Transcript Jaksa Cvitanic, Ali Lazrak, Lionel Martellini and Fernando

Conférence Gestion Alternative
2 Avril 2004
The Alpha and Omega of Hedge Fund Performance Evaluation
Joint work with Noël Amenc (EDHEC) and Susan Curtis (USC)
Lionel Martellini
Risk and Asset Management Research Center, EDHEC Graduate School of Business
[email protected]
Outline
•
•
•
•
•
•
•
•
•
•
•
•
Introduction
Standard CAPM Model
Adjusting CAPM for the Presence of Stale Prices
Payoff Distribution Model
Multi-Factor Models
Implicit Factor Model
Explicit Factor Model
Explicit Index Model
Peer Benchmarking
Comparative Performance Analysis
Impact on Attributes on Funds’ Performance
Conclusion
Introduction
Papers on MF and HF Performance
• There is ample evidence that portfolio managers following
traditional active strategies on average under-perform
passive investment strategies
– Examples are: Jensen (1968), Sharpe (1966), Treynor (1966), Grinblatt and
Titman (1992), Hendricks, Patel and Zeckhauser (1993), Elton, Gruber, Das and
Hlavka (1993), Brown and Goeztman (1995), Malkiel (1995), Elton, Gruber and
Blake (1996), or Carhart (1997), among many others
• Recently, many papers have focused on hedge fund
performance evaluation
– Examples are: Ackermann, McEnally, and Ravenscraft (1999), Amin and Kat
(2001), Agarwal and Naik (2000a, 2000b), Brown, Goetzmann and Ibbotson
(1999), Edwards and Caglayan (2001), Fung and Hsieh (1997, 2001a, 2001b),
Gatev, Goetzmann and Rouwenhorst (1999), Liang (2000), Lhabitant (2001), Lo
(2001), Mitchell and Pulvino (2001), Schneeweis and Spurgin (1999, 2000)
Introduction
Models
• Because these studies are based on a variety of models
for risk-adjustment, and also differ in terms of data used
and time period under consideration, they yield very
contrasted results
• The present paper can be viewed as an attempt to provide
an unified picture of hedge fund managers to generate
superior performance
• To alleviate the concern of model risk on the results of
performance measurement, we consider an almost
exhaustive set of pricing models that can be used for
assessing the risk-adjusted performance of hedge fund
managers.
Introduction
Preview of the Results
• While we find significantly positive alphas for a sub-set of
hedge funds across all possible models, our main finding
is perhaps that the dispersion of alphas across models is
very large
– Hedge funds appear to have significantly positive alphas on average when
normal returns are measured by an explicit factor model, even when
multiple factors serving as proxies for credit or liquidity risks are accounted
for
– However, hedge funds on average do not have significantly positive alphas
once the entire distribution is considered or implicit factors are included
• On the other hand, all pairs of models have probabilities of
agreement greater than .50
– In other words, while different models strongly disagree on the absolute
risk-adjusted performance of hedge funds, they largely agree on their
relative performance in the sense that they tend to rank order the funds in
the same way
Introduction
Data
• Our analysis is conducted on a proprietary data base of
1,500 individual hedge fund managers (MAR-CISDM data
base)
• We use the 581 hedge funds in the MAR database that
have performance data as early as January 1996
• The data base contains monthly returns and also
– Fund size (asset under management)
– Fund type (MAR classification system)
– Fund age (defined as the length of time in operation prior to the beginning of our
study)
– Location (US versus non US)
– Incentive fees
– Management fees
– Minimum purchase amount
Standard CAPM Model
Normal and Abnormal Returns
• Factor models allow us to decompose managers’
(excess) returns into
– Normal returns (risk premium)
– Abnormal returns (investment opportunity)
– Statistical noise (illusion)
• Normal returns are generated as a fair reward for the
risk(s) taken by fund managers
• Abnormal returns are generated managers’ unique ability
to “beat the market” in a risk-adjusted sense, generated
through superior access to information or better ability to
process commonly available information
• Need some model to understand what a “normal” return
is; benchmark model is the CAPM (Sharpe (1964))
Standard CAPM Model
Results
• The average alpha across all funds is significantly positive
• The majority of hedge funds have positive alphas, and
about a third are statistically significant
• Very few funds have significantly negative alphas
Statistic
Value under CAPM
Alpha (average fund)
5.83%
Std. Err. Alpha (average fund)
2.85%
p-value (for average alpha not 0)
0.045
St.Dev. Alpha (across funds)
10.02%
% of funds with alpha significantly 0
31.3%
% of funds with alpha significantly 0
0.7%
Standard CAPM Model
Distribution of CAPM Alphas
Distribution of CAPM Alphas
16%
14%
12%
10%
Percent
8%
of
Funds
6%
4%
2%
0%
-15 -13 -11
-9
-7
-5
-3
-1
1
3
5
7
9
11
13
15
Alpha Value (annual %, midpoint of bin)
17
19
21
23
25
Standard CAPM Model
Distribution of CAPM Betas
Distribution of CAPM Betas
25%
20%
15%
Percent
of
Funds
10%
5%
0%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Beta Value (midpoint of range)
1.2
1.4
1.6
1.8
2
Adjusting CAPM for Stale Prices
The Presence of Stale Prices
• It has been documented (Asness, Krail and Liew (2001))
that a fair number of hedge funds hold illiquid securities
• For monthly reporting purposes, they typically price these
securities using either the last available traded price or
estimates of current market prices
• Such non-synchronous return data can lead to
understated estimates of actual market exposure, and
therefore to mismeasurement of hedge fund risk-adjusted
performance
• In that context, some adjustment must be performed to
account for the presence of stale prices
Adjusting CAPM for Stale Prices
Model and Results
• Model: run regressions of returns on both contemporaneous
and lagged market returns
K
r i,t r f,t i  ik 
r M,tk r f,tk 
i,t
k0
• Results: the number of funds with alpha values significantly
greater than zero has been cut in half
Statistic
Value under CAPM Value under Lagged CAPM
Alpha (average fund)
5.83%
2.14%
Std. Err. Alpha (average fund)
2.85%
3.21%
p-value (average fund alpha not 0)
0.045
0.51
% of funds with alpha significantly 0
31.3%
16.9%
% of funds with alpha significantly 0
0.7%
2.8%
Adjusting CAPM for Stale Prices
Model and Results
• CAPM has more funds with alphas near 10%, and lagged
CAPM model has more funds with alphas between -10% and 0
Comparison of Alphas under CAPM and Lagged CAPM
16%
CAPM
Lagged CAPM
14%
12%
10%
Percent
8%
of
Funds
6%
4%
2%
0%
-23 -21 -19 -17 -15 -13 -11 -9
-7
-5
-3
-1
1
3
5
7
9
Alpha Values (bin midpoints)
11 13 15 17 19 21 23
Payoff Distribution Function Approach
Non-Linear Exposure to Standard Asset Classes
• Hedge fund returns exhibit non-linear option-like exposures
to standard asset classes because
– They can use derivatives
– They follow dynamic trading strategies
• Furthermore, the explicit sharing of the upside profits under
the form of incentive fees implies that post-fee returns have
option-like element even if pre-fee returns do not
• In this context, mean-variance CAPM based performance
measures will fail to account for non trivial preferences about
skewness and kurtosis
• There exists a method allowing an investor to account for
the whole distribution of returns
Payoff Distribution Function Approach
Methodology
• Methodology introduced by Dybvig (see Dybvig (1988a,
1988b)), applied to hedge fund performance evaluation
by Amin and Kat (2001)
• First step: recover the cumulative probability distribution
of the monthly hedge fund payoffs as well as the S&P 500
from the available data set assuming $100 are invested at
the beginning of the period
– A normal distribution is assumed for the S&P 500 (i.e., we only need to
estimate the mean and standard deviation of the monthly return on the
S&P 500 over the period), but not for the hedge funds
• Second step: generate payoff functions for each hedge
fund
– A payoff function is a function f that maps the return distribution of the S&P
500 into a relevant return distribution for the hedge fund
Payoff Distribution Function Approach
Methodology (con’t)
• Third step: we use a discrete version of a geometric Brownian
motion as a model for the underlying S&P price process
generate 20,000 end-of-month value
– From these 20,000 values, we generate 20,000 corresponding payoffs for
each hedge fund, average them, and discount them back to the present to
obtain a fair price for the payoff
– This “price” thus obtained can be thought of the minimum initial amount
that needs to be invested in a dynamic strategy involving the S&P and
cash to generate the hedge fund payoff function
– If the price thus obtained is higher than 100, this means that more than
$100 needs to be invested in S\&P to generate a random terminal payoff
comparable to the one obtained from investing a mere $100 in the hedge
fund. We therefore take this as evidence of superior performance.
– On the other hand, if the price obtained is lower than $100, we conclude
that one may achieve a payoff comparable to that of the hedge fund for a
lower initial amount.
– The percentage difference is computed as a relative measure of efficiency
loss
Payoff Distribution Function Approach
Cumulative Probability Distributions
•
The slope for the average hedge fund is much steeper than for the S&P 500,
indicating a much narrow distribution of returns
Comparison of Hedge Funds with S&P 500 (Real Data)
1.0
S&P
0.8
Average Fund
0.6
Cumulativ e
Probability
Distribution
0.4
0.2
0.0
85
90
95
100
105
Final Fund Value (Initial=100)
110
115
120
Payoff Distribution Function Approach
Performance of High- and Low-Rated Funds
•
•
The low-rated fund has a wide distribution of returns
Top rated funds were found to be of two types: high volatility funds with
exceptionally high returns, and low volatility funds
Comparison of Hedge Funds with S&P 500 (Real Data)
1.0
S&P
0.8
Top High Risk Fund
Top Low Risk Fund
Worst Fund
0.6
Cumulative
Probability
Distribution
0.4
0.2
0.0
85
90
95
100
105
Final Fund Value (Initial=100)
110
115
120
Payoff Distribution Function Approach
Distribution of Efficiency Gain or Loss
Distribution of Hedge Fund Efficiency
60%
50%
40%
Percent
of
30%
Hedge
Funds
20%
10%
0%
< -3%
-3 to -2%
-2 to -1%
-1 to 0%
0 to 1%
Efficiency Gain or Loss
1 to 2%
2 to 3%
> 3%
Payoff Distribution Function Approach
Performance of Hedge Funds
•
•
On average, hedge funds do not outperform the market
However, the statistics are influenced by a few funds with large negative
efficiencies. Over half of the funds have positive efficiency measures
PDPM
•
•
•
Mean Efficiency (annual rate)
-0.92%
St.Dev. Efficiency
10.66%
% of funds with efficiency 0
58%
Note that in the implementation of PDPM, we must make an assumption about
the volatility of the S&P 500
Here, we used a16% volatility as measured during the time period of the data
When we repeated the analysis with a higher volatility of 20%, the average
hedge fund has a slightly higher efficiency and is no longer significantly different
from zero
Multi-Factor Models
Other Sources of Risk
• Hedge funds are typically exposed to a variety of risk
sources including volatility risks, credit or default risks,
liquidity risks, etc., on top of standard market risks
• If one uses CAPM while the “true” model is a multi-factor
model, then estimated alpha will be higher than true alpha
• Modern portfolio theory and practice is based upon multifactor models (Merton (1973), Ross (1976))
• The return on asset or find i is
Rit = mi + bi1F1t + ... + biKFKt + eit
– Fkt is factor k at date t (k = 1,…,K)
– eit is the asset specific return
– bik measures the sensitivity of Ri to factor k, (k = 1,…,K)
Multi-Factor Models
Four Types of Factor Models
• Implicit factor models
– Factors: principal components, i.e., uncorrelated linear combinations of
asset returns
• Explicit factor models – macro factors
– Factors (Chen, Roll, Ross (1986)): inflation rate, growth in industrial
production, spread long-short treasuries, spread high-low grade corporate
interest rate
• Explicit factor models – micro “factors”
– Factors (actually attributes): size, country, industry, etc.
• Explicit factor model – index “factors”
– Factors are stock and bond market indices
Implicit Factor Model
The Model
• Use principal component analysis to extract statistical factors
(linear combinations of returns)
• Challenge is determine the optimal # of factors (K’)
–
–
–
Select K’ by applying results from the theory of random matrices
Compare the properties of an empirical covariance matrix to a null hypothesis purely
random matrix
Distribution function for eigenvalues under the null hypothesis
  max   min 
T
2N

N
N
1
2
T
T
f   
max
min  1 
–
N
2
T
N
T
Here, we regard as statistical noise all factors associated with an eigenvalue lower
than lambda min
Implicit Factor Model
The Results
• The mean alpha is less than zero under this model
• This suggests that there are factors influencing
hedge fund performance that are captured in the
Implicit Factor Model but not captured in CAPM
Statistic
Value under Implicit Factor Model
Mean Alpha (annual rate)
-1.04%
Std. Dev. Alpha
12.59%
p-value (for mean alpha not 0)
0.047
% of funds with alpha 0
44%
Explicit Factor Model
The Model
• We test an explicit macro factor model where we use financial
variables to proxy deeper economic effects
• The following factors are used
–
–
–
–
–
–
–
–
US equity risk is proxied by the return on the S\&P 500 index, and world equity risk is
proxied by the return on the MSCI World Index ex US
Equity volatility risk, proxied by using the changes in the average of intra-month
values of the VIX
Fixed-income level risk is proxied by the 3 months T-Bill rate
Slope risk or term premium risk is proxied by monthly differences between the yield on
3 months Treasuries and 10-year Treasuries
Currency risk is proxied by changes in the level of an exchange volume-weighted
index of currencies versus US dollar
Commodity risk is proxied by changes in the level of a volume-weighted index of
commodity prices
Credit risk is proxied by changes in the monthly observations of the difference
between the yield on long term Baa bonds and the yield on long term AAA bonds
Liquidity risk is proxied by changes in the monthly market volume on then NYSE
Explicit Factor Model
The Results
• Some of the above variables do not appear to command
a premium
• The following variables seems to be rewarded risk
factors: S&P 500, MSCI ex-US, oil price return, change in
credit spread, change in VIX
• This is the 5-factor model that we use
Statistic
Value under 5-Factor Macro Model
Alpha (average fund)
7.25%
Std. Err. Alpha (average fund)
2.35%
p-value (for average alpha not 0)
0.01
Std .Dev. Alpha (across funds)
9.81%
% of funds with alpha significantly 0
39%
% of funds with alpha significantly 0
1%
Explicit Factor Model
The Analysis
• The average alpha is higher than under the CAPM
• This is primarily due to the inclusion of the MSCI exUS index
– Many of the funds in our database are global funds, with a higher beta on
the MSCI index than on the S&P 500.
– Since the MSCI index underperformed the S&P 500 during this time period,
the inclusion of the MSCI factor makes the alpha values higher for these
funds
– Thus, in fact, these funds are outperforming the world index but are
underrated in the CAPM\ model since their performance is compared to the
S&P 500
– The inclusion of other factors (oil prices, change in credit spread, change in
VIX) tends to lower the alphas (compared to a 2-variable model using
S&P500 and MSCI only), but does not erase the gains made by including
the MSCI
– Thus, we conclude that when all of these significant factors are included,
the average hedge fund still has a positive alpha
Explicit Multi-Index Model
Return-Based Style Analysis
• Style analysis
– Sharpe (1992): equity styles are as important as asset classes
– Examples: growth/value, small cap/large cap, etc.
• Model: Rit = wi1F1t + wi2F2t + ... wikFkt + eit
– Rit = (net of fees) excess return on a given portfolio or fund
– Fkt = excess return on index j for the period t
– wik = style weight (add up to one)
– eit = error term
• Divide the fund return into two parts
– Style: wi1F1t + wi2F2t + ... wikFkt (part attributable to market movements)
– “Skill”: eit (part unique to the manager), emanates from 3 sources
• manager’s exposure to other asset classes not included in the analysis
• manager’s active bets: active picking within classes and/or class timing
• statistical error: if zero, Var(eit) can be regarded as selection return risk
Explicit Multi-Index Model
Style Analysis and Performance Evaluation
• Step 1: select a set of indices to perform returnbased style analysis
– CSFB/Tremont indices or (preferably!) EDHEC indices
• Step 2: perform style analysis of fund returns
– Constrained regression
• Step 3: form peer groups
– Use cluster analysis on style exposure
• Step 4: perform a risk-adjusted analysis of each
fund’s performance
– Unconstrained regression
Explicit Multi-Index Model
Performance Results
• We measure the excess return of hedge funds using the
primary indexes appropriate to each cluster as factors in the
model (average weight > 10%)
• The mean hedge fund has alpha not significantly different
from zero
• These results suggest that the CSFB indexes effectively
capture risk factors that are not captured by the standard
CAPM, and that fund managers with positive CAPM alphas
are often not outperforming hedge fund indexes
Statistic
Value under Multi-Index Model
Mean Alpha (annual rate)
0.79%
Std. Dev. Alpha
16.27%
p-value (for mean alpha not 0)
0.24
% of funds with alpha 0
57%
Peer Benchmarking
Cluster-Based Index
• Next, we regress hedge fund excess returns on the excess
return of the equally-weighted portfolio of all hedge funds
within a cluster
• This is formally similar to Sharpe's (1963) single-index model
except that perform a relevant peer benchmarking
• Cluster-index model has average alpha very close to zero
–
–
This should not be surprising since the same funds are used in the computation of
the index as are used for computation of alpha
Useful to spot the best performing funds in a peer group
Statistic
Value under Cluster-Index
Mean Alpha (annual rate)
0.06%
St.Dev. Alpha
15.02%
p-value (for mean alpha not 0)
0.92
% of funds with alpha 0
60%
Comparative Performance Analysis
Synthesis
• The standard deviations are across funds (not across time
periods)
Average St. Dev. % 0
CAPM
5.8%
10%
82.3%
Stale
2.1%
11.4%
65.2%
Cond
5.5%
10.2%
80.2%
Leland
5.3%
10.3%
78.7%
PPDM
-0.9%
10.7%
58.3%
PCA
-1%
12.6%
43.9%
Macro
7.3%
9.8%
86.7%
Index
0.8%
16.3%
56.5%
Cluster
0.1%
15%
59.4%
Av. Return
15.7%
9.8%
97.1%
Comparative Performance Analysis
Synthesis (con’t)
• Hedge funds appear to have significantly positive alphas for
CAPM-like models, even with multiple factors
–
–
However, hedge funds on average do not have significantly positive alphas once
the entire distribution is considered (PDPM) or implicit factors are included (PCA)
Nevertheless, many individual funds do have significantly positive alphas
Average St. Dev. % 0
CAPM
5.8%
10%
82.3%
Stale
2.1%
11.4%
65.2%
Cond
5.5%
10.2%
80.2%
Leland
5.3%
10.3%
78.7%
PPDM
-0.9%
10.7%
58.3%
PCA
-1%
12.6%
43.9%
Macro
7.3%
9.8%
86.7%
Index
0.8%
16.3%
56.5%
Cluster
0.1%
15%
59.4%
Av. Return
15.7%
9.8%
97.1%
Comparative Performance Analysis
Cross-Sectional Distribution of Average Alphas
• The mean of that distribution is 4.07%, the standard
deviation is 9.56%
• 276 (out of 581 hedge funds) have an average alpha across
methods larger than 4.5%
Cross-Sectional Distribution of Average Alphas
90
70
60
50
40
30
20
10
average alpha across models
38
40
M
or
e
34
36
30
32
26
28
22
24
18
20
14
16
8
10
12
6
4
2
0
-2
-4
-6
0
-3
8
-3
6
-3
4
-3
2
-3
0
-2
8
-2
6
-2
4
-2
2
-2
0
-1
8
-1
6
-1
4
-1
2
-1
0
-8
number of funds
80
Comparative Performance Analysis
Cross-Sectional Distribution of Standard Deviation
• The mean of that distribution is 7.66%, the standard
deviation is 4.60%
• One fund has a dispersion of alpha across methods larger
than 40%!
Cross-Sectional Distribution of Standard Deviation of Alphas
160
number of funds
140
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
dispersion of alphas across models
32
34
36
38
40
More
Comparative Performance Analysis
Correlation of Alphas
•
•
CAPM-related methods are highly correlated with each other, indicating that
the adjustments have small effects
The implicit factor model and clustering based methods have a smaller
correlation with the other methods, indicating that they pick up different
factors
Stale Cond Leland PPDM PCA Macro Index Cluster
CAPM 0.90
Stale
Cond
Leland
PPDM
PCA
Macro
Index
Cluster
1.00
0.96
0.998
0.72
0.52
0.97
0.59
0.73
0.88
0.90
0.71
0.44
0.86
0.53
0.74
1.00
0.96
0.66
0.50
0.93
0.58
0.71
1.00
0.71
0.51
0.97
0.60
0.73
1.00
0.42
0.68
0.38
0.73
1.00
0.55
0.27
0.33
1.00
0.54
0.64
1.00
0.61
1.00
Comparative Performance Analysis
Probability of Agreement
•
•
For any two models, we compute the probability that the two models will
agree on the rank order of a randomly-chosen pair of hedge funds
All pairs of models have probabilities of agreement > 0.50, even the model
that only computes the average return
Stale Cond Leland PPDM PCA Macro Index Cluster Av. Ret
CAPM
0.84
0.91
0.98
0.81
0.64
0.92
0.69
0.74
0.77
Stale
1.00
0.83
0.85
0.80
0.61
0.81
0.69
0.76
0.70
1.00
0.90
0.81
0.63
0.87
0.70
0.74
0.75
1.00
0.80
0.63
0.91
0.70
0.75
0.77
1.00
0.62
0.77
0.66
0.77
0.70
1.00
0.65
0.57
0.56
0.67
1.00
0.67
0.70
0.80
1.00
0.76
0.58
1.00
0.60
Cond
Leland
PPDM
PCA
Macro
Index
Cluster
Impact on Attributes on Fund Performance
Impact of Fund Size on Performance
•
•
Note that for all methods, the mean alpha for large funds exceeds the mean
alpha for small funds
This fact, combined with the observation that most of the results are
statistically significant, suggests that large funds do indeed outperform small
funds on average
Model
CAPM
Stale
Cond
Leland
PDPM
PCA
Macro
Index
Cluster
Avg Ret
Large Funds
mean
N
sd
stderr
6.75%
289
9.25%
0.54%
3.30%
289
10.22%
0.60%
6.30%
289
9.09%
0.53%
6.21%
289
9.44%
0.56%
0.95%
289
8.57%
0.50%
-0.50%
289
12.75%
0.75%
8.15%
289
9.34%
0.55%
1.70%
289
15.01%
0.88%
1.88%
289
12.67%
0.75%
15.94%
289
8.88%
0.52%
Small Funds
mean
N
sd
stderr
4.96%
290
10.66%
0.63%
1.01%
290
12.79%
0.75%
4.72%
290
11.29%
0.66%
4.49%
290
10.76%
0.63%
-2.72%
290
12.11%
0.71%
-1.51%
290
12.43%
0.73%
6.39%
290
10.20%
0.60%
-0.01%
290
17.33%
1.02%
-1.72%
290
16.88%
0.99%
15.58%
290
10.63%
0.62%
1.79%
0.03
2.29%
0.02
1.57%
0.07
1.73%
0.04
3.68%
< 0.01
1.01%
0.33
1.76%
0.03
1.71%
0.21
3.61%
< 0.01
0.36%
0.66
Difference
mean
p value
Impact on Attributes on Fund Performance
Impact of Fund Type on Performance
•
•
Event Driven
GL Macro
Global Emerg.
Global Est.
Global Intl.
Long Only
Median
Mkt Neutral
Sector
Short Sales
Unknown
Most models rate market neutral funds as outperforming the average of
other funds at a statistically significant level. However, two of the factor
models do not. Presumably a typical market neutral fund has a favorable
probability distribution of returns but is subject to some implicit or
macroeconomic risks not well captured by the other models.
The CAPM models rate short-selling funds the highest, although other
models did not. Short-selling funds tend to have negative betas, so even
absolute performance near the risk-free rate will result in positive CAPM
alphas.
# of Funds
66
28
27
125
20
5
14
101
27
8
160
CAPM
Stale
Cond
Leland
PDPM
PCA
Macro
4.96%
1.05%
4.45%
4.26%
0.44%
-1.13%
6.05%
4.15%
1.19%
2.56%
3.73%
-3.53%
-3.87%
5.75%
-2.66%
-5.33%
-0.96%
-3.98% -14.20% -0.66%
1.07%
6.93%
2.39%
6.71%
6.48%
-0.54%
-1.45%
8.75%
2.87%
-1.13%
1.77%
2.35%
-7.26%
-2.84%
5.56%
2.32%
-1.53%
-0.06%
1.53%
-3.41%
-5.18%
3.56%
4.87%
2.61%
4.63%
4.42%
1.89%
-2.77%
5.83%
9.40%
6.74%
9.28%
9.04%
2.88%
-0.52%
9.73%
10.47%
5.57%
8.44%
9.81%
-0.73%
3.27%
12.06%
13.65% 14.80% 15.11% 14.21% -19.62% -0.24%
13.34%
4.20%
0.20%
3.85%
3.72%
0.05%
-0.83%
5.65%
Index
Cluster
Avg Ret
1.79%
1.95%
13.46%
1.39%
1.79%
14.06%
-11.57% -15.14% 13.89%
-1.04%
-3.55%
21.05%
-2.23%
-7.38%
10.67%
-7.37%
-6.47%
18.02%
1.25%
0.82%
11.75%
8.17%
9.67%
15.48%
-1.14%
-2.44%
25.68%
20.34%
-2.96%
6.45%
-0.94%
-0.06%
12.96%
Impact on Attributes on Fund Performance
Impact of Fund Age on Performance
• Note that for all methods, the mean alpha for newer funds
exceeds the mean alpha for older funds
• The differences vary in significance across the methods
CAPM
Stale
Cond
Leland
PDPM
PCA
Macro
Index
Cluster
Avg Ret
Newer Funds
mean
7.34%
st.dev.
11.67%
2.90%
13.11%
6.88%
12.21%
6.84%
11.74%
-0.02%
11.16%
-0.50%
14.62%
8.67%
11.30%
2.40%
16.75%
1.63%
16.91%
17.65%
11.41%
Older Funds
mean
4.59%
st. dev.
8.16%
1.43%
10.10%
4.27%
8.19%
4.10%
8.37%
-1.50%
10.05%
-1.66%
10.39%
6.03%
8.13%
-0.26%
15.54%
-0.95%
12.97%
13.99%
7.75%
Difference
mean
p-value
1.47%
< 0.01
2.61%
< 0.01
2.74%
< 0.01
1.48%
< 0.01
1.16%
0.289846
2.63%
< 0.01
2.66%
0.011266
2.58%
< 0.01
3.66%
< 0.01
2.76%
< 0.01
Impact on Attributes on Fund Performance
Impact of Incentive Fee on Performance
• High incentive fees (>=20%; most were exactly 20%) versus
low incentive fees (<20%)
• Note that for all methods, the mean alpha for high incentive
funds exceeds the mean alpha for low incentive funds
• A strong significant effect is obtained with almost all of the
methods
CAPM
Stale
High Incentive Funds (N=334)
mean
6.11%
2.40%
st. dev.
8.43%
9.97%
Cond
Leland
PDPM
PCA
Macro
Index
Cluster
Avg Ret
5.56%
8.22%
5.64%
8.52%
-0.66%
10.57%
-1.10%
11.58%
7.57%
8.60%
2.49%
15.30%
0.55%
13.29%
15.48%
9.12%
Low Incentive Funds (N=99)
mean
0.73%
st.dev.
8.26%
-2.81%
10.75%
0.45%
7.85%
0.04%
8.56%
-4.38%
10.99%
-2.54%
11.12%
2.55%
8.03%
-5.23%
12.27%
-4.76%
13.82%
12.02%
8.27%
Difference
mean
p-value
5.22%
< 0.01
5.10%
< 0.01
5.60%
< 0.01
3.72%
< 0.01
1.44%
0.26
5.02%
< 0.01
7.72%
< 0.01
5.32%
< 0.01
3.46%
< 0.01
5.38%
< 0.01
Impact on Attributes on Fund Performance
Impact of Management Fee on Performance
• High management fees (>=2%) versus low management
fees (<2%)
• None of the reported differences is significant at the 0.05
level
• This suggests that there is no significant difference between
funds with higher or lower administrative fees
CAPM
High Fee Funds (N=133)
mean
4.46%
st. dev.
9.17%
Stale
Cond
Leland
PDPM
PCA
Macro
Index
Cluster
Avg Ret
0.58%
10.83%
3.78%
8.31%
3.92%
9.38%
-1.60%
10.72%
-1.11%
12.03%
5.94%
9.22%
-1.71%
12.61%
-0.47%
13.37%
14.17%
8.64%
Low Fee Funds (N=242)
mean
5.09%
st.dev.
8.56%
1.41%
10.24%
4.52%
8.73%
4.55%
8.69%
-1.43%
10.21%
-1.09%
10.57%
6.68%
8.59%
1.07%
16.04%
-1.39%
13.69%
15.60%
9.40%
Difference
mean
p-value
-0.82%
0.47
-0.75%
0.41
-0.63%
0.52
-0.17%
0.88
-0.02%
0.99
-0.74%
0.45
-2.78%
0.07
0.92%
0.53
-1.43%
0.14
-0.63%
0.52
Impact on Attributes on Fund Performance
Impact of Minimum Purchase Amount on Performance
• Minimum purchase amounts for the hedge funds in our study
ranged from 0 to \$25 million.
• High MPA (>=$300,000) versus low MPA (<$300,000)
• For all methods, the mean alpha for funds with the larger
minimum purchase amounts exceeds the mean alpha for the
other funds (statistically significant difference)
CAPM
Stale
Cond
High Mininum Purchase Funds (N=285)
mean
7.47%
4.34%
7.32%
st. dev.
10.60%
11.52%
11.23%
Leland
PDPM
PCA
Macro
Index
Cluster
Avg Ret
7.00%
10.67%
0.44%
10.25%
0.17%
12.94%
8.66%
10.41%
3.00%
16.93%
2.01%
16.39%
16.98%
10.43%
Low Minimum Purchase Funds (N=251)
mean
3.63%
-0.58%
3.19%
st.dev.
0.63%
0.68%
0.67%
3.09%
0.63%
-2.80%
0.61%
-2.69%
0.77%
5.28%
0.62%
-1.92%
1.00%
-2.46%
0.97%
14.09%
0.62%
Difference
mean
p-value
3.91%
< 0.01
3.24%
< 0.01
2.86%
0.01
3.38%
< 0.01
4.92%
< 0.01
4.47%
< 0.01
2.89%
< 0.01
3.84%
< 0.01
4.93%
< 0.01
4.13%
< 0.01
Conclusion
At the HF world's lies the Impersonal
• Alphas on active strategies, if they exist, are not easy to
measure with any degree of certainty
• In a companion paper, we test the impact of uncertainty in
alpha estimates on optimal allocation decision in a CT
Bayesian setting
• Hedge fund are exposed to a variety of risk factors, and, as a
result, generate normal, as opposed to abnormal, returns
• The hedge fund industry should perhaps focus on promoting
the beta-benefits of hedge fund investing, which are
significant and less arguable, as opposed to promoting the
alpha-benefits of hedge fund investing, which are very hard
to measure with any degree of accuracy
• This also suggests that the future of alternative investments
may lie in “the impersonal”, i.e., in passive indexing
strategies