Description
This study aims to explore whether a regularly updated portfolio of outperforming hedge funds can
consistently beat the corresponding hedge fund dataset index. If yes, moreover, the second question
concerns whether portfolio optimization approaches can lead to an even better performance than the
naïve equal-weighting method. The dataset spans the January-1994 to August-2008 period and is classified
into four main categories - Macro, Equity Hedge, Relative Value and Event Driven. Based on a
seven-factor model, this study applies the Step-SPA test to each category of funds and examines the
statistical significance of the studentized fund alpha over the selection period of 3e7 years in length. A
‘winner’ portfolio of funds, namely, consisting of funds with statistically significant, positive studentized
alpha, can be formed at the end of the selection period and held for 1 up to 3 years. We find that the
winner portfolio tends to beat the dataset indexes during the holding period, irrespective of the time
span for the selection and the holding periods investigated. Moreover, two of the three optimization
approaches employed, the Probabilistic Global Search Lausanne and the Genetic Algorithm, prove to
further enhance the performance of the equal-weighted winning portfolio.
Can hedge fund elites consistently beat the benchmark? A study of portfolio
optimization
St
ephane Meng-Feng Yen
a, 1
, Ying-Lin Hsu
b, 2
, Yi-Long Hsiao
c, *
a
Department of Accounting and Graduate Institute of Finance, National Cheng Kung University, Taiwan
b
Department of Applied Mathematics, National Chung Hsing University, Taiwan
c
Department of Finance, National Dong Hwa University, Taiwan
a r t i c l e i n f o
Article history:
Received 15 October 2014
Accepted 9 April 2015
Available online 26 July 2015
Keywords:
Hedge funds
Step-SPA test
GA
PGSL
Performance persistence
a b s t r a c t
This study aims to explore whether a regularly updated portfolio of outperforming hedge funds can
consistently beat the corresponding hedge fund dataset index. If yes, moreover, the second question
concerns whether portfolio optimization approaches can lead to an even better performance than the
naïve equal-weighting method. The dataset spans the January-1994 to August-2008 period and is clas-
si?ed into four main categories - Macro, Equity Hedge, Relative Value and Event Driven. Based on a
seven-factor model, this study applies the Step-SPA test to each category of funds and examines the
statistical signi?cance of the studentized fund alpha over the selection period of 3e7 years in length. A
‘winner’ portfolio of funds, namely, consisting of funds with statistically signi?cant, positive studentized
alpha, can be formed at the end of the selection period and held for 1 up to 3 years. We ?nd that the
winner portfolio tends to beat the dataset indexes during the holding period, irrespective of the time
span for the selection and the holding periods investigated. Moreover, two of the three optimization
approaches employed, the Probabilistic Global Search Lausanne and the Genetic Algorithm, prove to
further enhance the performance of the equal-weighted winning portfolio.
© 2015 College of Management, National Cheng Kung University. Production and hosting by Elsevier
Taiwan LLC. All rights reserved.
1. Introduction
The industry of hedge funds has consistently performed well
except in the year of 2008 when a ?nancial tsunami occurred as a
result of a substantial subprime mortgage default. Previous evi-
dence in the literature has shown from a variety of perspectives
that the hedge fund elites, namely, those beating the benchmarks,
are capable of consistently remaining outperformers over time.
Moreover, most previous efforts have ignored the data-snooping
bias problem. Controlling for the data-snooping bias, Kosowski,
Naik, and Teo (2007) apply the cross-sectional alpha bootstrap
technique, introduced by Kosowski, Timmermann, Wermers and
White (2006), to examine the statistical signi?cance of each
hedge fund's alpha in the presence of a large quantity. Their test
allows us to know whether a hedge fund whose alpha ranks with a
certain place delivers a statistically signi?cant alpha with that
certain ranking. Based on the bootstrapped alpha distribution
constructed by extracting and ranking from small to large the
bootstrapped alpha under each of a large number of, say 1000,
resamples, in particular, the observed sample alpha of a hedge fund
can be compared to such a bootstrapped distribution which then
leads to the p-value and statistical signi?cance according to a given
level of signi?cance. Similarly, Romano and Wolf (2005) pioneer an
alternative approach, known as the stepwise reality check (SRC), to
mitigating the adverse effect of data-snooping bias in the context of
large-scale multiple hypothesis testing. Instead of testing the null
hypothesis for each single hedge fund using its corresponding
bootstrapped distribution, Romano and Wolf's method focuses on
the bootstrapped distribution for the best-performing fund's alpha
and screens all resulting outperformers. Due to the different char-
acteristics of these two alternatives, conducting the former
approach is more time-consuming than the latter although they
tend to generate different statistical inferences. However, both
studies above select only a ?xed sample period for testing the
* Corresponding author. No. 1, Sec. 2, Da-Hsueh Road, Shou-Feng, Hualien 974,
Taiwan. Tel.: þ886 3 863 3147; fax: þ886 3 863 3130.
E-mail address: [email protected] (Y.-L. Hsiao).
Peer review under responsibility of College of Management, National Cheng
Kung University.
1
Tel.: þ886 6 275 7575x53443; fax: þ886 6 274 4104.
2
Tel./fax: þ886 4 2285 1590.
HOSTED BY
Contents lists available at ScienceDirect
Asia Paci?c Management Review
j ournal homepage: www. el sevi er. com/ l ocat e/ apmrvhttp://dx.doi.org/10.1016/j.apmrv.2015.04.001
1029-3132/© 2015 College of Management, National Cheng Kung University. Production and hosting by Elsevier Taiwan LLC. All rights reserved.
Asia Paci?c Management Review 20 (2015) 275e284
statistical signi?cance of the fund alphas without considering the
effect of a structural change of the hedge fund dataset on their
results. Also, they both fail to test the statistical signi?cance of the
alpha of the identi?ed hedge fund elites as a whole over the holding
period.
Another main issue that has been ignored in the literature of
hedge fund research involves the portfolio optimization. One
possible cause for the dearth of such efforts might be the size of the
amount for initial investment. Given that it is not extraordinary for
the typical hedge fund to require an initial investment of 200,000
USD up to 1,000,000 USD, the issue of constructing and managing a
portfolio for hedge funds only concerns fund of hedge funds, sizable
endowment funds, pension funds or other large ?nancial in-
stitutions, rather than wealthy individuals. However, if the union of
accessible hedge funds are reduced to only a few, e.g., less than ten,
elites, a portfolio with optimized weights on component funds will
be attractive to and much more affordable for both large ?nancial
institutions and individual wealthy investors.
It is the main thrust of this study to, in the ?rst place, investigate
whether the performance of outperforming hedge funds sustains
over the holding period of a variety of length in time while using a
recently proposed test, the stepwise test for superior predictive
ability (or Step-SPA test introduced by Hsu, Hsu, & Kuan, 2010;
hereafter HHK), to control for the data-snooping bias. The Step-SPA
test improves on the test power of Romano and Wolf's SRC. Second,
this study endeavors to extend the effort above to test whether
portfolio optimization techniques would enhance the performance
of an equal-weighted portfolio of hedge funds outperformers.
Having surveyed the recent development in the literature of opti-
mization techniques for portfolio, this study applies the recently-
developed probability global search Lausanne (hereafter PGSL),
the commonly-adopted genetic algorithm (hereafter GA) as well as
the outdated NewtoneRaphson algorithm (hereafter NR) as a
benchmark. In this study, empirical results suggest that both
equally-weighted and weights-optimized portfolios of good hedge
funds screened by the Step-SPA test are generally able to outper-
form the corresponding HFR database index.
The rest of the article is organized as follows. Section 2 reviews
the literature on performance persistence of hedge funds and on
portfolio optimization. Section 3 brie?y documents the dataset, the
three optimization methods and the Step-SPA test while Section 4
discusses the empirical results and brings about some implications
of them. Section 5 concludes.
2. Literature review
2.1. Performance persistence of hedge funds
Two main approaches to testing the performance persistence of
mutual funds or hedge funds have been developed in the literature.
The ?rst approach examines the entire universe of funds using
either the contingency table-based (nonparametric) method or the
regression-based (parametric) method. In particular, a fund is
referred to as a winner (loser) if its risk-adjusted return (alpha value
or information ratio) is larger than (less than) the mean or median
of the entire sample of funds. Following this categorization,
Goetzmann and Ibbotson (1994), Brown and Goetzmann (2003)
apply the Cross Product Ratio (CPR) test (also known as the Odds
Ratio test) to test whether past winners (losers) tend to be next
winners (losers). The CPR is given by
CPR ¼
ðno: of winners at tÞ Â ðno: of winners at t À1Þ
ðno: of losers at tÞ Â ðno: of losers at t À1Þ
:
Accordingly, the CPR equals 1 under the null hypothesis of no
persistence. The test statistic of the null hypothesis is given by
z ¼
logðCPRÞ
StdðlogðCPRÞÞ
;
where Std(log(CPR))¼
Under the assumption of independent observations, this z-sta-
tistic will follow a standard normal distribution asymptotically.
Agarwal and Naik (2000) adapt the method for multi-periods.
Given a series of nine consecutive periods, for instance, the proba-
bility for a fund to be winner for nine straight periods is (0.5)
9
under
the null hypothesis of no persistence. The probability for a fund to
be winner for ?ve straight periods and then loser for the remaining
four periods is (0.5)
5
. In this context, the Kolmogrov-Smirnov (KeS)
test is employed to test whether the observed probability for a fund
to be winner in all scenarios is signi?cantly different from its
theoretical counterpart as illustrated above. Statistical signi?cance
of the KeS test would then indicate performance persistence.
In contrast with the non-parametric approach above, Edwards
and Caglayan (2001) and Agarwal and Naik (2000) explore this
issue using a regression-based (parametric) method. In particular,
they calculated the risk-adjusted return (e.g., the alpha value by a
factor model) for a series of consecutive periods. The alpha values of
all funds of period tþ1 are regressed upon those of period t. For the
case of 10 consecutive sample periods, such regression will be
performed nine times and one can apply the FamaeMacbeth test to
check if the mean of the nine slope estimates is signi?cantly posi-
tive. If yes, the universe of funds tested demonstrate performance
persistence.
The second main approach, in contrast, sorts all funds into
different equally-weighted portfolios according to the funds' per-
formance (e.g., return in excess of the risk-free rate or risk-adjusted
return) during the portfolio-formation period, and tests whether
each portfolio's performance, if statistically signi?cant, persists into
the portfolio-holding period. Parametric (standard) p-value or
KTWW's cross-sectionally bootstrapped p-value is used to test
whether the portfolio's alpha value is statistically signi?cant. Their
relative performance, i.e., the spread between the returns of the
best portfolio and the poorest portfolio, can also be tested in this
way to see if it persists across time. (See Carhart (1997)).
The factor models such as CAPM, Sharpe's (1966) single-factor
model, three-factor model built by Fama and French (1993), and
Carhart's (1997) four-factor model are commonly used to evaluate
the abnormal returns of mutual funds. Mr. Lynch really owned
talent and skill in selecting underpriced stocks. Chen, Jegadeesh,
and Wermers (2000) study the stock positions and active trades
???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
1
no
f ðwinner
tÀ1
; winner
t
Þ
þ
1
nof ðwinner
tÀ1
; loser
t
Þ
þ
1
nof ðloser
tÀ1
; winner
t
Þ
þ
1
nof ðloser
tÀ1
; loser
t
Þ
s
S.M.-F. Yen et al. / Asia Paci?c Management Review 20 (2015) 275e284 276
of mutual funds and ?nd that managers of growth-oriented mutual
funds do possess skill in ?nding underpriced large-cap growth
?rms. Similarly, KTWW discover that quite a few managers of
American, domestic, open-end mutual funds are able to pick
underpriced stocks, which is also true even based upon net-of-fee
fund returns.
2.2. Portfolio optimization
Regarding the development on optimization, the literature has
witnessed a signi?cant amount of efforts dedicated to this issue. As
a conventional numerical method, Newton's (1736) approach
draws on a function's derivatives to approach the optimal solution,
which however does not guarantee global optimum. Given the
rapid improvement on PCs' computation ef?ciency over the past
decades, however, a variety of global search algorithms for the
optimal solution have been proposed with respect to different
practical problems. Since these algorithms involve iterative
computation, they are quite time-consuming and would have been
infeasible without the aid of mighty computation ability. For
instance, Gilli and Kellezi (2001) employ a global search approach
to optimizing a portfolio's weights on individual assets. Maringer
and Parpas (2009) apply a global search algorithm to optimize
the higher order moments in portfolio selection. Krokhmal,
Palmquist, and Uryasev (2002) devise a global search approach to
optimizing the expected returns of a portfolio given constraints on
the portfolio's conditional value-at-risk. For hedge funds, Minsky,
Obradovic, Tang, and Thapar (2009) survey the following global
optimization algorithms for adjusting the portfolio weights.
2.2.1. Newton's method
In the book, entitled ‘Method of Fluxions,’ Newton introduces
this seminal numerical approach to ?nding the optimal solution of
a function. It uses a tangent line on the objective function to
approach the function's solution, which is analytically insoluble.
Many extensions to the basic Newton's method have appeared in
the literature such as Broyden, Dennis, and Mor e’s (1973) quasi-
Newton method.
2.2.2. Genetic Algorithm (GA)
Based on the principle of natural selection in the course of living
being's evolution, Holland (1975) introduces the genetic algorithm.
Goldberg and Lingle (1985) applies it to the problem of optimiza-
tion. In the context of portfolio construction, the GA selects weights
on individual asset at random from the current population weight
range for each asset to be parents. They are then used to generate
the children for the next generation via crossing over the parents.
During the process of the population's evolution toward an optimal
solution, the GA allows a small probability for mutation.
2.2.3. Simulated annealing
Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953)
documents the simulated annealing algorithm. It concerns using
a probability search algorithm model that simulates the physical
process of heating a material and then gradually cooling down its
temperature to avoid defects, thus minimizing the system energy.
At each step of the simulated annealing algorithm, the current
solution is replaced by another solution which is selected
depending on the difference between the functional values at the
two points and the temperature variable, which is systematically
lowered during the process. However, this method does not ensure
global optimum. Kirkpatrick (1983) improves on Metropolis et al.’s
(1953) work and provides a similar but better algorithm.
2.2.4. Probabilistic Global Search Lausanne (PGSL)
Raphael and Smith (2003) propose a global search algorithm
based on the simulated annealing method mentioned above.
Following an initial global search based on a uniform distribution
assumed for all variables depending on the value of the target
function, the PGSL intensi?es the probability density on regions
corresponding to a good value of the target function. By iteratively
increasing the probability density for regions of a good solution and
reducing the search space along these regions, the PGSL approaches
the optimal solution.
2.2.5. Pattern search
The Pattern Search randomly selects a point (value) for each of
all driving variables along the initial search space. Each of these
initial values is multiplied by a vector (of a constant or variable
length) to form a region for further search. If any new point within
each generated region corresponds to a better solution for the
target function, the initial point is replaced by the new point.
Multiplying the new point by the vector above constructs a new
search region which substitutes for the previous search region.
Iteration of such a procedure will lead to the optimal solution. If the
vector length is constant, such a method is called the Generalized
Pattern Search (GPS). If the vector is of a variable length, in parallel,
this method is called the Mesh Adaptive Search (MADS).
Minsky et al. (2009) suggest that the PGSL performs best among
the methods introduced above in 21 out of 24 scenarios of
nonlinear optimization problems. As a result, we apply this method
in the following analysis. Due to its popularity in portfolio opti-
mization, however, the study also includes the GA as a benchmark
approach in addition to the Newton Raphson method.
3. Data and methodology
3.1. Data
The dataset was bought from the Hedge Fund Research, Inc and
spans the September 1994 to August 2008 period. During the sample
period, a total of 13098 hedge funds are covered by the dataset,
including 5023 funds still existent by the end of our sample period,
August 2008, and 8075 defunct funds.
3
Including the universe of
defunct funds help purge our results of the survivorship bias. As our
focus is onthebene?ts of usinga portfoliooptimizationtechnique on
its performance, we also categorize the dataset into ?ve sub-samples
according to the main strategy de?nedby the dataset vendor, HFR. In
particular, the?vestrategies are Marco, Event-Driven, Relative Value,
Equity Hedge, andFund of Funds. The monthly returns of each hedge
fund, net of all fees, are enteredintoour workhorse, theStep-SPAtest,
to screen signi?cant outperforming funds.
3.2. Step-SPA test
The literature substantially implements the bootstrap method
to control for the data-snooping bias. White (2000) pioneers the
use of bootstrapping by introducing the Bootstrap Reality Check
(hereafter BRC). White's BRC tests the null hypothesis under which
the best model (strategy) in a large group of competitors cannot
beat the benchmark model (strategy) in terms of a speci?c loss
function (e.g., average daily returns for funds). However, the BRC
method is less effective when the sample contains too many
underperforming models (strategies). In light of this drawback,
3
Funds might be moved from the live funds list to the defunct funds list for
reasons such as liquidation due to bad performance, having been closed to new
investors due to unmanageable size, being merged by other funds and so on.
S.M.-F. Yen et al. / Asia Paci?c Management Review 20 (2015) 275e284 277
Hansen (2005) devised a superior predictive ability (SPA) test,
which increases the rejection rate of the null hypothesis by
reducing the number of poor models in the sample. A drawback of
both the BRC and the SPAtest is that they only test the best model of
the entire union. In the context of portfolio management, however,
a fund-of-funds manager is inclined to pick as many good indi-
vidual funds as possible. Thus, this study incorporates the Step-SPA
test to screen as many good hedge funds as possible while con-
trolling for the data-snooping bias.
For a typical investor who allocates assets among hedge funds or
for a fund-of-funds manager, the challenge is how to identify
genuinely pro?table individual hedge funds but exclude at the
same time the lucky ones. To state this problem in mathematical
formulation, let n be the number of models for some variable and
let d
k,t
(k ¼ 1, 2, …, n and t ¼ 1, 2, …, T) denote their performance
measures (relative to a benchmark model). For each k, let E(d
k,t
)¼m
k
denote the mean of the k-th rule for all t. For each t, d
k,t
may be
dependent across k. We would like to test the following inequality:
H
k
0
: m
k
0; k ¼ 1; :::; n (1)
In the context of testing the hedge funds’ performance, m
k
may
refer to the alpha value of the k-th hedge fund whose return across t
is measured by a linear multi-factor model. The null hypothesis in
Eq. (1) simply states that none of the total of n hedge funds out-
performs the multi-factor benchmark portfolio.
Following Hansen (2005), HHK assume for {d
t
} ¼ (d
1,t
, …,d
n,t
)’
that {d
t
} is strictly stationary and alpha-mixing of
size À(2þh)(rþh)/(rÀ2) for some r > 2 and h>0,where Ejd
t
j
ðrþhÞ
This study aims to explore whether a regularly updated portfolio of outperforming hedge funds can
consistently beat the corresponding hedge fund dataset index. If yes, moreover, the second question
concerns whether portfolio optimization approaches can lead to an even better performance than the
naïve equal-weighting method. The dataset spans the January-1994 to August-2008 period and is classified
into four main categories - Macro, Equity Hedge, Relative Value and Event Driven. Based on a
seven-factor model, this study applies the Step-SPA test to each category of funds and examines the
statistical significance of the studentized fund alpha over the selection period of 3e7 years in length. A
‘winner’ portfolio of funds, namely, consisting of funds with statistically significant, positive studentized
alpha, can be formed at the end of the selection period and held for 1 up to 3 years. We find that the
winner portfolio tends to beat the dataset indexes during the holding period, irrespective of the time
span for the selection and the holding periods investigated. Moreover, two of the three optimization
approaches employed, the Probabilistic Global Search Lausanne and the Genetic Algorithm, prove to
further enhance the performance of the equal-weighted winning portfolio.
Can hedge fund elites consistently beat the benchmark? A study of portfolio
optimization
St
ephane Meng-Feng Yen
a, 1
, Ying-Lin Hsu
b, 2
, Yi-Long Hsiao
c, *
a
Department of Accounting and Graduate Institute of Finance, National Cheng Kung University, Taiwan
b
Department of Applied Mathematics, National Chung Hsing University, Taiwan
c
Department of Finance, National Dong Hwa University, Taiwan
a r t i c l e i n f o
Article history:
Received 15 October 2014
Accepted 9 April 2015
Available online 26 July 2015
Keywords:
Hedge funds
Step-SPA test
GA
PGSL
Performance persistence
a b s t r a c t
This study aims to explore whether a regularly updated portfolio of outperforming hedge funds can
consistently beat the corresponding hedge fund dataset index. If yes, moreover, the second question
concerns whether portfolio optimization approaches can lead to an even better performance than the
naïve equal-weighting method. The dataset spans the January-1994 to August-2008 period and is clas-
si?ed into four main categories - Macro, Equity Hedge, Relative Value and Event Driven. Based on a
seven-factor model, this study applies the Step-SPA test to each category of funds and examines the
statistical signi?cance of the studentized fund alpha over the selection period of 3e7 years in length. A
‘winner’ portfolio of funds, namely, consisting of funds with statistically signi?cant, positive studentized
alpha, can be formed at the end of the selection period and held for 1 up to 3 years. We ?nd that the
winner portfolio tends to beat the dataset indexes during the holding period, irrespective of the time
span for the selection and the holding periods investigated. Moreover, two of the three optimization
approaches employed, the Probabilistic Global Search Lausanne and the Genetic Algorithm, prove to
further enhance the performance of the equal-weighted winning portfolio.
© 2015 College of Management, National Cheng Kung University. Production and hosting by Elsevier
Taiwan LLC. All rights reserved.
1. Introduction
The industry of hedge funds has consistently performed well
except in the year of 2008 when a ?nancial tsunami occurred as a
result of a substantial subprime mortgage default. Previous evi-
dence in the literature has shown from a variety of perspectives
that the hedge fund elites, namely, those beating the benchmarks,
are capable of consistently remaining outperformers over time.
Moreover, most previous efforts have ignored the data-snooping
bias problem. Controlling for the data-snooping bias, Kosowski,
Naik, and Teo (2007) apply the cross-sectional alpha bootstrap
technique, introduced by Kosowski, Timmermann, Wermers and
White (2006), to examine the statistical signi?cance of each
hedge fund's alpha in the presence of a large quantity. Their test
allows us to know whether a hedge fund whose alpha ranks with a
certain place delivers a statistically signi?cant alpha with that
certain ranking. Based on the bootstrapped alpha distribution
constructed by extracting and ranking from small to large the
bootstrapped alpha under each of a large number of, say 1000,
resamples, in particular, the observed sample alpha of a hedge fund
can be compared to such a bootstrapped distribution which then
leads to the p-value and statistical signi?cance according to a given
level of signi?cance. Similarly, Romano and Wolf (2005) pioneer an
alternative approach, known as the stepwise reality check (SRC), to
mitigating the adverse effect of data-snooping bias in the context of
large-scale multiple hypothesis testing. Instead of testing the null
hypothesis for each single hedge fund using its corresponding
bootstrapped distribution, Romano and Wolf's method focuses on
the bootstrapped distribution for the best-performing fund's alpha
and screens all resulting outperformers. Due to the different char-
acteristics of these two alternatives, conducting the former
approach is more time-consuming than the latter although they
tend to generate different statistical inferences. However, both
studies above select only a ?xed sample period for testing the
* Corresponding author. No. 1, Sec. 2, Da-Hsueh Road, Shou-Feng, Hualien 974,
Taiwan. Tel.: þ886 3 863 3147; fax: þ886 3 863 3130.
E-mail address: [email protected] (Y.-L. Hsiao).
Peer review under responsibility of College of Management, National Cheng
Kung University.
1
Tel.: þ886 6 275 7575x53443; fax: þ886 6 274 4104.
2
Tel./fax: þ886 4 2285 1590.
HOSTED BY
Contents lists available at ScienceDirect
Asia Paci?c Management Review
j ournal homepage: www. el sevi er. com/ l ocat e/ apmrvhttp://dx.doi.org/10.1016/j.apmrv.2015.04.001
1029-3132/© 2015 College of Management, National Cheng Kung University. Production and hosting by Elsevier Taiwan LLC. All rights reserved.
Asia Paci?c Management Review 20 (2015) 275e284
statistical signi?cance of the fund alphas without considering the
effect of a structural change of the hedge fund dataset on their
results. Also, they both fail to test the statistical signi?cance of the
alpha of the identi?ed hedge fund elites as a whole over the holding
period.
Another main issue that has been ignored in the literature of
hedge fund research involves the portfolio optimization. One
possible cause for the dearth of such efforts might be the size of the
amount for initial investment. Given that it is not extraordinary for
the typical hedge fund to require an initial investment of 200,000
USD up to 1,000,000 USD, the issue of constructing and managing a
portfolio for hedge funds only concerns fund of hedge funds, sizable
endowment funds, pension funds or other large ?nancial in-
stitutions, rather than wealthy individuals. However, if the union of
accessible hedge funds are reduced to only a few, e.g., less than ten,
elites, a portfolio with optimized weights on component funds will
be attractive to and much more affordable for both large ?nancial
institutions and individual wealthy investors.
It is the main thrust of this study to, in the ?rst place, investigate
whether the performance of outperforming hedge funds sustains
over the holding period of a variety of length in time while using a
recently proposed test, the stepwise test for superior predictive
ability (or Step-SPA test introduced by Hsu, Hsu, & Kuan, 2010;
hereafter HHK), to control for the data-snooping bias. The Step-SPA
test improves on the test power of Romano and Wolf's SRC. Second,
this study endeavors to extend the effort above to test whether
portfolio optimization techniques would enhance the performance
of an equal-weighted portfolio of hedge funds outperformers.
Having surveyed the recent development in the literature of opti-
mization techniques for portfolio, this study applies the recently-
developed probability global search Lausanne (hereafter PGSL),
the commonly-adopted genetic algorithm (hereafter GA) as well as
the outdated NewtoneRaphson algorithm (hereafter NR) as a
benchmark. In this study, empirical results suggest that both
equally-weighted and weights-optimized portfolios of good hedge
funds screened by the Step-SPA test are generally able to outper-
form the corresponding HFR database index.
The rest of the article is organized as follows. Section 2 reviews
the literature on performance persistence of hedge funds and on
portfolio optimization. Section 3 brie?y documents the dataset, the
three optimization methods and the Step-SPA test while Section 4
discusses the empirical results and brings about some implications
of them. Section 5 concludes.
2. Literature review
2.1. Performance persistence of hedge funds
Two main approaches to testing the performance persistence of
mutual funds or hedge funds have been developed in the literature.
The ?rst approach examines the entire universe of funds using
either the contingency table-based (nonparametric) method or the
regression-based (parametric) method. In particular, a fund is
referred to as a winner (loser) if its risk-adjusted return (alpha value
or information ratio) is larger than (less than) the mean or median
of the entire sample of funds. Following this categorization,
Goetzmann and Ibbotson (1994), Brown and Goetzmann (2003)
apply the Cross Product Ratio (CPR) test (also known as the Odds
Ratio test) to test whether past winners (losers) tend to be next
winners (losers). The CPR is given by
CPR ¼
ðno: of winners at tÞ Â ðno: of winners at t À1Þ
ðno: of losers at tÞ Â ðno: of losers at t À1Þ
:
Accordingly, the CPR equals 1 under the null hypothesis of no
persistence. The test statistic of the null hypothesis is given by
z ¼
logðCPRÞ
StdðlogðCPRÞÞ
;
where Std(log(CPR))¼
Under the assumption of independent observations, this z-sta-
tistic will follow a standard normal distribution asymptotically.
Agarwal and Naik (2000) adapt the method for multi-periods.
Given a series of nine consecutive periods, for instance, the proba-
bility for a fund to be winner for nine straight periods is (0.5)
9
under
the null hypothesis of no persistence. The probability for a fund to
be winner for ?ve straight periods and then loser for the remaining
four periods is (0.5)
5
. In this context, the Kolmogrov-Smirnov (KeS)
test is employed to test whether the observed probability for a fund
to be winner in all scenarios is signi?cantly different from its
theoretical counterpart as illustrated above. Statistical signi?cance
of the KeS test would then indicate performance persistence.
In contrast with the non-parametric approach above, Edwards
and Caglayan (2001) and Agarwal and Naik (2000) explore this
issue using a regression-based (parametric) method. In particular,
they calculated the risk-adjusted return (e.g., the alpha value by a
factor model) for a series of consecutive periods. The alpha values of
all funds of period tþ1 are regressed upon those of period t. For the
case of 10 consecutive sample periods, such regression will be
performed nine times and one can apply the FamaeMacbeth test to
check if the mean of the nine slope estimates is signi?cantly posi-
tive. If yes, the universe of funds tested demonstrate performance
persistence.
The second main approach, in contrast, sorts all funds into
different equally-weighted portfolios according to the funds' per-
formance (e.g., return in excess of the risk-free rate or risk-adjusted
return) during the portfolio-formation period, and tests whether
each portfolio's performance, if statistically signi?cant, persists into
the portfolio-holding period. Parametric (standard) p-value or
KTWW's cross-sectionally bootstrapped p-value is used to test
whether the portfolio's alpha value is statistically signi?cant. Their
relative performance, i.e., the spread between the returns of the
best portfolio and the poorest portfolio, can also be tested in this
way to see if it persists across time. (See Carhart (1997)).
The factor models such as CAPM, Sharpe's (1966) single-factor
model, three-factor model built by Fama and French (1993), and
Carhart's (1997) four-factor model are commonly used to evaluate
the abnormal returns of mutual funds. Mr. Lynch really owned
talent and skill in selecting underpriced stocks. Chen, Jegadeesh,
and Wermers (2000) study the stock positions and active trades
???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
1
no
f ðwinnertÀ1
; winner
t
Þ
þ
1
no
f ðwinnertÀ1
; loser
t
Þ
þ
1
no
f ðlosertÀ1
; winner
t
Þ
þ
1
no
f ðlosertÀ1
; loser
t
Þ
s
S.M.-F. Yen et al. / Asia Paci?c Management Review 20 (2015) 275e284 276
of mutual funds and ?nd that managers of growth-oriented mutual
funds do possess skill in ?nding underpriced large-cap growth
?rms. Similarly, KTWW discover that quite a few managers of
American, domestic, open-end mutual funds are able to pick
underpriced stocks, which is also true even based upon net-of-fee
fund returns.
2.2. Portfolio optimization
Regarding the development on optimization, the literature has
witnessed a signi?cant amount of efforts dedicated to this issue. As
a conventional numerical method, Newton's (1736) approach
draws on a function's derivatives to approach the optimal solution,
which however does not guarantee global optimum. Given the
rapid improvement on PCs' computation ef?ciency over the past
decades, however, a variety of global search algorithms for the
optimal solution have been proposed with respect to different
practical problems. Since these algorithms involve iterative
computation, they are quite time-consuming and would have been
infeasible without the aid of mighty computation ability. For
instance, Gilli and Kellezi (2001) employ a global search approach
to optimizing a portfolio's weights on individual assets. Maringer
and Parpas (2009) apply a global search algorithm to optimize
the higher order moments in portfolio selection. Krokhmal,
Palmquist, and Uryasev (2002) devise a global search approach to
optimizing the expected returns of a portfolio given constraints on
the portfolio's conditional value-at-risk. For hedge funds, Minsky,
Obradovic, Tang, and Thapar (2009) survey the following global
optimization algorithms for adjusting the portfolio weights.
2.2.1. Newton's method
In the book, entitled ‘Method of Fluxions,’ Newton introduces
this seminal numerical approach to ?nding the optimal solution of
a function. It uses a tangent line on the objective function to
approach the function's solution, which is analytically insoluble.
Many extensions to the basic Newton's method have appeared in
the literature such as Broyden, Dennis, and Mor e’s (1973) quasi-
Newton method.
2.2.2. Genetic Algorithm (GA)
Based on the principle of natural selection in the course of living
being's evolution, Holland (1975) introduces the genetic algorithm.
Goldberg and Lingle (1985) applies it to the problem of optimiza-
tion. In the context of portfolio construction, the GA selects weights
on individual asset at random from the current population weight
range for each asset to be parents. They are then used to generate
the children for the next generation via crossing over the parents.
During the process of the population's evolution toward an optimal
solution, the GA allows a small probability for mutation.
2.2.3. Simulated annealing
Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953)
documents the simulated annealing algorithm. It concerns using
a probability search algorithm model that simulates the physical
process of heating a material and then gradually cooling down its
temperature to avoid defects, thus minimizing the system energy.
At each step of the simulated annealing algorithm, the current
solution is replaced by another solution which is selected
depending on the difference between the functional values at the
two points and the temperature variable, which is systematically
lowered during the process. However, this method does not ensure
global optimum. Kirkpatrick (1983) improves on Metropolis et al.’s
(1953) work and provides a similar but better algorithm.
2.2.4. Probabilistic Global Search Lausanne (PGSL)
Raphael and Smith (2003) propose a global search algorithm
based on the simulated annealing method mentioned above.
Following an initial global search based on a uniform distribution
assumed for all variables depending on the value of the target
function, the PGSL intensi?es the probability density on regions
corresponding to a good value of the target function. By iteratively
increasing the probability density for regions of a good solution and
reducing the search space along these regions, the PGSL approaches
the optimal solution.
2.2.5. Pattern search
The Pattern Search randomly selects a point (value) for each of
all driving variables along the initial search space. Each of these
initial values is multiplied by a vector (of a constant or variable
length) to form a region for further search. If any new point within
each generated region corresponds to a better solution for the
target function, the initial point is replaced by the new point.
Multiplying the new point by the vector above constructs a new
search region which substitutes for the previous search region.
Iteration of such a procedure will lead to the optimal solution. If the
vector length is constant, such a method is called the Generalized
Pattern Search (GPS). If the vector is of a variable length, in parallel,
this method is called the Mesh Adaptive Search (MADS).
Minsky et al. (2009) suggest that the PGSL performs best among
the methods introduced above in 21 out of 24 scenarios of
nonlinear optimization problems. As a result, we apply this method
in the following analysis. Due to its popularity in portfolio opti-
mization, however, the study also includes the GA as a benchmark
approach in addition to the Newton Raphson method.
3. Data and methodology
3.1. Data
The dataset was bought from the Hedge Fund Research, Inc and
spans the September 1994 to August 2008 period. During the sample
period, a total of 13098 hedge funds are covered by the dataset,
including 5023 funds still existent by the end of our sample period,
August 2008, and 8075 defunct funds.
3
Including the universe of
defunct funds help purge our results of the survivorship bias. As our
focus is onthebene?ts of usinga portfoliooptimizationtechnique on
its performance, we also categorize the dataset into ?ve sub-samples
according to the main strategy de?nedby the dataset vendor, HFR. In
particular, the?vestrategies are Marco, Event-Driven, Relative Value,
Equity Hedge, andFund of Funds. The monthly returns of each hedge
fund, net of all fees, are enteredintoour workhorse, theStep-SPAtest,
to screen signi?cant outperforming funds.
3.2. Step-SPA test
The literature substantially implements the bootstrap method
to control for the data-snooping bias. White (2000) pioneers the
use of bootstrapping by introducing the Bootstrap Reality Check
(hereafter BRC). White's BRC tests the null hypothesis under which
the best model (strategy) in a large group of competitors cannot
beat the benchmark model (strategy) in terms of a speci?c loss
function (e.g., average daily returns for funds). However, the BRC
method is less effective when the sample contains too many
underperforming models (strategies). In light of this drawback,
3
Funds might be moved from the live funds list to the defunct funds list for
reasons such as liquidation due to bad performance, having been closed to new
investors due to unmanageable size, being merged by other funds and so on.
S.M.-F. Yen et al. / Asia Paci?c Management Review 20 (2015) 275e284 277
Hansen (2005) devised a superior predictive ability (SPA) test,
which increases the rejection rate of the null hypothesis by
reducing the number of poor models in the sample. A drawback of
both the BRC and the SPAtest is that they only test the best model of
the entire union. In the context of portfolio management, however,
a fund-of-funds manager is inclined to pick as many good indi-
vidual funds as possible. Thus, this study incorporates the Step-SPA
test to screen as many good hedge funds as possible while con-
trolling for the data-snooping bias.
For a typical investor who allocates assets among hedge funds or
for a fund-of-funds manager, the challenge is how to identify
genuinely pro?table individual hedge funds but exclude at the
same time the lucky ones. To state this problem in mathematical
formulation, let n be the number of models for some variable and
let d
k,t
(k ¼ 1, 2, …, n and t ¼ 1, 2, …, T) denote their performance
measures (relative to a benchmark model). For each k, let E(d
k,t
)¼m
k
denote the mean of the k-th rule for all t. For each t, d
k,t
may be
dependent across k. We would like to test the following inequality:
H
k
0
: m
k
0; k ¼ 1; :::; n (1)
In the context of testing the hedge funds’ performance, m
k
may
refer to the alpha value of the k-th hedge fund whose return across t
is measured by a linear multi-factor model. The null hypothesis in
Eq. (1) simply states that none of the total of n hedge funds out-
performs the multi-factor benchmark portfolio.
Following Hansen (2005), HHK assume for {d
t
} ¼ (d
1,t
, …,d
n,t
)’
that {d
t
} is strictly stationary and alpha-mixing of
size À(2þh)(rþh)/(rÀ2) for some r > 2 and h>0,where Ejd
t
j
ðrþhÞ