Copyright
by
Cristian Ioan Tiu
2006
The Dissertation Committee for Cristian Ioan Tiu
certifies that this is the approved version of the following dissertation:
Systematic Risk in Hedge Funds
Committee:
Sheridan Titman, Supervisor
Laura Starks
Roberto Wessels
Lorenzo Garlappi
Rui de Figueiredo
Systematic Risk in Hedge Funds
by
Cristian Ioan Tiu, B.A., Ph.D.
Dissertation
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
The University of Texas at Austin
August 2006
To Mariana, who together with Andrei and Ioana (Ellie) supported me fully and
unconditionally.
Acknowledgments
The author thanks Keith Brown, Lorenzo Garlappi, Ilan Guedj, Cathy Iberg, Andrea
Reed, Laura Starks, Paul Tetlock, Sheridan Titman, Roberto Wessels and Uzi Yoeli
for fruitful discussions, and Aleksey Bienneman and Tina Gatch for data support.
Last but not least, I am thankful to UTIMCO for research support provided while
this thesis has been written.
Cristian Ioan Tiu
The University of Texas at Austin
August 2006
v
Systematic Risk in Hedge Funds
Publication No.
Cristian Ioan Tiu, Ph.D.
The University of Texas at Austin, 2006
Supervisor: Sheridan Titman
We document that hedge funds with lower systematic risk exposures have higher
Sharpe ratios. These funds are more successful: they are able to charge higher fees
and manage more assets. When pressed with inflows, fund categories on average do
not lose their ability to find investments bearing no systematic risk. By contrast,
individual funds experiencing inflows above and beyond their category average increase their systematic risk exposures. The tradeoff between performance and the
degree to which systematic risk exposures explain the returns of hedge funds has
implications for the latter’s transparency: the risks taken by outperforming hedge
funds cannot be understood solely from their monthly returns.
vi
Contents
Acknowledgments
v
Abstract
vi
List of Tables
x
List of Figures
xii
Chapter 1 Introduction
1
Chapter 2 Literature Survey
5
Chapter 3 Framework and Hypotheses
9
3.1
Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
3.2
Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
Chapter 4 Data
14
4.1
Hedge Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
4.2
Risk factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
Chapter 5 R-squares and Sharpe Ratios
5.1
20
Estimating R2 , Rsqr, T O1 and T O2 . . . . . . . . . . . . . . . . . .
20
5.1.1
20
Serial correlation in returns . . . . . . . . . . . . . . . . . . .
vii
5.2
5.3
5.1.2
Results - R2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
5.1.3
Results - Rsqr, T O1, T O2 . . . . . . . . . . . . . . . . . . . .
23
Testing Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
5.2.1
Cross-sectional tests: overall R2 and Sharpe ratios . . . . . .
24
5.2.2
Time series tests: Rsqr, T O1, T O2 and Sharpe ratios . . . .
27
Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
5.3.1
Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
5.3.2
Extensions: Sharpe ratios and R-squares,
or appraisal ratios and R-squares? . . . . . . . . . . . . . . .
32
Extensions: Idiosyncratic Risk by Strategy . . . . . . . . . .
33
5.4
Economic Significance . . . . . . . . . . . . . . . . . . . . . . . . . .
34
5.5
R-square and inflows . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
5.3.3
Chapter 6 Extensions: Other Measures of Success and R-squares
39
6.1
R-squares and fees . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
6.2
R-squares and assets under management . . . . . . . . . . . . . . . .
41
6.3
R-squares and age . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
6.4
R-squares and survival . . . . . . . . . . . . . . . . . . . . . . . . . .
44
Chapter 7 Implications for Risk Management
45
Chapter 8 Conclusions
47
Appendices
50
Methodologies to fit the factor model . . . . . . . . . . . . . . . . . . . . .
50
Spurious estimation of systematic risk: Estimation of the systematic models 55
Tables and figures
56
Bibliography
88
viii
Vita
94
ix
List of Tables
8.1
Summary Statistics for the Hedge Funds Industry.
8.2
Heterogeneity across net returns and assets under management from the Altvest, HFR
and TASS databases.
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
. . . . . . . . . . . . . . . . . . . .
59
. . . . . . . . . . .
60
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
8.3
Sample statistics for the risk factors used.
8.4
Summary of factor analysis applied to individual hedge funds.
8.5
R2 and talent proxies.
8.6
The relationship between the ability to explain a fund (high R2 or low T E) and fund
characteristics.
8.7
57
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
The relationship between the ability to explain a fund (high R2 or low T E), and the
fund’s performance, measured as Sharpe ratio adjusted for serial autocorrelation or as
the probability of survival.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
63
8.8
Out-of-sample fit of stepwise regression vs. five principal components.
. . . . . . . .
64
8.9
Fama-MacBeth regressions of Rsqr, T O1, T O2 on fund characteristics.
. . . . . . . .
65
8.10
Performance and the ability to infer a fund’s risk exposures.
. . . . . . . . . . . .
66
8.11
Economic significance of low Rsqr as talent indicator.
. . . . . . . . . . . . . . .
67
8.12
Determinants of the out-of-sample Rsqr.
. . . . . . . . . . . . . . . . . . . .
68
8.13
Determinants of the intra-factors timing.
. . . . . . . . . . . . . . . . . . . .
69
8.14
Determinants of inter-factor timing T O2.
. . . . . . . . . . . . . . . . . . . .
70
8.15
The link between R2 and fund fees.
. . . . . . . . . . . . . . . . . . . . . . .
71
x
8.16
Stepwise regression vs. Principal components goodness of fit.
8.17
Average Sharpe ratios and R-squares for hedge fund strategies.
8.18
Robustness check: repeating out hypothesis tests by strategy.
8.19
The relationship between appraisal ratios and R-squares.
xi
. . . . . . . . . . . .
72
. . . . . . . . . . .
73
. . . . . . . . . . . .
74
. . . . . . . . . . . . .
76
List of Figures
8.1
Distribution of data across databases merged.
8.2
Estimated Total Assets Under Management in the hedge fund industry.
8.3
Estimated Quarterly Flows into the hedge fund industry.
8.4
Assets under management distributed across strategies, when the strategies are inferred
using Sharpe regressions.
8.5
78
. . . . . . . . . . . . .
79
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
81
Differences in the means of the assets under management between groups of Low - High
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
Differences in the means of the management fees between groups of Low - High Rsqr,
T O1, T O2.
8.8
. . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rsqr, T O1, T O2.
8.7
77
Differences in the means of the Sharpe ratios between groups of Low - High Rsqr, T O1,
T O2.
8.6
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
Differences in the means of the incentive fees between groups of Low - High Rsqr, T O1,
T O2.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
. . . . . . . . . . . . . . . . .
85
. . . . . . . . . . . . . . . . . . . . . .
86
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
8.9
Stepwise regressions vs. principal components fit.
8.10
Length of backfilled histories in TASS.
8.11
Backfill bias correction.
xii
Chapter 1
Introduction
The hedge fund industry has doubled almost every two years, contains more than
8,000 active funds, and manages more than $ 1.2 trillion. With management fees
averaging 1.5% and 20% in incentive fees, hedge funds are also a very lucrative
industry. Given this explosive growth, identifying talented managers has become an
increasingly daunting task for the investor.
The returns of any fund can be divided into two parts: systematic and idiosyncratic. Since the talent is unobservable, a funds wants its investors to have
high confidence in its ability to generate returns. The investors’ t-statistic for ex√
cess returns is T (µ−rf )/σ , which justifies the motivation of the fund to maximize
Sharpe ratios. This is also a justification of why the Sharpe ratios are often used as
measures of performance by the hedge fund investors. In a simple setting in which
funds maximize their Sharpe ratios , we show that while it is optimal for a manager
to have some exposure to systematic risk, the proportion of the fund’s variance that
is systematic is inversely related to the manager’s ability to generate performance.
Simply put, if the manager is talented then the R-square of the regressions of the
hedge fund returns on systematic factors should be small.
This study tests the hypothesis that hedge funds which bear less systematic
1
risk outperform. Consistent with this hypothesis, we find that funds whose returns
have lower R-squares with respect to systematic factors have higher Sharpe ratios.
For example, comparing the funds in the highest R-square tercile with the funds in
the lowest, we find that the latter has a Sharpe ratio that is 0.38 higher and that this
difference is statistically significant. Furthermore, this relationship is economically
significant: a portfolio consisting of the low past R-square decile of hedge funds has
returns around 1% per year higher, and Sharpe ratios around 0.40 higher than the
portfolio of the high decile of past R-square funds. This difference is robust to the
size of the funds included in the analysis and to the frequency of rebalancing.
Low R-squares are achieved not only when the fund does not bear systematic risk but also when the fund is dynamically changing risk exposures so when
averaged, these exposures are small. We separate out the funds whose systematic
exposures change through time and show that on average, their Sharpe ratios are
lower. Therefore, we conclude that it is the ability of managers to make investments
uncorrelated with the systematic factors, rather than their ability to time these
factors that is positively related to the fund’s success.
Strategies with no systematic risk exposures arguably exist in finite supply
and may not accommodate all flows into hedge funds. Hence, the negative relationship between performance and systematic risk exposures may change when hedge
funds receive inflows. This is similar to the mechanism in which the growth of a
mutual fund renders the relationship between the manager’s talent and his performance insignificant, as in Berk and Green (2004). We show, however, that higher
inflows into categories of funds do not impede managers’ ability to find proprietary
strategies that are orthogonal to the space of systematic factors1 . Only in the case
of a fund that receives inflows above and beyond its category average do we find
evidence that manager’s ability to invest idiosyncratically is curtailed, causing the
1
This is not in contradiction with the fact that after receiving inflows, the performance of a
strategy may decrease due to decreasing returns to scale.
2
manager to increase exposures to systematic risk and in turn to under perform.
Do investors recognize the fact that low R-square funds are more talented?
We document that these funds are able to charge higher fees: the funds in the lowest
tercile of R-square charge, on average, 20 basis point more in management fees and
226 basis points more in incentive fees than the funds in the highest R-square tercile.
Additionally, low R-square as an explanatory variable for fees dominates measures
of realized performance such as the mean excess returns of the fund of the fund’s
Sharpe ratio.
Other measures of a fund’s success also favor the low R-square funds: the
funds in the lowest R-square tercile manage $ 9 million dollars more on average, live
about 10 months longer and are 5% less likely to exit the sample than the funds in
the highest R-square tercile.
Our paper extends the literature on understanding the sources of returns in
hedge funds by focusing on the analysis of individual funds. In this respect our
work differs from the literature directed at hedge fund risk adjusted performance,
which studies only portfolios of funds. Instead, our research is close to earlier studies
on risk factors that explain individual hedge fund returns such as Fung and Hsieh
(1997), Liang (1998) or Dor and Jagannathan (2002). Additionally, it builds on
more comprehensive and dynamic models, similar to Agarwal and Naik (2004), and
accounts for more sophisticated statistical properties of the returns of the hedge
funds a la Getmansky, Lo and Makarov (2004).
Furthermore, this study performs a comprehensive out-of-sample analysis of
the validity of risk models explaining individual hedge funds. As such, this analysis
is also close to the literature that links mutual funds style stability to performance.
From this point of view, we extend and apply to hedge funds what Chan, Chen
and Lakonishok (2002) and Brown and Harlow (2005) did for mutual funds. Our
conclusion is somewhat different from the conclusions of both of these studies: Chan,
3
Chen and Lakonishok (2002) asserts that managers stray from their “style course”
following periods of bad performance; Brown and Harlow (2005) asserts that better
performance is associated with “staying the course”. By contrast, our results on
the relationship between performance and the extent to which funds are exposed
to systematic factors show that hedge funds seem to be better off when they are
orthogonal to any investment style, at any point in time.
4
Chapter 2
Literature Survey
Our paper belongs mainly to the literature that examines whether hedge funds
are able to generate excess returns and examines links between performance and
fund characteristics. We draw from three relatively separate strands in the finance
literature.
The first strand, most related to this paper, addresses hedge funds performance. The fundamental question asked by this research is which hedge funds are
most likely to outperform. In contrast with the literature that addresses performance
of mutual funds (e.g. Carhart (1997)), the literature analyzing the performance of
hedge funds seems to be almost unified in the belief that hedge funds are capable
to produce positive risk adjusted excess returns (alpha). For example, Kazemi and
Schneeweiss (2003) show that managers in the CIDR database add value. Liang
(1998) argues that hedge funds offer better risk-return tradeoff than mutual funds.
Novikov (2003) argues that the returns of hedge funds are persistent. Aggarwal
and Naik (2004) find positive alphas on the hedge fund indices they study (except
for the short-selling index). Malkiel and Saha (2006) take the opposite side on
the hedge funds performance debate, arguing that various biases plague the performance studies and once they are taken into account hedge funds underperform
5
their benchmarks. Getmansky, Lo and Makarov (2004) report Sharpe ratios above
1 across hedge funds, way in excess of the modest Sharpe ratio of around 0.35 of the
US market, or the 0.4 of the mutual funds. Authors such as Lo (2002), Getmansky,
Makarov and Lo (2004) have argued that hedge funds exhibit smooth returns; after
adjustment for serial autocorrelations the median Sharpe ratio of the hedge funds
in the TASS database drops to a still impressive 0.69. Tied to this literature are the
studies linking outperformance to various fund characteristics, and in that respect
this study belongs to that literature, in the sense that we argue that there is a positive relationship between the degree to which a fund does not bear systematic risk
and the performance of the fund. Other characteristics than systematic risk have
been studied previously. One of these characteristics is the fund size. Gregoriou and
Rouah (2003) and Koh, Koh and Teo (2003) find no relationship. De Souza and
Gokcan (2003) and Amenc, Curtis and Martellini (2003) find a positive relationship
between size and performance. Getmansky (2004) finds a inverse quadratic relationship between size and funds returns, suggesting that funds have an optimal size. We
find that there is a positive albeit weak relationship between fund size and performance, consistent with the earlier studies. Another fund characteristic is the age of
the fund. Amenc, Curtis and Martellini (2003) find that younger funds outperform
the older ones, although this relationship varies across their models. Koh, Koh and
Teo (2003) find that age is unrelated to the performance of Asian hedge funds. De
Souza and Gokcan (2003) find that older funds outperform younger funds. We find
a positive relationship between the lack of idiosyncratic risk and the hedge fund’s
age, siding therefore with the latter studies in this area. A third fund characteristic
is the compensation structure. Koh, Koh and Teo (2003) find a negative relationship between incentive fees and net returns; Amenc, Curtis and Martellini (2003)
find a positive relationship between alphas and incentive fees. We find a positive
link between the lack of idiosyncratic risk and both management and incentive fees
6
- suggesting that better funds are the ones charging higher fees. One novel characteristic related to the funds’ performance is manager tenure. Boyson (2003) argues
that older managers are more risk averse and end up underperforming the younger
ones. We add one more fund characteristic - the degree to which the fund takes
systematic risk - that explains hedge funds performance.
Another strand of the finance literature is concerned with the relationship between fund performance and a certain stability of the investment process. Studying
mutual funds, Chan, Chen and Lakonishok (2002) find that following bad returns
mutual funds change their style exposures. Brown and Harlow (2005) find that
better performance is associated with more style stability. While styles are successful in explaining mutual funds returns (R squares in Brown and Harlow (2005)
are higher than 80%), the similar literature proposing more sophisticated risk factors for hedge funds (Agarwal and Naik (2004)) has a more limited success. Our
study could be seen as a generalization of the stability - performance studies from
mutual funds to hedge funds. We find that style analysis has a relatively small
success when used out-of-sample and applied to individual funds (rather than to
indices of funds like Agarwal and Naik (2004)); and we find that not stability nor
style instability is positively associated with performance, but rather that positive
performance is associated with the failure of the style classification procedure altogether. In other words, maverick hedge funds who are not taking risks mapped and
understood thrive.
Lastly, we touch into a growing literature in investments that attempts to
determine whether idiosyncratic risk is priced. Merton (1987) predicts that idiosyncratic risk should be priced when investors hold non-diversified portfolios, and that
it should be positively related to returns. Miller (1977) argues that a negative relationship arises between idiosyncratic risk and returns in the presence of trading
constraints. There is currently a vibrant debate in the empirical asset pricing liter-
7
ature siding with one side or another. For example, Ang, Hodrick and Zhang (2004)
find evidence that idiosyncratic risk and returns are negatively related. Boehme,
Danielsen and Sorescu (2006) argue that the two predicted effects are not complementary, and either one or the other may prevail. Fu (2006) estimates the idiosyncratic risk dynamically and finds a positive relationship between returns and
idiosyncratic risk. Our findings offer a class of portfolios - the hedge funds - for
which the relationship between performance and idiosyncratic risk is positive.
8
Chapter 3
Framework and Hypotheses
3.1
Framework
Assume that a hedge fund manager i chooses between three investments1 : a risk-free
asset, a publicly available index F and a proprietary strategy Ai for which
E[F − rf ] = µ > 0;
E[Ai − rf ] = αi > 0;
Corr(Ai , F ) = 0
std[F ]
=σ
std[Ai ] = T Ei
.
We denote by wF,i and wA,i the weights allocated by the manager to his
respective investment choices. The manager is able to borrow at the risk free rate
(i.e., we do not require that wA,i + wB,i = 1). The excess returns of the manager
are given by Ri − rf = wA,i (Ai − rf ) + wF,i (F − rf ), and his Sharpe ratio by
SR(wF,i , wA,i ) =
E[Ri − rf ]
αi + βi µ
=q
,
std[Ri ]
T Ei2 + βi2 σ 2
1
(3.1)
No generality is lost if we restrict the manager to two investments. A similar model would carry
though with more than one systematic factor, only the notations would become more cumbersome.
This model is a simple exposition of Treynor and Black (1973).
9
where βi = wF,i /wA,i .
If the manager maximizes his Sharpe ratio2 , he solves
max SR(wF,i , wA,i ).
wF,i ,wA,i
The solution to the above optimization problem is given by



βi∗ =

 wF,i
µ/σ 2
αi /T Ei2
.
= βi∗ wA,i
The Sharpe ratio of the optimal portfolio is
sµ
SRi∗
=
αi
T Ei
¶2
µ ¶2
+
µ
σ
.
An econometrician attempting to explain the systematic risk exposures of
the fund by regressing Ri − rf on the systematic factor returns F would obtain an
R2 of the OLS regression equal to
(R2 )∗i =
βi∗2 σ 2
=
T Ei2 + βi∗2 σ 2
1+
1
(αi /T Ei )2
(µ/σ)2
.
The first observation from the equation above is that (R2 )i , like the Sharpe
ratio, is independent of leverage; the second observation is that under the assumption
that αi > 0, (R2 )i decreases with the information ratio αi /T Ei of the proprietary
strategy, which leads to the following proposition:
Proposition 1 If a hedge fund is maximizing its Sharpe ratio, then the R2 of the
2
Hedge funds are often evaluated by their Sharpe ratios. Also a way to convince an external
observer that the fund generates statistically significant excess returns is for the fund to have a
high t-statistics of the excess returns. The t-statistic of the excess returns is equal to the Sharpe
ratio of the fund times square root of the length of the fund’s history. If we compare funds with
histories of equal length then comparing the t-stats of their expected excess returns is equivalent
to comparing their Sharpe ratios.
10
regression of the hedge fund’s excess returns on systematic factors is inversely related
to the fund’s Sharpe ratio.
3.2
Hypotheses
The main objective of this paper is to test the hypothesis that the fund’s performance
- measured as the Sharpe ratio of its returns - is inversely related to the R-squares.
To obtain the R-squares, we first explain the excess returns of individual
funds Rt − rf , t ≥ t0 , from some initial time t0 until the time T , which is either the
present period or the time the fund exited the sample, whichever is lower. Employing
a factor model with K factors amounts to fitting every fund to
Rt − rf =
K
X
β T,k Ftk + (αT + ²Tt ), t = t0 , t0 + 1, ..., T.
(3.2)
k=1
R-square can be calculated from Equation (3.2), as R2 = 1 −
V ar[²t ]
V ar[Rt ] .
We estimate the overall R-squares using the entire history of the fund. By
doing so, only average exposures to systematic factors observed throughout the
entire life of the fund are taken into account.
We then test the following
Hypothesis 1: Sharpe ratios are negatively related to R2 s.
The model presented above is one period, hence it ignores timing - or dynamic
portfolio allocation. In reality hedge funds attempt to time, with or without ability3 .
Therefore, low R-square in the regressions of the funds on systematic factors may
be due not only to predominant idiosyncratic investments but also to timing. To
exemplify this case, imagine a fund who trades only in the S&P 500 and has a beta
of -1 half of the time and a beta of +1 the rest. The fund’s R-square with respect to
3
Chen and Liang (2005) analyze the timing ability of 157 market timing funds from TASS, HFR
and TUNA databases and show that timing is related to fund characteristics and more pronounced
in bear markets.
11
the S&P 500 index is zero, however, the fund takes only systematic risks. Of course,
the fund may exhibit talent and add value by timing, but just as well the fund
may have no special information or timing ability. We therefore present tests which
separate the low R-squares due to idiosyncratic investments from the low R-squares
induced by timing.
Note that a separation of the selectivity of idiosyncratic strategies from the
timing of the systematic factors is impossible in the sense of Daniel, Grinblatt,
Titman and Wermers (1997) as holdings data are not available for hedge funds.
Thus, in order to separate them, we roll out-of-sample estimations of the extent
to which past systematic exposures explain the returns of the fund; if past factor
exposures explain the contemporaneous returns poorly, this may be due to the
idiosyncrasy of the fund manager, or to its timing attempts. We employ measures
of timing to separate away the latter case.
The measure of goodness-of-fit out of sample is given by
Definition 1 Given a hedge fund with rolling systematic risk exposures given by
β T,k , k = 1 : K, T , the out-of-sample R2 is defined as
V ar[Rt −rf −αT +β T,1 Ft1 +...+β T,K FtK ;t=T +1:T +12]
RsqrT := 1 −
.
V ar[Rt −rf ;t=T +1:T +12]
The Rsqr resembles an “out-of-sample” R-square or the statistic from a Chow
(1960) test of a structural break in a linear model explaining the returns of a hedge
fund. For example, suppose a fund has a beta of -0.5 with respect to the S&P 500
Index up to time T . Suppose that at time T the fund changes its exposure and
its beta becomes +1. Then the out-of-sample RsqrT = 1 − V ar[(0.5RS&P 500 ) −
(−0.5RS&P 500 )]/V ar[0.5RS&P 500 ] = −3 = −300%.
The timing measures are defined below. The first measure describes changes
in the exposures to the factors the fund continues to be exposed to. The cases in
which a fund invests in a new systematic factor, or if the fund ceases to be exposed
to a factor are not included in this measure.
12
Definition 2 Given a hedge fund with rolling systematic risk exposures given by
β T,k , k = 1 : K, T , the intra-factor timing4 T O1T at time T is defined as
T O1T :=
PK
k=1 |β
T −1,k
− β T,k |1{β T −1,k 6=0} 1{β T,k 6=0} .
The second measure is complementary to the first: it is the sum of the
numbers of factors the fund ceased to be exposed to and the number of factors the
fund started to be exposed to.
Definition 3 Given a hedge fund with rolling systematic risk exposures given by
β T,k , k = 1 : K, T , the inter-factor timing T O2T at time T is defined as
T O2T := #[({k : β T −1,k 6= 0} ∪ {k : β T,k 6= 0}) − ({k : β T −1,k 6= 0} ∩ {k :
β T,k 6= 0})].
A similar measure to T O2 may be constructed to capture not only changes in
the number of the factors, but also the magnitude of these changes. Although this
measure produces qualitatively the same empirical results exposed in this study, it
is noisier that T O2 defined above5 , and hence we prefer to use T O2.
We test that there is a negative relationship between Sharpe ratios and Rsquares, and that this is not due to timing:
Hypothesis 2: Higher Sharpe ratios correspond to lower Rsqr, T O1, T O2.
Simply put, managers who have zero exposures to systematic risk at each
moment in time perform better.
4
“TO” is an acronym for turnover in the investment sense of the word, i.e., the change in weights
in a portfolio.
5
Across funds with the same T O2T , the betas on the new factors may vary, thus making a
measure designed to capture changes in betas noisier.
13
Chapter 4
Data
4.1
Hedge Funds
We use a proprietary, comprehensive database consisting of the union of the Altvest,
HFR and TASS databases. The proportion of funds coming from each database is
described in Figure 8.1.
For each of the databases, the graveyards, i.e. the lists of funds that dropped
from the databases were obtained1 . Data of various complexity is collected for a
total of 8,542 funds. While smaller subsets of the database contain more information, for 7,429 funds we have monthly returns net of fees, assets under management,
whether the fund is a fund of funds, and the management and incentive fees the
fund is charging. Missing records for the assets under management are filled assuming that between the dates at which information is provided the funds received
uniform inflows (outflows). When a fund for which the data does not contain a
name2 is added to the merged database, we follow a procedure which eliminates the
1
To the best of my knowledge this is the first paper that uses the Altvest graveyard. The
graveyard data usually hide the names of the funds, due to non-disclosure agreements prohibiting
making information on hedge funds that decided to stop reporting public.
2
Altvest and HFR cease to report the names of the funds once the funds stop reporting to the
database, so their graveyards do not include names.
14
duplicates: when the correlation between the common net returns for two funds is
greater than 99.9% and the correlation between the common assets under management(after filling the missing records as described above) is greater that 99% and
the fees are identical the two funds are assumed duplicates and one is eliminated.
This procedure eliminates only no-name database duplicates, but if one manager
runs several funds, and the names of these funds are provided, then all the funds
are kept (this may result in funds with the same series of returns but different sizes
being kept in the database).
The number of funds in the database is presented in Table 8.1, while the
industry coverage of the data used is apparent in Figures 8.2 and 8.3. For December
2003, our database covers around $ 800 billion of assets under management.
Several biases have been documented that plague hedge fund data; we list
them below.
• Survivorship bias. Databases drop from the sample the funds that
stop reporting. This may be caused either by the fund going out of business or
to the fund closing to new investments and not having incentives to report any
longer. Fung and Hsieh (2000) estimate the difference in performance between the
portfolio of all surviving funds and the portfolio of all the funds to be 3% annually.
Similar estimations are found in Brown, Goetzmann, Ibbotson and Ross (1999). We
included in the database the funds who ceased reporting, making thus the data free
of survivorship bias.
• Self selection bias. The reporting is voluntary, so a bad fund has no
reason to report, and a fund that is too good closes quickly and does not have any
reason to “advertise”3 ; Fung and Hsieh (1997b) claim that these effects even out.
• Backfilling bias. The moment a fund decides to report to a database
might not coincide with the date the fund started, and when the fund start re3
Reporting to a database may be an indirect form of advertising.
15
porting it is free to backfill its history. Typically, hedge funds smooth their back
returns; in this study we use a procedure that removes the serial autocorrelation
induced by smoothing, and hence correct for this bias. Potentially, this may bias
the performance of hedge funds upward4 .
As we do not have data on the exact time of each fund joining the database
we have employed the following correction to the backfill bias.
Some databases calculate indices of hedge funds using the fund currently
existing in the database and these indices are not restated when a fund joins and
brings its history of returns to the database. Unfortunately, as several funds join
a database simultaneously, it cannot be directly inferred only from the returns of
the funds and of the indices alone when each individual fund joined. However, we
can discard a certain number of initial returns from the history of each fund, so
that the index build after discarding some initial history matches closer the index
reported by the database. Funds backfill great amounts of data (see a histogram for
the funds in TASS constructed a la Novikov (2004) in Figure 8.10); as a consequence
discarding initial histories may in fact reduce substantially the number of funds. If
we repeat this procedure on the HFR database, which reports indices, we obtain
that the distance between the HFR indices and the indices computed by us after
discarding n months of history is minimized for n = 24 months. This is consistent
with Novikov who finds n = 27 months. The correlation between the value weighted
HFR index and the one calculated after discarding 24 months of each fund’s history
is 0.988. The results of our analysis hold after correcting the history in this way.
For a quick comparison, the median (mean) Sharpe ratio of a fund in our
database, adjusted for serial autocorrelation of the returns a la Lo (2002) is 0.69
(0.80). To see the impact of the backfilling bias, we eliminated 24 months from the
history of each fund. The new median (mean) Sharpe ratio (corrected for serial
4
See Posthuma and van der Sluis (2003).
16
autocorrelation) becomes 0.66 (0.73). This difference could be explained not only
by the backfill bias but also by the fact that we capture only the last months of
returns of some defunct funds. The small difference between the backfilled, and
non-backfilled Sharpe ratios may partly be attributed to the fact that correcting for
smooth returns lowers the performance of the backfilling funds.
• Smooth returns. Several authors (e.g. Asness, Krail and Liew (2002))
present evidence that the returns of hedge funds are serially autocorrelated, and
so performance measures such as Sharpe ratios end up having difference statistical
properties than being normally distributed. We adjust the fund returns for serial autocorrelations such as in Getmansky, Lo and Makarov (2004), the backfilled returns,
which are generally smoother, decrease.
• Late reporting bias. Databases usually wait for funds to report, and
a fund can be as late as 8 months in reporting. This causes a fund to appear as
“defunct” while in reality it still exists and it is still willing to report. I We correct
for this bias using only data before December 2003, but collected in August 2004,
when all the funds that are late5 came back to report again. This bias has not, to
the best of my knowledge, been documented in the literature.
The three databases merged do not contain homogeneous fund information;
Table 8.2 documents the differences among them.
To examine the extent to which data coming from different databases are
structurally different, we perform a Kolmogorov-Smirnov test that net returns and
assets under management from each database were drawn from the same distribution; results are presented in Table 8.2; the p-values of the statistic are high when
differences between Altvest and HFR are the center of attention: we cannot reject
the null that Altvest and HFR net returns and respectively assets under management were drawn from the same distribution. However, we can reject at better than
5
This problem seemed the most severe with TASS, where some funds were 8 months late.
17
95% confidence level the null hypothesis that HFR and TASS, respectively Altvest
and TASS were drawn from the same distribution. The TASS database seems to
pick smaller funds that also have lower performance, which indicates that performance tests ran on TASS tend to produce rather pessimistic results on hedge funds
compared to studies based on different databases. This differences across databases
may bias the results of studies based on a single source, and make generalization
from one database to the whole industry of hedge funds problematic.
4.2
Risk factors
Due to their dynamic nature, hedge fund portfolios are hard to explain by traditional
buy-and-hold strategies, regardless of how sophisticated the latter might be. Failure
of traditional risk factors to explain hedge fund returns6 lead to a search for nonlinear
risk factors. Two main categories of nonlinear factors surfaced: the first category,
pioneered by Glosten and Jagannathan (1994), is motivated by the observation
that, unlike mutual funds7 , hedge funds employ derivative strategies, hence they
may take asymmetrical positions relative to a factor’s performance. Risk factors
resembling option payoffs are hence added to the factor models designed for hedge
funds. The second category stems from an extension of the previous: if hedge funds
employ derivatives, they are also cashing out or loosing on the premium that these
derivatives command; such views were confirmed by detailed analysis of particular
hedge fund strategies such as merger arbitrage (see Mitchell and Pulvino (2001)),
whose returns resemble those of a strategy that sells “merger insurance”, or more
6
Fung and Hsieh (1997a, b) find “styles” that explain successfully returns of mutual funds more than 50% of the mutual funds they analyze have R2 greater than 78%. But these styles fail
to explain hedge fund returns, nearly half of which have an R2 under 25%. The lack of success
of this early analysis generated subsequent studies with identical methodologies but looking at
different factors. Different asset classes or styles - as in Liang (1999) who uses 8 different “styles”
or Schneeweis and Spurgin (1998) who look at 13 variables, out of which some are volatilities of asset
classes, or Brealey and Kaplanis (2001) who use 31 factors - still kept the blur on the systematic
hedge fund risk.
7
See Koski and Pontiff (1999) or Almazan et. al. (2001).
18
precisely, out of the money puts. The most important of these aspects (classical
buy-and-hold risk factors and returns from option strategies have been combined
by Agarwal and Naik (2004) and further refined by practitioners (See for example
deFigueiredo and Meredith (2005)).
A refined factor model considers, as explanatory risk factors, several market
indices, both from US and abroad, as well as global; payoffs on a market index I of
the form max(RI − k, 0) or min(RI − k, 0) (these serve as factors capturing market
timing in the sense of Treynor and Mazuy (1966); market timing factors in the sense
of Henriksson and Merton (1981), such as (Returns on the Russell 3000)×(Returns
on the Russell 3000)8 ; market factors documented as successful in an equity factor
model, such as the Fama-French two factors HML and SMB, and the Jegadeesh
and Titman (1993) momentum factor MOM; returns on strategies involving selling
short term at- or out-of-the-money options (calls and puts) on some market index I;
fixed income factors, such as three “points” on the yield curve9 , indices of corporate,
municipal and mortgage backed securities; inflation.
The ideal factor model would include a minimal superset of the risk factors
used in the previous research, but not to the extent to which we have factors that
are collinear. Thus, this study uses to the 34 factors presented in Table 8.3.
Although some of these factors are redundant, the procedure we use for fitting
the model is insensitive to this problem.
8
In order to know that a fund is exposed to market timing factors dos not help an investor to
replicate to fund, but merely to understand it. As Chen and Liang (2005) make the argument that
some managers have the ability to time their focus market, we have included a term that model’s
managers’ ability to time the S&P500. Note that these factors are not investable, but we can only
assert that we “understand” the returns of fund or we can “proxy” them if we discover the fund is
exposed to these factors. As a robustness check we eliminate the non-investable factors from our
analysis, as shown in our section on robustness.
9
Litterman and Sheinkman (1991) showed that a three factor model explains 92% of the yield
curve.
19
Chapter 5
R-squares and Sharpe Ratios
In this section we shall argue that hedge funds performance, as expressed by the
fund’s Sharpe ratio, is inversely related to the extent to which systematic risk exposures explain the fund’s returns.
In the first subsection, we present the methodology used to estimate the
R-squares.
5.1
Estimating R2 , Rsqr, T O1 and T O2
5.1.1
Serial correlation in returns
The R-squares may be computed by estimating Equation (3.2) for the whole history
of each individual hedge fund. However, Asness, Krail and Liew (2002) argue that
hedge fund returns are autocorrelated; Getmansky, Lo and Makarov (2004) present
some of the causes contributing to the serial correlation observed in hedge fund
returns:
1. Hedge funds hold illiquid securities and use stale prices to compute returns;
2. Funds move their leverage ratios through time;
3. Managers smooth returns intentionally, for example by backfilling.
20
Getmansky, Lo and Makarov (2004) and Novikov (2004) estimate models
in which the returns of the funds are autocorrelated. We follow practitioners (see
deFigueiredo and Meredith (2005)) and assume serial correlation at the level of at
most a lag. Following Getmansky, Lo and Makarov (2004), we estimate a model in
which the observed returns of a fund follow:
Rto = (1 − ρT )Rt + ρT Rt−1 , t = t1 + 1, ..., T.
(5.1)
If the true returns are given by (3.2), then the observed returns follow:
1 ) + ... + β T,K ((1 − ρT )F K + ρT F K ) + uT ;
Rto − rf = αT + β T,1 ((1 − ρT )Ft1 + ρT Ft−1
t
t
t−1
uTt = (1 − ρT )²Tt + ρT ²Tt−1 , t = t1 + 1, t1 + 2, ..., T.
(5.2)
This is the factor model we estimate. In order to estimate the overall R2
used in the Hypotheses 1, we take t1 = (inception of the fund) and
T = min{(Dec 2003), (exit time from the database)}.
To estimate Rsqr, T O1, T O2 we estimate the model 5.2 starting with T being two
years after the fund’s inception date and continuing to roll T until one year before
the fund drops from the database or until December 2003, whichever comes sooner.
Not every hedge fund is exposed to each of our 34 risk factors. To capture
the factors relevant for each fund we shall use the stepwise regression to estimate
the model (5.2). Other methodologies include principal components, or imposing a
parsimonious model such as the CAPM or the Carhart (1997) 4-factors model. For
arguments supportive of the virtues of using stepwise regressions to explain hedge
fund returns, we send the reader to the appendix and we limit ourself to quote
21
Agarwal and Naik (2004), which assert that the “benefits of using the stepwise
regression [to explain hedge fund returns] ... outweigh the costs [of potential data
mining]”.
5.1.2
Results - R2
The summary of fitting model (5.2) for the whole life of individual hedge funds is
presented in section.
The distribution of the R2 estimates from the entire history of each fund
using stepwise regressions is presented in Table 8.8, along with the distribution of
the tracking errors and with the summary statistics of R2 if the estimation is applied
instead to mutual funds. The quality of fit is about three times worse for hedge funds
than for mutual funds - hedge fund explanatory regressions have a median adjusted
R2 of 42.10%, contrasting the 66.86% for mutual funds - consistent with the findings
of Fung and Hsieh (1997a) who show that hedge funds follow dynamic strategies, and
with the findings of Griffin and Xu (2005), who show that the hedge fund turnover
of the 13-F filed holdings alone is larger than that of mutual funds.
Consistent with Getmansky, Lo and Makarov (2004), hedge funds seem to
smooth returns. Consistent with Agarwal and Naik (2004), who show that hedge
fund indices are exposed to systematic risk, we find that individual hedge funds bear
systematic risk as well. The median adjusted R2 of 42.10% implies that hedge fund
investors pay for quite a lot of “beta”. We note that is not timing related beta:
when the non-investable factors related to the funds’ timing ability of the US equity
market are taken out, the median adjusted R2 drops only 0.6% to 41.50%.
On average, a fund is exposed to 5 different systematic factors from our set
of 34; the minimum number of factors a fund is exposed to is 0, the maximum is 10.
22
5.1.3
Results - Rsqr, T O1, T O2
Rolling estimates of the model (5.2) are produced using stepwise regressions; at
each time T , we estimate the model on the interval [T − 23, T ], and use the period
[T + 1, T + 12] as the out of sample period to calculate Rsqr as in Definition 1.
Out of sample tracking errors are also calculated, as well as in sample rolling R2 ’s
and in sample rolling tracking errors. The measures T O1, T O2 are calculated as in
Definitions 2 and 3. The summary statistics are reported in Table 8.8.
The median of the out-of-sample Rsqr is negative, consistent with the fact
that funds shift factor exposures. In sample R2 and tracking errors as comparable
with those obtained estimating the whole history of the fund. For comparison
reasons we report results produced using factor analysis (Panel B of Table 8.8)
as well.
We can paint the picture of the median hedge fund. The average fund is
exposed to 5 different factors; from one month to another the average fund almost
drops a factor in the favor of another (mean number of the factors switched out of
and into is 1.67). However, the median out-of-sample Rsqr is around -3%, which
indicates that the betas of the factor dropped and of the new factor as well are
relatively small compared to the betas with respect to the factors kept.
In order to compare the quality of the out-of-sample fit produced by the
stepwise regression, we also reproduce the same analysis in the case principal components are used; the median out-of-sample Rsqr is -7.16%, hence, the 5 principal
components model fares worse. However, a model with zero factors has an out-ofsample Rsqr of zero, thus seemingly exhibiting a better out-of-sample fit than both
stepwise regressions and the principal components. Yet, the zero factors model does
not exhibit any fit at all: the 80th percentile of the out-of-sample Rsqr estimated
from the stepwise regressions is 18.23%, much better than the zero percent of the
zero factors model !
23
Are the Carhart (1997) four factors more, or less helpful in describing the
hedge fund returns than the factors selected by the stepwise regression? In order to
answer this question we check the former’s out-of-sample quality of fit. The median
of the out-of-sample Rsqr is -19% - worse than the stepwise regression and much
worse than the zero factors model. This suggests that out-of-sample model stability
cannot be achieved simply by moving to more parsimonious models, and are better
off including more factors with potential in explaining the hedge fund returns.
When rolling the stepwise regression analysis, both in-sample and out-ofsample R-squares are serially autocorrelated across funds. The median autocorrelations are 0.6060 for in-sample R@ ’s and 0.5392 for the out of sample Rsqr (means
are 0.5126 and 0.4528 respectively).
5.2
Testing Methodology
In this subsection we present the methodology used to test Hypotheses 1 and 2.
5.2.1
Cross-sectional tests: overall R2 and Sharpe ratios
As a preliminary test, funds are sorted in terciles according to their R2 , and the
average size, fees charged, age, probability to remain in the sample and Sharpe ratios
are computed for each of the R2 terciles. Under the null hypothesis of no relationship
between the Sharpe ratios and R2 , the averages across R2 terciles should not differ.
The results are in the second column of Table 8.5. The table also presents averages
of other fund characteristics across different R2 terciles.
Several fund characteristics may influence the R2 : the fund’s age, size, the
degree to which the fund smooths its returns, the number of strategies in which the
fund plays and the fees charged by the fund. Consequently, we first estimate the
model:
24
Ri2 = f (sizei , size2i , mf eei , if eei , Agei , Alivei , rhoi , Complexityi , F OFi ) + ²i
(5.3)
for a linear specification f . We run a similar analysis using the tracking
error as a depend variable. Although the tracking error is not formally related
to our Hypotheses, we are interested if the idiosyncratic component of the funds’
returns is hedged (that is the tracking errors are small) or not.
The test of Hypothesis 1 is performed by estimating the following model:
c2 , size , Age , Alive , rho , Complexity , F OF , mf ee , if ee )
SRi = f (Ri2 − R
i
i
i
i
i
i
i
i
i
+²i
SRi = f (T Ei − Td
Ei , sizei , Agei , Alivei , rhoi , Complexityi , F OFi ,
mf eei , if eei ) + ²i
(5.4)
c2 are estimations from Equation
for a linear specification f . Above, Td
Ei and R
i
(5.3). The results are in the Panel A of Table 8.7.
c2 )is now
Note that R2 orthogonalized on fund characteristics (that is, R2 − R
an exogenous variable. We have chosen to make this assumption because there is a
large body of hedge fund literature studying the relationship between Sharpe ratios
and fund characteristics1 and we had to control for the latter. Although the tracking
error does not directly enter our tests, it is descriptive of whether the idiosyncratic
1
The relationship between size and performance has been studied by Getmansky (2004), by
Gregoriou and Rouah (2002); by Koh, Koh and Teo (2003) among others. The relationship between
performance and age of the fund has been studied by Howell (2001), Amenc, Curtis and Martellini
(2003) and De Souza and Gokcan (2003) among others. The relationship between performance
and fees has been studied by Kazemi, Martin and Schneeweis (2002), Koh, Koh and Teo (2003),
De Souza and Gokcan (2003) and Amenc, Curtis and Martellini (2003). Other fund factors (e.g.
manager tenure, redemption specifications, managerial investment in the fund) are also related to
performance but we lack data on these variables.
25
investments of a fund are hedged, and for comparison purposes we included in the
results reported.
The independent variables are described below.
• size is the size of the fund. As the analysis of this section is purely
cross-sectional, it is difficult to define the size of a fund (it varies through time).
We transform the assets under management in December 2003 dollars, and as a
proxy for size, we use the 25th percentile of the assets under management for the
history of the fund. The relationship between this proxy for size and the extent to
which a fund can be explained by systematic factors does not change if instead we
use the 10th percentile of the 2003 assets under management or the median, but
the significance decreases if we use the maximum assets under management or the
mean. As habitually, we use the natural logarithm of size. Its square is included as
well.
• Age is the age of a fund, measured in months, from the time when the
fund starts reporting until the minimum between December 2003 or the time the
fund ceased reporting.
• Alive is a dummy meant to separate funds that ceased to report from
funds that were still in existence in December 2003.
• rho is the degree to which returns are serially autocorrelated, precisely,
it is the smoothing coefficient from model (5.2).
• Complexity. There are structural differences in the fund managers’ talent, determined by the Complexity of the hedge funds they run; managers following
certain investment strategies may have different Sharpe ratios, may grow to different
sizes, or are more or less prone to smooth their returns. In order to address this
problem we have to control for the investment strategy of the fund. Unfortunately
most of the database used in this study does not contain information regarding
the strategy of the hedge fund. To resolve this weakness, we estimate each fund’s
26
investment strategy as follows. A Sharpe (1992) style regression is performed, having the fund’s returns as dependent variable and the returns of 15 HFR strategy
indices as independent variables. In this regression, some of the strategy indices
have significant t-statistics2 . We retain the number of significant t-stats (at 5%)
from each style regression, and define that number as the complexity of the fund.
If no t-statistics were significant, then the complexity of the fund is taken to be
equal to 16 (highest possible value). Funds of funds are also similar to funds we
call complex; we do include a control for funds of funds. This rough classification
results in a distribution of the assets under management across strategies as shown
in Figure 8.4.
• F OF is fund of funds dummy.
• mf ee is the management fees charged by the fund in percents and if ee
is the incentive fee. Note that the returns used throughout this study are net of
fees.
• SRi is the Sharpe ratio of the fund i, adjusted for serial correlation.
With a few exceptions the variables above are relatively uncorrelated: the
highest positive correlation is 30% (between Complexity and Age - we will therefore
run robustness tests due to this potential problem as described in Section ??).
The next positive correlation is 13% (between Alive and rho). The most negative
correlation is -40% (between F OF and if ee - we address this issue in the robustness
section as well). The next negative is -10% (between Lif e and mf ee).
5.2.2
Time series tests: Rsqr, T O1, T O2 and Sharpe ratios
Low overall R-squares does not mean that a fund never bears systematic risk - it
merely indicates that on average the systematic exposures are zero. In this section
we present a methodology to test Hypothesis 2, which asserts that higher Sharpe
2
The t-statistics from the Sharpe (1992) style regression cannot be estimated as in an OLS
regression, hence we use the methodology proposed by diBartolomeo and Lobosco (1997).
27
ratios correspond to low R-squares at any moment in time - precisely, high Sharpe
ratios are associated with low Rsqr, but with a low degree of variability in systematic
exposures - that is, low T O1 and T O2.
Much in the spirit of the sorting performed in the previous section, every
month T we sort portfolios based on Rsqr, T O1, T O2 and compute the difference
between the average Sharpe ratio of the lowest, respectively the highest Rsqr, T O1,
T O2 decile. The Sharpe ratios are from the period [T + 1, T + 12] and adjusted
for serial autocorrelation à la Lo (1992). We also perform a difference in mean test
between the Sharpe ratios in both deciles. The results are plotted in Figure 8.5. A
star signifies that the difference in means between the low and the high Rsqr, T O1,
T O2 deciles is significant at 5%.
In the same spirit, we run Fama-MacBeth regressions to isolate the effect of
fund characteristics on Rsqr, T O1, T O2:
RsqrTi = c + b1 aumT,i + b2 Last1Y StdT,i + b3 AgeT,i + b4 P ressureT,i
+b5 mktT + b6 F OFi + b7 mf eei + b8 if eei + b9 F lowF racT,i
+b10 AliveT,i + ²T,i
T O1iT = e + d1 aumT,i + d2 Last1Y StdT,i + d3 AgeT,i + d4 P ressureT,i
+d5 mktT + d6 F OFi + d7 mf eei + d8 if eei + d9 F lowF racT,i
+d10 AliveT,i + ²T,i
T O2iT = +f1 aumT,i + f2 Last1Y StdT,i + f3 AgeT,i + f4 P ressureT,i
+f5 mktT + f6 F OFi + f7 mf eei + f8 if eei + f9 F lowF racT,i
+f10 AliveT,i + ²T,i
The results are in Table 8.9.
28
(5.5)
We then estimate the following Fama-MacBeth model:
dT,i ) + d2 (T O1T,i − T O1
dT,i ) + d3 (T O2T,i − T O2
dT,i )
SharpeT,i = c + d1 (RsqrT,i − Rsqr
+d4 aumT,i + d5 F lowT,i + d6 Last1Y StdT,i
+d7 P ressureT,i + d8 F OFi + d9 mf eei + d10 if eei + ²T,i .
(5.6)
where Rsqr, T O1, T O2 are not simultaneously included in the equation, dues
dT,i , T O1
dT,i , T O2
dT,i are estimations of
to the fact that T O1, T O2 affect Rsqr. Rsqr
RsqrT,i , T O1T,i , T O2T,i from Equations (5.5). Results are in Table 8.10.
The variables in the right hand size are described below:
• RsqrTi is the out of sample R2 as described in Definition 1 of Section 3.
Note that the returns one year forward (the period [T + 1, T + 12] enter into the
definition of Rsqr;
• T O1iT and T OTi are the measures capturing changes in the systematic
exposures from Definitions 2 and 3 in Section 3.
• aumT,i is the natural logarithm of the assets under management of find
i at time T ;
• Last1Y StdT,i is the standard deviation of the monthly returns of the
hedge fund i calculated over the period [T − 23, T ]. We include this variable as
a control for the overall risk of the fund, as Kat and Menexe (2003) argued that
the risk level of a fund is persistent (rather than the fund’s performance). Overall
affects the out of sample Rsqr, and it also affects the extent to which funds may
time systematic risk exposures. For example a fund who has a high leverage ratio
is riskier than a fund with the same ratios of systematic exposures/idiosyncratic
exposures which is unlevered. The inclusion of the overall risk in the model has
the effect of equalizing two managers with the same proportion of idiosyncratic risk
relative to the total risk, but differently levered.
29
• AgeT,i is the age of the fund i at time T .
• P ressureT,i is a variable describing the flows into the category the fund
belongs to. More inflows into the same category generate competition among the
funds in that category. P ressureT,i is built as follows. First we employ the classification of the fund into strategies as in Section 5.2.1. The fund i is thus assigned weights
i (single strategy funds will have all w’s but one
into each of the strategies w1i , ..., w15
equal to zero). The inflows into each hedge fund (quarterly aggregation) are used
to compute the aggregate flows into each of the 15 strategies. For each strategy j =
1, ..., 15, the flows fT,j into each strategy are computed as the natural logarithm of
the (quarterly) dollar flow into the strategy divided by the assets under management
for that respective strategy (f = log[(dollar f low)/(assets under management)]).
The higher fT,j is, the more money flows into the strategy j at time T . The pressure
on fund i is defined as
P ressureT,i :=
15
X
wji fT,j .
j=1
• M ktRetT represents alternatively the returns on the US market portfolio;
mktcapT is the natural logarithm of the US market capitalization. Funds may be
tempted to become more systematic during a boom to exploit the potential benefits
of a bubble hence we included a control for this behavior. Also, when the market
cap is larger, funds may have a higher potential to find idiosyncratic trades.
• F OFi is a fund of funds dummy.
• mf eei and if eei are the management and the incentive fees charged by
the funds.
• F lowF racT,i is the natural logarithm of the dollar flow into the fund i
over the quarter [T − 3, T ] divided by the assets under management at time T . We
include both the pressure on a fund and the flow into that fund as we are interested
to capture the effect of inflows way and beyond the industry average on hedge fund
30
investment behavior (systematic/idiosyncratic/timing).
• AliveT,i is a dummy indicating that the fund does not drop from the
sample in the next two years.
• SharpeT,i is the Sharpe ratio of the fund on the time interval [T + 1, T +
12], corrected for serial autocorrelation of the returns.
5.3
Test Results
5.3.1
Main Results
Built based on the whole history of each individual fund, Table 8.5 shows that the
average Sharpe ratio of the funds with low R2 is 0.38 higher than the average Sharpe
ratios of high R2 funds, and that the difference is statistically significant.
Results in Table 8.7 further show that a negative, significant relationship
between Sharpe ratios and R2 ’s, hence we can reject the null of no relationship in
favor of Hypothesis 1.
On a rolling basis the statement is still valid: Figure 8.5 plots the differences
between the average Sharpe ratios of low, vs. high Rsqr, T O1, T O2 groups of
funds. In only two instances have the high Rsqr decile had an average Sharpe ratio
higher than the one of the lower Rsqr decile. This time instances are September
and October 1998 - the LTCM collapse3 . The lowest T O1, T O2 deciles also have
the highest Sharpe ratios. This is evidence supporting Hypothesis 2.
Table 8.10 further shows a negative, significant relationship between the
Sharpe ratio and Rsqr, T O1, T O2, hence, the null of no relationship can be rejected in favor of Hypothesis 2.
It is perhaps surprising that on average, funds attempting to time exposures
to systematic factors under perform - after all, hedge fund managers may have the
3
Although LTCM did not report in any of the Altvest, HFR or TASS databases, its collapse
meant a shock to the hedge fund industry, both literally and figuratively.
31
skill to time the markets. Despite evidence of timing abilities of certain managers4 ,
our results indicate that the average hedge fund is worse off by dynamically changing
the systematic risk exposures. To some extent, this is less surprising if we consider
recent evidence that simple, fixed allocation rules to asset classes dominate dynamic,
sophisticated allocation strategies: DeMiguel, Garlappi and Uppal (2005) show that
simple asset allocation rules such as the “1/N ” rule do not under perform sophisticated, dynamic asset allocation strategies. This result suggests that absent timing
talent, a fund investing in publicly available factors is better off by not changing the
allocation rules dynamically but by keeping them fixed.
As the literature argues that mutual fund managers cannot out-perform simple benchmarks (a la Carhart (1997)), the same argument is consistent with the
findings of Brown and Harlow (2004), who show that there is a positive relation
between mutual funds’ performance and their style stability.
5.3.2
Extensions: Sharpe ratios and R-squares,
or appraisal ratios and R-squares?
Can the finding that low R-square is associated with higher Sharpe ratio be translated into a similar claim about the appraisal ratio?
The short answer is yes, but there is a little caveat. The exception are a
class of funds which define themselves as hedge funds and report to hedge funds
databases, while in reality their nature is more that of an index fund. Precisely,
there are 69 funds in the database whose tracking error is smaller than 3 bp per
month (about two orders of magnitude less that the median of the sample). These
funds have an average alpha of 1% per month (yet half of them have alpha less
than or equal to zero), but the average information ratio are extremely large. We
windsorize the data at 1% and carry out a analysis similar with what we ran for
4
Brunermeier and Nagel (2004) show that several large funds rode the technology bubble and
Chen and Liang (2005) find managers may have timing skills.
32
Sharpe ratios. The results in Table 8.19.
5.3.3
Extensions: Idiosyncratic Risk by Strategy
We can question whether our results regarding the negative relationship between
R2 and performance is driven by a particular strategy who simultaneously have low
R2 and outperforms. For example it is apparent from Table 8.17 that Convertible
Arbitrage funds have smaller R-squares and higher Sharpe ratios compared to the
rest of the funds, so it is legitimate to ask if our results are driven by this relationship.
To check if this is the case, we have used our classification into strategies and
added strategy dummies in the performance regressions, as well as in the regression
studying the relationship between R-squares and fund characteristics. This was
done by first dropping the Complexity variable from the regressions, and adding
instead a strategy dummies. A strategy dummy can be computed in two ways: one
is to assign a value of one to the predominant strategy of the fund and zero to the
rest; another is to find all the strategies the fund is invested in, and assign to each
of those dummies a 1 times the weight the fund has in that strategy. In both cases,
c2 actually increased in magnitude when dummies were
The t-statistics of the R2 − R
added, so the documented relationship between R2 and performance is robust. A
similar effect is obtained in the regressions linking R2 and fund characteristics.
Furthermore, we reproduced our analysis within each strategy. The results
are presented in Table 8.18. We observe that our claim, that lower R-squares correspond to higher Sharpe ratios, is robust to all categories, except for the Macro and
Fixed Income Arbitrage categories. We note that the difference is negative (contrary
to our claim) in only one category, and in that case it is statistically insignificant.
The result in the Macro category may be due to excessive classification of the funds
as ’Macro’, while in reality they may be multi-strategy funds.
The claim that lower R-squares are associated with higher Management Fees
33
and Incentive Fees is robust to all categories.
The claim that lower R-squares are associated with longer lives also holds for
all categories but Event Driven and Emerging Markets. We note, again, that in the
cases when the direction of the difference goes against our findings, it is statistically
insignificant.
Some of the variables used in the hypotheses exhibit what we may consider
high correlations. Of concern is the correlation between Complexity and Age, at
30%. As point 6 below indicates, we have reproduced our results using strategy
dummies and thus eliminating the variable Complexity from the regressions. The
correlations between Age and these dummies are between less than 5%.
Of concern is also the negative correlation of -40% between F OF and if ee.
We have therefore projected if ee on F OF , and run the same analysis using F OF
and if ee⊥ , and we obtained similar results.
5.4
Economic Significance
The previous section argues that across time, low Rsqr funds outperform; in this
section we shall analyze the portfolio of the low Rsqr, respectively, the high Rsqr
funds.
For that, we form equally weighted portfolio of funds from the lowest past
Rsqr decile, and rebalance this portfolio on a quarterly or annual basis. We also
build portfolios drawing from all the funds, then from all the funds over $15 million,
then over $ 100 and over $ 300 million.
Note that in order to form portfolios based on past Rsqr, we need funds with
3 years of previous data, and in the case of annual rebalancing, with 1 more year of
data after the formation period. We do the same for the highest past Rsqr decile.
The timeline of portfolio formation is described in the diagram below:
34
T − 36
|
{z
T − 12
}||
construct benchmark
{z
calculate Rsqr
T
|
}|
{z
}
form low previous
Rsqr portfolios;
hold till rebalancing
The summary statistics of these portfolios are reported in Table 8.11. The
portfolio of low Rsqr exhibit higher returns (with only one exception) and higher
Sharpe ratios (both on an adjusted, or not adjusted for serial correlation) that the
portfolio of the high Rsqr funds. For example, if we look at the portfolio low Rsqr
funds over $ 300 million of size, rebalanced annually, versus the portfolio of high
Rsqr funds, they have close means but the standard deviation of the high Rsqr
portfolio is almost three times higher than the standard deviation of the low Rsqr
portfolio, and the Sharpe ratio is 0.45 higher. The portfolio consist of 69 funds, a
reasonable number to describe a fund of funds portfolio.
These differences prevail across portfolios drawn from funds of different sizes,
rebalanced quarterly or annually. The means are, with one exception, higher in the
case of the low Rsqr portfolio. Additionally, we can form random portfolio of funds,
equally weighted and containing the same number of funds as the corresponding
low Rsqr portfolio (for example we can form portfolio of funds over $ 300 million,
choosing the funds randomly from all the funds over $ 300 million and weighting
them equally). When the Sharpe ratio of the low Rsqr portfolio is compared to the
Sharpe ratios of the random portfolios containing the same number of funds, the
low Rsqr portfolio ends the contest in the top 5%.
Note that a portfolio long the low Rsqr funds has a good Sharpe ratio (0.62
is the worse Sharpe ratio of such a portfolio in Table 8.11, for the portfolio of funds
larger than $ 300 million and on an adjusted basis), while a portfolio long in the
35
low Rsqr funds and short in the high Rsqr funds5 has not. This is due to the fact
that the short leg has a standard deviation high enough so the effect of adding it to
the long leg would be a large drop in the Sharpe ratio.
We conclude that the negative relation between Rsqr and fund performance
is economically significant.
5.5
R-square and inflows
We have argued that managers with low R-squares due to idiosyncratic investments
are successful. Do managers keep their ability to find idiosyncratic investments when
the hedge fund receives inflows? Where do managers place the inflows? There are
four possibilities.
One possibility is that managers invest more into their systematic component.
In this case, Rsqr increases with the inflows, and the timing measure T O1 increases,
capturing a raise in the betas of the systematic component os the fund.
The second possibility is that the fund invests in new systematic factors. In
this case, T O2 increases because it captures timing among the factors, other than
ones the fund is already exposed to.
The third possibility is that the fund de-levers (invest the inflows in cash).
This would be consistent with a decrease in the riskiness of the fund following the
inflows and with no changes in the Rsqr.
The last possibility is that the fund invests idiosyncratically. The betas
stay the same, so the timing decreases, and the Rsqr decreases because the model
estimated before the inflows does even a worse predictive job than without the
inflows.
5
It is also unrealistic to short hedge funds. There have been recent attempts to create hedge
funds derivatives in the OTC markets, but shorting hedge funds has yet to be developed as a
process.
36
In order to investigate the effect of inflows on the ability of funds to find
investments uncorrelated with public indices, we estimate the following model:
RsqrTi = ci + b1 aumT,i + b2 Last1Y StdT,i + b3 AgeT,i + b4 P ressureT,i
+b5 mktT + b6 F OFi + b7 mf eei + b8 if eei + b9 F lowF racT,i
+b10 AliveT,i + ²T,i
T O1iT = ei + d1 aumT,i + d2 Last1Y StdT,i + d3 AgeT,i + d4 P ressureT,i
+d5 mktT + d6 F OFi + d7 mf eei + d8 if eei + d9 F lowF racT,i
(5.7)
+d10 AliveT,i + ²T,i
T O2iT = gi + f1 aumT,i + f2 Last1Y StdT,i + f3 AgeT,i + f4 P ressureT,i
+f5 mktT + f6 F OFi + f7 mf eei + f8 if eei + f9 F lowF racT,i
+f10 AliveT,i + ²T,i
The results are presented in Tables 8.12, 8.13 and 8.14.
To analyze the effect of the inflows on the extent to which managers can
invest idiosyncratically, we look at the coefficient of P ressure, which measures the
inflows into hedge fund strategies, from Tables 8.12, 8.13 and 8.14. We observe that
as strategies of funds receive inflows, Rsqr decreases when funds of all sizes are
included in the analysis. Both types of managers, of large and small funds, seems
to be timing the factor exposures less after inflows are received, consistent with the
hypothesis that managers invest idiosyncratically. The first three possibilities on
placing inflows are therefore eliminated, the alternative remaining being that funds,
on average, invest the new money idiosyncratically (so their talent materializes after
money flows into hedge funds).
However, analyzing the relationship between Rsqr, T O1, T O2 and inflows
37
not into strategies but into individual funds, controlling for the flows in strategies,
we observe, from Tables 8.12,8.13 and 8.14, that what we just showed to hold for
strategies pressed with inflows ceases to remain true at funds level. Precisely, if
funds receive inflows (expressed by F lowF rac) above and beyond their strategy
average inflows, we observe that Rsqr increases, while T O1 increases and T O2 is
not significantly affected. This is evidence consistent with the fact that managers of
funds receiving more money relative to their size than other funds in their industry
fall into the trap of making easy fees and boost the allocation to their systematic
component. As we have shown earlier, this behavior triggers under performance,
which Agarwal, Daniel and Naik (2004) show it conducts to outflows. This seems
to be a self regulatory mechanism of the size of hedge funds: managers receiving
more money than their industry average invest more systematically, under-perform
and subsequently experience outflows.
38
Chapter 6
Extensions: Other Measures of
Success and R-squares
The previous section argues that low R-squares are inversely related to one measure of a fund’s success: the Sharpe ratio. If low R-squares funds out-perform,
do investors recognize this? If they do, we expect the low R-squares funds to be
able to charge higher fees than the high R-square funds, have more assets under
management, be more likely to remain in the sample (i.e., survive) and be older.
In this section we investigate the relationship between R-squares and these other
measures of a fund’s success: fees, assets under management, age and the likelihood
to survive.
6.1
R-squares and fees
The objective of this section is to test the following hypotheses:
Hypothesis 3: Higher fees correspond to lower overall R2 .
Hypotheses 4: Higher fees correspond to lower Rsqr, T O1, T O2.
From Table 8.5, we observe that as we move from the low to high R2 terciles,
39
the average of both incentive and management fees decrease. There is a difference
of 20.20 basis points between the average management fees charged by the funds
with low R2 and the average management fees charged by the funds with high R2 .
the corresponding difference is 226.39 basis points for the incentive fees and both
difference are statistically significant. Hypothesis 3. is therefore strongly supported.
Figures 8.7 and 8.8 both show that funds with lower Rsqr, T O1, T O2 charge
higher fees. This is confirmed further by the Fama-MacBeth tests of Table 8.9.
Hypothesis 4 is thereby strongly supported.
Furthermore, Table 8.6 shows a negative and statistically significant relationship between R2 and the fees charged; we can therefore reject the null of no
relationship in favor of Hypothesis 3.
One result from Table 8.6 is that fees are not very strongly related to the
tracking error. In fact only the management fee seems to be strongly related to the
tracking error, and this is true only for the funds smaller than $ 15 million. If the
structure of the fees is what incentivizes the manager to take more or less risk, then
mutual funds, who charge only management fees, should have a different risk taking
behavior from hedge funds, whose manager extract rents from investors through
mostly through the incentive fees. Under this assumption, that fees drive the risk
taking, the weak link we find between the incentive fees and the tracking errors is
consistent with Brown, Goetzmann and Park (2001) who show that hedge funds are
less likely to engage in tournament behavior than their mutual funds counterparts.
Furthermore, the fact that management fees are positively related to tracking errors
are then consistent with Brown, Harlow and Starks (1996), who show that mutual
funds (who charge management fees) engage in tournaments behavior.
An interesting question is what do investors pay fees for. Are the hedge
funds compensated for performance, Sharpe ratios, or in fact investors recognize
the importance of the idiosyncratic investment ideas in the hedge fund world and
40
compensate the managers with these ideas? In order to answer this question, we
test whether fees explain the funds’ R2 s beyond Sharpe ratios or excess returns.
The results are presented in Table 8.15.
We observe that fees explain the R2 ’s of the funds above and beyond Sharpe
ratios or raw returns and that this relationship is more stronger for incentive fees.
If fees reflect talent, this evidence suggests that R2 is a better descriptor of the
manager’s talent, as differentiated from luck or any other apparent manifestations
of talent1 .
The Fama-MacBeth tests in Table 8.9 reject the null of no relationship between the Rsqr, T O1, T O2 and the fees in favor of Hypotheses 3 and 4.
The fixed fund effects tests continue to confirm the negative relationship
between fees and Rsqr, T O1, T O2. The null of no relationship between Rsqr, T O1
and T O2 respectively and fees can further be rejected at more than 1% confidence
given the results in Tables 8.12, 8.13 and 8.14, in favor of Hypothesis 4.
6.2
R-squares and assets under management
The objective of this section is to test the following hypotheses:
Hypothesis 5: Assets under management are inversely related to overall
R2 .
Hypothesis 6: Assets under management are inversely related to Rsqr,
T O1, T O2.
From Table 8.5, we observe that funds in the low R2 tercile are $ 9.21 million
larger on average (also statistically significantly) than the funds in the high R2
tercile. To gauge the magnitude of the difference, recall that the median size of
1
For example, Berk and Green (2004) imply that the proposition “talented mangers outperform”
is a myth (because talented managers get to manage larger funds and their talent cannot materialize
in performance regardless of scale). Hence, measuring manager’s talent by performance may be
wrong. Our results suggests that investors reward more a low R2 manager than a outperforming
one.
41
the hedge funds is around $ 38 million. This is evidence in favor of Hypothesis 5.
However the difference is not statistically significant (although economically large).
There is a concave, statistically significant relationship between R2 and size
of the fund (as captured by aum25, as apparent from Table 8.6. Thus we reject the
null of no relationship between R2 and size of the funds in favor of Hypothesis 5:
when we examine the concave relationship between R-squares and size, we observe
that it becomes negative only past a certain fund size. The coefficient of aum25 is
0.0107 for all funds, while the coefficient of (aum25)2 is -0.0014. This means that
the R2 decreases with fund size as the fund manages more that log(0.0101/0.0014) =
$2.0338 million.
On the panel data, Figure 8.6 indicates that low R-square funds manage more
money; this is confirmed by the Fama-MacBeth regressions of Table 8.9. Note that
the Fama-MacBeth regressions produce stronger results that a pure cross-sectional
regression using the whole history of the funds; the relationship between Rsqr and
size is linear, instead of quadratic. Although we can reject the null of no relationship between R-squares and size in favor of Hypothesis 6, the relationship between
T O1, T O2 and size is inconclusive. Some of the larger funds may, therefore, time
exposures as well as invest idiosyncratically.
The panel regressions do not need a quadratic size term as they capture
the dynamics of size through time. From Table 8.12, we observe that funds with
larger assets under management (aum) have also lower Rsqr (the relationship is
significant). Therefore the null of no relationship between Rsqr and aum is rejected
in favor of the alternative, which is Hypothesis 6. Again, the relationship between
growth ( as expresses by the coefficient on aum on the time series regressions) and
timing is inconclusive.
42
6.3
R-squares and age
The objective of this section is to test the following Hypotheses:
Older funds have lower overall R2 .
Older funds have smaller Rsqr, T O1, T O2.
Table 8.5 shows that funds with a lower R2 have been reporting to our
database 9 months more, on average, than the funds with a higher R2 . This difference is statistically significant and economically important as it represents 17%
of the median age of a fund in our database (which is 53 months), and constitutes
evidence in favor of Hypothesis 3a.
The coefficient of Age in the R2 regressions from Table 8.6 is negative and
statistically significant, so we can reject the null of no relationship between age and
R2 . The same relationship carries to larger funds although the coefficient of Age is
less significant.
When the relationship between age and R-squares is studied inter-temporally,
the sign of the coefficient on age in fact reverses: as the funds grow older, their Rsqr
in fact increases (see Table 8.12).
As the panel regressions capture time series effects, our result may be explained in the context of Boyson (2004), who finds that managers with longer tenure
(which older funds are more likely to have) tend to become less risky, and take actions
that are more moderate than managers who are younger. This causes the manager
of an aging fund to invest more conventionally - or equivalently less idiosyncratically. Hence, as managers get older they are less likely to use their investment talent,
they prefer to covary more with public indices and thus ensure that their potential
failures are “conventional”.
Although different in scope and performed on another database, this study
also shows that the magnitude of the idiosyncratic risk borne by hedge funds is
unrelated to management fees, while it is positively related to incentive fees. If the
43
pay structure is the driving force behind managers’ decisions on risk taking, then
our findings suggest that managers paid predominantly in management fees take
higher risk2 , while managers paid mostly in incentive fees do not3 .
We confirm the results of Boyson (2004). She shows that as a manager’s
tenure (interpreted here as the age of the fund) becomes longer, the manager’s
career concerns increase, which induces him to take less risk and to herd more.
Thus, with age, the conformity of a manager increases. This may be seen in our
Table 8.12, which shows that as the fund ages, the Rsqr increases.
6.4
R-squares and survival
The objective of this subsection is to test the following:
Hypothesis 9: Funds with a lower probability to exit the sample have
lower overall R2 .
Hypothesis 10: Funds with a lower probability to exit the sample have
lower Rsqr, T O1, T O2.
From Table 8.5, funds with lower R2 have 5.19% more probability to remain
in the sample than funds with high R2 , supporting Hypothesis 9.
Table 8.6, as well as Panel B in Table 8.7 further shows a negative, statistically significant relationship between probability to remain in the sample and the
R2 . We can reject the null of no relationship in favor of Hypothesis 9.
When testing Hypothesis 10, however, the tests do not have enough power
to be able to reject the null of no relationship.
2
Brown, Harlow and Starks (1996) show that mutual fund managers, who charge mostly management fees, engage in tournaments behavior.
3
Brown, Goetzmann and Park (2001) show that hedge funds, who profit mostly from charging
incentive fees (and also have watermarks), do not engage in tournaments behavior.
44
Chapter 7
Implications for Risk
Management
This study contributes to the current debate on the hedge fund transparency needs
of the hedge fund investors. Hedge funds do not disclose their positions and hedge
fund investors may only use returns to infer the risks embedded in their hedge funds.
In this section, we address an issue related to the risk management performed by
investors in hedge funds, as opposite to that performed by the funds themselves.
For the latter, see Lo (2001).
To asses the risk associated with a hedge fund, each investor estimates a
factor model from the history of the fund; this estimation is useful as long as it
is valid out of sample. In the language of the measures employed in this study,
inferring risk exposures from the monthly returns is useful only as long as Rsqr is
positive (and as close to the maximum of 1 as possible).
We argued that funds for which Rsqr is large are funds whose managers do
not exhibit talent; in other words, we document a tradeoff between the quality of
the fund and the extent to which monthly returns allow investors in hedge funds
to extract the risks the fund is exposed to. In particular, the better the returns of
45
the fund can be “explained” by systematic factors, the worse the Sharpe ratio of
the fund is. The top panel of Figure 8.5 plots the difference between the average
Sharpe ratios of the funds that are least likely to be explained by public factors,
compared to the average Sharpe ratios of the ones most likely to be explained. The
tradeoff between performance, and the extent to which a fund may be explained
by systematic factors exacerbates in 2000 (the difference in average Sharpe ratios
is close to 3 !), and it seems to have levelled in the recent years (2003), when the
volatility of the markets in general lowered.
These findings suggest that if an investor could understand the risk exposures
of her hedge funds from the past monthly returns of the fund, then the funds are
under performers. Combined with the fact that Rsqr has a negative median (see
Table 8.8), this seems to suggest that on the one hand, inferring risk exposures
of hedge funds from the past time series of monthly returns does not have much
success, and in the case it has, it is because the investor holds under performing
hedge funds.
This explains the thriving risk systems which, instead of using only the time
series of returns of a hedge fund to infer the inherent risks of the funds, actually
collect the fund holdings under mutual secrecy arguments and aggregate these holdings for the investor1 . The evidence presented in this study also suggests that more
transparency is needed from the hedge funds to their investors.
1
So the investor does not get to observe the positions of the fund, only the aggregate risks.
46
Chapter 8
Conclusions
It is almost a truism of the hedge fund universe that a talented manager is one with
investment ideas that are “out of the box” and whose strategies are uncorrelated
with publicly available indices. Intuitively, a less talented manager has to rely more
on investing correlated to public indices in order to produce returns. In turn, this
manager’s R-squares will be low, and a simple model shows that their performance
will also be low.
Consistent with the common wisdom confirmed by our simple model, we find
evidence in support of this hypothesis. Our finding, that the lack of covariance with
public indices is related to abnormal performance, is economically significant: we
show that a portfolio of low R-square funds outperforms a portfolio of high R-square
funds. In addition, we show that a portfolio of low R-square funds outperforms the
average portfolio of hedge funds, and that this relationship is robust to the size of
the funds considered or to the frequency of rebalancing the portfolio.
Additionally, we find mixed evidence on the funds’ ability to invest inflows
in idiosyncratic strategies. This study shows that inflows into fund strategies do
not trigger an increase in the systematic exposures of the hedge funds, on average.
Therefore, the relationship between R-squares and performance is robust to inflows
47
into hedge fund strategies. While strategies of hedge funds accept inflows if these
inflows can be invested idiosyncratically, the same ceases to hold true for individual
hedge funds who receive inflows above and beyond their category average. These
funds succumb to taking some systematic risk - thus, potentially, making easy fees off
beta exposures; eventually these funds under perform and thus experience outflows.
Not only do we find that funds whose strategies are more idiosyncratic have
higher Sharpe ratios, but also that these funds are recognized and compensated by
investors. For example, these funds have more assets under management. Additionally, we show not only that low R-square funds are able to charge higher fees,
but also that R-square dominates excess returns or Sharpe ratios as an explanatory
variable of the fund fees. This relationship is stronger for incentive fees. Simply
put, we show that investors pay for investment ideas with little systematic risk on
top of what they pay for fund performance.
To the best of our knowledge we are the first to document the tradeoff between the extent we can understand the risk exposures of a hedge fund, and its
performance. We show that if a manager is good, then his risk exposures cannot
be inferred only from the monthly returns of the fund. Thus, this study has implications for the risk management performed by investors holding hedge funds and
attempting to understand the risks associated with them. If investors attempt to
understand the systematic exposures of their funds using factor models, and succeed, then our results show that the fund manager either lacks talent, or that he is
overinvested. Returns based risk management is therefore problematic if the hedge
funds to be explained have talented managers and provide only monthly returns,
and additional transparency may be required by the investors of these funds.
48
Appendices
49
Methodologies to fit the factor model
In this section we argue that using stepwise regressions to estimate the model (5.2)
is superior to methodologies such as principal component analysis.
Equation (5.2) is fitted for each of the funds in our database; we use the whole
history of the fund (in-sample estimations), and we also roll estimations across time
(to study the out-of-sample goodness of fit).
Hedge fund histories are generally not very long - the median life of a fund
in our database is 53 months while 31% of the funds have less than 34 months of
history - and we employ K = 34 factors. Thus, while evaluating (5.2) in or out-ofsample we cannot simply run regressions on the fund returns on the set of all the
factors. We investigate two main methods used in the factor model literature to
reduce the number of factors.
Agarwal and Naik (2004) advocate the use of stepwise regressions to explain
hedge fund returns, claiming that the “benefits of using the stepwise regression [to
explain hedge fund returns] ... outweigh the costs [of potential data mining]”. The
first method considered is therefore the stepwise regression; the stepwise regression
is an OLS regression performed in stages, in which not all the independent variables are used. First only the independent variable the most correlated with the
dependent variable is considered (along with its first order lag), then new independent variables are included (with their first order lags) in the regression if and only
the introduction increases the R2 of the regression. Due to the presence of serial
autocorrelations in the time series of the returns, this study adapts the stepwise
regression so that the first order lags of the dependent variables are included along
with their contemporary counterparts at each stage of the stepwise regression, a la
Getmansky, Lo and Makarov (2004), Section 5.2.
The alternative method is factor analysis, where the model consisting of
34 factors is reduced to a model including only n < 34 factors, usually a linear
50
combination of the set of 34 factors. We take the first n principal components
as the factors. There are several criteria that help identifying the number n of
principal components that ought to be used: the Kaiser criterion selects only the
principal components whose corresponding eigenvalue is greater than one1 ; when
used in our case, it recommends selecting the first 6 principal components. The
Cattell criterion picks principal components until their explanatory power seems to
“level out” when plotted; applied to out case this criterion recommends selecting
5 principal components. The Akaike and Schwartz criteria minimize an expression
depending on the likelihood function of an explanatory regression of the factors
selected. When minimized in our particular case, these two criteria recommend to
pick 10, respectively 8 factors.
Although we have experimented with two other methods of fitting, namely
ridge regressions and the lasso method (see Hastie, Tibshirani and Friedman (2001)),
the results were similar to those obtained from the factor analysis and hence we only
present the latter.
To compare the two methodologies, we have simulated 10,000 funds under the
null that they hold systematic risk described by our set of 34 factors, and analyzed
which method better captures these risk exposures. We first simulate entire histories
(that is funds that invest in systematic risks on the whole time period January 1994
- December 2003), then we simulated funds whole life span spreads only on random
periods 24 months in length. We made the assumption that each fund does not
invest in more than 10 different factors2 . Each fund is simulated in the following
way:
1. A random number of factors is selected from a uniform distribution on
1
This criterion includes a principal component if and only if it’s explanatory power is at least
as high as of one individual factor.
2
When later fitting the model (3.2) to the hedge fund returns data, either using the whole history
or on a rolling basis, we observed that in all but 1% of the fund-month cases in which we estimated
the model, the funds were exposed to fewer than 9 different factors.
51
the interval [1, n]. We select n = 10 (the fund invests in maximum 10 factors), and
also n = 3 and n = 5 to compare the quality of fit with the case when the number
of factors decreases3 . On short, we choose k ∼ U [1..n], n = 3, 5, 10.
2. Once the number of factors, k, is selected, a number of k factors, j1 , ..., jk is
randomly drawn from the set of 34 factors in our data set. We choose j1 ∼ U [1..34],
then j2 ∼ U ([1..34] \ {j1 }), ..., jk ∼ U ([1..34] \ {j1 , ..., jk−1 }).
3. A beta for each of these factors is drawn from a normal distribution. That
is, we choose (βj1 , βj2 , ..., βjk ) ∼ N (0k , Ik ).
4. Another number, to represent the monthly idiosyncratic volatility of the
fund, is drawn from a normal distribution, scaled so that the monthly idiosyncratic
volatility cannot be larger than 5% with a probability of 99.9% (the typical overall
volatilities of funds in-sample have a median of around 1% per month in our sample,
when model 5.2 is estimated on rolling two year windows). That is, we choose
σ² ∼ |N (0, 1)|/50 (the median of this random variable is 1.00%).
5. If we are using rolling windows, we simulate a starting time t0 ∼ U [1..(120−
23)]. The ending time is t1 = t0 + 23. If the whole history of the fund is used, then
t0 = 1, t1 = 120.
6. A series of normal random noise is generated with a length equal to
the history of the fund (which may be January 1994 - December 2003 or random
subperiods of 24 months). That is, we simulate ² ∼ N (0T , IT ), where T = 24 (rolling
windows) or T = 120 (whole history).
7. The returns of the fund simulated are equal to the sum of the randomly
selected factors F j1 , ..., F jk multiplied with their corresponding betas simulated at
step 3, plus the noise simulated at step 6 multiplied with the idiosyncratic volatility
simulated at step 4. That is,
3
The motivation to pick 5 factors comes from the fact that the median number of factors the
fund is exposed to, as computed from fitting the model (3.2) to hedge funds data, is equal to 5.
52
Rt =
34
X
βm Ftjm + σ² ²t , t = t0 , t0 + 1, ..., t1 ,
m=1
where
βl =


 βj
m
, l = jm

 0
, l 6∈ {j1 , ...mjk }.
We then use stepwise regressions and factor analysis (we repeat the analysis
for the cases when 5 to 16 factors are used, as various criteria advise on any number
c1 , ...β
d
between 5 and 10) to infer the betas of these funds, (β
34 ), and we calculate the
square distances between the true betas and the inferred betas, that is,
34
X
2
|βc
m − βm | .
m=1
The distribution of these distances is presented in Table 8.16 for the various
cases considered.
The median differences between the true and estimated betas is the smallest
in the case we use the stepwise regression, in all cases analyzed. If the estimation
of the models is made for the whole history, stepwise regression clearly dominates
the other methods. We notice, however, that if the fund can be exposed to as many
as 10 systematic factors and the estimation is done on periods of 24 months, the
distribution of the differences from the stepwise regression is much flatter than the
similar distributions obtained when using principal components, indicating that the
stepwise regression has a potential for more serious spurious mismatches than the
multivariate factor analysis (or principal components analysis). However, in the
majority of cases the stepwise regression produces a better fit than the alternative
methodologies. Figure 8.9 shows, in each of the cases considered4 , the percentage
4
The fund is exposed to 3, 5 respectively 10 factors and the estimation is done for the whole
history of for rolling periods of 24 months.
53
of simulations in which the stepwise regression produces a better fit than using a
number of principal components. These comparison results are consistent with the
claim of Agarwal and Naik (2004) on the quality of the stepwise regression. Note,
however, that their statement and our comparison results are contingent upon the
time period used and the factors employed (specific for hedge funds), and it should
not be considered as an absolute proof of virtues for the stepwise regression in
general.
54
Spurious estimation of systematic risk: Estimation of the
systematic models
Although we show that stepwise regression is a better way of inferring funds’
systematic exposures, for comparison reasons, we perform our tests based on factor
analysis as a methodology to infer funds’ exposures. The results are qualitatively
similar, although the tests lose power. For example, the adjusted R2 of the panel
regressions presented in Table 8.12 drops 28 times (!) when factor analysis is used
instead of the stepwise regression.
As low out-of-sample R-squares may be of some concern, we experimented
with the CAPM and the Carhart (1997) four factor models as explanatory models
for hedge fund returns. Both produce negative out-of-sample R-squares, with the
Carhart (1997) model faring worse, at the median, than the model based on stepwise
regressions. This result show that naive smoothing of the out-of-sample fit is not
likely to be achieved.
Because it is built out of sample, Rsqr is less likely to be the subject of
spurious estimation and this is the reason we prefer to use it throughout this study.
However, we may use pure rolling R2 (an in-sample measure). If we do so then the
conclusions of our analysis do not change.
55
Tables and figures
56
Table 8.1:
Summary Statistics for the Hedge Funds Industry.
Databases started keeping track of the funds that ceased to report only after 1994. Second Panel
presents cross-sectional summary statistics of the funds.
Year
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Funds Born
83
159
214
278
404
508
506
683
722
666
667
611
803
877
767
25th percentile of size ($ mil)
Age
Still in-sample (Alive)
FOF
Management Fee (%)
Incentive Fee (%)
Mean Excess Return (annual)
Sharpe Ratio (annual)
Funds Died
2
1
0
1
0
61
186
182
316
497
458
381
316
174
516
Total Funds
363
520
733
1011
1414
1922
2367
2864
3404
3754
3924
4077
4499
5060
5653
Mean
Median
Std
53.3589
66.0582
72.84%
23.33%
1.3665
16.5776
7.32%
0.8018
11.9450
53.0000
N/A
N/A
1.2500
20.0000
6.21%
0.6657
388.0830
50.2813
N/A
N/A
0.7657
6.8582
14.69%
1.5797
57
Table 8.2:
Heterogeneity across net returns and assets under management from the Altvest,
HFR and TASS databases.
Means (with standard deviations in parenthesis) and Medians of the monthly returns net of fees
and Assets Under Management across Altvest, HFR and TASS, and the merged database. A
Kolmogorov-Smirnov test to check whether the distributions of assets under management and
net returns are similar among the databases. Low p-values for the Kolmogorov-Smirnov statistic
means that we are more likely to reject the null that the two samples are drawn from the same
distribution. TASS seems to be different than both Altvest and HFR, and seems to contain funds
with lower assets under management and with lower net returns.
Altvest
Net
AUM
.0133 (.0370)
122.52 (351.78)
HFR
2003 Mean (Std)
.0129 (.0345)
140.40 (815.93)
Entire database Mean (Std)
Net
AUM
TASS
.0131 (.0388)
99.05 (218.55)
.0099 (.0626)
85.05 (443.95)
Net
AUM
.0088
32
Net
AUM
Altvest-HFR
.2922
.0351
2003 Median
.0086
28.6
Kolmogorov-Smirnov p-values
Altvest-TASS
.0042
.0000
58
.0082
26.4
HFR-TASS
.0400
.0000
59
Sample statistics for the risk factors used.
FTSE 100
MSCI World ex US
MSCI EM
NAREIT Equity
NASDAQ
Russell 1000
RUSSELL 2000
Russell 3000
max(R3K, -.01)
min(R3K, -.01)
R3K*R3K
Russell Midcap Value
VIXret
MSCI EAFE
SMB
HML
MOM
Mean
0.53
0.35
0.08
1.01
1.14
0.98
0.92
1.11
1.56
-1.45
0.12
0.89
1.88
0.24
0.27
0.14
0.89
Median
0.40
0.55
0.49
1.19
1.57
1.38
1.68
0.94
0.94
-1.00
0.03
1.41
0.17
0.75
-0.13
0.11
1.08
Std
5.93
4.39
6.86
3.43
8.31
4.59
5.70
3.25
2.62
1.17
0.19
4.34
18.10
4.36
3.82
4.65
5.69
DXY
Lehman Agg
Lehman Agg - MBS
Lehman Munis 10Y
SB Currency Hedged
SB Wt Gvt 1 Yr
SB US Treas 10 Yr
SB US Treas 30 Yr
SB US Treas 5 Yr
DefSpread
CPI
AMEX Oil Index
GSCI
SPPo
SPPa
SPCo
SPCa
Mean
-0.07
0.57
0.56
0.51
0.58
0.57
0.52
0.57
0.51
0.81
0.20
0.80
0.52
-8.99
-85.35
6.01
-9.04
Median
-0.12
0.66
0.61
0.71
0.65
0.30
0.48
0.64
0.44
0.71
0.19
0.40
0.63
3.80
3.98
4.16
3.86
Std
2.21
1.15
0.90
1.34
0.93
1.91
2.14
3.16
1.34
0.23
0.23
5.25
5.54
124.22
1099.81
199.61
463.33
There are 17 equity indices (including timing terms), 11 fixed income indices, 2 commodities indices and 4 option strategies. All the option strategies are
written on the S&P 500 index, and the first two symbols in the factor name, “SP”, symbolizes that. The third letter is the name of the option used, “P”
for put and “C” for call. The last small letter indicates moneyness, with “a” indicating at the money and “o” indicating 1% out-the-money. The unit is
percent-per-month. Three of the factors are not investable: max(R3K, -.01), min(R3K, -.01) and R3K*R3K.
Table 8.3:
Table 8.4:
Summary of factor analysis applied to individual hedge funds.
Summary statistics for R2 and tracking errors from fitting the model (5.2) to individual hedge
funds and fitting the model (3.2) (no serial correlation) for mutual funds are presented. The
standard errors for the hedge fund model are adjusted for serial correlation.
Mean
Std
25th percentile
Median
adjusted R2 (stepwise regression)
adjusted R2 (investable factors)
adjusted R2 (Carhart 4-factor)
adjusted R2 (VW market returns)
TE
42.50%
42.15%
15.85%
5.99%
3.80%
26.89%
26.98%
25.86%
9.59%
6.10%
21.77%
20.91%
1.46%
0.52%
1.64%
42.10%
41.52%
13.71%
2.43%
2.71%
75th percentile
Hedge Funds
62.96%
62.22%
30.09%
7.16%
4.50%
adjusted R2 (stepwise regression)
TE
61.34%
1.82%
28.34%
1.90%
48.60%
0.53%
66.86%
1.26%
Mutual Funds
83.45%
2.61%
60
61
R2 and talent proxies.
12.14%(10.02%)
41.66%(7.65%)
72.79%(12.60%)
-0.6065
-6.0499
low R2
med R2
high R2
low-high mean
low-high t-stat
R2
0.3853
7.1255
1.0197(2.3064)
0.7564(0.9997)
0.6344(1.0644)
SR
0.2029
8.7329
1.4763(0.8905)
1.3525(0.7485)
1.2734(0.6254)
mfee
2.2639
11.0641
17.7291(6.3577)
16.5727(6.8616)
15.4652(7.1362)
ifee
9.21
0.81
57.53(439.8348)
54.38(416.6248)
48.32(294.6952)
aum25
9.2085
5.8381
69.2829(50.2678)
69.0009(45.6930)
60.0744(53.8956)
Age
0.0519
3.8358
0.7473(0.4346)
0.7436(0.4367)
0.6954(0.4604)
Pr(Alive)
We sort the funds by the R2 terciles and compute the average Sharpe ratio, Management Fee, Incentive Fee, size represented by aum25, Life of the fund
and probability of not exiting the database among each R2 tercile. The differences between the low R2 tercile and high R2 tercile and their t-statistics are
presented.
Table 8.5:
62
The relationship between the ability to explain a fund (high R2 or low T E) and fund characteristics.
Adjusted R2
cons
aum25
(aum25)2
Age
Alive
rho
Complexity
F OF
mf ee
if ee
Variable
Dependent Variable
0.0371
-0.0062
0.0003
0.0001
-0.0097
0.0344
0.0008
-0.0203
0.0030
0.0002
Coef
5.75%
4.6203
-7.2702
2.0468
2.1397
-5.6438
5.0552
0.4514
-8.3210
3.4015
0.9971
0.6126
0.0107
-0.0014
-0.0005
-0.0226
-0.1645
0.0004
0.0621
-0.0351
-0.0044
TE
All funds (6525 obs.)
t-stat
Coef
6.62%
29.4416
2.8590
-1.9770
-4.0246
-2.9282
-10.0601
0.0868
6.6304
-5.3650
-7.6269
t-stat
R2
0.0338
-0.0088
0.0007
0.0000
-0.0095
0.0254
0.0036
-0.0205
0.0016
-0.0002
Coef
8.36%
4.6101
-2.1628
1.4966
0.0539
-4.1099
3.6250
4.6738
-6.6159
1.6696
-0.8376
0.6197
0.0029
-0.0007
-0.0001
-0.0216
-0.1821
-0.0089
0.0868
-0.0287
-0.0034
7.60%
17.5849
0.1085
-0.2514
-0.3353
-1.7300
-6.3751
-1.3008
6.0016
-4.1779
-3.8812
TE
R2
Funds over $ 15 mil (4528 obs.)
t-stat
Coef
t-stat
Determinants of the ability to explain the risks specific to individual funds. For every fund, a stepwise regression is performed; this procedure generates a
benchmark for the fund. The adjusted R2 and the standard deviation of the error term (or the tracking error T E) are stored. We then run cross-sectional
regressions R̄i2 = f (f undi characteristics) + ²i and T Ei = f (f undi characteristics) + ²i and the results of this second stage regressions are reported in the
table.
Table 8.6:
Table 8.7:
The relationship between the ability to explain a fund (high R2 or low T E),
and the fund’s performance, measured as Sharpe ratio adjusted for serial autocorrelation or
as the probability of survival.
For every fund, a stepwise regression is performed and the R2 and T E are stored. Panel A reports
c2 and T E − Tc
the results of cross-sectional regression of Sharpe ratios on R2 − R
E, controlling
2
2
c
c
for fund characteristics. R and T E are estimations of R and T E from model (5.3). Panel B
presents the results of a probit regression where the dependent variable is a dummy for whether
the fund remained or not in our sample.
Panel A: OLS regressions explaining the Sharpe ratios.
Dependent
Variable:
Coef
t-stat
Coef
const
0.4400
3.9009
0.2416
c2
R2 − R
c
TE − TE
aum25
Age
Alive
rho
Complexity
F OF
mf ee
if ee
Adjusted R2
-0.3068
-4.5121
0.0007
-0.0001
0.4192
2.2341
-0.0982
-0.1330
-0.0085
0.0028
0.0633
-0.2694
10.2083
32.5069
-4.4663
-2.5702
-0.3634
0.8857
0.2593
0.0006
0.0000
0.4289
2.2753
-0.0985
-0.1464
0.0016
0.0041
18.53%
Panel B: Probit analysis explaining the fund’s probability of survival.
Dependent Variable:
Coefficient p-value
Coefficient
d
Rsqr − Rsqr
-0.1830
0.0244
T E − Tc
E
-1.3075
aum25
0.1000
0.0000
0.0921
Age
0.0045
0.0000
0.0048
rho
0.4964
0.0000
0.5733
Complexity
-0.1785
0.0000
-0.1794
F OF
0.4245
0.0000
0.3849
mf ee
0.1588
0.0000
0.1728
if ee
0.0112
0.0001
0.0122
Nobs=6525, McFadden R2
6.75%
63
SR
t-stat
2.2910
0.8672
0.0504
0.0052
10.4109
33.1188
-4.4748
-2.8148
0.0709
1.3108
18.28%
Alive
p-value
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
7.05%
64
Out-of-sample fit of stepwise regression vs. five principal components.
0.0000
41.66% are zeros;
Panel B:
0.0854
0.0089
0.0103
-0.03
-0.8781
T O1:
T O2:
In sample T E
Out-of-sample T E
In sample adj. R2
Out-of-sample Rsqr
T O1 (T O2 = 0)
0.28
-0.5608
0.0067
0.0106
In sample T E
Out-of-sample T E
In sample adj. R2
Out-of-sample Rsqr
Panel A:
20th
Percentile
0.11
-0.2064
0.18
-0.0716
0.0225
0.0261
0.3672
5 principal components
0.2442
0.0175
0.0200
0.0952
0.57
-0.0391
0.0093
0.0263
50th
0.0501
0.49
-0.1489
0.0083
0.0202
Stepwise regression model
40th
0.26
0.0277
0.0280
0.0334
0.5407
0.1595
mean=1.6708;
0.65
0.0012
0.0222
0.0334
60th
0.43
0.2611
0.0450
0.0577
1.2450
0.4022
std=1.9794
0.79
0.1823
0.0301
0.0567
80th
Each month from January 1997 to December 2002, the model (5.2) is estimated using two years of data prior to the current month, then the out of sample
Rsqr, T O1, T O2 and tracking errors are computed as described in Section 3. The fitting of the model (5.2) is first done by stepwise regression (Panel A),
then for comparison purposes using the first five principal components of the factors as explanatory variables (Panel B).
Table 8.8:
65
Fama-MacBeth regressions of Rsqr, T O1, T O2 on fund characteristics.
-0.3372
-0.0434
0.7326
0.0016
45.5204
-0.1087
-0.1231
-0.0073
-0.0118
0.0006
3.96%
const
aum
Last1Y Std
Age
P ressure
F OF
mf ee
if ee
F lowF rac
alive
R2 (t-stat)
Coef
2.8124
-1.0801
-2.8089
3.0591
4.8491
1.6977
-1.7078
-1.7578
-6.0181
-1.3469
0.0131
Rsqr
t-stat
2.70%
0.0569
0.0063
1.5360
-0.0001
-15.4336
0.0041
-0.0041
-0.0009
0.0003
-0.0062
Coef
10.0481
0.7282
1.2328
9.9399
-4.1735
-1.1248
0.6714
-2.0035
-2.3798
0.1626
-0.9509
T O1
t-stat
0.22%
0.5520
-0.0323
Coef
2.8729
17.9910
-5.9216
T O1
t-stat
0.89%
0.3808
0.0148
1.9101
0.0006
7.0870
0.2448
-0.0261
-0.0056
-0.0355
-0.0183
Coef
6.9527
0.429
1.4993
6.4909
3.0865
0.141
5.4464
-2.083
-2.6678
-2.0376
-0.7636
T O2
t-stat
0.15%
1.6754
0.0154
Coef
1.9052
23.0458
1.8434
Dep. Var.
T O2
t-stat
The Table shows Fama-MacBeth regressions of out-of-sample Rsqr, T O1, T O2 on fund characteristics. The average R2 of the cross-sectional regressions are
reported along with their t-statistics. t-statistics are Newey-West corrected for serial autocorrelation and heteroscedasticity.
Table 8.9:
Table 8.10:
Performance and the ability to infer a fund’s risk exposures.
The Table shows Fama-MacBeth regressions of funds’ performance calculated as out of sample
d T O1 − Td
Sharpe ratio, on Rsqr − Rsqr,
O1, T O2 − Td
O2, the estimations are from cross-sectional
regressions of Rsqr, T O1, T O2 on fund characteristics. The average R2 of the cross-sectional
regressions are reported along with their t-statistics. t-statistics are Newey-West corrected for
serial autocorrelation and heteroscedasticity. Similar results are obtained if instead of using Rsqr−
d T O1 − Td
Rsqr,
O1, T O2 − Td
O2, we use Rsqr, T O1, T O2.
const
T O1 − Td
O1
T O2 − Td
O2
d
Rsqr − Rsqr
aum
F low
Last1Y Std
P ressure
F OF
mf ee
if ee
Average R2
Coefficient
2.7797
-0.1338
t-statistic
4.9571
-3.4956
Coefficient
2.7628
t-statistic
4.8282
-0.0237
-3.1949
Dep Var:
SharpeRatio
Coefficient
2.9070
t-statistic
5.0144
0.1338
0.0370
-29.2579
32.8599
0.2249
-0.0892
0.0296
4.7098
2.5797
-6.3776
0.4227
2.0833
-1.7663
8.8985
0.1342
3.7231
-29.3194
25.7952
0.2279
-0.0873
0.0298
3.1712
2.0421
-6.3447
0.2764
1.4895
-1.6846
9.4913
-0.8613
0.1112
0.0181
-29.0717
10.9429
0.1401
-0.1820
0.0234
-7.9673
3.7857
1.2003
-5.9801
0.1281
1.0547
-1.7683
8.0403
8.65%
12.0817
8.64%
9.4143
15.35%
8.1409
66
Table 8.11:
Economic significance of low Rsqr as talent indicator.
Hedge fund long portfolios formed based on out-of-sample goodness of fit. At the beginning of
every formation period (every month, quarter or year, between Jan 1998 and Dec 2003) portfolios
are formed containing all the funds in the smallest decile of out-of-sample Rsqr. These funds are
held until the next rebalancing period, when the procedure repeats. The table shows summary
statistics of these portfolios: mean, standard deviation, Sharpe ratios, Sharpe ratios adjusted for
serial autocorrelation, average number of funds in the portfolio, and the turnover (in number
of funds) at the time of the rebalancing. Similar statistics are reported for the portfolio of the
high decile of Rsqr (the low talent funds). On a Sharpe ratio ranking (adjusted or not for serial
autocorrelation) the portfolio of the low Rsqr funds is in top 5% of portfolios of hedge funds
formed at random, on an equally weighted basis, containing the same number of funds as the low
Rsqr portfolio.
Panel A: quarterly rebalancing
all funds
funds over $ 15 mil
funds over $ 100 mil
funds over $ 300 mil
low
high
low
high
low
high
low
high
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Mean
Std
Sharpe
Ratio
Adj. Sharpe
Ratio
No. of
funds
7.80%
6.78%
7.95%
6.76%
8.11%
7.32%
8.36%
7.19%
3.19%
14.20%
3.25%
14.17%
3.28%
13.73%
3.50%
13.88%
1.16
0.19
1.18
0.19
1.22
0.23
1.21
0.22
1.06
0.18
1.07
0.18
1.08
0.23
1.09
0.21
231
Turnover
89%
122
88%
100
87%
69
87%
Panel A: annual rebalancing
all funds
funds over $ 15 mil
funds over $ 100 mil
funds over $ 300 mil
low
high
low
high
low
high
low
high
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Rsqr
Mean
Std
Sharpe
Ratio
Adj. Sharpe
Ratio
No. of
funds
8.19%
7.23%
8.03%
7.41%
8.58%
8.82%
8.11%
7.27%
4.55%
12.81%
4.59%
12.79%
5.13%
12.72%
5.83%
12.95%
0.90
0.24
0.85
0.25
0.87
0.37
0.69
0.24
0.80
0.23
0.75
0.24
0.77
0.34
0.62
0.23
231
67
Turnover
89%
122
88%
100
87%
69
87%
68
Determinants of the out-of-sample Rsqr.
1.2738
0.7881
0.1370
2.2281
0.8059
1.0133
-0.6308
-0.0484
-0.8295
0.9914
0.7165
17.4423
0.0025
57.5338
14.4138
2.0368
-0.7154
-0.0084
-0.0123
1.4388
aum
Last1Y Std
Age
P ressure
M ktRet
mktCap
F OF
mf ee
if ee
F lowF rac
alive
0.04%
64,366
t-statistic
Coefficient
Variable
Adj. R2
Obs.
1.12%
116,167
-5.4897
-1.8663
-4.7817
2.8371
-0.0500
-0.1610
-0.1155
-0.0080
0.0001
-0.0031
Adj. R2
Obs.
-5.9640
-0.6333
8.3820
-2.6255
5.2458
-0.0459
-0.2051
0.0018
-0.9785
0.4814
aum
Last1Y Std
Age
P ressure
M ktRet
mktCap
F OF
mf ee
if ee
F lowF rac
alive
t-statistic
Coefficient
Variable
-10.8935
-5.2042
-1.8877
-4.7273
3.2150
0.0441
-0.6806
-0.1514
-0.1165
-0.0078
0.0001
0.0027
2.7828
0.8242
-0.5766
-0.1061
-0.6923
0.9257
20.0465
1.5396
-0.6597
-0.0185
-0.0114
1.3340
0.09%
64,366
1.0670
0.1881
0.1523
0.1011
5 principal components model
t-statistic
Panel B:
Coefficient
All Funds
0.5594
4.0477
0.0027
2.0421
1.66%
116,167
-5.6648
0.7912
8.4150
-0.3351
Stepwise regression model
t-statistic
Panel A:
Coefficient
All Funds
-0.0428
0.2744
0.0017
-0.1312
1.1464
-2.9739
0.0463
0.0057
-0.7477
-0.6373
-5.7762
0.0159
61.4839
-6.8190
Coefficient
-0.1274
-0.1302
-0.0059
0.0001
-0.0409
-0.0604
0.2497
0.0018
-1.3409
0.3844
Coefficient
1.33%
56,320
t-statistic
Coefficient
Funds over $ 15 mil.
-1.8110
-0.6561
-0.6444
-16.2182
3.2925
0.0158
4.5086
49.9335
-5.3073
10.7111
1.5005
0.9386
-1.2274
-2.9999
0.8303
0.0441
1.9633
0.0056
-0.3184
-0.8008
1.45%
82,739
t-statistic
Coefficient
Funds over $ 15 mil.
-4.3821
-0.0577
0.6408
1.0073
7.7150
0.0018
-2.8110
-0.0911
5.0670
-0.8512
-3.8494
-0.1182
-1.6521
-0.1304
-3.4048
-0.0060
2.8978
0.0001
-0.4396
-0.0325
Dependent Variable:
Rsqr
1.76%
56,320
6.0665
1.2652
-1.2376
0.7966
1.9681
-0.3427
-1.8676
-1.9815
3.2554
3.5157
t-statistic
2.44%
82,739
-10.7543
-3.6446
-1.6579
-3.4862
3.3808
-0.3509
-4.2543
2.5167
7.7581
-0.1777
t-statistic
For every month from January 1996 until December 2002, and for every hedge fund in the sample that existed for at least two years before the current
month, we use the previous years of data and a stepwise regression to determine the factors best explaining the fund returns. This procedure produces a
i F
i
2
benchmark Bτi = αit + β1t
1τ + ... + βkt Fkτ , τ = t − 23, ..., t. The out-of-sample R is the percentage of the variance of the fund returns not explained by
the benchmark B i over the time interval [t, t + 12]. To find the determinants of the out-of-sample R2 we run a panel regression using the tracking error as
dependent variable. Fixed fund effects are included. The t-statistics are Newey-West corrected for serial autocorrelation. The coefficients significant over
1% are bolded.
Table 8.12:
69
Adj. R2
Obs.
0.0015
0.5590
0.0001
-0.1859
0.0511
aum
Last1Y Std
Age
P ressure
M ktRet
mktCap
F OF
mf ee
if ee
F lowF rac
alive
0.0513
-0.0033
-0.0016
0.0000
0.0145
Coefficient
Variable
0.46%
116,167
t-statistic Coefficient
All Funds
1.0380
0.0012
8.2644
0.5091
2.1656
0.0001
-1.4280
-0.3840
1.8104
0.0725
6.9990
0.0502
-0.8586
-0.0032
-3.9026
-0.0016
1.8669
0.0000
0.9582
0.0138
0.52%
116,167
6.1633
6.8909
-0.8336
-3.9770
1.7216
0.9023
0.8081
7.6045
2.1718
-2.9436
t-statistic
0.0585
0.0014
-0.0010
0.0000
-0.0129
0.0015
0.7348
0.0001
-0.0828
0.0788
Coefficient
0.52%
82,739
t-statistic
Coefficient
Funds over $ 15 mil.
0.6598
0.0012
8.5101
0.6733
1.4203
0.0001
-0.5377
-0.3047
2.5051
0.0717
6.9430
0.0577
0.3106
0.0014
-2.0426
-0.0010
1.9151
0.0000
-0.7637
-0.0138
Dependent Variable:
Determinants of the intra-factors timing.
The model (5.2) is estimated at time t − 1 then at time t. There are differences between the set
of factors the funds has non-zero exposures to between time t − 1 and time t. The intra factor
timing turnover measures the extent to which exposures to factors common in periods t − 1 and t
changed.
Table 8.13:
0.57%
82,739
5.2201
6.8617
0.3154
-2.0563
1.7513
-0.8132
0.5384
7.7269
1.4211
-1.9795
t-statistic
TO1
70
Adj. R2
Obs.
0.0233
1.5063
0.0004
-0.0510
0.8557
aum
Last1Y Std
Age
P ressure
M ktRet
mktCap
F OF
mf ee
if ee
F lowF rac
alive
0.2531
-0.0277
-0.0059
0.0000
0.0189
Coefficient
Variable
0.56%
116,167
t-statistic Coefficient
All Funds
3.6362
0.0211
5.3183
1.2069
1.7606
0.0004
-0.0945
-1.8366
7.8133
0.4442
7.9401
0.2463
-2.1364
-0.0269
-3.2953
-0.0062
0.1307
0.0000
0.2810
0.0133
0.64%
116,167
8.3214
7.7944
-2.1159
-3.4449
0.0392
0.1969
3.3009
4.3291
1.7238
-3.4203
t-statistic
0.2771
-0.0173
-0.0048
0.0000
-0.0212
0.0334
2.0864
0.0003
-0.1499
1.0842
Coefficient
0.61%
82,739
t-statistic
Coefficient
Funds over $ 15 mil.
3.1060
0.0313
5.5722
1.7014
1.2531
0.0003
-0.2322
-2.1872
8.3552
0.4635
7.3189
0.2716
-1.2042
-0.0172
-2.2161
-0.0049
0.0862
0.0000
-0.2606
-0.0281
Dependent Variable:
Determinants of inter-factor timing T O2.
The model (5.2) is estimated at time t − 1 then at time t. The inter-factor timing measures the
number of factor that dropped from the funds’ exposures plus the number of factors the fund
started being exposed to from t − 1 to t.
Table 8.14:
0.67%
82,739
7.3993
7.2291
-1.2214
-2.2724
-0.0264
-0.3444
2.9269
4.5282
1.2233
-3.3981
t-statistic
TO2
71
The link between R2 and fund fees.
Adjusted R2 of regression
const
Mean Excess Returns
Sharpe Ratio
Management Fee
Incentive Fee
Dependent
0.4291
-0.0556
0.07%
102.8040
-2.0421
-3.0605
-0.0186
1.17%
74.6021
0.4399
t-stat
-0.0339
0.4713
Coef
0.91%
-4.5487
44.4271
t-stat
-0.0056
0.5183
Coef
2.04%
-11.3786
58.9489
t-stat
-0.0056
-0.0184
0.5326
Coef
3.19%
-11.4321
-3.0507
54.1895
t-stat
Coef
-0.0186
-0.0346
-0.0056
0.5804
4.15%
-3.0200
-5.1037
-11.4938
44.0571
t-stat
Coef
Coef
t-stat
R-square
Variable:
R2 ’s of the fund with respect to an exhaustive set of systematic factors care regressed on fees. Fees are related to R2 even after controlling for
Sharpe ratios and raw returns.
Table 8.15:
72
Stepwise regression vs. Principal components goodness of fit.
P34
0.0006
0.0332
0.3982
1.9649
10.724
0.0010
0.0791
0.6453
2.6393
20.5660
0.0045
0.409
2.1402
6.6221
54.0681
5th
25th
50th
75th
95th
5th
25th
50th
75th
95th
5th
25th
50th
75th
95th
Stepwise
0.0005
0.0167
0.2289
1.3934
8.2157
0.0001
0.0059
0.0705
0.6089
4.4015
5th
25th
50th
75th
95th
5th
25th
50th
75th
95th
0.0001
0.0045
0.0424
0.4252
3.8706
5th
25th
50th
75th
95th
Stepwise
0.4128
2.1469
4.226
7.4305
12.6552
0.2326
1.1592
2.6098
4.7152
8.8259
0.1112
0.776
1.8253
3.7316
7.2368
0.3422
1.9728
4.2562
6.9316
12.129
0.2078
1.0772
2.6547
4.7633
8.6219
5
0.0963
0.8129
1.8966
3.5044
7.2898
0.395
2.0419
4.0945
7.2617
12.3001
0.2260
1.1154
2.5158
4.5037
8.6149
0.0923
0.7321
1.7651
3.5884
7.011
24 months history
Panel B:
0.0926
0.6837
1.6644
3.3553
6.7443
holds
0.2177
1.0367
2.2479
4.1401
8.2041
holds
0.3836
1.8726
3.7838
6.6829
11.6437
Fund
0.2169
1.0962
2.3420
4.3273
8.3445
Fund
0.3889
1.9763
3.9075
6.9889
12.0878
holds
0.2871
1.7532
3.8386
6.2922
11.2975
0.0927
0.6989
1.69
3.417
6.9045
Fund
0.2889
1.8349
3.9366
6.3922
11.6054
holds
holds
0.1644
0.9598
2.4003
4.3717
7.8541
Fund
0.1750
1.0117
2.5000
4.4586
8.0012
Fund
8
0.0832
0.6505
1.6843
3.0878
6.4751
holds
7
0.0854
0.6917
1.7504
3.2623
6.7747
Fund
Entire history
0.3008
1.9392
4.0919
6.7303
12.042
0.1773
1.0305
2.5611
4.5881
8.2466
6
0.0901
0.7305
1.793
3.3824
7.0561
Panel A:
1–10
0.3731
1.7829
3.6521
6.4203
11.2178
1–5
0.2066
0.9995
2.1757
3.9903
7.9086
0.0974
0.6678
1.6248
3.2177
6.6679
Principal
1–3
0.2523
1.6429
3.7316
6.0814
10.8034
1–10
1–5
0.1559
0.9094
2.2972
4.2098
7.5084
9
0.0758
0.6243
1.6189
2.9971
6.3151
Principal
1–3
factors
0.3784
1.748
3.5436
6.1507
10.9514
factors
0.2105
0.9875
2.0890
3.8795
7.7715
0.1056
0.6464
1.5826
3.1192
6.4628
factors
0.2139
1.5898
3.509
5.9128
10.5786
factors
factors
0.1477
0.8488
2.1730
3.9938
7.4333
10
0.0754
0.6074
1.5184
2.8948
6.2375
factors
0.3835
1.645
3.3791
5.8724
10.5735
0.2186
0.9261
2.0231
3.7976
7.4963
0.1064
0.6094
1.5144
2.9688
6.3216
Components
0.2078
1.5348
3.3976
5.5732
10.2806
0.1330
0.8281
2.0272
3.8137
7.3487
11
0.0762
0.5463
1.4573
2.7753
5.9294
Components
0.3739
1.6379
3.3098
5.6119
10.2542
0.2192
0.9047
1.9540
3.6162
7.2950
0.118
0.6099
1.4702
2.8734
6.2224
0.1997
1.4693
3.2243
5.4343
9.4435
0.1249
0.7824
1.9016
3.6730
7.0267
12
0.0708
0.5277
1.3766
2.6729
5.7499
0.3551
1.59
3.1792
5.4141
10.1234
0.2196
0.8861
1.9502
3.5261
7.0942
0.1248
0.6067
1.4628
2.8356
5.9364
0.181
1.412
3.0213
5.2021
9.0744
0.1205
0.7169
1.8104
3.5193
6.8754
13
0.063
0.4883
1.2816
2.5626
5.5738
0.3511
1.5817
3.1151
5.2542
9.7521
0.2108
0.8779
1.9013
3.4424
7.0530
0.1352
0.626
1.4188
2.7938
5.8114
0.1649
1.2458
2.8872
4.9472
8.7103
0.1100
0.6382
1.6740
3.3926
6.7625
14
0.0601
0.4333
1.209
2.4231
5.4058
0.364
1.5178
3.0059
5.1933
9.3876
0.2066
0.8898
1.8947
3.4434
7.0300
0.144
0.6468
1.4141
2.7719
5.6741
0.1612
1.1427
2.7179
4.757
8.3085
0.1060
0.6083
1.5948
3.2205
6.5826
15
0.0591
0.4086
1.1282
2.336
5.2101
0.3658
1.5095
2.9896
5.1849
9.1449
0.2055
0.9017
1.9063
3.4153
7.1437
0.1475
0.6734
1.4636
2.8199
5.6754
0.1457
1.0331
2.5862
4.4797
7.8198
0.0781
0.5456
1.5038
2.9971
6.4722
16
0.0471
0.3479
1.0427
2.2894
4.9446
bk using stepwise regression or principal components (5 to 16 components are used). For each method, the quantity k=1 |βbk − β k |2 , which
of the betas, β
represents the distance between the true betas and their estimation, is calculated. The distribution of this difference is presented in the Table. Panel A
presents the case when the estimation is run over 120 months, while Panel B presents the case when the estimations are run over random periods of 24
months. There are 10,000 simulations in each case.
Distributions of the differences between true betas and betas estimated by stepwise regression of by factor analysis, P
under the null that funds bear a certain
34
number of randomly weighted systematic risks. For each simulated fund whose returns are given by Rtf und −rf = α+ k=1 β k Ftk +²t , we produce estimators
Table 8.16:
Table 8.17:
Average Sharpe ratios and R-squares for hedge fund strategies.
Funds are classified into strategies using Sharpe (1992) regressions and average Sharpe ratios and
R-squares with respect to a comprehensive set of risk factors are calculated.
Short Selling
Relative Value Arbitrage
Macro
Fixed Income Arbitrage
Event Driven
Equity Market Neutral
Emerging Markets
Distressed Securities
Convertible Arbitrage
Mean R-square
0.4029
0.3605
0.3894
0.3666
0.5411
0.2954
0.4769
0.3983
0.2760
73
Mean Sharpe ratio
0.5426
1.0876
0.6137
0.9132
0.7598
1.0440
0.5881
1.0035
1.2968
Table 8.18:
Robustness check: repeating out hypothesis tests by strategy.
Short Selling (500 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
low R2
med R2
high R2
0.0876
0.3601
0.7504
0.5780
0.7552
0.3020
1.5095
1.3936
1.3179
18.4434
20.0133
18.3843
45.8779
27.1642
25.6438
66.6667
65.3212
51.7118
0.6970
0.7515
0.7000
low-high mean
low-high t-stat
-0.6628
-58.0526
0.2760
1.5836
0.1916
2.5501
0.0591
0.0982
20.2341
1.5702
14.9549
2.6400
-0.0030
-0.0602
Relative Value Arbitrage (528 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.0869
0.3384
0.6465
1.2929
1.0415
0.9337
1.3882
1.2516
1.3981
16.4225
15.5948
14.5861
42.0909
40.7858
98.5649
72.0575
69.0632
48.2167
0.7816
0.8333
0.7556
low-high mean
low-high t-stat
-0.5595
-41.2381
0.3593
2.6767
-0.0098
-0.1537
1.8364
2.3368
-56.4740
-1.1439
23.8408
4.4663
0.0261
0.5795
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.1295
0.3628
0.6673
0.6340
0.5779
0.6286
1.6984
1.6811
1.3124
18.1336
16.2985
14.5163
51.4024
132.1998
58.9728
85.8764
81.1517
61.8392
0.7612
0.7107
0.6649
low-high mean
low-high t-stat
-0.5378
-58.7237
0.0055
0.0847
0.3860
7.0427
3.6172
7.1709
-7.5704
-0.5027
24.0372
5.8824
0.0964
2.8746
Macro (1079 funds)
Fixed Income Arbitrage (346 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.0637
0.2983
0.7252
0.9103
0.8431
0.9838
1.4252
1.7763
1.5312
18.9942
17.3202
15.6412
46.2808
38.0041
114.5614
63.7982
60.5000
26.8644
0.5965
0.7368
0.7288
low-high mean
low-high t-stat
-0.6616
-42.3199
-0.0735
-0.3080
-0.1061
-0.6072
3.3529
3.8013
-68.2805
-0.8482
36.9338
9.8339
-0.1323
-2.1448
Event Driven (1640 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.2730
0.5605
0.7822
1.0092
0.6714
0.6039
1.2539
1.1860
1.2080
17.2878
16.8510
15.7008
38.8002
28.4088
46.7416
73.6913
76.0351
77.4301
0.7616
0.7726
0.7366
low-high mean
low-high t-stat
-0.5093
-72.1377
0.4052
6.6809
0.0459
1.3337
1.5870
3.8345
-7.9414
-1.0038
-3.7388
-1.0262
0.0250
0.9547
continued on the next page . . .
74
Equity Hedge (444 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.0172
0.2406
0.6194
1.6161
0.7659
0.7558
1.3320
1.3281
1.2775
18.6723
17.2541
17.8576
170.6210
57.8628
57.7703
55.3605
65.8699
40.1722
0.7891
0.7260
0.6887
low-high mean
low-high t-stat
-0.6022
-39.2235
0.8603
1.5068
0.0545
0.9581
0.8147
1.3361
112.8507
0.8973
15.1884
3.4067
0.1004
1.9770
Emerging Markets (1050 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.2008
0.4872
0.7353
0.7692
0.5618
0.4375
1.3810
1.3575
1.3179
17.3804
15.7746
14.3870
42.0243
32.5751
28.5119
56.5447
68.0116
61.3585
0.6916
0.7139
0.7255
low-high mean
low-high t-stat
-0.5345
-57.6295
0.3318
3.6362
0.0630
1.8271
2.9934
5.7631
13.5123
1.1330
-4.8139
-1.4585
-0.0338
-0.9876
(cont.)
Distressed Securities (462 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.1084
0.3699
0.7066
1.3228
0.9106
0.7849
1.3563
1.3651
1.2447
17.5164
15.2903
13.7480
61.1693
37.3040
38.7168
74.7829
67.2614
44.3248
0.7961
0.6667
0.4331
low-high mean
low-high t-stat
-0.5982
-41.6203
0.5380
3.1881
0.1116
2.1775
3.7685
4.7815
22.4525
1.0917
30.4581
5.1302
0.3629
7.0281
Convertible Arbitrage (476 funds)
R2
SR
mfee
ifee
aum25
Life
Alive
2
low R
med R2
high R2
0.0238
0.2139
0.5805
1.4052
1.3873
1.1042
1.5207
1.4022
1.2737
18.1985
16.8185
15.1687
59.5569
73.4153
41.8154
52.6752
66.2038
45.4444
0.8280
0.7771
0.7160
low-high mean
low-high t-stat
-0.5567
-32.6518
0.3010
2.2426
0.2470
3.2196
3.0298
4.2289
17.7415
1.1112
7.2307
1.5641
0.1120
2.3940
75
Table 8.19:
The relationship between appraisal ratios and R-squares.
We repeat our analysis, that low R-square is associated with good quality funds, using the appraisal
ratio as a proxy for performance instead of the Sharpe ratio.
R2
IR
mfee
ifee
aum25
Life
Alive
low R2
med R2
high R2
0.1180
0.4056
0.6988
0.1745
0.1161
-0.1433
1.4753
1.3627
1.2598
17.7729
16.5946
15.5176
58.1031
55.2410
45.0337
69.1581
69.8308
64.2132
0.7492
0.7428
0.6987
low-high mean
low-high t-stat
-0.5809
-178.3719
0.3178
3.9397
0.2155
9.0955
2.2552
10.8607
13.0694
1.2086
4.9449
3.0972
0.0505
3.6717
76
Altvest
HFR
13 %
18 %
29 %
15 %
7%
5%
13 %
TASS
Figure 8.1:
Distribution of data across databases merged.
77
900
Total Assets Under Management (bil)
800
700
600
500
400
300
200
100
0
1988
Figure 8.2:
1990
1992
1994
1996
1998
2000
2002
Estimated Total Assets Under Management in the hedge fund industry.
78
Figure 8.3:
Estimated Quarterly Flows into the hedge fund industry.
79
4%
5%
7%
1%
2%
< 1%
<<1%
1%
11%
24%
< 1%
Short Selling
Relative Value Arbitrage
Merger Arbitrage
Macro
Fixed Income Arbitrage
Event Driven
25%
Equity non Hedge
Equity Market Neutral − Stat Arb
Equity Market Neutral
Equity Hedge
Emerging markets
Distressed Securities
Convertible Arbitrage
COnvertible Bonds
Managed Futures
25%
18%
< 1%
Figure 8.4:
Assets under management distributed across strategies, when the strategies
are inferred using Sharpe regressions.
80
low Rsqr − high Rsqr
3
2
1
0
−1
1997
1998
1999
2000
2001
2002
2003
1998
1999
2000
2001
2002
2003
1998
1999
2000
Time
2001
2002
2003
low TO1 − high TO1
1
0.5
0
−0.5
−1
1997
low TO2 − high TO2
1
0.5
0
−0.5
−1
1997
Figure 8.5:
Differences in the means of the Sharpe ratios between groups of Low - High
Rsqr, T O1, T O2.
Each month from December 1997 to December 2002 the hedge funds are sorted based on their
Rsqr, T O1, T O2, and the average Sharpe ratios are computed across the lowest, respectively the
highest Rsqr, T O1, T O2 deciles. These differences are plotted. A star on the x-axis signifies that
the difference in means between the low and high Rsqr, T O1, T O2 deciles is significant at 5%.
81
low Rsqr − high Rsqr
low TO1 − high TO1
300
200
100
0
−100
1997
1999
2000
2001
2002
2003
1998
1999
2000
2001
2002
2003
1998
1999
2000
Time
2001
2002
2003
100
0
−100
−200
−300
1997
low TO2 − high TO2
1998
100
50
0
−50
−100
1997
Figure 8.6:
Differences in the means of the assets under management between groups of
Low - High Rsqr, T O1, T O2.
Each month from December 1997 to December 2002 the hedge funds are sorted based on their
Rsqr, T O1, T O2, and the average assets under management are computed across the lowest,
respectively the highest Rsqr, T O1, T O2 deciles. These differences are plotted. A star on the
x-axis signifies that the difference in means between the low and high Rsqr, T O1, T O2 deciles is
significant at 5%.
82
low Rsqr − high Rsqr
low TO1 − high TO1
1
0.5
0
1997
1999
2000
2001
2002
2003
1998
1999
2000
2001
2002
2003
1998
1999
2000
Time
2001
2002
2003
0.2
0.1
0
−0.1
−0.2
1997
low TO2 − high TO2
1998
0.2
0.1
0
−0.1
−0.2
1997
Figure 8.7:
Differences in the means of the management fees between groups of Low High Rsqr, T O1, T O2.
Each month from December 1997 to December 2002 the hedge funds are sorted based on their
Rsqr, T O1, T O2, and the average management fees are computed across the lowest, respectively
the highest Rsqr, T O1, T O2 deciles. These differences are plotted. A star on the x-axis signifies
that the difference in means between the low and high Rsqr, T O1, T O2 deciles is significant at
5%.
83
low Rsqr − high Rsqr
low TO1 − high TO1
low TO2 − high TO2
6
4
2
0
−2
−4
1997
1998
1999
2000
2001
2002
2003
1998
1999
2000
2001
2002
2003
1998
1999
2000
Time
2001
2002
2003
4
2
0
−2
1997
2
1
0
−1
1997
Figure 8.8:
Differences in the means of the incentive fees between groups of Low - High
Rsqr, T O1, T O2.
Each month from December 1997 to December 2002 the hedge funds are sorted based on their
Rsqr, T O1, T O2, and the average incentive fees are computed across the lowest, respectively the
highest Rsqr, T O1, T O2 deciles. These differences are plotted. A star on the x-axis signifies that
the difference in means between the low and high Rsqr, T O1, T O2 deciles is significant at 5%.
84
% of cases when stepwise regression is better than princ. comp.
90
85
whole history, 3 factors
whole history, 5 factors
80
whole history, 10 factors
2 years history, 3 factors
2 years history, 5 factors
75
2 years history, 10 factors
70
65
60
4
6
Figure 8.9:
8
10
12
Number of principal components used
14
16
Stepwise regressions vs. principal components fit.
For each simulated fund whose returns are given by Rtf und −rf = α+
P34
k=1
β k Ftk +²t , we produce
estimators of the betas, b using stepwise regression or principal components (5 to 16 components
P34
bk − β k |2 , which represents the distance between
|β
are used). For each method, the quantity
k=1
the true betas and their estimation, is calculated. This figure represents the percentage of cases
in which this distance is smaller in the case the stepwise regression was used than in the case a
number of principal components were used.
βk
85
140
120
Number of funds
100
80
60
40
20
0
0
50
Figure 8.10:
100
Months backfilled
150
200
Length of backfilled histories in TASS.
The TASS database reports the time at which hedge funds join. The figure above represents a
histogram of the lengths of the backfilled histories of funds in the TASS database between January
1994 and December 2003.
86
350
300
|I−J|2
250
200
150
100
0
10
20
30
40
50
Months cut
Figure 8.11:
Backfill bias correction.
TASS database reports the date at which a fund joins. By eliminating a number of months n
from a fund’s history and comparing the database-reported index I with the index replicated
after removing the first months of data J, we can infer the number n for which the difference
P
|I(t) − J(t)|2 is minimized.
t
87
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93
Vita
Cristian Ioan Tiu was born in Giurgiu, Romania on 22 January 1975, the son of
Ionel and Elena Tiu. He received a Bachelor of Science degree in Mathematics from
the University of Bucharest in 1998 and a PhD in Mathematics from the University
of Texas at Austin in 2002. He is married to Mariana Tiu and has two children, a
son, Andrei and a daughter, Ioana (Ellie) .
Permanent Address: 3573 E Lake Austin Blvd., Austin, TX 78703
This dissertation was typeset with LATEX 2ε 5 by the author.
5 A
LT
EX 2ε is an extension of LATEX. LATEX is a collection of macros for TEX. TEX is a trademark of
the American Mathematical Society. The macros used in formatting this dissertation were written
by Dinesh Das, Department of Computer Sciences, The University of Texas at Austin, and extended
by Bert Kay, James A. Bednar, and Ayman El-Khashab.
94