.52%
9.43%
8.32%
5.42%
4.63%
3.96%
3.55%
3.27%
3.01%
40.43%
5
Relative Managed
Value
Futures
41.93%
19.34%
11.27%
12.21%
8.54%
8.53%
6.26%
6.69%
3.86%
5.38%
3.30%
4.81%
2.74%
4.36%
2.26%
4.08%
2.01%
3.27%
1.92%
3.17%
61.74%
40.08%
4
5
BARCLAYS GLOBAL INVESTORS
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)
25
BARCLAYS GLOBAL INVESTORS
Mean/Median Forecast Error at successive steps
Equity Hedge Funds
60
Mean
50
Median
Forecast Error
40
30
20
26
STP19
STP18
STP17
STP16
STP15
STP14
STP13
STP12
STP11
STP10
STP9
STP8
STP7
STP6
STP5
STP4
STP3
STP2
0
STP1
10
BARCLAYS GLOBAL INVESTORS
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
Out-of-Sample
15%
In-Sample
Frequency
12%
9%
6%
3%
More
75%
70%
65%
60%
55%
50%
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
0%
Adjusted Fit
27
BARCLAYS GLOBAL INVESTORS
28
Median
Top Quartile
200401
200307
200301
200207
200201
200107
200101
200007
200001
199907
199901
199807
199801
199707
199701
Alpha p.a. (36m rolling estimation)
Equity Hedge Fund In-Sample Alpha
30%
25%
20%
15%
10%
5%
0%
-5%
Bottom Quartile
BARCLAYS GLOBAL INVESTORS
Mean/Median Forecast Error at successive steps
Fixed Income Hedge Funds
25
Median
Mean
20
15
10
5
0
1
29
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
BARCLAYS GLOBAL INVESTORS
Explanatory power of a factor risk model
(Fixed Income Funds)
25%
in-sample
out-of-sample
Frequency
20%
Median
Median*
21.97% 31.19%
10.26% 30.48%
Out-of-Sample
In-Sample
15%
10%
5%
More
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0%
Adjusted Fit
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%).
30
BARCLAYS GLOBAL INVESTORS
Fixed Income Fund In Sample Alpha
25%
Alpha p.a.
20%
15%
10%
5%
Median
Q3
200401
200307
200301
200207
200201
200107
200101
200007
200001
199907
199901
199807
199801
199707
199701
0%
Q1
Fund-level rolling 36m estimation
31
BARCLAYS GLOBAL INVESTORS
HFR Hedge Fund Index Returns: Where is the Hedge?
T-Stat of Systematic Factors
Adjusted R Squared
Intercept
Inflation % change
Inflation level
VIX % change
Vix level
S&P 500 return
Credit spread % change
US small - large return
US Value-growth return
Slope of yield curve % Change
Slope of yield curve
Risk appetite
32
LONG/ RELATIV FIXED GLOBAL FUND OF
SHORT E VALUE INCOME MACRO FUNDS
0.85
0.63
0.53
0.32
0.64
2.29
1.54
2.91
2.77
2.02
0.29
1.42
0.88
0.23
1.21
-0.19
0.23
0.81
-0.45
0.39
-0.19
-1.9
-0.62
0.35
-0.52
-0.73
0.74
-2.8
-2.13
-1.46
11.92
4.73
-1.32
3.44
5.1
-0.47
-4.03
-2.9
-0.92
-2
9.43
2.8
0.19
3.36
4.9
6.22
-0.56
0.49
1.92
3.74
0.8
-2.5
-6.01
-0.41
-0.03
-3.78
-3.49
0.07
-0.62
-1.56
1.97
2.99
-0.5
-0.97
1.54
BARCLAYS GLOBAL INVESTORS
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
33
BARCLAYS GLOBAL INVESTORS