Board of Governors of the Federal Reserve System

International Finance Discussion Papers

Number D2014-4

Returns to Active Management: the Case of Hedge Funds∗

Mazi Kazemi and Ergys Islamaj

April 2014

∗NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussionand critical comment. References to International Finance Discussion Papers (other than an acknowledgmentthat the writer has had access to unpublished material) should be cleared with the author or authors. RecentIFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded withoutcharge from Social Science Research Network electronic library at www.ssrn.com

Returns to Active Management: the Case of Hedge Funds1

Mazi Kazemi2 and Ergys Islamaj3

Abstract

Hedge funds often change their exposure to market risk in response to market conditions

and private information. Do more active portfolio managers perform better? Using a sample of

284 hedge funds covering 2007-2011, we study the relationship between activeness and various

measures of performance. More specifically, we use dynamic estimates of exposure to market

risk to construct a measure of activeness and examine the relationship with various measures of

hedge fund performance. We find that more active managers tend to provide higher raw returns

to their clients. However, once we adjust these raw returns for their riskiness, the relationship

changes such that more active hedge fund managers do not earn higher risk-adjusted returns on

their portfolios.

Keywords: Hedge Funds, Fama-French, Active Management, Dynamic Trading

JEL classifications: G11, G12, G14, G23

1The views in this paper are solely the responsibility of the author(s) and should not be interpreted as reflectingthe views of the Board of Governors of the Federal Reserve System or of any other person associated with theFederal Reserve System.

2The author is a Research Assistant in the Division of International Finance, Board of Governors of the FederalReserve System, Washington, D.C. 20551 U.S.A.

3The author is an economist in the Department of Economics, Vassar College, Poughkeepsie, NY, 12604,U.S.A.

1 Introduction

This paper investigates whether active portfolio managers perform better than those who are

less active. Using a sample of 284 equity long-short hedge funds covering 2007-2011, we study

the relationship between a constructed measure of activeness, calculated from estimates of funds’

dynamic exposures to risk factors, and various measures of performance, such as realized returns

and risk-adjusted realized returns. We use the Fama-French-Carhart factors in both static and

dynamic frameworks to construct performance benchmarks and to measure the level of activeness

of each hedge fund. This measure is then employed to test our main hypothesis that there is no

relationship between the level of activeness and the risk-adjusted performance of hedge funds.

While more active funds tend to provide higher average raw returns, they do not provide higher

risk-adjusted returns.

Since 1997, the hedge fund industry’s assets under management (AUM) has increased by

more than 14 times, with AUM growing at an average pace of $100bn per year.4 Hedge funds

are defined as absolute return investment vehicles, seeking to generate some positive return in

any market condition. They can take short positions and are not subject to the stricter charters

that govern mutual funds. Having such freedom of investment puts extra emphasis on the

importance of the hedge fund manager. The incentive fee structure employed by the hedge fund

industry is supposed to align the interest of shareholders.5 In addition, given that hedge fund

managers receive a share of their funds’profits in the form of incentive fees, it is argued that the

industry attracts the most skilled asset managers.6 Numerous academic studies have examined

the performance of hedge funds and their managers. Generally, the primary goal of these studies

has been to determine whether hedge funds are able to outperform a passive benchmark, such

as the S&P 500 Index.7

The evidence in the hedge fund literature is mixed. Some studies, such as Capocci (2001),

found significant positive abnormal returns for a significant portion of hedge funds, whereas

more recent papers, such as Ding and Shawky (2007), reported that the majority of hedge funds

are not able to outperform buy-and-hold investment strategies on a risk-adjusted basis. To the

degree that some hedge funds may provide positive abnormal returns, it would be instructive

4http://www.barclayhedge.com/research/indices/ghs/mum/Hedge_Fund.html5 In addition, most hedge fund managers have a significant portion of their personal wealth invested in the

fund, aligning their interests with those of their investors even further.6 Incentive fees are typically 20% of a fund’s profits above its previous high water mark. For instance, John Paul-

son, the founder of Paulson and Co, reportedly earned $5 billion in 2010. See http://www.forbes.com/profile/john-paulson/

7The anecdotal and academic evidence, at least for mutual funds, is fairly clear. For example, In 2011, 84% ofactively managed U.S. equity mutual funds underperformed their benchmarks. For example, see Fama and French(2010), Wermers (2011), and http://www.prnewswire.com/news-releases/84-of-actively-managed-us-equity-funds-underperformed-their-benchmark-in-2011-57-trail-over-3-year-period-142356285.html.

1

to find out whether these funds share some common characteristics. For example, Boyson

(2008) reports that smaller and younger funds display better and more persistent performance.8

However, none of the previous studies have examined whether those funds who display positive

abnormal are relatively more active in managing their portfolios. In other words, even if the

majority of hedge funds may not be able to outperform buy-and-hold investment strategies, it

is of interest to determine whether those who outperform their peers do so because they are

unusually active in managing their portfolio allocations —does active hedge fund management

mean skilled management?

The contribution of this paper is to test for a relationship between activeness and perfor-

mance. The activeness measure is constructed from dynamic risk exposure estimates. Papers,

such as Monarcha (2009), Roncalli and Tieletche (2007), and Bollen and Whaley (2009) have

employed dynamic regression models with time-varying coeffi cients to explain hedge funds’ab-

normal returns. As will be discussed later, dynamic regressions allow the researcher to better

capture the hedge fund manager’s reallocations into different risk factors. These changes can

be in response to macro-economic conditions, like the Great Recession, arbitrage opportunities,

costs of leverage, and varying performance of equity indices (Patton and Ramadorai (2010)).

We apply the Kalman Filter methodology to a dynamic version of the model first proposed by

Carhart (1997) and use the estimated time-varying hedge fund risk-exposures to generate a mea-

sure of activeness for each fund. We also employ various cross-sectional regressions and find that

more actively managed funds tend to provide higher raw returns to their clients. However, after

adjusting for riskiness , the relationship changes such that more active hedge fund managers do

not earn higher risk-adjusted returns on their portfolios.

2 Literature Review

The key question that we wish to study in this paper is whether more actively managed hedge

funds are able to generate higher returns. According to the effi cient market hypothesis (EMH),

asset prices reflect all available information, and, therefore, actively managed portfolios should

not outperform passive investments on a risk adjusted basis.9 However, this does not imply that

investors should be indifferent between passive investment products (e.g., index funds) and those

that are actively managed (e.g., hedge funds). If markets are effi cient, the returns on actively

managed portfolios will be lower by the amount of fees and transaction costs.

8Boyson (2008) contains numerous references to papers on varying aspects of hedge funds’performance per-sistance, which is beyond the scope of this paper.

9For a discussion of the EMH see Bodie, et al (2011).

2

We conduct a returns-based analysis to evaluate performance.10 Wermers (2011) warns of

three potential problems when conducting returns-based analysis. First, in determining a per-

formance model, one must have an accurate measurement of the risk exposures of the managers.

That is, one must have the correct benchmark. Second, one must be aware of the difference

between idiosyncratic and systematic risks in the fund’s holdings. Finally, one should have a

good understanding of the return distribution, which may deviate from the normal distribution.

This paper concentrates on hedge fund managers who invest in U.S. equity markets, and we con-

struct a model that reflects the risks they take. This is the model developed in Carhart (1997).

Second, the model differentiates between systematic and idiosyncratic risks. Finally, while we

assume that hedge fund returns are normally distributed, we correct our results for potential

heteroskedasticity when estimating the relationship between performance and the measure of

activeness.

The development of the Capital Asset Pricing Model (CAPM) in the 1960’s provided a

testable model of risk for financial assets. Jensen (1968) was one of the first to use this new

tool to evaluate fund performance. An econometric representation of the CAPM to model the

ex post returns would be,

Rjt −Rft = αj + βj(Rmt −Rft) + µjt, j = 1, ..., J, t = 1, ..., T, (1)

where αj is the intercept of interest and µjt is a random error term with expected value equal

to zero.

The interpretation of αj is the average excess return on portfolio j. Thus, this is the average

return on a portfolio that can be attributed to the manager’s investment skills. This variable

is colloquially known in the financial literature as Jensen’s alpha. If managers are consistently

generating returns in excess of those predicted by their risk-factor exposures, it would appear

that managers are extracting economic rents by trading on certain information. Jensen selected

a sample of 115 open-end mutual funds covering 1955-1964. Only 13 intercepts are positive and

significant at the 5% level.11 One of the shortcomings of the CAPM is that it only includes one

risk factor to model returns. Many researchers have expanded the CAPM to create multi-factor

models. Fama and French (1992, 1993, 1996) develop a widely employed model of risk and

10There are two broad categories of performance analysis used to study both hedge funds and mutual funds:portfolio holdings and returns-based analysis. The former involves obtaining information regarding the portfoliostructure of each fund. This is not feasible for hedge funds since, unlike mutual funds, most hedge funds are notrequired to disclose their holdings on a regular basis and when they do, they report only their long positions.However, for hedge funds, the latter method offers the possibility of obtaining estimates of portfolio holdings aswell as risk-adjusted performance.11Jensen (1968) states, “The model implies that with a random selection buy and hold policy one should expect

on average to do no worse than α = 0 . Thus it appears from the preponderance of negative α̂’s that the fundsare not able to forecast future security prices well enough to recover their research expenses, management feesand commission expenses.”(pg. 22).

3

return where they describe a set of three risk factors, which was used to analyze stock returns.

Fama and French (2009) apply their model to 1,308 equity mutual funds with monthly data

from January 1984 to September 2006.12 The estimated annualized alpha was -0.93.

Carhart (1997) combines the three-factor model, developed by Fama and French (1992,

1993, 1996), and the momentum factor, developed by Jegadeesh and Titman (1993).13 Equation

(3) represents the four-factor Fama-French-Carhart model:

rpt = α+ β(RMRFt) + s(SMBt) + b(HMLt) + u(UMDt) + εt, t = 1, ..., T. (3)

Here rpt and the Fama-French factors are as before, and UMDt is the excess return of the

stocks that were winners in the past period over those that were the losers, and εt is white noise.

Carhart showed that funds that had a positive performance in one year tended to perform above

average the following year. However, in subsequent years this abnormal return vanished.

Studies of hedge funds’performance have approached the subject in a similar fashion.14

Table 1 of the Appendix summarizes the results of some of the papers on the topic. Capocci

(2001) uses 198 monthly returns (1984-2000) for 2,154 hedge funds to test the viability of the

CAPM as a performance metric for hedge funds. The author finds an estimated monthly alpha

of 0.65% and estimated beta of 0.41. Both of these estimates are significantly different from

zero.15 Then, the author applies Carhart’s (1997) four-factor model (equation (3)) to hedge

funds. The author shows that in a sample of 2,154 funds the estimated monthly alpha is 0.66%,

and the estimated betas are 0.23, 0.05, and 0.03 for SMBt, HMLt, and UMDt, respectively.

Only the coeffi cient on the momentum factor is not significantly different from zero. The data

indicated that the hedge fund managers’abilities are significant and positive.

Asness, Krail, and Liew (2001) also use the CAPM with lagged market returns to analyze

hedge fund performance. The authors consider a sample of 656 funds with data spanning from

1994 to 2000. For long short equity funds, the authors find a value of alpha equal to 3.82% and

beta equal to 0.55. However, neither of these values are significantly different from zero at the

12They estimate model (2) below.

rpt = α+ β(RMRFt) + s(SMBt) + b(HMLt) + εt, t = 1, ..., T. (2)

Here rpt is the excess return in month-t of the portfolio over the T-Bill, RMRFt is the excess return of the marketin month-t, SMBt is the excess return of small cap stocks over large cap stocks in month-t, HMLt is the excessreturn of value stocks over growth stocks in month-t, and εt is white noise. Since the authors were examiningequity funds, the coeffi cient on the market beta was close to one, 0.98, and the coeffi cients on SMBt and HMLtwere close or equal to zero, 0.18 and 0.0, respectively.13Aptly refered to as the four-factor Fama-French-Carhart model.14For a discussion of hedge funds see Lhabitant (2006).15The small beta coeffi cient implies that hedge funds do not have much exposure to traditional market risk.

This motivates the use of extended models to evaluate hedge funds performance.

4

5% level.

Brown, Goetzmann, and Ibbotson (1999) consider hedge fund performance for the years

1988 to 1995. However, they divide their analysis into each individual year, for instance, 1988-

1989, 1989-1990, etc. The authors find positive significant alphas in the years 1991-1992 and

1992-1993. However, they also find negative and significant alphas for the years 1993-1994 and

1994-1995.

In recent years, the performance of hedge funds has suffered. Some argue that because

of significant inflows of capital into this industry, sources of excess return have gradually dis-

appeared. Recent papers on the performance of hedge funds seem to support this hypothesis.

These studies have reported zero or even negative alphas for hedge funds using the four-factor

Fama-French-Carhart model. Agarwal and Naik (2004) add non-linear variables to the four-

factor model and show that hedge funds had significant risk exposures to both the non-linear

and the original four factors. The authors also compare long-run hedge fund returns to their

recent performances and find that in the long-run, returns are lower, volatility is higher, and

tail-losses are higher.

This evidence suggests that hedge fund returns fluctuate over time and across different

samples. The models mentioned make a central assumption that is frequently violated in real

life: They assume constant parameter values. However, as new information becomes available to

fund managers, they are likely to make material changes to the fund’s composition. For instance,

they may take on more leverage or change their allocations to securities. A basic solution for

this dynamism is to partition the sample and test for structural shifts. This was presented by

Bollen and Whaley (2009) who show that they could apply these tests to basic linear models by

using the change-point regression of Andrews, et. al. (1996).16 The above method suffers from

the fact that the researcher must have some prior knowledge as to when this structural break

occurs.

Hasanhodzic and Lo (2006) also recognize that non-dynamic regression coeffi cients could

be problematic. The authors use a rolling-window regression as an alternative. In their paper,

the window is 24 months. While this methodology offers more insights into the fluctuations of

returns over time, there is still some ambiguity in choosing the window size. Also, shifts and

16Consider rewriting the single-factor return model as,

rt = α1 + β1xt + εt, t = 1, ..., T1

rt = a2 + α1 + (β2 + β1)xt + εt, t = T1 + 1, ..., T.

Once the above models are estimated, then one would proceed to test the null hypothesis,

H0 : β2 = α2 = 0.

5

changes that occur within the window can be lost.

The shortcomings of the above two dynamic methods can be overcome through the use of

the Kalman Filter methodology. The Kalman Filter uses observable data (hedge fund returns) to

provide the best estimate for an unobservable stochastic random variable (hedge funds’exposures

to various risk). For mutual funds, Mamaysky, et al (2004) show that a dynamic regression using

the Kalman Filter does a better job of fitting historical mutual fund returns data and provides

a better forecast of the out-of-sample returns than the static OLS models. For hedge funds,

Monarcha (2009) compares the explanatory power of a mutli-factor model using a dynamic

regression with the Kalman Filter with those of a static linear model. The author uses a sample

of 6,716 funds with monthly data from January 2003 to December 2008. Monarcha finds that

the mean adjusted R2 rises from 0.60 for the static linear model to 0.72 for the dynamic case

with the Kalman Filter. Even a linear static model with non-linear variables yields an adjusted

R2 of only 0.62. Roncalli and Teiletche (2007) compare the dynamic regression applied to hedge

funds with the Kalman Filter to rolling window OLS estimates. They find that the Kalman

Filter produces smoother estimates of the funds’sensitivity to different indexes and reacted to

new information much quicker than either the 12 month, 24 month, or 36 month rolling window

techniques. Bollen and Whaley (2009) also comment on the use of a dynamic regression with

stochastic betas, using the Kalman Filter to estimate these betas, as an effective way to capture

the time-dynamics of hedge fund allocations. Table 1 in the Appendix summarizes the three

key performance measuring results mentioned above.17

3 The Model

Since we are considering a sample of U.S. long-short equity hedge funds, it makes sense to

select a multi-factor model whose risk-factors are equity-related. The goal is to estimate hedge

funds’exposures, or weights, to these factors and, in the spirit of Sharpe style analysis, create

a benchmark for each manager.18 Consider the general case of the excess return on a portfolio:

rp,t − rf,t =n∑i=1

ωi,t−1(ri,t − rf,t) p = 1, ...,K (4)

In equation (4) , rp,t is the hedge fund’s portfolio returns at time t, rf,t is the risk-free rate at

time t, ωi,t−1 is the weight on asset i decided at time period t − 1, and ri,t is the return on17The Table includes our results as well. These were calculated by taking the mean weighting on each risk-factor

across all time periods and managers. Further details on my model will be discussed later.18Since the Fama-French-Carhart factors are in excess returns form, we do not need to impose a restriction that

the weights have to add up to one. Further, since hedge funds can take long and short positions, we do not needto impose the restriction that the weights should be positive.

6

asset i. The weight on risk-free rate in the portfolio is given by (1−∑n

i=1 ωi,t−1). The above

expression is, in fact, an economic identity, as it describes how the excess return on a portfolio

is simply a weighted average of the excess returns of securities that constitute the portfolio.

In practice, one does not know the exact composition of the portfolio and thus the weights

have to be estimated using available returns on a set of asset classes or risk factors that approx-

imate the investment universe considered by the portfolio manager. We employ the four-factor

Fama-French-Carhart model as described in equation (3).19 Thus, the econometric representa-

tion of the model is equation (5) below.

rp,t − rf,t = w′p,t−1ft + εp,t p = 1, ...,K, t = 1, ..., T. (5)

The weights wp,t, a 5× 1 vector, will be estimated by the Kalman Filter. ft is a 5× 1 vector ofFama-French Carhart factors (including the constant term, alpha). The error term is represented

by εp,t. The weights are assumed to follow the following autoregressive process.

wt = wt−1 + µt, t = 1, ..., T.

The variance of the error terms, εt and µt, is described as follows.

V ar

[(εt

µt

)|ft, t = 1, ..., T

]=

[Q Σ

′εµ

Σεµ R

].

Note that we have assumed that the weights could change through time. As the portfolio

manager receives new information at time (t − 1), the portfolio weights are adjusted and thenthe time t realized returns on the risk factors will determine the return on the portfolio.

Having estimated the parameters of equation (5), we then attempt to measure the variation

in the weights, which will represent the degree of activeness of each fund. We use the sum of

absolute changes in wi,t−1 to measure the activeness of each portfolio. In particular, we define,

φp =4∑i=1

T−1∑t=1

|wi,t − wi,t−1| , p = 1, ..,K, (6)

as the measure of activeness of fund p.20

Once the measure of activeness is obtained, we focus on investigating our question of

19For a description of all the risk-factors see http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html20One possible approach is to use the average standard deviation of the time-series of the estimated weights.

We decided not to use this approach because it will not adequately capture the degree of activeness of a portfoliowhere the weights are trending in a predictable way.

7

whether more active funds are associated with higher returns. First, we divide the sample into

the most active and least active funds and compare the alphas of the Fama-French-Carhart

regressions for the two samples. Second, we use cross-sectional regressions to determine if there

is a relationship between the average return on a hedge fund and its degree of activeness. That

is,

Zp = γ0 + γ1φp + ε̃ p = 1, ...,K (7)

In equation (7), Zp represents the performance of hedge fund p. The hypothesis is that γ1 = 0;

i.e., higher activity does not lead to better performance. We use three different measures to

represent the dependent variable Zp. First, we use the average return on each manager to

represent Zp.This will determine if more active funds lead to higher average return. Of course,

higher returns could come with higher risk. Thus, we use two different measures of risk-adjusted

returns to determine if more active funds are able to provide higher risk-adjusted returns. First,

we run the above regression using the manager’s Sharpe ratio across the time period. With this

metric, risk is measured as volatility, without any adjustment for systematic or idiosyncratic

risk. Thus, second, we consider the above regression using the manager’s mean alpha across the

time period as our measure of risk. This method will allow us to consider the effect of activeness

while considering returns adjusted for systematic risk specifically.

4 The Data

The data is obtained from the Center for International Securities and Derivatives at the Uni-

versity of Massachusetts-Amherst (CISDM). We consider 284 hedge funds whose Morningstar

category is listed as U.S. Long/Short Equity. These funds, as their name suggests, invest in

U.S. stocks, taking both long and short positions. We have restricted the sample to equity

funds to avoid the mistake of having misspecified risk factors. The factors in the four-factor

Fama-French-Carhart model are appropriate risk factors to use, as suggested by the literature.

The reported monthly returns are net of fees, calculated as percentage change in the net asset

value. For each of the funds, we use 5 years of data, covering 2007-2011.

Since we consider funds that have survived for 5 years, the results might be impacted

by survivorship bias. This means that considering only surviving hedge funds can lead to the

overestimation of returns. However, the problem is mitigated a bit by the fact we are only

comparing survivors to other survivors. Tables 2 and 3 below present summary statistics for the

fund returns, and summary statistics for the risk-factor returns, respectively.

Tables 2 and 3 Here

8

5 Results

We begin by estimating the following static OLS regression (8) for 60 months across 284 funds.

rpe,t = αp + w1p(RMRFt) + w2p(SMBt) + w3p(HMLt) + w4p(UMDt) + εtp (8)

where rpe,t is the excess return on fund p. This regression is simply the standard four-factor

Fama-French-Carhart model as was discussed in equation (3). We begin with the static model

because it is the building block of the dynamic regression to follow. In addition, this allows us to

compare our preliminary results with those reported in previous papers. We estimate regression

(8) for each manager and then we average the estimated coeffi cients. These averaged estimates

are presented in Table 4.

Table 4 Here

Note that most alphas are not significantly different from zero. In equation (8), the esti-

mated mean abnormal return, αp, was 0.144% per month. Of all 284 funds, 31 had significantly

positive alphas at the 5% level, and 15 had negative alphas significant at the 5% level. Since

the funds in the sample are, by virtue of still existing, the most successful funds over the four

year span, one would expect them to have better performance than an average fund selected at

random from one of the time periods in the sample.21 Keeping these results in mind, we now

turn to the dynamic regression.

Next, we estimate regression (8) with time-varying coeffi cients, using the Kalman Filter

methodology.22 Figure 1 displays the dynamics of the average estimated weights of the four

factors.23 As can be seen from the figure, the weights are indeed time-varying, suggesting that

the managers have actively adjusted exposure to market risks across the period.

Figure 1 Here

21 If this model were to be applied to all the funds that were available in 2007, the results would be different.One would most likely see alpha drop closer to 0, based on the evidence in the previous literature and by theEMH.22All empirical tests were carried out in MATLAB using the State Space Model toolbox developed by Peng

and Aston (2011).23We ignored the first 10 observations of {wt}p, the sequence of weights on the risk-factors. The justification

behind this is that the Kalman Filter is exceptionally volatile for the early observations, as it is still "learning"the trends in the data.

9

Having estimated the times series of each manager’s exposures to the four equity factors,

we are now prepared to use these estimates to create a measure of activeness for each fund

manager. As described in equation (6), we construct a measure of activeness, φp, for each fund.

We normalize each manager’s measure of activeness in following manner

ρp =φp

φ− 1,

where φ is the mean of measure of activeness across the sample. Therefore, ρp represents how

much more active fund p is, as a percentage relative to the mean. A value of 0 would indicate

that a fund’s amount of activity is average while a positive (negative) value means the manager

is more (less) active than average.

We first divide the sample into highly active and highly inactive funds and compare the

Fama-French-Carhart alpha’s coming from pooled OLS regressions. We use the top 40 percent

most active and bottom 40 percent least active funds for these comparisons.24 Table 5 shows the

results. The second row of each group shows t-statistics. Our focus is on alpha, and examining

the data suggests that the top 40 % most active funds have generated a higher Jensen alpha.

Table 6 shows summary statistics for each group.

Table 5 Here

Table 6 Here

To be able to make a more robust comparison across the two groups, we re-run the regression

adding a dummy variable to identify firms in the top 40% of activeness, as follows:

rpe,t = αp + w1p(RMRFt) + w2p(SMBt) + w3p(HMLt) + w4p(UMDt) +

+Dp ∗ [αD + w1D(RMRFt) + w2D(SMBt) + w3D(HMLt) + w4D(UMDt)] + εtp(9)

where Dp takes on a value of one if the observation comes from a top 40% manager and zero

otherwise. The parameter of interest is Dp∗αD, which is the upward "shift" in abnormal returnsthat come from being a member of the most active group. We find an estimated coeffi cient value

of 0.13 with a t-statistics of 1.6223. This is just barely significant.

Next, we re-run the four-factor OLS regression for each fund in the top and bottom 40%

and calculate the percentage of funds with statistically significant positive and negative alphas24The results are similar when we use the 50 percentile benchmark to define different groups.

10

for each fund. Table 7 shows the results. The percentage of positive and statistically significant

alphas is higher for the group of top 40% most active hedge funds (15.79% compared to 9.49%

for the least active). This would suggest that most active funds perform better. But, the

percentage of statistically significant negative alphas is also larger (6.14% vs. 4.31), suggesting

that the higher percentage of alphas for the most active group may stem from higher risk taking

behavior.

Table 7 Here

The results from OLS estimates for different groups are intriguing. To gain further insights,

we consider three cross-sectional regressions using the constructed measure of activeness. In

addition to serving as an alternative test, this allows us to also control for various measures of

risk. First, we run the following cross-sectional regression:

rp = γ0 + γ1(ρp) + v. For p = 1, ..., 284 (10)

where, rp represents the mean excess return of fund p, and v is the error term. The regression

employs White estimates of the variance covariance matrix of errors to correct for heteroskedas-

ticity.25 Table 8 presents the results of this regression.

Table 8 Here

We find that, γ1, the coeffi cient on the measure of activeness is statistically significant

and different from zero at the 5% level. The results indicate that activeness is associated with

positive returns. It is important to point out that this result may be time period specific. The

time span of the sample covers the financial crisis of the late 2007-2008. Thus, much of the

activity might be attributable to nimble managers who were able to shed toxic assets and avoid

losses.

However, the above regressions do not take into account the relationship between increased

activeness and risk. That is, the managers who are more active may also be taking on riskier25Given an n × n regressor matrix, X, and OLS residual ui for each observation, White’s estimated variance-

covariance matrix for β̂ is,

V ar[β̂]=(X′X

)−1X′diag

(u21...u

2n

)X(X′X

)−1.

11

assets, leading to higher returns. It is, therefore, necessary to consider some risk-adjusted

measures of return. Consider the definition of a portfolio’s Sharpe ratio.

SR =E[rp]

σp.

Here rp is the excess return on a portfolio and σp is the standard deviation of rp.26 The Sharpe

ratio can be thought of as a measure of effi ciency. In comparing managers, the ones with higher

Sharpe ratios for their portfolios are able to extract higher returns for the same level of risk.

In this context, risk is measured as volatility, which includes both systematic and idiosyncratic

risks. Later, we will use the alpha from the four-factor model to only consider returns adjusted

for systematic risk. Thus, we estimate regression (11), using White’s approach.

srp = γ0 + γ1(ρp) + µ. (11)

The results of regression (11) are presented in Table 9.

Table 9 Here

The results indicate a negative relationship between activeness and the Sharpe ratio, but

very close to zero. Higher activeness seems to be correlated to a lower ratio of reward to risk.

The above results seem to indicate that there is, proportionally, more risk taken on than excess

return achieved.

To account for systematic risk of the manager, we examine the relationship between the

mean alpha of each manager and the manager’s activeness.

αp = γ0 + γ1(ρp) + ν. (12)

Here αp is the mean value of {αt}p, sequence of risk-adjusted excess returns for fund pas estimated by the dynamic four-factor model. That is, this is the average of alpha for each

fund across the entire sample time period. The motivation behind regression (12) is to adjust

for systematic risk. The results are presented in Table 10. We use White’s standard errors to

correct for heteroskedasticity.

Table 10 Here

26For a discussion of the Sharpe ratio see Bodie, et al (2011).

12

Clearly, the results of the regression are not significant. The sign is negative, but the

coeffi cients are not statistically different from zero. The results show that activeness is not

associated with fund managers’ abnormal returns after adjusting for systematic risk. Given

these results, why are certain managers more active than others, and why do investors allocate

funds to these managers, if they are not generating alpha through their methods? The answer

to this question is open for further research. A quick hypothesis is that it is diffi cult for investors

or managers to recognize the relationship between active management and returns. Even the

analysis presented above relies on the assumption that we have chosen the appropriate risk-

factors in the regressions. Being able to separate the returns generated by activeness and those

generated by luck can be very diffi cult.

6 Conclusion

Do active portfolio managers perform better than their peers? The empirical evidence presented

in this paper cannot reject the hypothesis that more active managers do not provide higher risk-

adjusted return for their investors. Using a sample of 284 U.S. equity long-short hedge funds

covering 2007-2011, we find that while active hedge funds provide higher raw returns, their risk

adjusted returns are, in fact, the same.

Using a state space methodology, we estimated the exposures of these funds to the Fama-

French-Carhart factors. We then developed a measure of activeness, which is used as an explana-

tory variable in a series of cross-sectional regressions. Three dependent variables were employed

in these cross-sectional regressions. First, we examined the relationship between average un-

adjusted return on each manager and his/her degree of activeness. The results show that the

estimated mean return is an increasing function of activeness. Therefore, active managers tend

to outperform their peers when their returns are not adjusted for risk.

Second, we used two different measures of risk-adjusted returns to determine if the above

higher raw returns are associated with higher risk. The first measure of risk-adjusted return

employed was the Sharpe ratio. As is well known, this measure does not distinguish between

systematic and idiosyncratic risks. The results show that active managers have lower Sharpe

ratios. This indicates that while active hedge fund managers are able to increase their returns

by actively managing their portfolios, they are not able to do so without a substantial increase

in return volatility.

Finally, we considered using the fund managers’mean alpha as a dependent variable. Each

manager’s alpha was derived from a dynamic regression model, and it accounted for the man-

ager’s exposures to systematic sources of risk, namely market, size, value, and momentum. The

13

results showed that there was no relationship between alpha and activeness. This indicates that

the increase in an active manager’s mean return is accompanied by an equivalent increase in the

systematic risk of the portfolio.

The results for pooled OLS regressions for the most active and least active groups of hedge

funds are also not robust. While the alpha for the most active group is statistically different from

zero and positive, we could not determine that the alpha’s of the two groups were statistically

different from each other. Furthermore, time series OLS regressions for each fund show that

both the percentage of positive and negative statistically significant alphas was higher for the

most active group of funds.

Among the questions which this paper brings up is the issue of survival bias. All the funds

in the sample were in existence in 2007 and were still in operation by the end of 2011. Since this

period covers the financial crisis, it is safe to assume that these surviving funds were managed

by rather skilled managers.27 As a part of future research, we plan to examine the return to

activeness for defunct hedge funds. The question would be whether less active funds were not

able to survive the downturn. By the same token, future research should extend the results

of this paper in two other directions. First, the methodology developed in this paper can be

applied to other hedge fund strategies to determine if returns to activeness are different for other

hedge fund strategies.28 Next, the research could be applied to a larger database of hedge funds

covering a longer time period. It is possible that results reported in this paper are time specific,

and therefore return to activeness could be different during less turbulent times.

27For example, a study by Liang and Park (2008) shows that for the period of 1995-2004, the attrition rate ofhedge funds was about 8.7%. This rate is likey to be much higher during 2007-2011.28Other hedge fund strategies are: convertible arbitrage, merger arbitrage, fixed income arbitrage, distressed

debt, event-driven, global macro and so on.

14

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16

Tables and Figures

Table 1: Studies on Hedge Fund Performance

Study Model Data Betas

α (%) RMRF t RMRF t−1 RMRF t−2 RMRF t−3

Capocci (2001) CAPM 1984-00 0.65 0.41

Asness, et al (2001) CAPM 1994-00 3.82 0.55

Asness, et al (2001) Lag CAPM 1994-00 −2.83 0.57 0.1 0.18 0.14

Brown, et al (1999) CAPM 1988-95 4 0.664

α (%) RMRF t SMBt HMLt UMDt

Capocci (2001) 4-Factor 1984-00 0.66 0.4 0.23 0.05 0.03

This Paper 4-Factor 2007-11 0.06 0.49 0.11 −0.11 0.04

α (%) RMRF t SMBt HMLt GSCIt

Agarwal & Naik (2004) Non-Linear 1990-00 0.99 0.41 0.33 −0.08 0.08

Monarcha (2009) Kalman Filter increases R2

Roncalli et al(2007) Kalman Filter smoother estimates than rolling window OLS

Table 2: Average of Fund Monthly Returns (%)

Mean Max Min

Average of Return, 2007-2011 0.177 3.542 -2.055

Standard Deviation 5.007 19.216 0.399

Skewness -0.325 3.882 -3.082

Table 3: Average of Risk-Factor Monthly Returns (%)

Mkt-rf SMB HML MOM

Mean 0.09 0.243 -0.311 -0.166

Max 11.53 5.77 7.59 12.53

Min -18.55 -4.21 -9.78 -34.74

Stand. Dev 5.78 2.406 2.87 6.385

Skewness -0.518 0.323 -0.203 -2.825

17

Table 4: Results: Regression (8)

Variable Mean Coeffi cient Value % t-stat sig. at 5%

αp 0.144 16.9

w1p 0.526 85.9

w2p 0.099 16.9

w3p -0.21 34.2

w4p -0.022 36.3

% F-stat sig. at 5% 88.7

Mean R2 0.486

.

Table 5: Pooled OLS Regressions for Top and Bottom 40%

α RMRF SMB HML UMD R2 F − StatTop 40 0.222 0.466 0.068 −0.180 −0.019 0.239 4.625

3.878 38.731 2.523 −7.591 −1.904Bottom 40 0.056 0.527 0.139 −0.219 −0.05 0.261 5.213

0.877 39.392 4.61 −8.25 −4.368

.

Table 6: Summary Statistics for Returns

Top 40% Bottom 40%

Mean 0.344 0.21

Standard Dev. 5.316 6.038

Skewness −0.334 −0.152Kurtosis 21 20.778

Table 7: Pooled OLS Regressions for Top and Bottom 40%

αp Mean Coeffi cient %(+)ve sig. at 5% %(-)ve sig. at 5%

Top 40% 0.26 15.79 6.14

Bottom 40% 0.22 9.49 4.31

Table 8: Regression (10) w/ 4-Factor Model

Variable Estimated Value t-Stat

γ0 0.283 8.478

γ1 0.183 2.015

F − stat 12.577

R2 0.043

18

Table 9: Results of Regression (11)

Variable Estimated Value t-Statistic

γ0 0.082 9.343

γ1 -0.035 -2.299

F − stat 6.797

R2 0.024

.

Table 10: Results of Regression (12)

Variable Estimated Value t-Statistic

γ0 -0.007 -0.148

γ1 -0.047 -0.348

F − stat 0.448

R2 0.002

.

Figure 1

Dynamics of the average factor loadings of the funds in our

sample.

21