Hedge Fund Performance Predictability

Hedge Fund Predictability Under the Magnifying Glass:
The Economic Value of Forecasting Individual Fund Returns

Doron Avramovy Laurent Barrasz and Robert Kosowskix
, ,

First version, June 5th 2008;
This version, July 27th 2010

JEL Classi…cation: G11, G23, C12
Keywords: Hedge Fund Performance, Return Predictability, Combination
Forecasts

ABSTRACT
The recent …nancial crisis has highlighted the need to search for suitable models
forecasting hedge fund performance. This paper develops and applies a framework in
which to assess return predictability on a fund-by-fund basis. Using a comprehensive
sample of hedge funds during the 1994-2008 period, we identify the fraction of funds
in each style that are truly predictable, positively or negatively, by macro variables.
Out-of-sample, exploiting predictability can be di¢ cult as estimation risk and model
uncertainty lead to imprecise fund forecast. Moreover, in our multi-fund setting,
investors face a trade-o¤ between unconditional and predictable performance, as
strongly predictable funds may exhibit low unconditional mean. Nevertheless, a
strategy that combines forecasts across predictors circumvents all these challenges
and delivers superior performance. We highlight the statistical and economic drivers
of this performance, especially in periods when predictor values strongly depart from
their long run means. Finally, we use one such period– 2008 crisis–as a natural
the
out-of-sample experiment to validate the robustness of our …ndings.

We thank Tarun Ramadorai, Olivier Scaillet, Jialin Yu, as well as the seminar participants at HEC-
Montreal, Imperial College, McGill University, Tilburg University, the University of Rotterdam, the Uni-
versity of Toronto, the 4th Imperial College London conference on hedge funds, the 2nd INSEE/CREST
conference on hedge funds, the 2009 Annual Meeting of the European Finance Association (EFA), and
the 2010 Annual Meeting of the Institute for Mathematical Finance (IFM2) for their comments.
y
Hebrew University of Jerusalem and University of Maryland. email: davramov@rhsmith.umd.edu
z
Desautels Faculty of Management, McGill University. email: laurent.barras@mcgill.ca
x
Imperial College Business School, Imperial College London. email: r.kosowski@imperial.ac.uk

1

Electronic copy available at: http://ssrn.com/abstract=1650293

I Introduction

During the recent …nancial crisis, the hedge fund industry su¤ered its worst performance
ever. While predicting crises is inherently di¢ cult, traditional measures that built on
past stellar performance conclusively failed. For one, the formerly best performing
styles, long-short equity and emerging markets, recorded a 13.8% and 29.3% loss in
2008. Chicago-based Citadel is yet another piece of anecdotal evidence that expected
fund returns are time varying. This $11 billion investment …rm founded by Ken Gri¢ n,
posted a mid-year 21% return in 2009 after betting that out‡ows from and price drops
of convertible bonds were excessive at the beginning of 2009.1 Such events raise essential
questions that we attempt to address here. First, does future hedge fund performance
depend on the state of the economy? If yes, does this predictability vary across predictive
variables and investment styles? Second, can hedge fund investors successfully exploit
predictability out-of-sample? Of special interest is to examine the economic value of
predictability in times when predictors depart dramatically from their long run levels,
as in 2008.
Hedge funds follow a wide range of strategies, even within pre-established investment
styles. While we expect some funds to perform well under speci…c economic conditions,
others will do poorly. To incorporate this diversity, this paper examines hedge fund pre-
dictability at the individual fund level –we scrutinize both in-sample and out-of-sample
predictability "under the magnifying glass". Compared to our approach, using broad
hedge fund indices is less informative, as cross-fund di¤erences may simply average out.
For example, if one half of the funds are positively related to a given predictor, while the
other half has a negative exposure, an index-based analysis would detect no predictabil-
ity at all. Furthermore, any realistic portfolio advice based on predictability boils down
to selecting individual funds, since broad hedge fund indices are not investable.
Our paper uses three ingredients to deal with a challenging environment of several
thousand individual funds. The unique combination of these ingredients allows to estab-
lish important links between in-sample and out-of-sample predictability, and to clearly
explain the performance of conditional strategies that incorporate predictability.
The …rst ingredient is a precise measure of in-sample predictability that determines
the proportion of funds in the population having returns (or alphas) that are (i) nega-
tively related; (ii) unrelated; or (iii) positively related to any given predictive variable.
In a large fund population, it is not guaranteed that funds exhibiting the strongest
predictability also deliver the highest unconditional performance. Therefore, when ex-
1
See "Canyon, Citadel Ride Convertibles to Recoup Losses", Bloomberg article, June 11, 2009.

1

Electronic copy available at: http://ssrn.com/abstract=1650293

ploiting predictability, investors face a trade-o¤ between unconditional and predictable
performance: when they invest in predictable funds, they may fail to capture the high
unconditional performance of the funds they do not select. Our second ingredient is a
conditional strategy that explicitly incorporates this trade-o¤. Speci…cally, this strategy
selects, at each rebalancing date, the top decile of funds with the highest conditional
mean. Since the latter is the sum of both unconditional and predictable performance,
predictive information is used with parsimony, that is, only when the predictor value is
away from its average level.
From an out-of-sample perspective, the identity of predictable funds must be de-
tected from the data, thus confronting estimation risk. In addition, model instabilities
may arise from policy surprises, institutional changes, or advances in information tech-
nology. If the quality of the predictive information is poor, even a parsimonious use of
predictability may not be economically valuable. The third ingredient is an extended
version of the conditional strategy above. We use a combination strategy in which the
fund conditional means, obtained from each predictor separately, are averaged to form
a combined forecast. Intuitively, the combination strategy diversi…es across predictors
to reduce the impact of poor information quality, just like a portfolio diversi…es across
assets to reduce risk.
Armed with these three ingredients, we examine a universe of 7,991 individual hedge
funds across ten distinct investment categories between January 1994 and December
2008. To predict future monthly returns, we use four economically motivated predictors
(appropriately lagged): the default spread, the dividend yield, the VIX, and the monthly
net aggregate in‡ows into the hedge fund industry. In addition, we develop and apply
a uni…ed econometric framework that controls for both the well-known small sample
bias in predictive regressions, as well as return autocorrelation caused by hedge fund
illiquidity.
In-sample analysis reveals that predictability is a widespread phenomenon –we …nd
that the future returns of 60.5% of the funds in the population can be predicted by
including the four predictors above in the predictive regression. In addition, we inves-
tigate whether this predictability is driven by time-varying benchmark returns or by
time-varying skills of the hedge fund managers. Using the Fung-Hsieh (FH) seven risk
factor model to disentangle these two sources of predictability, we conclude that the
bulk of predictability comes from time-varying alphas. Stated di¤erently, the FH risk
factors are largely unpredictable based on the four predictors.
As expected, hedge funds following di¤erent strategies tend to react di¤erently to
changes in predictor values. For instance, we …nd that a high proportion of emerg-

2

ing market funds (33.5%) have future returns that are positively related to the de-
fault spread. Widening credit spreads typically coincide with a ‡ight to quality, widen-
ing emerging market sovereign bond spreads, and higher future returns (e.g., Jostova
(2006)). Another example is managed futures, which is the only category with funds
(16.7% of them) that are predominantly positively exposed to the VIX. Extreme volatil-
ity may trigger trend reversals which is generally bene…cial to these funds. However, we
also observe some common patterns across hedge fund styles. For most categories, we
…nd that a high dividend yield signals lower future returns, consistent with more limited
access to leverage during recessions. Moreover, there is strong evidence of negative ex-
pected returns after money in‡ows, consistent with the idea that the hedge fund industry
is subject to capacity constraints (e.g., Naik, Ramadorai, and Stromquist (2007)).
Importantly, we uncover a clear asymmetry in the direction of predictability, in the
sense that most predictable funds react in a similar manner to changes in the predictor
value. To illustrate, we …nd that while 13.4% of the funds are positively predicted by
the default spread, only 2.8% have a negative exposure to it. As a result, a rise in the
default spread leads to an increase in expected returns for more than 90% (13.4/16.2)
of predictable funds.
Having documented ample evidence of in-sample predictability, we next turn to
the analysis of its economic value. We carry out a range of out-of-sample tests that
carefully incorporate several real-world investment constraints faced by institutional
investors. In particular, we only allow for annual portfolio rebalancing to account for
liquidity constraints (i.e., lock-up periods). Over the period 1997-2007, we …nd that
an unconditional portfolio that simply uses past returns to select funds produces a very
high performance, consistent with Jagannathan, Malakhov, and Novikov (2010) –its FH
alpha (b ); Information Ratio (IR) and Sharpe ratio (SR), amount to 5.8%, 2.4, and 1.8
per year, respectively. In addition, we observe that single-predictor conditional strategies
that use one of the four predictors to forecast returns underperform the unconditional
portfolio on a risk-adjusted basis. In contrast, the combination strategy achieves the
highest risk-adjusted performance (IR = 2:7; SR = 1:9), and produces a FH alpha of
7.0% per year. From an investor perspective, this strategy also o¤ers other advantages,
such as a low tail risk, a low exposure to the FH risk factors (like a "pure alpha"
strategy), as well as reasonable levels of turnover and serial correlation.
Why do the single-predictor strategies fail? These strategies exploit predictive infor-
mation whenever the predictor moves either below or above its long-run mean. In these
two cases however, the information quality is not the same because of the asymmetric
nature of predictability. Consider the default spread again. When it is below average,

3

we need funds with a negative exposure to exploit predictability. However, since there
are only 2.8% of the funds with this correct exposure, data will surely be of little help to
detect these funds, leading to poor information quality. Indeed, we …nd that the out-of-
sample performance of the single-predictor strategies perfectly re‡ects the asymmetry
documented in-sample. For instance, in times of a lower-than-average default spread,
performance decreases substantially.
The combination strategy is more robust to this asymmetry, because it diversi…es
across predictors. First, it leads to a very conservative strategy that invests on average
80% in the unconditional portfolio. While this shrinkage e¤ect is discussed in Rapach,
Strauss, and Zhou (2010) for the US stock index, we argue that it is even more important
in a multi-asset setting, because investors are potentially hit twice–…rst, by choosing
funds with low predictability and, second, by excluding funds with high unconditional
performance. Second, diversifying reduces the out-of-sample forecast error variance, and
helps detect the predictable funds from the data. Indeed, the "active" portfolio chosen
by the combination strategy (that is, the remaining 20%) produces an additional FH
alpha up to 5.3% per year over the unconditional portfolio. Moreover, the performance
asymmetry observed for single predictor strategies disappears.
The 2008 …nancial crisis was accompanied by large ‡uctuations of the predictor val-
ues around their long-run means. This provides us with an additional out-of-sample
experiment to measure the economic value of predictive information. After incorporat-
ing 2008, we …nd that the risk-adjusted performance of the combination strategy is still
superior to that of the unconditional portfolio (b = 6:0% versus 4.1%; IR = 1:9 versus
1.2). Among the single-predictor strategies, we observe that the VIX strategy resisted
remarkably well, posting the lowest …nal quarter loss among all strategies (3.1% versus
10.8% on average for the other strategies). We …nd that part of this positive perfor-
mance comes from the higher stability of the VIX predictive power during the crisis.
However, this result should be treated with caution because it is subject to speci…cation
uncertainty, i.e., investors would have had to know back in December 2007 that the
VIX strategy would outperform in 2008. Finally, we examine the cost of the additional
liquidity constraints imposed by hedge funds to prevent massive out‡ows during the
crisis. We …nd that the cost borne by investors was substantial –had they been able to
rebalance at a monthly frequency in 2008, the maximum annual loss across all strategies
would have decreased from 18.7% to only 6.1%.
Our paper relates to the vast literature on return predictability (e.g., Keim and
Stambaugh (1986), Fama and French (1989), Ferson and Harvey (1991)). In particular,
Amenc, El Bied, and Martellini (2003) examine hedge fund predictability using broad-

4

based hedge fund indices, while Avramov, Kosowski, Naik, and Teo (2010; AKNT)
examines the hedge fund portfolio choice of a Bayesian investor that incorporates pre-
dictability. On the methodological front, our paper mostly borrows from the previous lit-
erature on combination forecasts (e.g., Bates and Granger (1969), Hendry and Clements
(2002), Timmermann (2006)), while using and extending the method proposed by Ami-
hud, Hurvich, and Wang (2008) to correct for small sample bias in predictive regressions.
The paper proceeds as follows. Section II discusses the methodology. Section III
describes the data. Section IV contains the empirical results of the paper, while Section
V concludes.

II Understanding Hedge Fund Predictability
A Measuring Return and Alpha Predictability

Our investment universe consists of M individual hedge funds. To predict future hedge
fund returns, we consider a set of J macroeconomic variables that potentially capture
evolving economic conditions. Hedge fund return predictability is analyzed based on the
time series predictive regression, run separately for each of M funds,

J
X
ri;t+1 = bi;0 + bi;j Zj;t + ui;t+1 : (1)
j=1

The dependent variable ri;t+1 denotes the time t + 1 excess hedge fund return (over
the riskfree rate), Zj;t (j = 1; :::; J) is the time t realized value of the j-th predictive
variable, bi;0 is the intercept, bi;j is the slope coe¢ cients associated with each predictor,
and ui;t+1 denotes the unpredictable fund speci…c innovation.
Hedge funds typically follow a wide range of strategies and trade many di¤erent
assets. As a result, some funds are likely to perform better under speci…c economic
conditions, while others will do poorly. This heterogeneity, captured by cross-fund
variation in the predictive regression slope coe¢ cients, provides a strong motivation to
examine predictability at the individual fund level.
To precisely assess the ability of each predictor j to forecast future fund returns, we
decompose the fund population into three distinct categories:
funds with unpredictable returns (bi;j = 0);
funds with predictable returns and a negative relation with predictor j (bi;j < 0);
funds with predictable returns and a positive relation with predictor j (bi;j > 0):
Then, we measure the proportions of funds in the population, denoted by 0 (j);
R R (j);

5

+
and R (j); that fall into one of these three categories. The estimation procedure bor-
rows from Barras, Scaillet, and Wermers (2010, henceforth BSW), and uses as input
the estimated slope coe¢ cients, bi;j ; across all funds. Importantly, this approach allows
b
to measure true predictability, because it explicitly accounts for funds that exhibit pre-
dictability by luck alone (i.e., funds with high bi;j , while their true coe¢ cient, bi;j ; equals
b
zero). We display the main formulas in Appendix B, and refer the interested reader to
BSW for further detail.
While the predictive regression in Equation (1) helps determine whether a given
fund exhibits predictable returns, there are various sources for predictability, which we
analyze below. First, hedge fund benchmark returns can vary with changing economic
conditions. This variation is in turn transmitted into individual hedge fund returns.
Denoting by ft+1 the K-vector of portfolio-based benchmark excess returns in time
t + 1, we measure predictable risk premia using the regression

J
X
ft+1 = bf;0 + bf;j Zj;t + uf;t+1 ; (2)
j=1

where bf;0 is the K-vector of intercept coe¢ cients, bf;j is the K-vector of slope coe¢ cients
associated with predictor j (j = 1; :::; J), and uf;t+1 denotes the K-vector of factor
innovations. While there is a large literature analyzing predictability of equity and
bond factors (e.g., Fama and French (1989), Ilmanen (1995), and Ferson and Harvey
(1999)), studying predictability of option-based factors included in hedge fund models
is novel.
Second, hedge fund managers may have skills in security selection and benchmark
timing that depend on the state of the economy. Indeed, Christopherson, Ferson, and
Glassman (1998) and Avramov and Wermers (2006) document predictability of mutual
fund managerial skills. If managers have specialized skills that best apply under speci…c
economic conditions, their private information correlate with the predictive variables,
making fund alphas predictable. To capture this intuition, we follow past work on
mutual fund performance and model the dynamics of hedge fund return using

J
X
0
ri;t+1 = ai;0 + ai;j Zj;t + i ft+1 + i;t+1 ; (3)
j=1

where ai;0 is the intercept, ai;j is the alpha slope coe¢ cient associated with each pre-
dictor, i the K-vector of fund risk loadings, and i;t+1 is the idiosyncratic fund-speci…c
term. We decompose again the fund population into three predictability categories, now

6

based on alpha variations, and denote by 0 (j); (j); and + (j); the proportions of
funds whose alphas are unrelated (ai;j = 0); negatively related (ai;j < 0), and positively
related (ai;j > 0) to predictor j; respectively.

To disentangle the two sources of hedge fund return predictability (benchmark re-
turns versus alpha variation), we employ the restrictions imposed by the hedge fund
benchmark model on the relation between the slope coe¢ cients in Equations (1) and
(3). In particular, replacing ft+1 in Equation (3) with its expression in Equation (2),
0
the predictive regression slope coe¢ cient in Equation (1) becomes bi;j = ai;j + i bf;j .

By comparing bi;j and ai;j ; we can easily determine the source of predictability for
fund i: For one, if the explanatory power of predictor j is entirely driven by risk factors
(as opposed to alpha), we would observe bi;j 6= 0 and ai;j = 0. This idea can be
extended to examine the source of predictability in the entire cross-section of hedge
+
funds by comparing the proportions of funds with predictable returns, R (j) and R (j);
with the proportions of funds with predictable alphas, (j) and + (j).

Given the large number of factors used in Equation (3) (typically seven factors in the
Fung-Hsieh (2004) model), we assume that benchmark risk loadings are time-invariant.
Using more parsimonious models, Bollen and Whaley (2009) and Patton and Ramadorai
(2010) …nd that hedge fund betas are subject to structural breaks. Such breaks are less
of a concern here since we are mostly interested in the estimated slope coe¢ cients,
bi;j . While unmodeled beta variations can potentially bias the estimated unconditional
a
alpha, they do not a¤ect bi;j as long as the relation between the predictors and factors
a
remains unchanged after the break.2 To empirically verify this property, we examine
the impact of changing betas associated with the prominent market and size factors.
Following Fung et al. (2008), we allow for breaks after September 1998 and March 2000
and …nd in unreported results that the estimated proportion of predictable funds in the
population remain virtually unchanged.

2
To see this, consider a simple model with one centered predictor; zj;t = Zj;t E(Zj;t ); one factor,
fk;t+1 ; and one structural break at time t+1 = : ri;t+1 = i;0 +ai;j zj;t + i;k fk;t+1 + i;k fk;t+1 + i;t+1 ;
where i;0 is the unconditional alpha and fk;t+1 = fk;t+1 1ft+1 g : Assuming that the relation between
zj;t and fk;t+1 is constant over time, we have cov( zj;t ; fk;t+1 fk;t+1 ) = 0; and the bias in bi;j in a
a
cov( zj;t ;fk;t+1 jfk;t+1 )
constant-beta model is equal to zero: E(bi;j a ai;j ) = i;k var( z f = 0: However, the
j;t j k;t+1 )
estimated unconditional alpha is biased: E(b i;0 i;0 ) = i;k E(fk;t+1 ) 6= 0:

7

B Measuring the Economic Value of Predictability

B.1 The Trade-o¤ between Unconditional and Predictable Performance

Previous studies and real-world investors typically rank funds based on expected perfor-
mance. In a large population of hedge funds following di¤erent strategies, it is unlikely
that funds with the highest unconditional mean are also those with the strongest pre-
dictability. In this multi-fund setting, investors willing to exploit predictability face a
potential trade-o¤ between unconditional and predictable performance. More formally,
we can write the di¤erence in expected returns between a conditional strategy with
c
time-varying weights, wi;t (i = 1; :::; M ); and an unconditional strategy with constant
u
weights, wi ; as

M
X M
X
c u c u c
= cov(wi;t ; ri;t+1 ) wi E(wi;t ) i; (4)
i=1 i=1

where i is fund i unconditional (excess) mean. When investing in predictable funds,
the investor tries to generate a positive covariance between the portfolio weights and
the future returns of the predictable funds (the …rst term in the RHS). However, there
is a cost as she sacri…ces high unconditional performance of the funds that are excluded
from the portfolio (the second term in the RHS). Excessive tilts towards predictable
funds could in‡ this second term and make the conditional strategy unpro…table.
ate

A simple way to incorporate this trade-o¤ into the fund selection process is to rank
funds according to the conditional (excess) mean, i;t = E[ri;t+1 jZt ]; where Zt stands
for the J-vector of predictor values observed at the portfolio rebalancing time t: For
simplicity, we start with the single-predictor case (J = 1); and discuss richer dynamics
below. Denoting the centered predictor value by zj;t (zj;t = Zj;t E(Zj ), where E(Zj )
is the predictor mean), we see that i;t is the sum of the unconditional and predictable
performance:
i;t = i + bi;j zj;t ; (5)

where i is the fund unconditional excess mean and bi;j zj;t is the predictable component.
Equation (5) leads to a parsimonious use of predictive information. Predictable funds
are chosen when the predictive component, zj;t bi;j ; is large enough, i.e., when Zj;t is
su¢ ciently far away from E(Zj ):

8

B.2 Implementing the Conditional Strategy

Implementation of the conditional strategy recognizes that the parameters in Equation
(5) have to be estimated and involves three steps. First, at each rebalancing time t
and for each existing fund (i = 1; :::; Mt ), we use past data to compute the estimated
conditional mean, b (j) = b + bi;j zj;t , where the sample mean, Z j , replaces E(Zj ) in
i;t b i
the de…nition of zj;t .
Most likely, the conditional mean is not estimated with the same accuracy across
funds with varying lives and investment strategies. To account for estimation uncer-
tainty, the second step consists of computing the t-statistic of the estimated conditional
mean:
bi;t (j)
t(bi;t (j)) = 1 ; (6)
d
v ar(bi;t (j)) 2
where v ar(bi;t (j)) is the estimated variance of bi;t (j) : The conditional t-statistic indi-
d
cates how precisely the unconditional mean, i, and the predictable component, zj;t bi;j
are estimated. Funds that exhibit higher t(bi;t (j)) are likely to perform better.3
The third step of our dynamic setup consists of investing in 10% of the funds with the
highest t(bi;t (j)). This portfolio is held over the next period, after which the selection
procedure is repeated (based on the new predictor value at time t+1). Our approach ex-
tends the decile portfolio approach of Elton, Gruber, and Blake (1996), Carhart (1997),
which use unconditional performance measures, such as past returns, to rank funds.
Understanding the investment process is straightforward, once we decompose the
1
conditional t-statistic. Speci…cally, let the unconditional t-statistic be t (bi ) = bi =d i ) 2 ,
v ar(b
1
and let the slope t-statistic be t(b bi;j ) = bi;j =d bi;j ) 2 : Using Equation (6), we can
b v ar(b
write the conditional t-statistic as a weighted average of the unconditional and slope
t-statistics:
1 !1
d
v ar(bi ) 2 v ar(bi;j )
d b 2

t(bi;t (j)) = t (bi ) + zj;t t(bi;j )
b
d
v ar(bi;t (j)) d
v ar(bi;t (j))

= w (zj;t ) t (bi ) + wb;j (zj;t ) t(bi;j );
b (7)

where the weights, w and wb;j ; depend on the di¤erence, zj;t ; between the current value
of the predictive variable, Zj;t ; and its long run mean Z j :
When Zj;t is close to Z j , the strategy invests in the "unconditional" portfolio–the

3
In an unconditional setting, the use of the t-statistic as an improved performance measure is advo-
cated, among others, by Kosowski et al. (2006) and Kosowski, Naik, and Teo (2007).

9

portfolio holding the top decile of funds with the highest unconditional t-statistic, t (bi ) :
By contrast, when Zj;t moves away from Z j , the predictable component, zj;t bi;j ; grows
large, and the strategy invests in the "slope" portfolio, the portfolio holding the top decile
of funds with the highest slope t-statistic, t(bi;j ) sign(zj;t ); where sign(zj;t ) denotes the
b
sign of zj;t . That is, the slope t-statistic is multiplied by the sign of zj;t to guarantee
that the slope portfolio contains funds with the correct exposure (bi;j < 0 when zj;t < 0,
b
and vice-versa).
In Figure 1, we con…rm the existence of a trade-o¤ between unconditional and pre-
dictable performance using our comprehensive hedge fund dataset (discussed below).
To illustrate, we plot in Panel A the relation between the average t-statistic of funds
included in the unconditional portfolio, denoted by t(bu ); and the default spread (using
t
other predictors provide similar insights).4 To ease interpretation, zj;t is standardized,
i.e., a value of one indicates that the predictor value is one standard deviation above
its average. In a nutshell, we …nd that funds with high unconditional mean tend to be
unpredictable. While the conditional t-statistic, t(bu ); is high when zj;t is close to zero
t
(driven by the high t (bi ) across funds), it quickly goes down as jzj;t j increases because
of the low and noisy estimate of the predictable component, zj;tbi;j (i.e., t(bi;j ) is low
b b
across funds):
Panel B plots the relation between the conditional t-statistic of the slope portfolio,
t(bs );
t and the default spread. In this case, we observe the exact opposite pattern:
while t(bs ) is low when zj;t is close to zero; it progressively increases as jzj;t j grows,
t
implying that predictable funds exhibit low unconditional mean. Finally, Panel C plots
the investment process described in Equation (7)– conditional strategy moves away
the
from the unconditional portfolio when jzj;t j gets large.

Please insert Figure 1 here

B.3 The Combination Strategy: Dealing with Estimation Risk and Model
Instability

The trade-o¤ between unconditional and predictable performance suggests that investing
in the slope portfolio is only advisable when jzj;t j is su¢ ciently large. In this section,
we go further and argue that, even in this situation, being fully invested in the slope
portfolio may actually hurt performance for two reasons.
4
Speci…cally, for each fund i included in the unconditional portfolio in month t, we use past returns
(over the last 36 months) to estimate t (bi ) ; v ar(bi ); t(bi;j ), and v ar(bi;j ): Then, we compute averages
d b d b
of these quantities across funds (i 2 unconditional portfolio in month t) and months (t = 1; :::; T ). These
averages are inserted in Equation (7) to compute t(bU ); as a function of the predictor value, zj;t :
t

10

First, in the presence of estimation risk, it may be quite di¢ cult to detect predictable
funds (i.e., funds with zj;t bi;j > 0) from the data. For instance, we see in Panel C of
Figure 1 that while funds with a positive unconditional mean can easily be detected
from the data (when zj;t = 0, t(bu ) = 3:5); the signal accuracy associated with funds
t
included in the slope portfolio is much lower, especially when the default spread is
negative (when zj;t = 2:5; t(bs ) = 1:6): This suggests that when jzj;t j gets large, the
t
conditional strategy may sometimes trade funds with high unconditional performance
for funds with low predictability.
Second, even if at some point in time, we can precisely estimate the predictive
regression slope coe¢ cients, numerous factors, such as the investors’search for successful
forecasting models, technological shocks, or institutional changes, make the predictive
model unstable (e.g., Timmermann (2008)). Since we expect both the identity of the
relevant predictors as well as their associated slope coe¢ cients to change over time, the
single-predictor model considered so far may not capture all variation due to changing
economic conditions. If the predictive power of a given predictor follows short-term
cyclical patterns, there are periods when the estimated predictable component, zj;tbi;j ;
b
conveys a wrong signal about future performance, and guides the slope portfolio to a
poor fund selection.
To address these obstacles, we implement an alternative conditional strategy building
on the combination forecast literature (e.g., Bates and Granger (1969), Timmermann
(2006)). In particular, for each existing fund i at the rebalancing time t (i = 1; :::; Mt );
we estimate its conditional t-statistic, t(bi;t (j)); using each predictor j separately (j =
1; :::; J): Second, we compute the simple average across all J conditional t-statistics:

J J
1X 1X
t(bi;t ) = t(bi;t (j)) = w t (bi ) + wb;j (zj;t ) t(bi;j );
b (8)
J J
j=1 j=1

1 PJ
where w = J j=1 w (zj;t ):5 We ultimately design an investment strategy that holds
the top decile of funds with the highest combination t-statistic, t(bi;t ):
This combination strategy exhibits several appealing properties. First, since it is
unlikely to observe extreme values for all predictors simultaneously, the total weight,
w ; associated with the fund unconditional t-statistic, t (bi ), remains high: At the same
time, the importance of the slope signals in the investment process decreases because
5
While more complex weighting schemes exist, the simple average tends to perform well, as the
weights do not have to be estimated (see Timmermann (2006)). As an alternative to combination
forecast, previous papers use Bayesian averaging, where the weight associated with each predictive
model depends on the model prior distribution (e.g., Avramov (2002) and Cremers (2002)).

11

each individual weight, wb;j (zj;t ); is divided by J: The combination strategy shrinks the
portfolio towards the unconditional portfolio and reduces the impact of both estimation
risk and model instability (see Rapach, Strauss, and Zhou (2010) for a discussion in
a single-asset setting). Second, similar to portfolio diversi…cation, combining forecasts
generally reduces the out-of-sample forecast error variance (see Timmermann (2006)). In
particular, Hendry and Clements (2002) show that combining forecasts provides a good
hedge against structural breaks in the data generating process. Hence, the combination
strategy should be more likely to consistently detect those funds with predictable returns.
The all-inclusive model, which includes all J predictors simultaneously in the regres-
sion, can also be considered to assess predictability. However, this speci…cation typically
delivers poor performance. As shown by Avramov (2002) and Goyal and Welch (2008),
the forecast errors of this multi-predictor model are large, as multiple slope coe¢ cients
are estimated with less accuracy. Since there is no shrinkage towards the unconditional
portfolio, performance deteriorates because large positions are taken in slope portfolios
that exhibit low or no predictability out-of-sample.6 For comparative purposes, we do
report the performance of the conditional strategy based on the all-inclusive speci…ca-
tion.

C Estimation Issues

C.1 Correcting for Small Sample Bias

It is well-known that the ordinary least-square (OLS) estimation of the predictive re-
gression slope coe¢ cients is subject to the small-sample bias. That is, the expected
value of estimated slope coe¢ cients, E(bols ) = E(bols ; :::; bols )0 ; is di¤erent from its true
b ib b
i;1 i;J
parameter value; bi (e.g., Stambaugh (1999)). While this bias disappears in large enough
samples, it is an important concern here because the return history for many hedge funds
is short. For one, survivorship bias-free databases only start in January 1994.
To illustrate the magnitude of this bias, we estimate that a one-standard deviation
increase in the dividend yield leads to a large overestimation in the expected fund return
greater than 26 bp per month (3.1% per year) for 25% of the funds in the population.
This bias is even more pronounced for speci…c investment categories. Ignoring small
sample bias is likely to a¤ect the estimated proportions of predictable funds, as well as
the fund estimated t-statistics, leading to a poor fund selection.
6
To see why there is no shrinkage, note that in the multi-predictor case, the conditional t-statistic
has a similar expression as in Equation (7): t (bi ) = w (zt ) t (bi ) + wb (zt ) t(bi ); where zt ; wb ; and
0
b
bi ) are all J-vectors. When the kth element in zt gets large, the conditional strategy invests in the kth
t(b
slope portfolio that holds funds with the highest kth slope t-statistic, t(bi;k ):
b

12

The small sample bias arises under two conditions frequently met empirically: 1) the
predictors are persistent, e.g., Zt+1 has an autoregressive VAR(1) structure:

Zt+1 = + Zt + t+1 ; (9)

where is the J J companion matrix, and t+1 is the J-vector of innovation; 2) the
hedge fund innovation, ui;t+1 ; is contemporaneously correlated with t+1 . That is, we
0
can express the hedge fund innovation using ui;t+1 = i t+1 + ei;t+1 ; where i denotes
the J-vector of innovation coe¢ cients, and ei;t+1 is the fund residual term (orthogonal
to both t+1 and Zt ).7 Since the OLS-estimated companion matrix, b ; is biased in small
samples (Nicholls and Pope (1988)), the slope estimate, bi ; inherits some of the bias in
b
b because of condition 2): Following Stambaugh (1999), this bias can be written as8

0
bias(bols ) = E(bols
bi bi bi ) = E b i: (10)

Intuitively, Equation (10) can be interpreted as an omitted variable bias, since bi captures
b
the in‡uence of the omitted innovation vector, t+1; on ri;t+1 . Therefore, as noted by
Amihud and Hurvich (2004) and Amihud, Hurvich, and Wang (2008, AHW hereafter),
if we include the J-vector t+1 as an additional explanatory variable and write

J
X 0
ri;t+1 = bi;0 + bi;j Zj;t + i t+1 + ei;t+1 ; (11)
j=1

the small-sample bias disappears as the orthogonality holds, i.e., E (ei jX ) = 0; where
ei = [ei;1 ; :::; ei;T +1 ]0 ; X = [x1 ; :::; xT +1 ]0 ; and xt = [1; Zt
0
1;
0 ].
t Of course, we cannot
observe the true innovation vector thus we have to …nd a proxy for it denoted by c .
t+1
To compute c ; we use a simple procedure proposed by AHW described in Appendix
t+1
B. After replacing with c in Equation (11), we can compute the bias-corrected
t+1 t+1
estimated slope coe¢ cients, bi;j ; using the standard OLS technique. Using extensive
b
simulation tests, AHW …nd that their approach achieves a substantial reduction in the
small-sample bias (bi;j is not totally bias-free though, as we use c instead of the true
b t+1
7
Unless the J-vector of predictor innovations, t+1 ; is strongly correlated with news about current
and future expected cash ‡ ows, there must be a contemporaneous correlation between t+1 and ui;t+1 .
Changes in future expected returns captured by t+1 a¤ect both prices and the contemporaneous fund
return, ri;t+1 (e.g., Cochrane (2008) and Pastor and Stambaugh (2009)).
8
Using X(T J+1) = [(1; Z1 )0 ; :::(1; ZT )0 ]0 ; and Yi(T 1) = [ri;2 ; :::; ri;T +1 ]0 ; we can write Yi =
0 0

Xbi + V i + ei ; where V(T J) = [ 2 ; :::; T +1 0 ]0 : Replacing V with Z
0
X 0 ; where Z(T J) =
[Z2 ; :::ZT +1 ] ; we can use the standard OLS formula to get E(bi ) = E (X 0 X) 1 X 0 Yi = bi +
0 0 0
b ols
0
0 1 0
E (X X) X (Z X ) 0
= bi + E b :
i i

13

t+1 ). While other approaches are also feasible, such as the bootstrap (see Nelson and
Kim (1993)), the AHW procedure is computationally much faster as it boils down to
estimating a single regression for each fund. Given the great number of funds in our
sample, as discussed below, computational e¢ ciency is strongly appealing.
The framework proposed by AHW focuses on traditional predictive regressions. Here,
we extend their methodology on several fronts: 1) to examine predictability in a richer
setting that incorporates alpha predictability and di¤erent time horizons (monthly and
quarterly); 2) to account for potential hedge fund illiquidity (discussed below). All the
technical details on these extensions are detailed in Appendix B.

C.2 Accounting for Hedge Fund Illiquidity

Some hedge funds invest in illiquid assets, such as emerging market debt, asset-backed se-
curities, or over-the-counter derivatives. Such assets may be a¤ected by non-synchronous
trading (stale prices) and may also facilitate return misreporting activities, as docu-
mented by Bollen and Pool (2009). Illiquidity tends to smooth hedge fund returns over
time, and induce positively correlated residuals, ei;t+1 ; in Equation (11) (see Getman-
sky, Lo, and Makarov (2004)). All else equal, the standard deviation of the estimated
coe¢ cients, bi;0 ; and bi;j ; is higher for funds with positively correlated residuals. Failing
b b
to adjust for this correlation, we may wrongly conclude, based on the t-statistics of bi;0 ;
b
and bi;j ; that illiquid funds generate a higher unconditional mean and/or have highly
b
predictable returns.
To explicitly control for illiquidity when computing the variance of bi;0 ; and bi;j , we
b b
model the residual, ei;t+1 , of each fund i as an AR(p) process (i = 1; :::; M ):

p
X
ei;t+1 = i;l ei;t+1 l + i;t+1 ; (12)
l=1

where i;l is the autoregressive coe¢ cient at lag l (l + 1; :::; p); and i;t+1 is the inno-
b
vation term. We use the estimated residuals, ei;t+1 ; to obtain consistent autoregressive
coe¢ cient estimates. To determine the appropriate number of lags, we compute the pro-
portions of funds with non-zero autocorrelation coe¢ cients at di¤erent lags (using the
approach of BSW described in Appendix B). The results displayed in Appendix C reveals
that 29.1% and 28.1% of the funds have a one-month and two-month lag coe¢ cients dif-
ferent from zero, respectively, while the proportion falls to 4.9% at a three-month lag.
The results are qualitatively similar across investment styles (some categories such as
convertible arbitrage exhibit higher proportions, consistent with Getmansky, Lo, and

14

Makarov (2004)). Based on this evidence, we use an AR(2) model that we estimate for
each fund separately to control for the cross-fund variation observed in the data. As an
alternative to the AR speci…cation, we also compute the variance of the estimated re-
gression coe¢ cients using the Newey-West (1987) methodology, and …nd that the results
(to be presented) remain unchanged.

III Data Description
We use four economically motivated instruments to predict future hedge fund returns:
the default spread, the dividend yield, the VIX, and aggregate fund ‡ows. Given the
relatively small number of monthly observations for hedge funds, model parsimony is an
important consideration in our choice of predictors. Parsimony also avoids the search
over a large number of predictors which could invoke data-mining concerns.9 All pre-
dictors are observed at a monthly frequency and appropriately lagged to forecast hedge
fund returns over the next month.
The default spread is the yield di¤erential between Moodys BAA and AAA rated
bonds. Previous studies (e.g., Kandel and Stambaugh (1986)) show that the yield spread
can predict future stock and bond returns. The dividend yield is the total of annual
cash dividends on the value-weighted CRSP index divided by the current index level.
Fama and French (1989) suggest that the dividend yield is a business cycle indicator that
peaks in recession when expected returns required by investors are high. We also use
the VIX index from the CBOE. Taylor, Yadav and Zhang (2006) present evidence that
implied volatilities help predict stock returns. Moreover, volatility may capture some
of the option-like features in hedge fund returns (Agarwal and Naik (2004)). Finally,
aggregate ‡ows are calculated as the value-weighted percentage net in‡ows into the
hedge funds in our database. As discussed in Naik, Ramadorai, and Stromqvist (2007)
and Fung et al. (2008), new money can create capacity constraints, leading to lower
future returns.
Figure 2 shows that during the …nancial crisis of 2008, the dividend yield, the default
spread, and the VIX exhibited extreme deviations from their past historical average. For
this reason, we initially focus on the period 1994-2007 to assess hedge fund predictability,
and run a separate analysis to check the robustness of our results during the 2008 crisis.

9
Patton and Ramadorai (2010) address the need for a parsimonious model by examining a large
number of predictors and risk factors and selecting for each fund one predictor and two factors based
on a statistical criterion.

15

Panel A of Table I reports descriptive statistics for the hedge funds included in our
sample between January 1994 and December 2007. We evaluate hedge fund performance
using monthly net-of-fee returns using a new data base that aggregates for the …rst
time data reported by …ve di¤erent providers (BarclayHedge, TASS, HFR, CISDM and
MSCI). To create this data set, we carefully control for a number of potential biases that
are discussed in Appendix A. To estimate the coe¢ cients in the predictive regression,
each fund is required to have at least 36 monthly return observations, which leads to a
…nal sample of 7991 funds.10
We observe from Panel B that the default spread, the dividend yield, and the VIX
exhibit high positive autocorrelation ( = 0:95; 0:97; and 0:84; respectively). These large
coe¢ cients highlight the importance of controlling for small sample bias in the estimation
process. In addition, correlations across predictors are low on average, suggesting that
each variable capture speci…c variations in economic conditions. In this context, the
combination strategy could be able to add value over individual predictors.
Finally, Panel C contains summary statistics for the risk factors included in the Fung
and Hsieh (2004) seven factor model. Equity Market is the S&P 500 return minus risk
free rate, Equity Size is the Wilshire small cap minus large cap return, Bond Term
is the change in the constant maturity yield of the 10–year Treasury appropriately
adjusted for duration (to represent returns on a traded portfolio), Bond Default is the
change in the spread of Moody’ Baa minus the 10–
s year Treasury (also adjusted for
duration), and Trend Bond, Currency, and Commodity are the straddle-type trend
following strategies.11
Please insert Table I here

IV Empirical Results
A Hedge Fund Return Predictability
A.1 Return versus Alpha Predictability

We begin our empirical analysis by measuring return and alpha predictability across
individual hedge funds over the period 1994-2007. While Panel A of Table II reports the
evidence for all funds in the population, Panels B to K focus on the di¤erent investment
categories. For each panel, the …rst row (Return) contains the estimated proportions of
+
funds with predictable returns, R (j) and R (j); associated with each predictor using
10
While this requirement may lead to survivorship bias, unreported results show that our results are
robust to using funds with 24 monthly observations.
11
We thank David Hsieh for making these factors available on his website.

16

the (bias-corrected) estimated slope coe¢ cients, bi;j ; in Equation (1). As a measure of
b
overall predictability, the last row-element displays the proportion of predictable funds
using all predictors simultaneously, bJoint . Similarly, the second row of each panel
R
(Alpha), reports the estimated proportions of funds with predictable alphas, (j);
+ Joint
b (j); and b , obtained from the (bias-corrected) estimated slope coe¢ cients, bi;j ;
a
in Equation (3). All details on the estimation procedure are explained in Appendix B.
Overall, two insights stand out from Table II. First, the measure of joint predictabil-
ity, bJoint ; reveals that there is ample evidence of return predictability. In the entire
R
population, we …nd that 60.5% of the funds are predictable, while this proportion ranges
from 31.1% (managed futures) to 83.7% (convertible arbitrage) across investment cat-
egories. Second, most of this predictability is due to alpha variation. Comparing the
Return and Alpha rows, we observe that for most hedge fund styles, the proportions of
funds exhibiting return and alpha predictability are almost identical (i.e., bR b and
b+
R
+
b ): This interpretation is corroborated by the evidence, reported in Appendix C,
that the Fung-Hsieh benchmark factors are largely unpredictable. This result is consis-
tent with the interpretation that total returns are predictable due to predictable alpha
or skill that manifests itself under speci…c economic conditions. Another interpretation
is that the Fung-Hsieh model fails to include relevant risk factors. While sensitivity tests
in Section IV.E.1 show that alpha predictability is robust to additional risk factors, we
leave the …nal interpretation to the reader.

Please insert Table II here

Several hedge fund styles exhibit a high fraction of funds that are positively pre-
dictable by the default spread. The strongest relation is found among emerging markets
funds, with 33:5% of them being positively related with this predictor (consistent with
Jostova (2006)). Looking at the median of the (standardized) slope coe¢ cient, bj ; we
conclude that a one standard deviation increase in the default spread causes a large re-
turn jump of 43 bp per month (5% per year). Widening credit spreads typically coincide
with ‡ight to quality, which could in turn forecast higher returns in the future. A similar
reasoning holds for the carry trade strategies in FX markets followed by global macro
funds (b+ = 13:2%). Widening credit spreads can trigger the unwinding of carry trades,
R
which leads to increasing future expected returns (e.g., Jylha and Suominen (2010)). Fi-
nally, 32.3% of the convertible arbitrage exhibit positive predictability, re‡ecting again
the exposure of these funds to the default spread.
The dividend yield shows a very consistent pattern across all fund styles, except

17

for managed futures: while only few funds have a positive slope coe¢ cient, a large
number of them have a negative exposure (bR ranges from 14.8% to 37.8%). One
possible explanation, consistent with the business cycle interpretation of the dividend
yield, is the role of leverage in hedge fund performance. In recessions, it is likely that
leverage availability from prime brokers is constrained, forcing hedge funds to reduce
their exposures. Such impediments are consistent with low returns and alphas in times
of high dividend yield. 12 This could also explain why the opposite pattern holds for
managed futures funds. Since these funds trade on futures markets that remain liquid
over the business cycle and that allow them to determine the margin to equity ratio
themselves, they face fewer leverage constraints.
The vast majority of fund styles exhibit a negative relation with the VIX. For in-
stance, we …nd that 38.9% of event-driven funds have a negative relation with the VIX,
consistent with the higher deal failure rate in turbulent periods (e.g., Mitchel and Pul-
vino (2001)). Convertible arbitrage funds often exploit mispriced volatility in convertible
bonds (e.g., Choi, Getmansky, Henderson and Tookes (2010)). Increasing VIX may re-
duce opportunities of cheap volatility and explain the negative exposure of these funds
(bR = 24:9%). On the contrary, managed futures are one of the few categories that ben-
e…t from higher uncertainty (b+ = 16:7%). Extreme values in the VIX could indicate
R
trend reversals. Since managed futures funds (which include CTAs) tend do well after
trend reversals, this would could explain this positive relation. During the 2008 …nancial
crisis, a Financial Times article observed that "CTAs as an investment typically do best
in periods of market chaos[...] they performed relatively well when implied volatility of
equities rose on fears of Russian default and the Long Term Capital Management crash
in 1998. A similar picture emerged in the run up to the Iraq war in 2002-2003, and now
the credit crunch of 2008 ".13
The strongest evidence for negative return predictability is found for aggregate ‡ows.
Looking at the entire population, an increase in ‡ows leads to a decrease in returns
and alpha for 33:2% and 26:7% of the funds, respectively. This ‡ return relation
ow
con…rms the …nding of Naik, Ramadorai, and Stromquist (2007) who argue that capacity
constraints, attributable to excessive in‡ows, hurt performance.14 Unsurprisingly, this
e¤ect is particularly strong for the crowded market for convertible arbitrage that is
12
Our results contrast with the positive relation between the dividend yield and future mutual fund
returns (Ferson and Qian (2004)). Mutual funds have a strong exposure to the stock market, whose
returns tend to be positively related to the dividend yield (e.g., Fama and French (1989)).
13
"One investment that loves chaos", Financial Times, 23 November 2008.
14
The existence of capacity constraints is con…rmed by our subperiod analysis: while b equals 6:5%
of the entire population between 1994 and 2000, it jumps to 38.9% during the most recent period
(2001-2007).

18

dominated by hedge funds (bR = 44:7%). It is also strong for funds of funds, suggesting
that they struggle to generate performance by deploying capital after large fund in‡ows.
Importantly, Table II documents a clear asymmetry in the direction of predictability,
since most predictable funds share the same exposure to the predictor. To illustrate, we
observe for the dividend yield that bR = 22:2% and b+ = 4:1% in the entire population,
R
implying that close to 80% (=4.1/22.2) of the predictable funds have a negative slope
coe¢ cient, bi;j : This result may have an impact on performance. If the dividend yield is
well above its mean (i.e., zj;t > 0), the conditional strategy will …nd it di¢ cult to …nd
funds with the correct exposure (i.e., funds with bi;j > 0):
Arguably, liquidity constraints (such as lock-up periods) may prevent investors from
rebalancing their fund portfolio at a monthly frequency.15 For hedge fund predictability
to be exploitable out-of-sample, it must be present at lower frequencies. As a …rst test,
we examine predictability at a quarterly frequency. The results reported in Appendix C
con…rm that quarterly returns are predictable. This suggests that the economic value of
predictability can be positive even after accounting for these constraints. This is what
we examine next.

B The Economic Value of Predictability
B.1 Performance Analysis

While our previous analysis documents ample evidence of predictability, institutional
investors (such as funds of funds) willing to take advantage of it face several issues
discussed in Section II.B. First, the identity of these predictable funds is unknown, and
must be inferred from the data (estimation risk). Second, the in-sample predictability
documented so far may not carry forward if the predictive relation changes over time
(model instability). To address these issues, we carry out a range of out-of-sample tests
that carefully incorporate real-world investment constraints.
First, we account for liquidity constraints by excluding closed funds, and by con-
sidering a one-year lock-up period (i.e., annual rebalancing). Second, there is a limit
in the number of individual funds that funds of funds hold in practice. While data
on these holdings is not publicly available, Lhabitant (2006) indicates that the typical
number is about 40. As a result, we limit the minimum and maximum number of funds
in the portfolio to 25 and 75, respectively. Third, investors typically do not invest in
funds that are too small relative to their own size. As discussed in Ganshaw (2010),
15
Since liquidity constraints prevent the investor from investing additional money into hedge funds,
it may also explain why alphas are predictable in the …rst place. Baquero and Verbeek (2010) raise a
similar argument when they examine the performance of "smart money" strategies in hedge funds.

19

few institutional investors want to represent more than 10% of a fund’ assets under
s
management. We use this rule to set up a dynamic AuM cuto¤ equal to the minimum
fund size such that a "typical" fund of funds does not breach this 10%-threshold.16 The
resulting cuto¤ rises from $12 million at the beginning to $63 million at the end of our
sample. Contrary to the constant cuto¤s used in previous studies (e.g., $20 million),
our …lter explicitly accounts for the growth in hedge fund industry over time. Finally,
we exclude funds of funds since we assume that institutional investors only focus on
individual funds to avoid an additional layer of fees.
We consider four distinct strategies presented in Section II.B, each of which utilizes
the following signal to select the top decile of funds: (i) the unconditional portfolio uses
the unconditional t-statistic; (ii) the single-predictor strategy ranks funds according
to the conditional t-statistic obtained from each predictor (default spread, dividend
yield, VIX, and aggregate ‡ows); (iii) the multi-predictor strategy uses all predictors
simultaneously; (iv) the combination strategy averages across the single-predictor t-
statistics. The construction of the di¤erent portfolios proceeds as follows. At the end
of each year, we estimate, for each strategy, the appropriate signal for each existing
fund using past three-year returns, and form the top decile portfolio. This portfolio
is kept during one year, after which the entire procedure is repeated. When a fund
stops reporting returns after being selected into the portfolio, we assume that its capital
allocation is invested at the riskless rate. Therefore, we avoid look-ahead bias since we
do not condition on a fund being alive until the rest of the year.
Panel A of Table III reports the out-of-sample performance of the di¤erent strategies
between January 1997 and December 2007 (the period 1994-1996 is used for estimation).
First, the unconditional portfolio obtains a solid performance– annual Fung-Hsieh al-
the
pha and Information ratio are 5.8% and 2.4, respectively, thus easily beating the value-
(VW) and equal-weighted (EW) hedge fund indices. This performance re‡ects the high
signal accuracy of the unconditional mean (see Panel C of Figure 1), and is consis-
tent with the results obtained by Kosowski, Naik, and Teo (2007), and Jagannathan,
Malakhov, and Novikov (2010). Second, none of the single-predictor strategies out-
perform the unconditional portfolio on a risk-adjusted basis (Information and Sharpe
ratios). Third, consistent with the previous literature (e.g., Goyal and Welch (2008)),
the multi-predictor strategy that uses all predictors simultaneously produces to the
worst performance (IR = 1:5), suggesting that conditional means based on multiple
regressions cannot be precisely estimated. Finally, the combination strategy is the only

16
The "typical" fund has an average size (as measured from the funds of funds AuM in our sample)
and invests in 50 funds (the midpoint in our investment strategy).

20

conditional strategy that dominates the unconditional portfolio – the Information and
Sharpe ratios which amount to 2.7 and 1.9, respectively, are statistically signi…cantly
higher than that of the unconditional strategy (at the 5% level). In addition, the combi-
nation strategy does not introduce higher tail risk. The 1% and 5% Value-at-Risk equals
-1.4% and -0.7% per month, respectively, and are thus the lowest among all competing
strategies.

From an investor perspective, the superior performance of the combination strategy
is accompanied by several additional advantages displayed in Panel B. First, the strat-
egy does not involve extensive (and possibly unrealistic) portfolio turnover– exhibits
it
the second lowest (66%) annual turnover of constituent funds. Second, the autocorre-
lation coe¢ cients suggest that performance is not due to holding illiquid funds. The
coe¢ cients are comparable in magnitude to the other strategies, and are lower than
the typical hedge fund autocorrelation coe¢ cients (e.g., Lo (2002)). Finally, the per-
formance of the combination strategy is not driven by concentrated bets on speci…c
investment categories. The highest weight, invested in long-short equity funds, is only
equal to 10.8% on average over the period.

Please insert Table III here

In a recent study, Avramov, Kosowski, Naik, and Teo (2010; AKNT) form hedge
fund portfolios that exploit predictability using a Bayesian framework. A comparison
of the combination strategy with their portfolios shows important di¤erences. First, by
focusing on the t-statistic (as opposed to the estimated conditional mean), the combi-
nation strategy achieves an important reduction in total risk (b = 4:5% is almost three
times lower on average). Second, the strategy invests in a larger number of funds (68
against 12 in AKNT), suggesting that it may be more robust to extreme market condi-
tions, as discussed in Jagananthan and Ma (2003). Third, Panel C of Table III shows
that the combination strategy behaves more like a pure alpha strategy, as its exposures
to the Fung-Hsieh risk factors are extremely low. But perhaps more importantly, the
conditional strategies considered here are very intuitive–the investment process boils
down to investing in only two portfolios, the unconditional and the slope portfolios.
While less sophisticated than the Bayesian approach in AKNT, they allow for a deeper
understanding of the drivers of out-of-sample performance, which we examine below.

21

B.2 Explaining the Performance of Single-Predictor Strategies

As shown in Equation (7), when the predictor value is di¤erent from its normal level
(i.e., when zj;t is low or high), the single-predictor strategy invests in the slope portfolio
(i.e., in funds with high bi;j sign(zj;t )). Therefore, an important driver of performance
b
should depend on the slope portfolio’ ability to detect the (truly) predictable funds
s
from the data. We examine this issue in Table IV.
Consider, for instance, the default spread. We group the values of the default spread;
zj;t ; observed at each rebalancing date into quintiles, and examine the strategy alloca-
tion when zj;t is either very low (bottom quintile) or very high (top quintile). As
expected, Panel A shows that when the default spread takes extreme values, the condi-
tional strategy has a large exposure to the slope portfolio (for instance, when zj;t > 0,
wslope = 77:2%).17 But more importantly, we …nd that the quality of the predictive
information is very di¤erent according to the value taken by zj;t . While the cross-fund
average slope t-statistic is quite low when zj;t is negative (t(bj ) = 0:96); it is very high
b
bj ) = 2:03): This result re‡
when zj;t is positive (t(b ects the strong asymmetry documented
in-sample. Since there are a lot more funds with a positive exposure to the default spread
+ +
in the population (in Panel A of Table II, R (j) = 14:5% versus R (j) = 1:6%), it should
be much easier to identify these predictable funds from the data when zj;t is positive.
As suggested, Panel B reveals that the performance of the default spread strategy
is strongly dependent on the signal accuracy of the slope portfolio. The Fung-Hsieh
annual alpha, for instance, is equal to 14.8% after observing a high default spread at
the rebalancing date (as opposed to 6.0% when it is low).
The analysis is exactly the same for the remaining predictors (dividend yield, VIX,
and aggregate ‡ows). In each case, Panel A documents a strong asymmetry in the
quality of predictive information, which matches the asymmetry observed in Table II.
This, in turn, leads to a strong asymmetry in future performance, as shown in Panel B.
Observing such a clear-cut pattern in performance is striking given that all measures
are computed out-of-sample.

Please insert Table IV here

Figure 3 illustrates the relation between the predictor value and out-of-sample per-
17
The sum of the weights does not necessarily equal 100%. It can be slightly above 100% if the
unconditional and slope portfolio have a few funds in common. It can be below 100% if the conditional
strategy selects funds that are neither in the unconditional nor in the slope portfolios (for moderate
values of zj;t ; some funds can have a high t(bi;t (j))), despite having components, t(bi ) and t(bi;j ) that,
b
individually, do not belong to their respective top decile).

22

formance over time, where performance is measured this time as the di¤erence between
the Information ratio of the single-predictor strategy and the unconditional portfolio.
The result con…rm those in Table IV. For instance, the performance of the dividend yield
strategy goes up in times when the dividend yield is below average, which is consistent
with Table II ( R (j) = 22:6%; as opposed to R (j) = 3:6%).


B.3 Explaining the Performance of the Combination Strategy

We …nd that taking large positions in the slope portfolio hurts performance when the
quality of the predictive information is poor. The combination strategy overcomes these
di¢ culties by diversifying across predictors. As shown in Equation (8), such diversi…ca-
tion creates a shrinkage e¤ect towards the unconditional portfolio. To illustrate, Figure
4 plots the evolution of the weight invested in the unconditional portfolio over time.
Although we observe large variations for both single- and multi-predictor strategies, the
weight associated with the combination strategy is close to 80%. While Rapach, Strauss,
and Zhou (2010) highlight the bene…ts of shrinkage in a single-asset environment, we
argue that this is even more important with multiple assets because of the trade-o¤
between unconditional and predictable performance. Indeed, by investing in the slope
portfolio at the wrong time, the investor picks up funds with low predictability, and, in
addition, fails to capture the relatively high performance produced by the unconditional
portfolio.


Where does the combination strategy allocate the remaining 20%? As any active
strategy, the portfolio selected by the combination strategy can be decomposed into (1)
the unconditional portfolio plus (2) a long/short portfolio. The long portfolio contains
those funds selected by the combination strategy, but not by the unconditional portfolio.
The short portfolio consists of funds that are selected by the unconditional strategy, but
not by the combination strategy.
Intuitively, the construction of the long and short portfolios can be described as
a two-step process. First, with an increased emphasis on unconditional performance
(shrinkage e¤ect), the combination strategy focuses on a subset of funds with a su¢ -
ciently high unconditional signal, t (bi ) : This subset is not necessarily identical to and
may be larger than the top decile chosen by the unconditional portfolio. Second, in this

23

subset, the combination strategy looks for predictable funds using all predictors. Funds
having a positive (and precisely measured) predictable component are included in the
long portfolio, at the expense of funds with low predictable component that are put in
the short portfolio.
An important question is to know whether the performance of the combination strat-
egy is still subject to the asymmetry uncovered in Table IV. For each predictor, Table
V examines the annual out-of-sample performance of the long and short portfolios after
observing very low (bottom quintile) or very high (top quintile) predictor value, zj;t .
By combining across predictors, the long portfolio is able to use some new predictive
information. This information is orthogonal to the one produced by each predictor –
Panel A shows that the long portfolio never invests heavily in the di¤erent slope port-
folios. As seen from the performance analysis, this new information is richer and not
asymmetric anymore. For instance, the Fung-Hsieh alpha di¤erential against the un-
conditional portfolio, b b U ; is equal to 5.3% per year, even when the default spread
has the "wrong" value, i.e. when it is below average (zj;t < 0). Panel B shows the
combination strategy is also very good at excluding funds when they are expected to
underperform– annual performance of these funds is on average much lower than the
the
one produced by the unconditional portfolio.

Please insert Table V here

Is the superior performance of the combination strategy due to a few lucky years or
does the combination strategy outperform the unconditional strategy consistently over
2
time? To address this issue, we compute the out-of-sample ROOS of combining forecasts
of the monthly return, rt+1 ; of the long-short portfolio:

T
X T
X
2
ROOS = 1 (rt rt )2 =
b (rt rt )2 ; (13)
t=1 t=1

b
where rt+1 is the time t + 1 …tted value from a model that combines the forecasts
(estimated through time t) across all predictors; and rt is the forecast based on past
2
returns. The ROOS statistic measures the reduction in Mean Squared Prediction Error
(MSPE) for the combining model relative to historical average forecasts. Panel A of
2
Figure 5 plots the evolution of ROOS between January 2000 and December 2007 (using
2
an expanding window). Despite starting at a negative level, the ROOS jumps right after
January 2000, and increases steadily afterwards to reach a positive value at the end of the
period. This steadiness in performance is further con…rmed in Panel B which compares

24

the cumulative wealth produced by the combination strategy over the unconditional
portfolio.


C Impact of the 2008 Financial Crisis

C.1 Performance Analysis

The 2008 …nancial crisis is arguably the biggest crisis in modern …nancial history. Ac-
cording to Figure 2, this period witnessed a dramatic deviation of all predictors from
their historical means. For investors, it is of great practical importance to determine
whether the superior performance of the combination strategy is robust to the inclusion
of 2008, and which conditional strategy would have best anticipated the 2008 events,
thus steering the investor clear of the crisis.
In Panel A of Table VI, we report the out-of-sample performance of the unconditional
and conditional strategies (single-, multi-predictor, and combination) between January
1997 and December 2008. Despite the crisis, we …nd that the combination strategy still
achieves a strong performance– information ratio is not only the highest (IR =1.9),
its
but is also statistically signi…cantly higher than that of the unconditional portfolio (the
associated p-value is below 1%). In general, all strategies have been hit quite hard
during the crisis. For instance, the cumulative loss during the …nal quarter of 2008
amounts to 14.1% for the unconditional portfolio, and to 12.3%, and 14.1% for the
default spread, and aggregate ‡ows strategies, respectively. There is one exception
though: the conditional strategy based on the VIX. It not only yields the highest Sharpe
ratio (SR=1.4), it also resisted remarkably well during the …nal quarter of 2008 (with a
3.1% cumulative loss).
Please insert Table VI here

Of course, such performance should be viewed with caution because it is subject to
speci…cation uncertainty, that is the investor would have had to know back in December
2007 that the VIX strategy would outperform in 2008.18 However, it is interesting
to understand the drivers of this positive performance. To this end, we compare the
characteristics of the single-predictor strategies in 2008. Consistent with Figure 2, we
observe in Panel B that the value of all predictors in December 2007 (denoted by zj ); was
18
See Barras (2007) and Pesaran and Timmermann (1995) for further discussion. Note that the
combination strategy is robust to speci…cation uncertainty since the investor does not have to choose
among predictors.

25

very di¤erent from their average, leading to a large investment in the slope portfolios
(the weights range from 48.0% to 76%). How appropriate were these slope portfolios in
2008? To answer this question, we compute the hit ratio that determines the proportion
of months in 2008 when the portfolio predictable component, bj;t zj;t ; is positive, where
b
zj;t is the predictor value at the start of the month, and bj;t is the cross-fund average slope
b
coe¢ cient, estimated with the 36 most recent monthly observations. The results suggest
that the VIX strategy performs well in 2008, because its predictive power was much more
stable– hit ratio is extremely high (83.3%), as opposed to the other predictors.
its

The low hit ratios observed for the default spread and the dividend yield (25.0%
and 16.6%, respectively) are not due to a change in sign in the predictor value–Panel
B shows that the proportion of months in 2008 when the predictor keeps the same sign
(zj zj;t > 0); equals 100%. Therefore, the poor hit ratios are due to a change in sign
in the estimated slope coe¢ cients of the selected funds (from positive to negative). It
seems that the events in 2008 have caused important structural breaks in the predictive
relations that, for some reasons, did not a¤ect the VIX. The unique nature of 2008 is
con…rmed by our comparative analysis–computing the hit ratios of the default spread
and dividend yield during similar periods of extreme positive values for zj during 1997-
2007, we …nd a much higher stability in the predictive relation (i.e., the hit ratio amount
to 87.5% and 83.3%, respectively).

During the 2008 crisis, many investors tried to withdraw their money out of the hedge
fund industry. To prevent these massive out‡ows, hedge funds reacted by lengthening
redemption notice periods, erecting gates, or creating side-pockets. To measure the costs
of these liquidity constraints, we measure the performance of the di¤erent strategies
between January 1997 and December 2008 after exceptionally allowing the investor to
rebalance his portfolio monthly during 2008 (using all information available at the start
of the month). The results in Panel C show that allowing for monthly rebalancing leads
to a large improvement in performance compared to annual rebalancing (Panel A). For
instance, the increase in annual alpha ( ) is equal to 1.5%, 2.4%, and 1.7% for the
unconditional, aggregate ‡ows, and combination strategies, respectively. We conclude
that liquidity constraints imposed to investors carry an important cost–investors would
have been able dramatically reduce their losses in 2008, had they been able to rebalance
monthly (the cumulative returns during the …nal quarter of 2008 are positive in all but
two cases).

26

C.2 Further Evidence on the Performance of the VIX Strategy

To further interpret the performance of the VIX strategy, we compare its selection of
hedge fund investment styles with that of the unconditional portfolio. Figure 6 plots
the value of the VIX at each formation date (Panel A), next to the style composition of
the unconditional portfolio (Panel B), and the VIX strategy (Panel C).


First, the VIX strategy invests more in market neutral funds than the unconditional
portfolio. Market neutral funds were among the best performers in 2008, as the equal-
weighted style index produced a 1% annual return. Second, the VIX strategy reduced
its exposure to convertible funds, which heavily collapsed in 2008 (-21%). Thus, part of
the superior performance of the VIX strategy is due to overweighting good performers
(market neutral) and underweighting bad performers (convertible bonds) relative to the
unconditional strategy.
Should these choices make investors con…dent that the VIX strategy will perform
well again under similar circumstances in the future? One may argue that the 2008
performance is more driven by luck, as opposed to clever allocation choices. First,
contrary to past periods of high volatility (1997-2001), the strategy did not invest in
managed futures. However, there are good reasons to believe that this category performs
well in volatile periods, as discussed in Section IV.A–this category was indeed the best
performer in 2008 with outstanding 14% annual return. Second, the large drop in the
convertible bond market was caused by a spike in risk aversion, which led to signi…cant
out‡ows. In the Citadel example given in the introduction, we report that in early
2009 convertible bond hedge funds returned large pro…ts. As a result, underweighting
convertible arbitrage could eventually be a losing bet, if we incorporate the few …rst
months following the crisis.

D Additional Results

D.1 Sensitivity Tests

So far our results indicate that the combination strategy generates higher risk-adjusted
performance (Information and Sharpe ratios) than all other strategies. To determine
whether this conclusion is robust to alternative speci…cations, we perform a range of
sensitivity checks reported in Panel A of Table VII. First, our conclusions are robust
to reducing the maximum number of funds from 75 to 50, or to removing this upper

27

bound (i.e., holding the top decile portfolio even when it contains many funds). Second,
repeating our analysis including small funds (rather than imposing the AuM cuto¤)
leaves the performance of the combination strategy nearly unchanged. Funds generally
disappear from the database because they are liquidated. To account for the potential
impact of liquidation, we penalize any missing monthly observation with a -25% return,
after which the remaining funds are invested in the riskfree rate. While the annualized
alpha and mean of all strategies decrease by around 2%, the relative performance of the
combination strategy, on the other hand, slightly increases.
One important constraint is that of redemption notice periods– investor who
an
wishes to rebalance his hedge fund portfolio in December has to give notice to the
fund some time in advance, typically three months. To address this issue, we carry
out a robustness test in which the investor has to decide in September which funds to
hold in January of the following year. While overall performance slightly decreases, the
combination strategy still outperforms the unconditional portfolio.
Finally, while our baseline speci…cation is based on return predictability, we could
also rank funds based on the t-statistic of the conditional alpha in Equation (3). The
results indicate that the performance of the combination strategy based on alpha pre-
dictability is even better than that in Table III. This is consistent with our previous
discussion that most in-sample return predictability is driven by alpha predictability.
However, this approach is more sensitive to the potential bias caused by omitted risk
factors, as we use the same model to form the portfolio and evaluate subsequent perfor-
mance (see Carhart (1997)).

Please insert Table VII

To guard against the possibility of omitted risk factors, we also examine whether the
alpha and Information ratios computed using the Fung-Hsieh model change under alter-
native asset pricing models. We consider the four-factor model (market, size, book-to-
market, and momentum factors) and extended versions of the Fung-Hsieh model that
include the Pastor and Stambaugh (2003) liquidity factor, the emerging market port-
folio, and an additional equity straddle. The results, shown in Panel B of Table VII,
remain qualitatively unchanged.

D.2 Performance across Investment Categories

The superior performance of the combination strategy documented for the entire fund
population also holds across di¤erent investment categories. The results in Appendix

28

C show that for the two broadest investment categories, long-short equity and direc-
tional funds (which includes global macro, managed futures, and emerging markets),
the combination strategy still outperforms the unconditional portfolio by a substantial
margin.
In our discussion of the performance of the VIX strategy in Section IV.C, special
attention is given to two smaller investment categories: market neutral and convertible
arbitrage. Consistent with the performance of their respective equal-weighted indices, we
…nd that the unconditional and conditional strategies applied to market neutral funds
provides a fairly robust performance during the crisis, contrary to their convertible
arbitrage counterparts.

V Conclusions
The recent …nancial crisis has not spared the hedge fund industry and has highlighted
the need to search for a suitable forecasting models for hedge fund performance. This
paper develops a uni…ed framework to assess hedge fund return predictability on a fund-
by-fund basis. Using a large sample of funds during 1994-2008 along with a set of macro
variables, we …nd ample evidence of in-sample predictability, both across predictors and
investment styles. In addition, the bulk of return predictability is due to time-varying
alphas, whereas predictable benchmark returns play only little role.
To examine whether predictability can be exploited out-of-sample, we carry out a
range of tests that carefully incorporate several real-world investment constraints faced
by institutional investors. In a multi-fund setting, the impact of estimation risk and
model uncertainty on performance can be dramatic because of the trade-o¤ between
unconditional and predictable performance. When using poor predictive information,
the investor not only selects funds with low predictability, but may also exclude funds
with high unconditional performance. We …nd that a conditional strategy that com-
bines forecasts across predictors circumvents all these challenges and delivers superior
performance.
Our results make several contributions to the hedge fund literature and also have
implications for future work. First, we provide one of the most detailed analyses to date
of the statistical and economic drivers of conditional strategies’performance, especially
in periods when predictor values strongly depart from their long run means. Finally, we
use one such period– 2008 crisis– as a natural out-of-sample test to test the robust-
the ,
ness of our …ndings. Previous studies have often focused on unconditional measures of
hedge fund indices while we are able to shed light on predictability on a fund by fund

29

basis. Second, our results also have implications for the forecasting literature. Many
previous studies combine forecasts in an ad hoc way. Important insights can be gained
by studying the sources of the superior performance of combination strategies. We
compare our approach to studies of Bayesian predictability. In future work we plan to
study the economic and statistical drivers of strategies based on Bayesian predictability
models in more detail.

30

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33

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