Jesse Väisänen EMBEDDED LEVERAGE AND

OULU BUSINESS SCHOOL
Jesse Väisänen
EMBEDDED LEVERAGE AND PERFORMANCE OF HEDGE FUND SHARE CLASSES
Master’s Thesis
Department of Finance
August 2013
UNIVERSITY OF OULU
Oulu Business School
ABSTRACT OF THE MASTER'S THESIS
Unit
Department of Finance
Author
Supervisor
Jesse Väisänen
Joenväärä Juha Ph. D.
Title
Embedded leverage and performance of hedge fund share classes
Subject
Type of the degree
Time of publication
Number of pages
Finance
Master’s Thesis
August 2013
76+3
Abstract
Some investors may not be able to use leverage at all or they face different margin requirements.
Investing in securities with high-embedded leverage enables those investors to obtain desired level of
market exposure without violating their margin constraints. Investors in hedge funds can gain access to
this high-embedded leverage by investing in hedge fund share classes that have leverage multipliers
higher than one.
Hedge funds characteristically exploit different arbitrage and speculative investment strategies. These
strategies typically entail illiquid assets, and to obtain the flexibility hedge funds often restrict investors’
ability for capital redemptions. This is done by applying different share restrictions. Illiquid investments
can also yield to serially correlated returns.
This study employs extensive hedge fund database, which is constructed by merging five individual
databases. The use of this database contributes to previous academic studies, since such thorough
database has not been employed in studies concerning hedge funds. Furthermore, this study contributes
to the recent academic studies by investigating the return differences between unleveraged and leveraged
hedge fund share classes. Additionally, this study considers, whether the return spread is larger for hedge
funds that invest in illiquid assets. Finally, this study investigates whether some predefined
macroeconomic and risk factors are able to explain those returns differences.
This study finds two specific implications that contribute to the previous academic literature. First, there
exists a return difference between unleveraged and leveraged share classes, and that difference is
statistically and economically significant. Second, return difference can be partly explained by some
macroeconomic and risk variables. Aggregate hedge fund flow has a positive relationship with the return
difference and it acts as a key variable in explaining those return differences.
Additionally, this study finds that overall movements in financial markets affect the returns of leveraged
hedge fund share classes. Increases in different risk variables cause leveraged share classes to reduce
their exposures and their leverage is not constantly at the promised level. This makes them to resemble
more their unleveraged pairs and induces return difference to decrease.
As a conclusion, returns of leveraged share classes, scaled with their respective leverage, are lower than
the returns of unleveraged share classes. This finding brings important implications for hedge fund
investors. Ability of some macro and risk variables to explain the return difference helps investors to
understand the factors affecting the return spread and help them to time leveraged hedge fund
investments properly.
Keywords
Leverage aversion, Share restrictions, Liquidity, Betting-against-beta
Additional information
CONTENTS
Abstract
Contents
Figures and tables
1
2
INTRODUCTION…............................................................................ 6
1.1
Motivation for the study.............................................................. 6
1.2
Aim of the study and hypotheses development ………………..8
1.3
Main findings and related literature …………………………. 12
LEVERAGE AVERSION THEORY AND
LIQUIDITY OF
HEDGE FUNDS ...................................................................................................... 17
3
2.1
Zero-beta CAPM and leverage aversion theory …………….. 17
2.2
Empirical findings on the leverage aversion models……...... 22
2.3
Hedge fund leverage ….……………………............................. 24
2.4
Hedge fund liquidity and serial correlation.............................. 28
2.5
Measuring of fund asset illiquidity........................................... 30
DATA……………………………….…………………………………. 33
3.1
Hedge fund data …………………………………………...... 33
3.2
Data biases …………………………………………………...37
3.2.1 Backfill bias ……..…………………………………… 37
3.2.2 Survivorship bias. ……………………………………..38
3.2.3 Multi-period sampling bias …………………………... 39
3.2.4 Other biases related to hedge fund databases …………39
3.3
4
Macro and risk factors ………………………………………. 40
METHODOLOGY AND EMPIRICAL FINDINGS……………... 44
4.1
Construction of BAB portfolios ……………………………. 44
4.2.
Fund-level BAB regression ………………………………... 48
4.2.1 Sub-period samples for fund-level regression ……….55
4.3
Equally-weighted BAB regression ………………………… 59
4.3.1 Sub-period samples for equally-weighted BAB regression
…………..………..…………………………………………………….................... 67
5
CONCLUSION……………………………………………………... 70
REFERENCES……………………………………………………………………..73
APPENDICES
Appendix 1 Correlations of parameters in equally-weighted regression ….…… 77
Appendix 2 Additional empirical results ………………………………………...78
FIGURES
Figure 1. Annualized equally-weighted returns …...………………………………. 47
TABLES
Table 1. Embedded leverage ratios in different derivative instruments……………..27
Table 2. Summary statistics of hedge fund share classes……........... ………………35
Table 3. Summary statistics of each hedge fund strategy …………………………. 37
Table 4. Summary statistics of the BAB portfolios ……………………………...... 45
Table 5. Results for all funds in the fund-level regressions ……………………….. 51
Table 6. Funds with at least 12 monthly return observations. …………………….. 52
Table 7. Results for data without funds of hedge funds…………… ………………53
Table 8. Funds of hedge funds only. ………………………………………………. 55
Table 9. Summary of all funds in the fund-level regression for a period between
December 1993 and December 2002. …………………………………………....56
Table 10. Summary of all funds in the fund-level regression for a period between
January 2003 and June 2012. ……………………………………………………57
Table 11. Summary of sample without funds of hedge funds for a period between
January 2003 and June 2012……………………………………………………. 58
Table 12. Summary of all of the share classes …………………………………...... 61
Table 13. Summary statistics of data without funds of hedge funds …………….... 63
Table 14. Summary statistics of funds of hedge funds only ………………………. 66
Table 15. Summary statistics of the first sub-period sample……….. ………………68
Table 16. Summary statistics of the second sub-period sample……. ………………69
Table 17. Correlation coefficients of different macro and risk factors ……………. 77
Table 18. Summary of funds with at least 1 year of data for the second sub-period. 78
1
1.1
INTRODUCTION
Motivation for the study
One of the characterizing aspects of hedge fund industry is the refined use of
leverage to enhance returns, manage liquidity, and provide investment flexibility.
Since hedge funds are only open to certain type of individual and institutional
investors, funds can employ very complex strategies, where leverage acts as a key
element. Little is known about the level of leverage and liquidity of hedge funds,
because of the lack of regulatory oversight concerning the industry. After the most
recent financial crisis, industry has experienced several changes, such as Alternative
Investment Fund Managers Directive in Europe, to become more transparent.
However, this development is just in its starting stage and the results can be found
out later on.
Fierce competition among hedge funds contributes to the funds’ willingness to turn
to leverage. With the help of leverage, funds may be able to amplify their returns to
attract investors’ attention and funding. Funding is especially important, since it
results in management and performance fees, which are the drivers for keeping funds
in business eventually. Use of leverage is not totally riskless, since it demands
careful leverage management and follow-up of fund’s positions. Funds also have to
comply with margin constraints imposed by lenders. Funds may also choose to rely
on outside lending to obtain their leverage, or they may use different kinds of
leveraged securities.
One of those leveraged instruments that funds could use is a security with embedded
leverage, where embedded leverage means the amount of market exposure per unit of
capital committed. Nowadays, they have become an integral part of financial
markets. Different kinds of derivative securities and options have been traded for
decades, but instruments with embedded leverage, such as leveraged exchangetraded funds (LETFs), have been developed recently. Leverage constraints faced by
investors and their inability to use leverage in order to get desired market exposure,
are some of the reasons for increased demand of these products. Individual and
7
institutional investors may not be able to use leverage at all or they often face margin
requirements, which they need to fulfill. Embedded leverage brings investors various
facilitations, since securities with embedded leverage can be purchased without
breaching leverage constraints and without having a risk to lose more than 100 % of
initial investment.
A hedge fund share class that embed leverage, i.e. leveraged hedge fund share class,
is a quite recent phenomenon in asset management industry. They have been
developed to boost the returns of hedge fund investors and to attain the desired
market exposure. Many investors are willing to lever their holdings, but rather than
making the individual investor to borrow from commercial banks, hedge funds have
recently found it more efficient to set up share classes with embedded leverage for
those investors. First, investors who are qualified to invest in hedge funds, have an
option to choose the hedge fund with strategy and investment policy appealing to
them. Second, they can choose in an increasing amount the share class within a
hedge fund, which will match their desired level of market exposure by investing in
share classes, which have different leverage multipliers to the underlying. To
compensate for their risks of acquiring more leverage, hedge funds typically charge
investors with higher fees than traditional mutual funds.
The use of different hedge fund share classes is chosen for this study, since they offer
unique tool for research of embedded leverage due to existence and quantity of
leveraged and unleveraged share classes within hedge fund industry. Returns
generated by hedge fund share classes with embedded leverage are of especial
concern for hedge fund analysis, since unleveraged and leveraged hedge funds
deviate at least by the leverage multiplier and maybe in the levels of absolute returns.
Theoretically, leverage should not affect the risk-adjusted return within a hedge fund,
but leveraged share classes may use different investment tools to reach their return or
volatility targets, which can induce deviations in returns.
This study finds a few key results that contribute to ongoing research of hedge fund
leverage. Following the method of Frazzini & Pedersen (2011) we construct a
betting-against-beta (BAB) factor for hedge fund share classes. BAB factor is the
return difference of being long in both unleveraged and leveraged hedge fund share
8
classes. First, this study finds that positive BAB factor indeed exists between
unleveraged and leveraged share classes. This BAB factor is also statistically and
economically significant. Second, fund-level BAB factors exhibit serial correlation,
which relates to use of different illiquid assets by funds. Finally, this study finds that
some macro variables, such as aggregate hedge fund flow, are able to explain the
equally-weighted BAB returns. These results afford valuable knowledge for investors
in their efforts to time hedge fund investments.
This study is one of the first ones to cover the effects of embedded leverage on the
returns of different hedge fund share classes, where a gap in academic research has
existed. This study highlights important implications for individual investors and
institutional fund managers considering investing in leveraged hedge fund share
classes. Different macro variables and the overall state of financial markets can help
them to understand more comprehensively the factors affecting returns of leveraged
share classes.
This study is organized as follows. This section presents empirical hypotheses and
recent academic literature. Section 2 goes deeper in related literature by concerning
leverage aversion model, hedge fund leverage, serial correlation, and returnsmoothing in hedge fund returns. Section 3 describes the combined database used in
this study and highlights different well-known biases related to commercial hedge
fund databases. It also provides closer look on different variables used in regression.
Section 4 portrays the methodology and empirical results of this study. Section 5
completes this study by concluding the results.
1.2
Aim of the study and hypotheses development
This subchapter outlines the key hypotheses used in this study and links them to the
theory outlined in the next chapter. Since hedge fund share classes with different
leverage multipliers have not been a subject for a thorough study in the academic
literature before, the starting point for this thesis is to identify leveraged hedge fund
share classes and their corresponding unleveraged pairs from the combined hedge
fund database.
9
Previous studies of hedge funds industry, such as Kosowski, Naik & Teo (2007),
have concentrated more on risk-adjusted performance of hedge funds and hedge fund
managers’ ability to generate any alpha. Previous academic studies have not
discussed topics related to hedge fund share classes that have embedded leverage,
and do investors gain real value by investing in those shares. Increasing demand for
leveraged exchange-traded funds also serves as evidence that many investors are not
able to use leverage directly and may prefer securities with embedded leverage
(Frazzini & Pedersen 2011).
There is a lot of room in that field for further studies and this study contributes to that
gap by investigating, whether there exists economically and statistically significant
return spread, i.e. the BAB factor, between unleveraged and leveraged share classes.
Particularly, this study considers, whether those return spread are larger for hedge
funds using illiquid investment strategies. In addition, we investigate, whether the
BAB factor can be explained by some pre-defined macroeconomic and risk
variables. To test the explaining power of those variables, cross-sectional regression
analyses are conducted. Regressions are run such that each variable is added solely to
the regression, and eventually all of them are added together to the joint regression.
Hedge funds typically seek for arbitrage and speculative opportunities and according
to Kat & Palaro (2005) funds claim to do something exclusive and difficult-toreplicate. In order to have the flexibility and freedom in their investment strategies,
hedge funds often restrict the liquidity of fund’s investors. This is done by applying
several share restrictions that limit investors’ ability for capital redemptions. Aragon
(2007) argues that investors in funds with share restrictions can expect a higher
illiquidity premium and share restrictions are positively related to risk-adjusted
performance. Liang & Park (2008) compare illiquidity premium between offshore
and onshore hedge funds. They find that offshore hedge fund investors gather higher
illiquidity premium when their investments have the same level of share illiquidity as
the investments of onshore investors. Implementation of a lockup provision increases
the abnormal return for offshore funds by 4.4% per year compared to 2.7% for
onshore funds. They conclude that the difference is explained by the stronger
relationship between share illiquidity and asset illiquidity in offshore funds.
10
Aragon (2007) describes these share restrictions more closely. A lockup period
means, that an investor needs to wait a predetermined length of time after the initial
investment, typically from six months to even three years, before investment can be
redeemed from the hedge fund. Redemption period is the time period an investor in
hedge fund must wait before withdrawing capital. A notice period is the time period
of advance notice, typically one to three months, which investors are required to give
to managers in advance of the redemption period. This period gives managers time to
plan the liquidation in an orderly fashion. Unlike a lockup period, notice period is a
rolling restriction and applies throughout the time.
This study also considers, whether hedge fund returns entail autocorrelation
generated by illiquid investments and does it affect the magnitude of the BAB factor.
Getmansky, Lo & Makarov (2004) show that the reported returns of hedge funds
having illiquid assets in their portfolios appear to be smoother than true economic
returns (returns that fully reflect all available market information). Consequently,
smoothed returns lead to a downward bias on the estimated return variance and thus
yield serial correlation, i.e. autocorrelation. Autocorrelation coefficients of with 1month and 2-month lags and share restrictions are used as proxies for illiquid
investments in the cross-sectional regression. This study contributes to the previous
study of Aragon (2007) by examining, whether share restrictions have any impact on
the level of the BAB factor between different unleveraged and leveraged hedge fund
share classes. The impact of share restrictions on the return differences between
unleveraged and leveraged share classes is analyzed so that inferences of the impact
of illiquid holdings of hedge funds can be made. Thus, the first hypothesis of this
study is:
Hypothesis 1 (share restrictions and serial correlation): The BAB factor is larger for
funds that invest in illiquid assets.
Ang, Gorovyy & van Inwegen (2011) study whether some macroeconomic variables
are able to predict and explain the level of hedge fund leverage. They argue that
during times of low funding liquidity, hedge funds tend to decrease their level of
leverage. They represent also that hedge fund leverage tend decreases when asset
11
volatility increases. These results could lead to deteriorated returns for leveraged
hedge fund share classes when some economy-wide variables change. Thus, our
second hypothesis states:
Hypothesis 2 (different macro variables): The BAB factor is larger during the times
of low asset and funding liquidity.
To investigate the second hypothesis, cross-sectional regression analyses with
different macro and risk variables are conducted to find out, whether some of those
variables have any explaining power to the movements in the equally-weighted BAB
factor. Risk factors, such as TED spread and VIX, are used as proxies in the second
hypothesis. Changes in TED spread have an effect on the hedge funds’ funding costs
of acquiring leverage, which directly affects the performance of hedge funds.
According to Fostel & Geanakoplos (2008) leverage decreases during the times of
high volatility. We test these propositions for hedge fund share classes to find out,
whether leveraged share classes reduce their leverage with contemporaneous
decrease in asset liquidity.
Previous studies have been conducted by using just single hedge fund database. In
contrary, this study applies combined data base of five different hedge fund
databases. Also our database covers the period from December 1993 to June 2012,
which is far longer than data periods in most studies concerning hedge fund leverage.
Thus, the results of this thesis are more comprehensive and shed light to the effects
of embedded leverage on hedge fund returns. Since in depth analyses of these topics
have not yet been conducted for different hedge fund share classes, this study clears
the path for the future studies in this field.
The combined database also includes funds of hedge funds (FOFs). According to
Ang, Rhodes-Kopf & Zhao (2008) funds of hedge funds are pooled investment
vehicles that invest in individual hedge funds; hence they are basically hedge funds
themselves. Since many of the most famous hedge funds are closed to new
investments, Brown, Goetzmann & Liang (2004) argue that through FOFs investors
can gain exposure to those funds, since they usually hold shares in many attractive
hedge funds otherwise closed from new investments. However, investors gain all of
12
this with a cost; investors in FOFs typically face double fee structure, even though
FOFs may charge lower fees than traditional hedge funds. They conclude that
individual hedge funds have outperformed FOFs on after-fee return or on Sharpe
ratio basis. The empirical part is conducted with (i) data including FOFs; (ii) data
without FOFs; (iii) and for FOFs only to find out, whether there are differences
between traditional hedge funds and funds of hedge funds. Ang et al. (2011) use
database consisting of FOFs only, thus results of regressions with FOFs only are
comparable to their findings.
1.3
Main findings and related literature
One of the main findings of this study is that there exists a positive BAB return and it
is statistically significant. Unleveraged share classes have outperformed leveraged
ones almost year after year. That is, there exists a negative relation between
embedded leverage and returns of leveraged share classes; portfolios with higher
embedded leverage have lower returns. The equally-weighted BAB return is 2.2%
annually with very low volatility. Positive BAB return is consistent with strong tstatistics for the samples (i) including funds of hedge funds; (ii) for sample including
only share classes with at least 1 year of return observations; (iii) sample omitting
FOFs; (iv) and sample consisting of FOFs only.
Since hedge funds try to generate positive returns by maintaining both long and short
positions, they often employ illiquid trading strategies. According to Getmansky et
al. (2004) serial correlation between hedge fund returns arising from illiquid holdings
of hedge funds is a significant characteristic of hedge funds and it can yield
misleading performance statistics. Observed hedge fund returns can yield serial
correlation, which is created by intentional performance smoothing when trying to
mark illiquid holdings. Asness, Krail & Liew (2001) claim that hedge funds hold
illiquid exchange-traded securities or over-the-counter securities1, which are difficult
1
Liquidity is the degree to which a security can be traded without affecting significantly its market
prices. For a liquid security, a buyer is expected to be found in a relatively short period of time. An
13
to price, thus nonsynchronous price reactions can exist from those holdings. They
continue to argue that illiquid exchange-traded assets often do not trade at all every
month and are subject to very thin trading. They conclude that the lack of prices may
leave hedge funds with an option for marking these assets, and this option can be
used to manage hedge fund returns. Jagannathan, Malakhov & Novikov (2010)
claim, that if serial correlation is not taken into consideration properly, fund
manager’s performance measure will be biased. However, according to Kosowski et
al. (2007) top hedge fund performance is persistent and alternative explanations, such
as short-term serial correlation, are not able to explain performance persistence.
Asness et al. (2001) argue that hedge fund managers have a powerful incentive to
report monthly returns that are both consistent and uncorrelated with the overall
market. We find statistically significant autocorrelation between fund-level BAB
factors, indicating that hedge fund returns yield some serial correlation. These results
support the findings of Asness et al. (2001) and Getmansky et al. (2004) by
illustrating that hedge funds hold illiquid investments to various degrees and may use
different
methods
to
mark their
assets
for
month-end
reporting. Thus
nonsynchronous price reactions can exist.
Aragon (2007) argues that illiquid investments of hedge funds are often followed by
the use of different share restrictions. He continues to purport that hedge funds with
illiquid portfolio holdings impose longer share restrictions compared to funds with
more liquid portfolios. He concludes that share restrictions are especially suitable for
hedge funds to manage illiquid holdings effectively. Hedge funds typically try to take
advantage of different arbitrage opportunities, exploitation of these opportunities
may typically call for long-term horizon, since it may take a long time for those
trades to become profitable. Hence, hedge funds impose share restrictions to
promptly predict the redemption cycles of investors and to manage illiquid holdings
effectively. He concludes that investors in hedge funds with greater share restrictions
can expect higher illiquidity premiums. Liang & Park (2008) argue that illiquidity
premium is higher for investors in offshore hedge funds due to stronger relationship
illiquid security, such as real estate, is more difficult to sell. Holders of less liquid securities demand
higher returns on those securities, called liquidity premiums.
14
between share illiquidity and asset illiquidity. We do not divide share classes into
offshore and onshore funds, since it is not the primary point of this study.
Several hedge fund specific characteristics also exhibit that hedge funds hold illiquid
investments in their portfolios. Aragon (2007) argues that restrictions imposed on
investor redemptions make hedge funds an illiquid investment in contrast to mutual
funds, which provide investors option to sell at the end of each trading day. He
continues to argue that investors in funds with greater share restrictions have higher
expected returns, since share restrictions provide fund managers flexibility to utilize
arbitrage and more speculative strategies. This allows them to manage illiquid assets
efficiently. Agarwal, Daniel & Naik (2009) show in their study, that hedge funds with
greater share restrictions are likely to deliver superior performance. They conclude
that the level of managerial incentives affects hedge fund returns. They study
different databases and find negative relationship between share restrictions and the
liquidity of the hedge fund portfolio. Aragon (2007) finds similar results.
Related to the findings of Aragon (2007), we do not find significant relation between
share restrictions and the BAB factor. However, as Aragon (2007) infers, leveraged
hedge fund funds are less likely to impose lockup restrictions, which we directly
observe from the empirical results. Only statistically significant proxy for share
restrictions is the redemption period for sample consisting only of funds of hedge
funds. Even, when dividing the sample period for two sub-periods, we do not find
any statistical significance for different share restrictions in those sub-periods for the
sample including all the share classes or for the sample omitting FOFs.
Few studies, such as Ang et al. (2011) and Schneeweis, Martin, Kazemi & Karavas
(2005), have covered the effect of leverage on hedge fund returns and return
predictability. Ang et al. (2011) argue that leverage permits funds to gain notional
exposure at levels greater than the capital base of funds. Leverage is also applied to
target a level of return volatility and constantly changed to respond to arising
investment opportunities. They are first to use actual leverage ratios of funds of
hedge funds from December 2004 to October 2009. Schneeweis et al. (2005) use
point in time leverage ratios in their study of the relation between hedge fund
leverage and returns They find little evidence of a considerable difference between
15
risk-adjusted performance of hedge funds with above-median and below-median
level of leverage. Ang et al. (2011) conclude that leverage of hedge funds affects
many institutions besides hedge funds themselves because of scale of hedge fund
industry and trading activity nowadays. Acharya & Viswanathan (2011) show, that
deleveraging worsens bad shocks in financial markets even in good times.
Hedge funds can acquire their leverage in two ways. The first contains outright
borrowing and is called funding leverage. The second option is to use securities with
embedded leverage, which creates exposures to underlying assets that are much
higher than the original cash outlay. The cost of acquiring leverage depends
primarily on the method applied to obtain leverage. When obtaining leverage from
prime brokers, they typically charge a spread over LIBOR to hedge funds who are
borrowing to fund their long positions, and brokers pay a spread below LIBOR for
cash deposited by funds as collateral for short positions. Spreads depend on the
volatility of securities being financed and the creditworthiness of the fund with the
spread being higher for less creditworthy funds. Additionally, the strategy that fund is
applying and correlations of the fund’s investments with each other are taken into
consideration by prime brokers, if credit requested is for longer period use. The
length of the redemption period has an effect on the spread also, since it can have a
direct influence on the level of fund’s cash balance and hence to the collateral. (Ang
et al. 2011.)
Our empirical results indicate that the aggregate hedge fund flow is a key
explanatory variable in the equally-weighted BAB regressions. Ang et al. (2011)
argue that the aggregate hedge fund flow is positively related to the hedge fund
leverage. Increase in aggregate hedge fund flow increases the hedge fund leverage
contemporaneously. Wang & Zheng (2008) study the relation between quarterly
aggregate hedge fund flows and aggregate hedge fund returns. They find positive and
significant relation between hedge fund flows and past, as well as contemporaneous,
hedge fund returns. We find similar empirical results indicating positive relation
between the equally-weighted BAB return and aggregate hedge fund flow.
Additionally, Ang et al. (2011) argue that hedge funds target a specific risk profile of
their returns, where a rise in the riskiness of the assets leads to reduction in their
16
exposure. They study the capability of different macro variables to predict hedge
fund leverage. Changes in hedge fund leverage are found to be more predictable by
economy-wide factors than by fund-specific characteristics. Especially, decreases in
funding costs, measured by TED spread, forecast the increase in leverage. They find
statistically significant evidence that hedge fund leverage tends to decrease over the
next month when VIX increases, a proxy of volatility, or when TED spread increases.
They conclude also that hedge funds increase (decrease) their level of leverage
during less (more) volatile times to obtain desired target level of volatility. This is
consistent with Fostel and Geanakoplos (2008) prediction that leverage decreases
during the times of high volatility measured by VIX. Adrian & Shin (2010) draw
same kind of results for financial intermediaries. They adjust their balance sheets
actively by increasing leverage during booms and decreasing it during busts, thus
leverage being procyclical. Our empirical findings support the previous academic
findings, since increase in VIX leads to a fall in the BAB return in the regression for
the whole sample period. Share classes with embedded leverage may reduce their
leverage and exposures during more volatile times, thus resembling more of their
unleveraged pairs. Especially, positive changes in VIX lead to lower BAB returns,
thus indicating reductions in the exposures of leveraged share classes. Thus, we do
not find positive relation between low asset and funding liquidity and the BAB factor
for the whole sample period.
Frazzini & Pedersen (2010) use TED spread as a proxy of funding tightness in the
market. They hypothesize that an abrupt tightening of funding liquidity2, realizes a
simultaneous loss for the BAB factor and makes its expected future return to rise.
This takes place when leveraged investors face margin constraint and they must delever their investments and shift to more risky portfolios, which causes the spread
between the high-beta and low-beta assets to decrease and betas are compressed
towards one. Our empirical results support these findings, since tightening of funding
liquidity causes leveraged share classes to de-lever, which reduces their returns.
Consequently, their leverage is not at the targeted level anymore, which makes them
to resemble unleveraged share classes.
2
Brunnermeier & Pedersen (2009) define funding liquidity as an ease with which traders can obtain
funding from various sources.
17
2
LEVERAGE AVERSION THEORY AND LIQUIDITY OF HEDGE
FUNDS
This chapter introduces the concept of leverage aversion, which is the fact that in
financial markets not all investors are able or willing to borrow at the risk-free
interest rate (Frazzini & Pedersen 2010). Zero-beta capital asset pricing model is
presented to illustrate, why the intercept of the security market line is not always the
risk-free rate. Empirical evidence of the leverage aversion models is also presented in
this chapter. This chapter also represents topics related to leverage and illiquidity of
hedge funds. The relationship between illiquidity and share restrictions is scrutinized.
Also serial correlation arising from illiquid holdings of hedge funds and measuring
of the asset illiquidity is provided.
2.1
Zero-beta CAPM and leverage aversion theory
One of the basic assumptions behind the capital asset pricing model (CAPM) is that
an investor can take a long or short position of any size in any asset, also including
the riskless asset. This means that any investor is able to borrow and lend any
amount she wants at the riskless rate of interest. Black (1972) argues that this
assumption of all investors being able to borrow at the risk-free interest rate is the
most controversial of the all assumptions behind CAPM. He points out that CAPM
would be changed substantially if this assumption would be eliminated.
Recently, several academic papers have shown renewed interest in Black’s zero-beta
CAPM. First, Asness, Frazzini & Pedersen (2012) argue that according to CAPM of
Sharpe (1964), Lintner (1965) and Mossin (1966), tangency portfolio  should be
equal to market portfolio . However, they show in their study that the historical
performance of market portfolio is rather different from that of tangency portfolio by
producing significantly lower Sharpe ratio than the tangency portfolio. They infer
that this is because stocks are much riskier than bonds, thus stocks would need to
execute much higher Sharpe ratio for market portfolio to be optimal.
18
Second, Frazzini and Pedersen (2010) argue that CAPM assumes all investors to
invest in the portfolio with the highest expected excess return per unit of risk, that is.
to maximize their Sharpe ratio, and then level or de-lever that portfolio to fit their
personal risk preferences. However, according to Asness et al. (2001) various
investors, including mutual and pension funds, face leverage constraints, thus they
are forced to overweight risky assets in their portfolios instead of using leverage.
Also demand for assets with built-in leverage, such as leveraged exchange-traded
funds, highlight the issues investors not being able to use leverage directly, but
instead preferring assets with embedded leverage. Black (1992) points out, that
investors who cannot use leverage to their desired levels prefer high-beta stocks,
which makes their prices to increase and produce lower risk-adjusted returns
compared to the returns of low-beta stocks.
The first case to be considered is the case when there is no risk-free asset available.
However, investors can still take long or short positions of any size in risky assets.
Now every efficient portfolio  can be expressed as a linear combination of two
basic portfolios  and , which have different beta coefficients and which need not
be efficient themselves. If the weights of the portfolios are selected such that
 = 1;
 = 0,
(1)
as the beta of the first portfolio  is one, then it must the market portfolio . The
second portfolio  is called zero-beta portfolio . Since the return on portfolio  is
independent of the return on portfolio , and the weighted combinations of  and 
are efficient, portfolio  can be specified as the minimum-variance zero-beta
portfolio. (Black 1972.)
The return on efficient portfolio  is the weighted combination of the returns on
portfolios  and , then the weight of the market portfolio  in the efficient
portfolio  must be  . Now the return of portfolio  can be written as
 =   + (1 −  ) .
(2)
19
Taking expected values of both sides of equation (2) result in
( ) =  ( ) + (1 −  )( ).
(3)
Rewriting the results of equation (3) gives
( ) = ( ) +  [( ) − ( )].
(4)
Equation (4) implies that the expected return on any efficient portfolio  is a linear
function of its 
and every efficient portfolio can be written as a weighted
combination of the market portfolio  and the minimum-variance zero-beta portfolio
. Furthermore, the same holds for individual assets as well and the expected return
on every asset is a linear function of its . (Black 1972.)
Now let’s turn to the case in which there exists a risk-free asset, but in which
investors are not allowed to take short positions in the risk-free asset meaning that
the borrowing at the risk-free rate is prohibited. Defining 
,
and 
as the
weights on portfolios ,  and the risk-free asset in an efficient portfolio . As
defined earlier that the return on portfolio  is independent of the return on portfolio
, the expected return on portfolio  can be written as
( ) = 
( ) +  ( ) +   .
(5)
The weights must also satisfy following constraints (6) and (7):

+
+
=1
(6)

≥ 0.
(7)
Now it can be inferred that ( ) must satisfy
 < ( ) < ( ).
(8)
20
If the expected return of the zero-beta portfolio ( ) is less than or equal to risk-free
rate  , then increase in 
and decrease in 
by the same amount would reduce
the variance of portfolio  and increase or leave unchanged its expected return. But
this to be possible, it would mean that portfolio  is not efficient. Thus the equation
(8) must hold (Black 1972). Black et al. (1972) call the second risk factor ( ) as
the beta factor. More about the beta factor and testing of it is discussed later.
Under assumptions of CAPM, when there is a riskless asset available and riskless
borrowing and lending is not restricted, the risk-free rate  replaces the expected
return of the zero-beta portfolio ( ) as the intercept of the security market line.
Otherwise the intercept of the security market line will be ( ). However, the
introduction of the riskless asset changes the equilibrium in just one way. Now the
efficient set of portfolios is comprised of two parts. One part still continues to consist
of portfolios  and , and the other part is the mixture of the risk-free asset and a
single risky portfolio . Portfolio  is the so called tangency portfolio of the efficient
frontier of risky assets and as such is a combination of portfolios  and . Still the
expected return on portfolio or individual security continues to be a linear function of
its . (Black 1972.)
Frazzini & Pedersen (2010) supplement the model with an introduction of an
individual funding constraint. As discussed earlier, some investors are not able to
borrow at the risk-free rate at all and other investors need to have part of their wealth
in cash all the time. Asness et al. (2012) conclude that an investor who would like
higher expected return than the tangency portfolio and is willing to take extra risk,
but is not allowed to use leverage would prefer investing more in stocks. Some
investors may also be able to use leverage to some extent but face margin constraints.
Taking these conditions into consideration and solving the utility maximization
problem for all the investors results in a model, in which the expected return ( )
for any security  in equilibrium is
( ) =  +  +   ,
(10)
21
where the risk premium is  = ( ) −  − , and  is measuring the tightness of
funding constraints. Tightness of funding constraints is determined by the aggregate
risk aversion and portfolio constraints by all investors and larger  represents tighter
funding constraints. Larger values of  lead to lower risk premium , which results
into flattening of security market line. Leverage constrained investors’ demand for
high-risk securities causes the prices of those securities to rise and subsequently to
lower their returns. As in Eq. (4), the required return in Eq. (10) is a constant plus
beta times a risk premium. Tighter constraints flatten the security market line, thus
indicating a lower compensation for a marginal increase in systematic risk. This is
because constrained investors need an access to high un-leveraged returns and are
willing to reconcile to lower returns with riskier assets. (Frazzini & Pedersen 2010.)
However, in comparison to standard CAPM, in which the intercept of the security
market line is  , in Eq. (10) the intercept is increased by the amount of . It might
be ambiguous, why zero-beta assets should require returns higher than the risk-free
rate. The explanation is that binding capital in such assets precludes a constrained
investor from executing other more profitable trades. Moreover, if unconstrained
investors buy a significant amount of those securities, then this risk is no longer
idiosyncratic to them, since additional exposure to such assets would increase the
risk of their overall portfolio. Thus, it can be concluded that, in equilibrium, even
zero-beta risky assets must offer higher returns than the risk-free rate of return.
(Frazzini & Pedersen 2010.)
According to Asness et al. (2012) investors who are able to obtain leverage and
willing to apply it, can attain higher risk-adjusted returns by overweighting safer
assets. That is, leverage risk is compensated in equilibrium through the relative
pricing of assets. Since some investors choose to overweight riskier assets, either
purposely or by their inability to use leverage, prices of riskier assets are increases
and consequently expected return of those assets is reduced. Now safer assets are
underweighted by these investors and therefore offer higher expected returns.
Frazzini & Pedersen (2011) argue that some investors are willing to pay a premium
for products with high-embedded leverage, thus overweighting those securities,
22
which reduces the expected return of those assets compared to the assets without
leverage at all.
2.2
Empirical findings on leverage aversion models
Black (1992) test the beta factor presented in previous subsection with securities
listed on the NYSE using ten beta-sorted portfolios with a sample from 1931 to 1991.
The beta factor portfolio is formed to be long in low-beta stocks and short in highbeta stocks. This is accomplished by weighting the excess returns of the ten
portfolios by 1 −  , where  is the beta of portfolio . He concludes the beta of the
factor portfolio to be approximately zero, and by following CAPM, its excess return
should be also very near to zero. However, the excess return on the beta factor
portfolio differs statistically from zero (even at the 1% level) during the whole
sample period. This indicates that the beta factor ( ) is a risk factor, which is
priced in the market and it accounts for the cross-sectional variation in asset returns.
Test results support the model presented in Eq. (4), and therefore imply the rejection
of the CAPM.
Frazzini & Pedersen (2011) test in their study a dynamic model with a factor that is
long in a portfolio of low-embedded-leverage assets and selling short highembedded-leverage assets. This factor is called betting against beta (BAB) factor.
The construction of BAB portfolio is now explained in more detailed manner. The
weighted average embedded leverage of the high (H) and the low (L) embedded
leverage portfolio for underlying  is denoted by Ω
,
and Ω , , respectively. The
corresponding excess returns are denoted similarly by 
,
and  , . With these
notations, the excess return of the BAB portfolio for underlying security  can be
expressed as
 = (1/Ω
,
)
,
− (1/Ω
,
)
,
.
(11)
Equation 11 gives the excess return on a zero-beta self-financing portfolio that is
long low-embedded-leverage assets and short high-embedded-leverage assets. Long
side of portfolio is scaled to have an exposure to the underlying of one, since it is
23
divided by the embedded leverage Ω of the low-embedded-leverage securities. The
same applies to the short side of portfolio as well. Thus, these portfolios are market
neutral, since both sides now have the same market exposure. The portfolios are
effectively bets against embedded leverage, and therefore worthwhile to test the
return premium associated with embedded leverage. The BAB return does not reflect
moves in the underlying, but rather the discrepancy between getting market exposure
using high-embedded-leverage assets relative to that of low-embedded-leverage
assets. (Frazzini & Pedersen 2011.)
Frazzini & Pedersen (2011) first examine overall returns of asset classes with
embedded leverage and find that those asset classes offer low risk-adjusted returns.
They also test BAB factors for equity options, index options and leveraged ETFs.
They find for each BAB factor large and statistically significant average returns.
Alphas for option BABs vary between 14 and 44 basis points per month with highly
significant t-statistics. They conclude that there exists a premium for securities that
embed leverage and investors prefer instruments with embedded leverage. This is
consistent with the finding of Frazzini & Pedersen (2010) that more leverage
constrained investors hold riskier assets on their portfolios.
Frazzini & Pedersen (2011) second study the effect, whether high embedded leverage
is associated with lower subsequent returns. Their empirical results confirm that
hypothesis. The negative coefficients range between 72 and 151 basis points with
large t-statistics for equity and index options. The effect is also negative but
marginally significant for ETFs.
Frazzini & Pedersen (2011) finally consider alternative explanations for investors’
preference for securities with embedded leverage. They argue that one possible
hypothesis could be that alphas reflect poor statistical properties due to highly nonnormal return patterns. However, their portfolios are statistically well behaved with
skewness and kurtosis in line with those of standard risk factors, contrary to many of
the previous studies have argued (e.g. Broadie, Johannes & Chernov (2009)).
Frazzini & Pedersen conclude that the BAB factors are less extreme than the full
history of standard risk factors, such as SMB and HML, which does not support the
alternative explanation of poor statistical properties. They argue also that other
24
possible explanation could be that those positive alphas reflect tail risk. Returns of
the BAB factors are calculated during severe bear and bull markets and they find no
evidence of the compensation for the tail risk.
Contrary to Frazzini & Pedersen (2011), which focuses on assets with different
embedded leverage on the same underlying asset, Frazzini & Pedersen (2010) study
instruments that differ both in the level of risk and in their fundamentals. Frazzini &
Pedersen (2010) test BAB model with a factor that is long on low-beta assets and
shorts high-beta assets. Low beta (assets with beta below one) and high beta (assets
with beta above one) assets are set to corresponding portfolios. The BAB portfolio is
created by being long on the low-beta portfolio and shorting high-beta portfolio with
weights of the component portfolios being inverses of their betas. They find positive
excess returns on the BAB portfolio for U.S. and international equities. Excess
returns are positive and statistically significant even at the 1% level and results are
consistent with the model. Excess returns are highest for Canadian equities and are
positive in every country except in Austria in a period between 1984 and 2009.
Results also show that alphas decrease with beta in all the asset classes.
2.3
Hedge fund leverage
Leverage plays a pivotal role in hedge funds’ investment strategies. Since hedge
funds typically take an advantage of mispricing opportunities by simultaneously
buying underpriced assets and shorting overpriced assets, they rely on leverage to
enhance returns on assets which on an unlevered basis would not be sufficiently high
to attract funding from investors (Ang et al. 2011). Lan, Yang & Wang (2013) argue
that the use of leverage also increases volatility of the fund, and thus the possibility
of weak performance, which often results in money outflows and withdrawals. They
continue to argue that optimal level of leverage increases with alpha and decreases
with fund volatility. Stein (2009) shows that leverage can be chosen optimally by
individual hedge funds, but this could create a fire-sale type of pressure if hedge
funds simultaneously unwind their positions and reduce leverage.
25
Lan et al. (2013) propose an analytically tractable model of hedge fund leverage and
valuation where manager maximizes the present value of management and incentive
fees from present and forthcoming managed funds. The ratio between assets under
management (AUM)  and high-water mark (HWM)  is
= , in which 
measures the hedge fund manager’s moneyness and is a crucial determinant of
leverage and valuation. They propose a model of dynamic leverage with some
essential determinants, such as fund’s investment opportunity, management
compensation contracts and contractual constraints on leverage. They impose
following leverage constraint at all times :
 ≤ ,
(12)
where  ≥ 1 is the exogenously determined maximally allowed leverage. For assets
having different liquidity and risk profiles,  may differ. Lan et al. (2013) denote the
risk attitude of a manager by (), referring the manager being risk averse
when () > 0. Manager is referred to be risk seeking when () ≤ 0. The
optimal leverage policy for a fund, when the risk-neutral manager is behaving in a
risk-averse manner () > 0, is determined by
() =  {
( )
, }.
(13)
If () is sufficiently large, then the optimal leverage depends on the ratio between
the excess return  and the product of variance 
and endogenous risk
attitude (). However, when manager is behaving in risk seeking manner, () ≤
0, the optimal leverage policy for fund is
() = .
(14)
Now the manager is behaving in risk-seeking manner and chooses the maximally
allowed level of leverage and leverage constraint in equation (14) is binding.
As we can see, leverage depends on the manager’s moneyness in the fund (), which
is the ratio between AUM and HWM as defined earlier. As this ratio increases, the
26
manager also increases the level of leverage. This happens because when the ratio of
moneyness is higher, the manager is closer to collecting incentive fees and more
distant the fund is from forced liquidation. However, Lan et al. (2013) show in their
study that the path for optimal fund leverage to increase and decrease corresponding
to changes in  is nonlinear.
Buraschi, Kosowski & Sritrakul (2013) contemplate a model of a hedge fund
manager, who is subject to a many of the contractual features that affect his payoff,
such as (i) performance fee-based incentives; (ii) funding options by the prime
broker, (iii) and equity investor’s redemption options. These characteristics create a
nonlinear payoff structure that has an effect on manager’s leverage decision. The call
option-like performance fee incentive encourages the manager to employ more
leverage, while put option-like characteristics persuade the manager to decrease
leverage. They conclude that the relative importance of these two features depends
on the distance between AUM and HWM, the moneyness of the manager, which
determines the level of optimal leverage.
Usually hedge funds acquire leverage in two ways. The first is called funding
leverage, which contains outright borrowing. Taking on debt bolsters the potential
return, since returns are earned on a portfolio of securities that is larger than the
funds they contributed. How much to obtain this debt, depends usually on the type of
assets traded by the hedge fund, the creditworthiness of the fund, and the exchange,
if any, on which securities are traded. Commonly leverage for the hedge fund is
provided by fund’s prime broker, but not all hedge funds use prime brokers for
obtaining leverage. Since there are very few hedge funds that are able to directly
obtain long-term borrowing, the majority of leverage is acquired through short-term
funding from prime brokers. Another way to amplify returns is to use instruments,
such as derivatives, which create exposures to underlying assets that are much higher
than the original cash outlay. This type of leverage is labelled as instrument or
embedded leverage, and the effects of embedded leverage are the main research
subjects of this study. (Ang et al. 2011 and McGuire & Tsatsaronis 2008.)
As discussed earlier in section 1, investors’ inability to obtain enough leverage
emphasizes the importance of embedded leverage. It relieves investors’ leverage
27
constraints without risking a loss of more than 100 % of initial investment.
Embedded leverage, denoted by Ω, of a derivative security with price  with respect
to exposure to underlying asset  is given by
Ω=|
/ | = |∆/|,
(15)
where ∆= / is the security’s delta. A security’s embedded leverage is its
percentage change in price for a one percentage change in the underlying asset. Thus,
a security’s embedded leverage measures its return magnification relative to the
return of the underlying (Frazzini & Pedersen 2011). Computing Ω for the leveraged
hedge fund share classes used in this study is pretty effortless. For instance, the
embedded leverage of 2-times leveraged share class is naturally 2 and so on.
Breuer (2002) provides measures of embedded leverage ratios in different derivative
contracts by decomposing the contracts into cash market equivalents. The basic
derivative instruments, such as forwards and options, can be replicated by holding
appropriate positions in the underlying asset, and by borrowing or lending. This
replication can be applied to map the individual components into own funds
equivalents (equity) and borrowed funds equivalents (debt). These components can
be used to measure the leverage embedded in long and short forward and option
positions. These leverage ratios are provided in Table 1.
Table 1. Embedded leverage ratios in different derivative instruments.
Derivative security
Long position
Forward contract
Call option
Put option
 /
∆ /
|∆  / |
Short position
|− / |
|−∆  / |
−∆  /
Table 1 describes closely embedded leverage ratios.  denotes the current price of the underlying asset,  the
value of a long forward contract at time ,  the value of a short forward contract, ∆ denotes the delta of the
call option3,  is the current value of long call option,  is the current value of a short call option, ∆ is the
delta of a put option,  is the current value of long put option and  denotes the current value of a short put
option.
3
According to Breuer (2002) the delta of an option is defined as the rate of change of the option price
with respect to the price of the underlying asset.
28
Prime brokers may keep back an option to specify a NAV trigger for periodic falloffs below which they may terminate funding. This trigger is particularly effectual,
since as mentioned before, most of the hedge funds do not have admittance to equity
or other capital markets for funding. Increased margins4 can also lead to involuntarily
deleveraging for hedge funds. These haircuts were indeed increased in the second
half of 2008 and hedge funds found themselves in a need of deleveraging (Dai &
Sundaresan 2010). Breuer (2002) highlights, that larger level of leverage increases
the potential for swift deleveraging, which can cause major disturbances in financial
markets.
2.4
Hedge fund liquidity and serial correlation
Serial correlation is one of the most considerable characteristics of hedge fund
returns and has been the subject of many studies in recent years. In one of the most
comprehensive studies, Getmansky et al. (2004) conclude that the returns of hedge
funds are often highly serially correlated and the economic impact of serial
correlation can be quite real for most hedge funds. Serial correlation yields
misleading performance statistics, which are commonly used by investors to decide
in which fund to invest and how much capital to allocate to a fund.
Second, Getmansky et al. (2004) consider several possible explanations for serial
correlation in hedge fund returns. These include: (i) market inefficiencies, (ii) timevarying expected returns, (iii) time-varying leverage, and (iv) incentive fees with
high water marks.
However, after taking these four possible explanations into
account, they argue that the most likely sources for serial correlation are the
illiquidity exposure and smoothed returns. Despite of differences between illiquidity
exposure and smoothed returns, they should be considered concurrently, since one
facilitates the other (Getmansky et al. 2004).
4
Brunnermeier & Pedersen (2009) define margin, also known as haircut, a difference between the
security’s price and its collateral value.
29
Asness et al. (2001) show that hedge funds seem to price their assets at a lag either
intentionally or unintentionally, and thus biasing downward simple risk estimates
based on monthly returns. Getmansky et al. (2004) argue that a positive serial
correlation in hedge fund returns could be due to nonsynchronous trading, which
refers to trading of securities, whose prices are not readily available. They also claim
that hedge funds have possibilities to deliberately smooth their reported returns. This
kind of intentional smoothing can be carried out by managerial discretion for the
purpose of performance manipulation, since hedge funds hold hard-to-value assets to
a certain extent.
Lo (2001) infers that nonsynchronous trading is a common feature of hedge fund
returns, because they invest in assets that are not actively traded (illiquid) and so
market prices are hard to obtain. Thus, one approach to value illiquid securities is
linear extrapolation from the most recent transaction price, which generates a price
path that is at best a series of straight lines. Returns computed in that way are
smoother and exhibit higher serial correlation that returns computed from mark-tomarket prices. Therefore, serial correlation acts as proxy for a fund’s illiquidity
exposure. Even though hedge fund manager does not utilize any form of linear
extrapolation, the manager could still be exposed to smoothed returns if market
prices are obtained from brokers or dealers that apply such extrapolation. In that case
the manager is inadvertently downward-biasing price volatility (Getmansky et al.
2004).
Lo (2005, 42) argues that linear extrapolation is quite widely used technique by
brokers, since they might not be able to update their price quotes because of thin
trading volume of illiquid securities. Getmansky et al. (2004) infer that eventually,
serial correlation could also arise from intentional “performance-smoothing”, which
refers to unpalatable conventions of the hedge fund industry of reporting merely part
of the gains in months with positive returns in order to cover potential future losses
and reduce volatility. This practice also leads to improved risk-adjusted performance
measures. Asness et al. (2001) argue that lack of publicly available traded prices
could give hedge funds flexibility in how they mark these positions for month-end
reporting. Chandar & Bricker (2002) report that accounting discretion is applied to
manage fund returns in closed-end mutual fund industry.
30
As discussed earlier, hedge fund share restrictions make a hedge fund an illiquid
investment for investors. Aragon (2007) finds 4-7 % lockup premium, the difference
in excess returns between funds with and without lockup restrictions, per annum. He
also finds that positive alphas turn to either negative or insignificant after controlling
for lockup period, notice period and minimum investment size. This means that
hedge funds generate positive returns by holding illiquid investments in their
portfolios. Liang & Park (2008) compare illiquidity premiums between offshore and
onshore hedge funds. They find that premium is higher for investors in offshore
funds.
Aragon (2007) suggests in his study that illiquidity of a hedge fund’s portfolio results
in share restrictions. Hence, there exists a positive relationship between share
restrictions and the illiquidity of the hedge fund portfolio. Ding, Getmansky, Liang &
Wermers (2009) infer that the ability to quickly withdraw money is a real valuable
option for investors. Aragon (2007) continues to conclude that investors in funds
with share restrictions can expect a higher illiquidity premium and share restrictions
are positively related to risk-adjusted performance. Results show that lockup and
notice periods are connected with higher excess returns, e.g. 30-day notice period is
associated with over 3 % higher average fund performance annually. He finds also
that leveraged hedge funds are less likely to have lockup restrictions. Liang & Park
(2007) find similar results showing that share restrictions are positively linked to the
risk-adjusted returns. Ding et al. (2009) also find results that hedge funds with
illiquid holdings in their portfolios are likely to apply share restrictions to prevent a
premature liquidation of the fund. Thus, they are able to keep themselves in the
business for a longer period.
2.5
Measuring fund asset illiquidity
According to Aragon (2007), if hedge funds share restrictions are related to
underlying asset illiquidity, then investors in funds with share restrictions can
anticipate higher illiquidity premium. Since the secretive and unregulated nature of
hedge funds, holdings data for hedge funds are usually not available. Getmansky et
31
al. (2004) have developed a model to quantify the impact of possible sources of serial
correlation, from which asset illiquidity is the most likely explanation. Denote by 
the observed return of a hedge fund in period  , and let
 =  + 
+…+ 
,
(16)
where  ∈ [0,1] and  = 0,…, . The following constraint is set up for the
parameters
1 =  +  +…+ .
(17)
In equation (16),  is a weighted average of the fund’s true returns over the most
 + 1 periods, including the current period. Equation (16) captures deliberate
illiquidity-driven performance smoothing. The constraint in equation (17) that
weights sum to 1 indicates that the information driving the fund’s performance in
period  will eventually be fully reflected in observed returns. However, this process
may take up to  + 1 periods from the time the information is generated. Thus a
larger  implies a more liquid portfolio, since greater fraction of fund’s economic
return is simultaneously reflected in its reported return. (Getmansky et al. 2004.)
The smoothed returns indicate positive serial correlation up to order , the magnitude
of the effect is dictated by the pattern of weights  . Since even the most illiquid
funds will trade eventually and all of the cumulative information will be fully
reflected into its prices, thus the parameter  should be chosen to match the kind of
illiquidity of the fund. For private equity funds, much higher value of  would be
required than to funds comprised of exchange-traded equities. Higher serial
correlation will result, if the weights are evenly distributed among many lags instead
if they would be concentrated on a small number of lags. Getmansky et al. (2004)
present following summary statistics to measure the concentration of weights,
=∑
 ∈ (0,1),
(18)
32
which is called the Herfindahl index. Since the Herfindahl index has boundaries
between 0 and 1, and in the context of smoothed returns, a lower value of  implies
more smoothing, and the upper bound of 1 implies no smoothing at all. (Getmansky
et al. 2004.)
To conclude, the observed hedge fund returns generated by the model in equation
(16) can either reflect nonsynchronous effects or innocuous courses of action, such as
linear extrapolation methods, when marking illiquid assets. However, the observed
hedge fund returns can still reflect intentional performance smoothing, as discussed
earlier.
33
3
DATA
This chapter presents an overview of the data used in this study. Data for this study is
collected from various sources. Some well-documented biases in hedge fund
databases are reported also. The chapter begins with a presentation of the hedge fund
database used in this study. Descriptive statistics of data are displayed and presented.
Risk and macro factors used in this study as variables in regressions are presented
and discussed later in this chapter.
3.1
Hedge fund data
As hedge funds do not face same disclosure requirements as other investment
vehicles, such as mutual funds, the main source of information on hedge funds is a
small number of commercial databases containing data, which is voluntarily
provided by the funds. This study applies hedge fund data, which is put together by
combining five different hedge fund databases. These five databases are
EurekaHedge, TASS, Morningstar, BarclayHedge and Hedge Fund Research. Since
many of the hedge funds may report to multiple databases, combined database have
to be scrutinized and overlapping observations have to be removed before closer
analyses and conclusions can be made5. This combined database includes also details
of AUM, share restrictions and strategy applied by each hedge fund.
Since hedge funds are not required to report to commercial databases, choice of
reporting can be defined as a cost-benefit trade-off. Reporting to a database can be a
benefit for younger and smaller funds, which often tend to employ complex and
higher-frequency trading strategies, desiring potential investors and capital and are
therefore willing to slightly open their privacy and secrecy. Committing to reporting
at fixed time intervals dispossesses fund’s option in releasing information that would
be most favorable to fund. Fund may also cease to report to database due to various
reasons, from which demeaning losses can be a one key reason. The end of reporting
5
Data found from multiple databases is identical in almost all cases. In few occasions when
disagreements between two or more databases exist, those funds are left out the combined database.
34
can also be due to more positive factors, such as fund closing its doors from new
capital due to its success. (Agarwal, Fos & Jiang 2013.)6
There are altogether 292 unlevered and leveraged hedge fund share classes in data,
138 of these are unlevered (1X) hedge fund share classes and the rest are divided as
shown in Table 2. From these funds, 138 hedge fund groups can be comprised, since
every group needs to have one unleveraged share class to be able to calculate the
BAB factor. A hedge fund group means that one hedge fund can have multiple share
classes offered to investors with at least one matching unleveraged share class and
leveraged share class. Also if a hedge fund has one unleveraged share class and also
two leveraged share classes, e.g. two and three-times leveraged, then those share
classes compose one hedge fund group. If so, returns of those leveraged share classes
are averaged and that average return is used. The calculation of the spread between
unleveraged and leveraged share classes is presented later. The history of leveraged
hedge fund share classes is only few decades long, hence the amount of leveraged
share classes in data is not that numerous, although statistical inferences can still be
made.
Combined database includes total of 19257 return observations. Hedge fund return
data comprises the period between December 1993 and June 2012, thus the database
used covers wider time period than databases used in previous studies concerning
hedge fund leverage, e.g. Ang et al. (2011). However, not all the hedge funds report
their returns throughout the whole period, such as leveraged share classes of funds of
hedge funds. Hedge fund returns are reported as net-of-fees. The sample period
includes the recent financial crisis, which is an important feature, especially when
examining the hypothesis 2, since asset and funding liquidity have seen some very
substantial changes during this period. Additionally, when dividing the sample period
into two sub-periods, we can consider impacts of recent financial crisis more closely.
The majority of leveraged hedge fund share classes are two-times (2X) leveraged
with 96 different share classes belonging to that category. Hedge fund share classes
6
End of reporting does not mean liquidation of the fund. Fund closing its doors to new investors
continues to manage the funds of current investors.
35
having two (2X) or three (3X) times leverage comprise almost 80 % of the leveraged
share classes in data. All hedge funds in data are USD nominated. Hedge fund share
classes nominated in different currencies than USD are dropped out from this study7.
All hedge fund returns are monthly returns. Pairs of hedge fund share classes with at
least one monthly return observation are included in the sample when calculating
return differences.
Table 2. Summary statistics of hedge fund share classes.
Level of leverage
Number of share classes
Percentage of leveraged share classes (%)
1.0
138
-
1.5
4
2.60
1.6
1
0.65
2.0
96
62.34
2.5
8
5.19
3.0
30
19.48
3.3
1
0.65
4.0
7
4.55
4.5
1
0.65
5.0
6
3.90
Total
292
100.008
Hedge funds that do not exactly specify the level of embedded leverage of their
respective share classes are not included in this study. This drops substantial amount
of leveraged share classes on databases out, but the inclusion of those share classes
would cause bias in the estimates and results. It is vital for the purpose of this study
to have knowledge of the specified level of leverage of each share class. Without the
knowledge of the accurate leverage multiplier, scaling the return with the right
multiplier could cause undesirable detriment. Thus, only share classes with exact
definitions of their level of leverage are included in the sample. In some cases, there
are several share classes with different level of leverage in one hedge fund family,
which explains the difference in numbers between unleveraged and leveraged share
classes.
7
Ang et al. (2011) use the same approach as used in this study. They include both U.S. and
international hedge funds, but all returns and AUMs are in U.S. dollars.
8
Due to rounding specifications, the total percentage may not exactly add up to 100 %.
36
Table 3 describes the dispersion of hedge funds strategies more closely and presents
summary statistics of different hedge fund strategies. The largest amount of return
observations belongs to Commodity Trading Advisor (CTA) category with 8260
individual return observation and 96 individual share classes, which is also the
largest amount. The largest average AUM belongs to Sector strategy. However, since
there are only two share classes in this category, the robustness of this issue can be
questioned. It may be that only the largest funds belonging to that category have
reported their returns and AUM numbers. The second largest average AUM is in
Relative Value strategy. Since not all the hedge funds report their AUM every month,
estimates of average AUM of each strategy could be biased and are also suggestive.
Since empirical part of this study is performed in a way that the length of the return
time series of leveraged share classes are matched to those of unleveraged share
classes to be able to calculate the BAB factor for each pair, total number of return
observations is bit specious. Even though in some cases leveraged share class may
have more return data available, a hedge fund pair consisting of unleveraged and
leveraged share class has time series length of unleveraged share class. If not, the
BAB spread for each group would be impossible to obtain.
We can see that there are also 58 share classes of fund of hedge funds (FOF) in data,
from which 30 pairs of hedge fund share classes can be composed. FOFs have an
average of 176$M in assets under management. As described earlier, funds of hedge
funds are pooled investment vehicles that invest in individual hedge funds. A closer
look into FOFs is needed to be taken, since they differ from conventional hedge
funds. Analyses in this study are conducted in a way that fund of funds (i) are either
taken out of the sample; (ii) included in the sample; (iii) or are analyzed separately to
give comparative perspective for the results, since they differ from other hedge funds
by their structure. Managers of funds of hedge funds have the freedom to invest
different individual hedge funds, and according to Brown, Goetzmann & Liang
(2004) they hold share in many funds that have closed their doors from new
investments. Thus, investors can gain access to these funds through FOFs.
Investigating samples including and omitting FOFs gives us valuable knowledge
about the effects that FOFs might bring to the estimates.
37
Table 3. Summary statistics of each hedge fund strategy.
Strategy
Number of return
observations
(total)
Number of
share classes
Number of leveraged
share classes
Average
AUM of
each strategy
($M)
CTA
8260
96
51
140.7
Emerging Markets
135
2
2
120.7
Funds of hedge funds
3383
58
30
175.9
Global Macro
3466
62
34
82.9
Long/Short
2001
36
18
161.4
Market Neutral
100
6
3
11.3
Multi-Strategy
1089
22
11
121.1
Relative Value
730
8
4
277.5
Sector
93
2
1
690.3
Total
19257
292
154
198.09
3.2
Data biases
It is a well-known fact that hedge fund databases feature multiple biases because of
the unregulated nature of the industry. Hedge fund industry is an area of extensive
and rapidly growing research and reliance on commercial hedge fund databases may
impede researchers gaining important knowledge of hedge funds. Since hedge funds
are not compelled to report to databases, the quality of their reporting can also be
questioned. Hedge fund may have different motives for not reporting to databases or
choosing to report some information. Some of the well-documented biases, such as
survivorship bias, are presented in more detail.
3.2.1
Backfill bias
When entering a databases, a hedge fund may add its past performance history prior
to the inception data to the database, which creates backfill bias (also sometimes
called instant history bias) (Agarwal & Naik 2004). They also argue that backfill
bias could lead to an upward bias in reported returns, since typically unfavorable
9
Denotes the average calculated from the total averages of each hedge fund strategy giving a rough estimate of
average AUM for hedge fund used in this study.
38
early returns are not reported. Also data vendors can backfill the fund’s performance,
which will bias the fund’s return upwards. Fung & Hsieh (2004) contend that new
hedge funds enter to databases to seek for new prospective investors, if those funds
perform well enough. There is also a possibility that hedge funds may cease reporting
their returns to data vendors, if they conclude that their recent performance is not
adequate to attract new investments into the fund. Posthuma & Van der Sluis (2003)
infer in their study that over 50% of all returns in TASS database are backfilled
returns and also estimate backfill bias of about 400 basis points over the period 19962001. Ackermann, McEnally & Ravenscraft (1999) argue that one possibility to deal
with the backfill bias is to exclude the first two years’ data of each fund from the
analysis. They claim that the first two years are most likely to entail the most
backfilled return observations. Analyses in this study are conducted either with full
sample or including only funds with at least 1 full year of return observations.
Another alternative option to reduce backfill would be to eliminate 12 first return
observations. However, this option is omitted from this study.
3.2.2
Survivorship bias
Most hedge fund databases provide information only on operating funds. Normally
funds that have stopped reporting are eliminated from the databases, since such funds
are considered to be unappealing to investors. Also according to Ibbotson et al.
(2010), funds that failed are usually eliminated from the databases. Since the
performance of extinct funds is typically worse that the performance of survived
funds, the consequence is survivorship bias. Hence, survivorship bias could affect
upward biasing estimates of the performance of hedge funds (Fung & Hsieh 2004).
Liang (2000) conducts a study using HFR and TASS databases to see, whether there
is a survivorship bias existing and how large the effect is. He finds positive evidence
on survivorship of 2.24% per annum. Amin & Kat (2001) report similar results
showing that concentrating on survivors only will bias return estimates upwards by
2% per annum. However, Ackermann et al. (1999) only estimate 0.2% survivorship
bias in their study. Ibbotson et al. (2010) conclude that the lower estimate of
39
Ackermann et al. (1999) could be due to their use of combined HFR/MAR
database10. Following this method, empirical estimations in this study are conducted
with a combined database of hedge funds in order to alleviate problems arising from
the survivorship bias.
3.2.3
Multi-period sampling bias
Agarwal & Naik (2004) define multi-period sampling bias as a result of imposing a
requirement for funds to have a certain length of history to be included in the sample.
In some academic studies a minimum of 24-months or 36-months of return data is
required for a hedge fund to be included in the sample. One part of this study is
conducted by imposing an extra filter of including only hedge funds with at least one
full year of observations. Imposing a filter of 24-months or 36-months would cause
some difficulties for the statistical properties of this study, since leveraged hedge
fund share classes are relatively new invention and therefore many share classes do
not have multiple years of return history. Also bad results of some hedge fund share
classes with embedded leverage may have affected hedge funds’ interest on reporting
their returns to data vendors. This could have some impact on the empirical results of
this study. However, as Fung & Hsieh (1997) report, multi-period sampling bias is
relatively small with its magnitude being close to 0.6% when 36-months of minimum
return history is required. Therefore, multi-period sampling bias is not likely to create
significantly biased results in analyses conducted in this study.
3.2.4
Other biases related to hedge fund databases
Databases can also entail other biases. Bollen & Pool (2009) report that hedge funds
may avoid reporting negative returns, which could lead them to report returns such as
0.0001. This can be also due to managers’ choice not to alter the portfolio’s value
when there are no reliable market prices available, or when manager is applying
10
Ackermann et al. (1999) combine Hedge Fund Research (HFR) and Managed Account Reports
(MAR) databases.
40
some illiquid strategies. They also find that the number of small gains far exceeds the
number of small losses in commercial hedge fund databases.
Agarwal et al. (2013) document several biases related to self-reporting in hedge fund
databases. They argue that several studies before have totally forgotten one of the
most important biases in hedge fund databases, the self-reporting bias. It is a type of
selection bias, since it stems from hedge fund’s choice not to report, commence
reporting at some point, or to abolish reporting. They also argue that hedge funds
choice to voluntarily report is not likely to be random. They find evidence that hedge
fund performance worsens by 73 basis points after the first reporting date and by 24
basis points after reporting is discontinued. Hedge funds strategically start reporting
after a run of brilliant performance, whereas discontinuing the reporting can be seen
as a sign of deteriorating performance. Also net flows to funds tend to shrink after
the termination of reporting.
One way to scale down some of these aforementioned data biases according to Fung
& Hsieh (2000) is to use return data of funds of hedge funds. They claim that return
data of FOFs is less prone to database biases. They continue to assert that, if FOF
invests in a hedge fund that does not report to any of the databases, the performance
of that fund is still reflected in the performance of that particular FOF. Even if FOF
invested in a fund that discontinued its operations, the performance of that fund is
still included in the historical performance of FOF. This is turn reduces the
survivorship bias.
3.3
Macro and risk factors
In this subchapter we take a closer look into different parameters used in crosssectional analyses. In order to test the hypothesis number 1, we use different hedge
fund share restrictions and fund-level autocorrelation coefficients between hedge
fund return series as parameters in regressions. The fund-level autocorrelation
coefficients are obtained by using the Arima procedure in SAS. Data for aggregate
41
hedge fund flow, LIBOR and VIX is obtained from Datastream. Data for 3-month Tbill rate is from St. Louis Fed.11
As discussed in previous sections, hedge funds apply different restrictions on
investors’ ability to withdraw their capital from funds. Share restrictions are also
applied because strategies used by hedge funds may involve notable losses before
returns are produced according to Ding et al. (2009). Since these different restrictions
are chosen at the inception of the fund, they do not change during the life of the fund.
Agarwal et al. (2009) conclude that the longer those restrictions periods are, the
greater is the hedge fund manager’s discretion to employ different and sometimes
very illiquid strategies without having to worry about redemption requests. Also
during low funding liquidity, funds with longer restriction periods may not have to
engage in fire sales. They also argue that share restrictions provide incentives for
managers to perform better, since shorter restriction periods enable investors to
withdraw capital faster following poor performance.
Chicago Board Options Exchange Market Volatility Index (VIX) is a measure of the
implied volatility of S&P 500 index options. It portrays a measure of market’s
expectation of stock market volatility over the next 30-day period. It is quoted in
percentage points and is then annualized. Low levels of VIX imply that market is
expecting future volatility to be low and thus assets to be more liquid. Higher levels
of VIX refer to coming volatile periods, which are regarded to be poor for asset
liquidity. Thus, in this study VIX is used as a measure for asset liquidity and higher
level of VIX is referred as low asset liquidity. Also the change in the level of VIX,
∆VIX, is used as a risk factor. ∆VIX is the change in the value of VIX index from
month  − 1 to month . Sudden sizeable movements in the VIX could have major
impact on asset liquidity and consequently to funding liquidity, as perceived during
the latest financial crisis.
TED spread is used as a proxy for periods when credit constraints are more likely to
be binding, and so as a proxy of funding tightness and funding liquidity. TED spread
11
3-month T-bill rate is available at: http://research.stlouisfed.org/fred2/series/TB3MS/.
42
is the difference between the interest rate of interbank loans (3-month London
Interbank Offered Rate, LIBOR) and the short-term U.S. Treasuries rate (3-month TBills). An increase in TED spread is seen as a sign that liquidity in financial markets
is being withered. Therefore, interbank lenders demand a higher rate of interest, or
accept lower returns on investments considered to be safe, such as T-bills. Data for
both TED spread and VIX cover the period between December 1993 and October
2012. TED spread is denominated is basis points.12
Aggregate hedge fund flow is used also as a parameter in regressions. Monthly hedge
fund flow is constructed by following the method of Ang et al. (2011):
 =
− (1 +  ),
(19)
in which  is the aggregate monthly flow to hedge fund industry,  is assets
under management at time  and  is the hedge fund return from  − 1 to .
Although the monthly hedge fund flow may be quite volatile estimate, it is chosen
for this study, since it serves the purpose of this study more precisely than longer
period hedge fund flows and it matches the monthly return data. Data for aggregate
hedge fund flow runs from the period between January 1994 and December 2011.
Hedge fund flow has been positive almost the entire period except for the final
quarter of 2008 and some months in 2010 and 2011. This is confirmed also by
Ibbotson et al. (2011), who state that hedge funds faced net withdrawals during 2008.
According to Wang & Zheng (2008) aggregated hedge fund flows reflect correlated
trading activities of all hedge fund investors and may have cumulative effect on
market wide price movements. That is, aggregate hedge fund flow may have
explaining power for the movements of the BAB spread.
12
We use similar approach as Frazzini & Pedersen (2010) as we are reckoning TED spread merely as
a measure of credit conditions, not as a return even if TED spread is a difference in interest rates that
would be earned over time.
43
Pastor (2013)13 provides the data for traded liquidity factor, which is the spread
between value-weighted 10-1 portfolio sorted on historical liquidity betas. Liquidity
is the extent to which a security is easily tradable. If a security is continuously traded
in large quantities at low cost and without moving the price significantly, then this
security can be concluded to be liquid. (Pastor & Stambaugh 2003.)
13
Data for traded liquidity factor, the 10-1 portfolio return, is obatained from Lubos Pastor’s
homepage http://faculty.chicagobooth.edu/lubos.pastor/research/liq_data_1962_2011.txt.
44
4
METHODOLOGY AND EMPIRICAL FINDINGS
4.1
Construction of BAB portfolios
To build the BAB portfolio and to test the existence of the return spread between
unleveraged and leveraged hedge fund share classes, data of hedge fund share classes
is first divided to unlevered and leveraged categories. Second, we identify for each
unique unlevered (1X) share class the matching leveraged share class (leverage
greater than 1X) from the same hedge fund. Following the method of Frazzini &
Pedersen (2011), the return on BAB portfolio, i.e. the difference between returns of
unleveraged, which has a fixed leverage of 1, and leveraged share class for the hedge
fund  at time , is calculated in the following way
 = 
in which 
and 
,
,
,
− (1/Ω) ∗ 
,
,
(20)
denotes the return of the unleveraged hedge fund share class  at time 
denotes the return of the leveraged share class from same hedge fund at
time . The specified level of leverage for the leveraged share class is denoted by Ω.
For instance, if one pair consists of unleveraged and two-times leveraged share class,
then Ω equals 2 in the equation (20). The return of the BAB portfolio is also called as
the BAB spread, because of its nature as a difference between returns.
All the return differences are first studied within the fund-level. Second, from the
time series of those return differences mean returns are calculated. This analysis is
carried out for each leverage level. As shown in Table 4, unleveraged share classes
have outperformed leveraged share classes in aggregate level in each type of BAB
portfolio. This indicates a negative relation between embedded leverage and BAB
returns: portfolios with higher embedded leverage have lower mean returns. For
example, BAB portfolio comprising of unleveraged and three-times leveraged pairs
of hedge fund share classes, has resulted in unleveraged share class producing 305
basis points annualized excess return over leveraged share class with large t-statistics
supporting the outperformance of unleveraged share class. This outperformance in
45
the favor of unleveraged share class is also in net-of-fees. Comparing this to hefty
fees, which investors investing in leveraged share classes face, they are at a
disadvantage because of the weaker performance by leveraged share classes. As we
can see from Table 4, the return difference, as well as the volatility of the excess
return, increases with the level of leverage. Consistent with the findings of Black
(1972) of investors preferring riskier assets to safer assets and Frazzini & Pedersen
(2010) high-beta assets delivering lower alphas than low-beta assets, empirical
evidence suggests that leveraged share classes produce lower returns than
unleveraged share classes.
Table 4. Summary statistics of the BAB portfolios.
Type of BAB
portfolio
Number of
observations
Annualized mean
excess return %
T-statistics
Annualized
volatility %
1X*(R) –
(½)*2X*(R)
3646
1.33
5.18
4.25
1X*(R) –
(1/3)*3X*(R)
1528
3.05
3.97
8.52
1X*(R) –
(1/Lev)*(R)
6636
1.82
7.14
5.82
EWR BAB
6636
2.20
5.89
1.56
WFOF
5453
1.82
6.06
6.15
FOF
1183
1.95
4.66
3.96
1X*(R) - ½*2X*(R) denotes the return difference between unleveraged share classes and two-times leveraged
share classes with leveraged share classes scaled with their corresponding leverage. 1X*(R) - (1/3)*3X*(R) is the
return difference between unleveraged and three-times leveraged share classes with leveraged share classes
scaled with their leverage. 1X*(R) – (1/Lev)*(R) includes all share classes in the data and is the difference
between the returns of unleveraged share classes and leveraged share classes with the return of leveraged share
classes scaled with their respective leverage. EWR BAB denotes the equal-weighted return of the return
differences between unleveraged and leveraged share classes running from December 1993 to June 2012. WFOF
denotes sample without funds of hedge funds, thus consisting only of traditional hedge funds. FOF denotes
sample consisting only of funds of hedge funds. The biggest 1-month deviation in the sample is 23.9% for the
pair of 3x leveraged share class and unleveraged share class.
46
Also mentioned in Table 4 is the equally-weighted return (EWR BAB), which gives
the equal weight for every return observation of leveraged share classes and then
compares that return to the return of 1X share classes. An equal-weighted monthly
return data, i.e. an equal-weighted return index, is created by scaling the each
individual group-level BAB factors, i.e. BAB spreads, with 1/, where  denotes
the amount of funds reporting their returns in that month. Thus, the equal weight is
given to each hedge fund group’s BAB factor. The equal-weighted return index has
generated 2.2% annualized excess return with just 1.6% annual volatility. These
results support our views that leveraged share classes have not been able to lever
their returns in an orderly manner throughout the whole sample period. Factors
affecting that underperformance are analyzed later on. Also the detailed look into
construction of the equally-weighted BAB portfolio is given later on this chapter.
Figure 1 illustrates equally-weighted annualized returns of unleveraged and
leveraged share classes. Figure 1 also features the equally-weighted return of the
BAB factor. The equally-weighted BAB return (BAB) has fluctuated substantially
throughout the data period. It has been constantly different than zero and seen its
peaks in 1996 and 2002, when it has been around 5%. BAB has been negative in
recent years indicating that leveraged share classes have generated even higher
returns than their unleveraged counterparts. In period between 2003 and 2007, which
was the period for very stable growth in stock markets, BAB has been quite stable
and slightly positive. After that it turned to slightly negative in 2008 and again in
2011 and 2012. Figure 1 also indicates that when returns of both unleveraged and
leveraged share classes have been negative, returns of unleveraged share classes have
been worse than those of leveraged share classes. Thus, we can infer that leveraged
share classes have reduced their leverage and exposures during the times of low asset
and funding liquidity, and consequently resembling their unleveraged counterparts.
47
0,25
0,2
0,15
BAB
0,1
1X
Leveraged R
0,05
0
-0,05
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Figure 1. Annualized equally-weighted returns.
The figure illustrates annualized equally-weighted returns of the BAB factor, unleveraged share class (1X), and leveraged share class (Leveraged R) from 1994 to June 2012.
48
4.2
Fund-level BAB regression
To investigate earlier presented hypothesis 1, the BAB factor being larger for funds
investing in illiquid assets, a cross-sectional regression analysis is conducted. This is
done to find out variables that explain cross-sectional differences and magnitude in
fund-level BAB factors. For each pair of hedge fund share classes, the mean BAB
factor is calculated from their time series. To test the hypothesis 1, we first take all
the funds in the sample into consideration. Second, we conduct regression analysis
only for the funds with at least 1 year of return data. To exclude funds with fewer
return observations is done, since those funds may cause aforementioned biases to
estimates. However, that does not drop the amount of hedge funds significantly from
the sample.
Third, we exclude funds of hedge funds (FOFs), since FOFs have some differences
to conventional hedge funds. Results are reviewed for this sample to find out,
whether FOFs cause any significant changes in sample data. Finally, the same
analysis is also carried out only for funds of hedge funds to analyze the impacts they
may have solely.
According to Aragon (2007) hedge funds with share restrictions are assumed to
engage themselves in more illiquid assets, thus the effect of those restrictions to the
level of BAB factor is under examination. Also hedge funds using illiquid investment
strategies tend to produce serially correlated returns as discussed earlier. If hedge
funds do exhibit positive autocorrelation coefficients, it can be concluded that they
invest in illiquid assets and use methods to mark their investments that exhibit serial
correlation. Autocorrelation coefficients for each hedge fund group are calculated
and lags up to 2 periods are taken into consideration. To study these issues, i.e.
whether funds with illiquid investments are producing larger BAB factor, a following
regression is estimated:
 =  +   +   +   +
  ,
(21)
49
in which 
denotes the mean of time series differences between
unleveraged and leveraged share class,  ,  and  are
denoting lockup, advance notice and redemption period of pair of hedge fund share
classes  respectively.  denotes the autocorrelation of the BAB factor for
hedge fund pair . Lockup, notice and redemption periods are selected from the
leveraged share class.
Ding et al. (2009) study the relation between liquidity and capital flow restrictions,
including outflow restrictions, of investors. They use the liquidity proxy  , as
proposed by Getmansky et al. (2004), and infer that it is highly correlated with
outflow restrictions, i.e. lockup periods and redemption and notice periods. In this
subsection, analyses of BAB spreads is conducted to gain insight, whether those
share restrictions or autocorrelations cause any movements in the BAB factors.
The regression model described in equation 21 is estimated. First of all, t-test is
performed for the BAB spread alone in model [1]. We find that the intercept is highly
significant and robust, thus indicating that the BAB factor exists and has statistical
significance. Then in Tables 5-7 all variables are tested one by one in from model [2]
to model [5]. In model [6] both autocorrelation coefficients are used as explanatory
variables. In the last model, all variables are taken into joint regression [7] as
explanatory variables.
As shown in Table 5, none of the share restrictions that hedge funds can apply have
any statistical significance to explain the deviations between returns of unleveraged
and leveraged share classes. However, when adding autocorrelation coefficients into
regressions, they shed new light on results. Even though 1st-lag autocorrelation
coefficient does not have any statistical significance alone, when adding 2nd-lag
autocorrelation coefficient into regression, 1st-lag autocorrelation also turns slightly
significant in joint regression. Also 2nd-lag autocorrelation coefficient is robust in
both regressions [5] and [6]. This may indicate hedge funds using illiquid assets, for
which market prices are hard to obtain every month.
According to Lo (2001) hedge funds may use different extrapolation methods to
mark their assets. Getmansky et al. (2004) argue that funds may use intentional
50
“performance-smoothing” just to report part of the gains or losses in particular
month. If using some of those methods to value their assets, funds may alter the
prices of those assets without knowing the real price movements. Since illiquid assets
may not even trade every month, funds using different techniques to value those
assets at the end of the month may obtain prices for those assets not until next month
to find out that prices have not changed for few months14. Thus the impact of serial
correlation may be left out from the 1st-lag autocorrelation and arise later on.
In Table 5, all the funds are included in the sample, i.e. funds with less than one full
year of return observations also. This may cause biases to estimates and robustness
of parameters. Whereas in Table 6 results are presented for funds with at least one
year of return observation to find out, whether funds with shorter history induce any
biases to results. The most considerable difference between Table 5 and Table 6 is
that when controlling for all variables in joint regression [7], the 1st-lag
autocorrelation coefficient is not anymore statistically significant for funds with at
least 12 months of return data.
When looking at a magnitude of R2, we can see that autocorrelation coefficients add
much more explanatory power to cross-sectional regressions in Tables 5 and 6.
Adding the 2nd-lag autocorrelation coefficient, R2 increases dramatically compared to
models [1] to [5] in every table, even though the level of R2 is still quite low.
However, surprisingly the sign of 2nd-lag autocorrelation is negative in all of the
tables. This could be due to multicollinearity, meaning that 1st-lag and 2nd-lag
autocorrelation coefficients are highly correlated (Damodar 2003, 363).
14
This is typical for very illiquid investments, such as real estate.
51
Table 5. Results for all funds in the fund-level regressions.
Parameters
Intercept
Lockup
[1]
[2]
[3]
Model
[4]
[5]
[6]
[7]
0.002
(5.89)
0.001
(3.02)
0.001
(1.95)
0.001
(1.99)
0.001
(3.17)
0.001
(1.98)
0.001
(2.09)
0.001
(1.26)
Notice
0.001
(0.97)
0.005
(1.11)
Redemption
0.003
(0.55)
0.003
(1.40)
1st-lag corr
0.002
(0.05)
0.001
(0.92)
2nd-lag corr
R2
0.01
0.01
0.01
0.01
0.003
(2.16)
0.003
(2.01)
-0.005
(-2.75)
-0.05
(-2.80)
0.06
0.08
Table shows hedge fund share restriction variables. Parameters for ,  and  measure the redemption-, advance notice- and lockup periods in days. 1  −  
denotes the 1st-lag autocorrelation coefficient and  −   denotes 2nd-lag autocorrelation coefficient. T-statistics are in parentheses. R2 denotes the coefficient of determination for each
model. Data includes 138 pairs of hedge fund share classes, which are composed of 138 unleveraged and 154 leveraged share classes. That is, 138 hedge fund groups.
52
Table 6. Funds with at least 12 monthly return observations.
Parameters
Intercept
Lockup
[1]
[2]
[3]
Model
[4]
[5]
[6]
[7]
0.001
(3.31)
0.001
(2.63)
0.001
(1.95)
0.001
(1.66)
0.001
(2.94)
0.001
(3.72)
0.001
(1.31)
0.002
(1.75)
Notice
0.001
(0.89)
0.005
(1.00)
Redemption
0.001
(0.13)
0.004
(1.62)
1st-lag corr
0.005
(0.74)
0.001
(0.90)
2nd-lag corr
R2
0.02
0.01
0.01
0.01
0.003
(2.12)
0.003
(1.80)
-0.01
(-2.71)
-0.05
(-2.61)
0.06
0.08
Data includes 128 pairs of hedge fund share classes. Table shows hedge fund share restriction variables. Parameters for ,  and  measure the redemption-, advance
notice- and lockup periods in days. 1  −   denotes the 1st-lag autocorrelation coefficient and  −   denotes 2nd-lag autocorrelation coefficient. T-statistics are in parentheses.
R2 denotes the coefficient of determination for each model.All share classes in the sample are required to have at least one year of return data.
53
Table 7. Results for data without funds of hedge funds.
Parameters
Intercept
Lockup
[1]
[2]
[3]
Model
[4]
[5]
[6]
[7]
0.001
(3.00)
0.001
(1.54)
0.001
(2.54)
0.001
(2.00)
0.001
(2.81)
0.001
(3.35)
0.001
(1.98)
0.001
(1.13)
Notice
0.001
(0.94)
0.01
(1.24)
Redemption
0.01
(0.93)
0.003
(0.76)
1st-lag corr
-0.002
(-0.44)
0.001
(0.41)
2nd-lag corr
R2
0.01
0.01
0.01
0.01
0.002
(1.75)
0.003
(1.69)
-0.01
(-2.65)
-0.01
(-2.70)
0.05
0.07
Data includes 112 pairs of hedge fund share classes. Share classes of funds of hedge funds are removed from the sample. Redemption, notice and lockup periods are measured in days. 1 st-lag
corr denotes the 1st-lag autocorrelation coefficient and 2nd-lag corr denotes 2nd-lag autocorrelation coefficient. T-statistics are in parentheses. R2 denotes the coefficient of determination for each
model.
54
None of the proxies for share restrictions in the full period sample is statistically
significant in Tables 5-7 for all the funds and for sample without FOFs. Only
statistically significant proxy for share restrictions is the redemption period in Table
8 for a sample consisting of FOFs only. Increasing the redemption period with 30
days for FOFs will lead to 0.3 % increase in the BAB spread. Also the level of R2 is
much higher for redemption period than in the previous tables. The statistical
insignificance of other share restrictions proxies can be partly explained with the
finding that many of the hedge funds having leveraged share classes are quite young
and small in size. These are funds that are fiercely competing against other funds for
new money inflows from investors. According to Ding et al. (2009) these funds tend
to impose fewer restrictions on investors ability to redeem their capital, even though
this may put them more at-risk for failure. The desire to increase fund’s AUM, and in
consequence management fees obtained, could supersede the imposition of share
restrictions, thus funds are more willing to relax restrictions on withdrawals. Aragon
(2007) states that leveraged hedge funds are less likely to impose share restrictions,
which could partly explain our empirical results.
As discussed earlier, FOFs differ from traditional hedge fund share classes in several
ways. Funds of hedge funds may be issued by banks themselves and as a
consequence, these funds have direct access to the banks’ credit lines, which makes
them less vulnerable for investor redemptions. Thus, they can be relatively safe from
portfolio liquidations resulting from redemption requests. FOFs can manage their
capital more efficiently because of this. Also by imposing redemption periods, FOFs
are aware of periods when capital could be withdrawn, since they may not have
accurate knowledge of strategies used by hedge funds in which they have invested.
Hence imposing redemption restrictions for investors, they know in advance the
periods when investors are able to take money out of the fund and FOFs can prepare
for those periods beforehand.
From Table 8 we can find out also that 1st-lag autocorrelation coefficient has become
statistically significant, even when it is the only variable as in model [5]. Its sign is
also positive in every model. Consequently, the returns of fund of funds’ tend to
exhibit positive serial correlation. Hence, it could signify that, as FOFs do not have
direct knowledge of the holdings of underlying hedge funds, they do employ some
55
kinds of return smoothing tools. Also the underlying funds may exploit these
techniques and the impact is diffused to FOFs. However, the 2nd-lag autocorrelation
coefficient is not anymore significant and it reduces the coefficient of determination
in model [6]. Level of R2 is the highest in joint regression [7] for FOFs indicating
that redemption period and positive serial correlation can explain over third of the
BAB factor. However, amount of data for FOFs is quite low, which could lead to
biased estimates.
Table 8. Funds of hedge funds only.
Parameters
Intercept
Lockup
[1]
[2]
[3]
Model
[4]
[5]
[6]
[7]
0.001
(2.92)
0.001
(2.48)
0.0004
(0.46)
-0.001
(-0.72)
0.001
(1.95)
0.001
(2.08)
-0.001
(-0.80)
0.001
(0.70)
Notice
-0.001
(-0.68)
0.005
(1.01)
Redemption
-0.002
(-0.33)
0.01
(2.55)
1st-lag corr
0.01
(2.25)
0.003
(2.19)
2nd-lag corr
R2
0.003
(2.03)
0.003
(2.15)
0.004
(0.86)
0.02
0.04
0.22
0.17
0.14
0.37
Data includes 26 pairs of hedge fund share classes. Parameters for ,  and  measure
the redemption-, advance notice- and lockup periods in days. 1  −   denotes the 1st-lag autocorrelation
coefficient and  −   denotes 2nd-lag autocorrelation coefficient. T-statistics are in parentheses. R2
denotes the coefficient of determination for each model. 2nd-lag autocorrelation coefficient is left out from the
joint regression [7] because of the lack of its statistical properties, causing the level of R2 to decrease.
4.2.1
Sub-period samples for fund-level regression
To further investigate, whether some specific periods of time have affected our
earlier results, sample is divided into two consecutive periods. The first sub-period
sample covers the period between December 1993 and December 2002. The second
sub-period sample covers the period between January 2003 and June 2012. However,
none of the funds of hedge funds have reported to different databases in the first
defined sub-period for some reasons. This can also be due to fact that FOFs are very
56
recent invention in hedge fund industry and there were no FOFs existing in that
period. Thus, Table 8 describes the results for FOFs also for the second sub-period.
Hedge funds that have reported their returns during the first period have at least 12
months of data and in other words, Table 9 contains all of the funds, total of 27 pairs
of hedge fund share classes, in the first sub-sample.
The most significant distinction between Table 9 and previous tables presenting the
whole sample period, is that 1st-lag autocorrelation coefficient does not become
statistically significant in joint regression [7] anymore. However, 2nd-lag
autocorrelation coefficient is still the only robust parameter in all of the models.
Levels of R2 are quite low and do not explain the magnitude of the BAB factor very
well. When running the regression alone in model [1], t-statistics of the intercept is
just slightly significant in 95% level. It infers that the BAB spread is non-zero and
there exists a spread between unleveraged and leveraged share classes in the first
sub-period also.
Table 9. Summary of all funds in the fund-level regression for a period between December 1993
and December 2002.
Model
Parameters
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Intercept
0.003
(1.97)
Lockup
0.004
(1.89)
0.004
(1.62)
0.003
(1.29)
0.004
(2.14)
-0.001
(-0.22)
Notice
0.001
(0.04)
0.00004
(0.08)
0.01
(0.54)
1st-lag corr
0.03
(0.86)
0.01
(0.87)
2nd-lag corr
0.00
0.003
(1.32)
-0.01
(-0.93)
Redemption
R2
0.003
(1.79)
0.00
0.00
0.03
0.004
(0.37)
0.01
(0.84)
-0.01
(-3.07)
-0.01
(-2.58)
0.08
0.08
Data includes 27 pairs of hedge fund share classes. Share restrictions parameters ,  and
 measure the redemption-, advance notice- and lockup periods in days. 1  −   denotes the 1st-lag
autocorrelation coefficient and
 −   denotes 2nd-lag autocorrelation coefficient. T-statistics are in
parentheses. R2 denotes the coefficient of determination for each model. Data covers the period between
December 1993 and December 2002.
57
Diverging from Tables 5-9, the sign of 2nd-lag autocorrelation coefficient in Table 10
has now turned other way round for a period between 2003 and 2012. This time
autocorrelation coefficients are consistent as it could be expected as both signs are
positive. However, as in the first-sub period the 1st-lag autocorrelation does not
become significant even after adding the 2nd-lag autocorrelation into regression.
Table 10 includes 128 hedge fund groups indicating that there is far more data for
that period than for the first sub-period. This confirms our earlier inferences about
leveraged share classes being quite recent evolution.
Table 10. Summary of all funds in the fund-level regression for a period between January 2003
and June 2012.
Model
Parameters
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Intercept
0.002
(5.89)
Lockup
0.001
(2.60)
0.001
(1.65)
0.001
(1.68)
0.001
(2.75)
0.001
(1.16)
Notice
0.005
(1.00)
0.003
(0.46)
0.003
(1.06)
1st-lag corr
0.0005
(0.10)
0.001
(0.98)
2nd-lag corr
0.01
0.001
(1.69)
0.001
(0.91)
Redemption
R2
0.001
(3.14)
0.01
0.01
0.01
0.003
(1.83)
0.003
(1.68)
0.004
(1.98)
0.004
(2.05)
0.06
0.08
Data includes 128 pairs of share classes. Share restrictions parameters ,  and 
measure the redemption-, advance notice- and lockup periods in days. 1  −   denotes the 1st-lag
autocorrelation coefficient and
 −   denotes 2nd-lag autocorrelation coefficient. T-statistics are in
parentheses. R2 denotes the coefficient of determination for each model.
When taking funds of hedge funds out of the sample in Table 11, none of the proxies
for share restrictions possess any statistical significance. However, in model [6] and
in joint regression [7], both autocorrelation coefficients are positive and slightly
significant. The intercept in the model [1] is still statistically significant indicating
that the BAB factor exists. There are 103 pairs of leveraged and unleveraged hedge
fund share classes in Table 11.
58
Table 11. Summary of sample without funds of hedge funds for a period between January 2003
and June 2012.
Model
Parameters
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Intercept
Lockup
0.001
(2.94)
0.001
(2.45)
0.001
(1.56)
0.001
(1.95)
0.001
(2.52)
0.001
(1.19)
Notice
0.01
(1.11)
0.006
(0.90)
0.003
(0.81)
1st-lag corr
-0.002
(-0.42)
0.002
(1.19)
2nd-lag corr
0.01
0.001
(1.86)
0.002
(0.94)
Redemption
R2
0.001
(2.86)
0.01
0.01
0.01
0.003
(2.03)
0.003
(2.02)
0.004
(1.98)
0.004
(2.04)
0.05
0.07
Funds of hedge funds are left out of data and sample includes 103 pairs of hedge fund share classes. Share
restrictions parameters ,  and  measure the redemption-, advance notice- and lockup
periods in days. 1  −   denotes the 1st-lag autocorrelation coefficient and  −   denotes 2ndlag autocorrelation coefficient. T-statistics are in parentheses. R2 denotes the coefficient of determination for each
model. Data covers the period between January 2003 and June 2012.
If we assume that hedge funds with more illiquid assets in their portfolios would
impose share restrictions and the BAB factor to be larger for those funds, results
estimated do not comprehensively indicate that the BAB factor would be larger for
those funds. Although for funds-of-hedge funds the redemption period has statistical
influence on the BAB factor throughout the sample period, the number of FOFs in
databases is unfortunately quite small and statistical properties may be affected by
that. However, autocorrelation coefficients address that, for both traditional hedge
funds and FOFs, BAB spreads are serially correlated indicating some illiquid
exposure by hedge funds. This is consistent with Getmansky et al. (2004) who
conclude that serial correlation arises mainly from the illiquid holdings of hedge
funds. Nevertheless, the economic impact of serial correlation is not that eminent.
Results could indicate that funds trade very illiquid assets, for which market prices
may not be available every month.
Surprisingly, the 2nd-lag autocorrelation
coefficient is negative in estimates for the whole sample period. It could be assumed
that both of the autocorrelation coefficients would be positive, as they are in the
59
second sub-period sample. Since there were no FOFs reporting their returns in the
first sub-period, Table 8 presents statistics of the second sub-period for them. For
them autocorrelation coefficients behave as expected.
4.3
Equally-weighted BAB regression
In this section, the ability of various macro and risk variables to explain the BAB
spread is studied. In order to be able to conduct analyses of different variables,
equally-weighted time series data of BAB spread is needed to construct. An equalweighted monthly return data, i.e. an equally-weighted return index, is created by
scaling the each individual hedge fund group’s BAB factors with 1/, where 
denotes the amount of funds reporting their returns in that month to combined
database. Hence, the equal weight is given to each group’s BAB factor. In this way,
equally-weighted time series of return differences between unleveraged and
leveraged share classes is obtained. Use of equally-weighted return data is chosen,
since not all hedge funds report their AUM numbers, thus we omit the construction
of value-weighted index.
As stated in hypothesis 2, it is assumed that low asset and funding liquidity affect the
level of the BAB factor. Since when funding liquidity is low and funding constraints
are tightened, leveraged funds may find difficulties to obtain their desired level of
leverage. They may also be charged with higher fees when obtaining leverage from
prime brokers or from other sources, as explained in a more detail way in section 2.3.
This may cause them to de-lever, which can have outright effects on the real return of
the leveraged share class. Consequently, this can affect the difference between
returns of unleveraged and leveraged share classes. To test these assumptions, a
following cross-sectional regression is estimated:
 =  +   +   +   +    +
 Δ ,
(22)
where  is the return of equally-weighted BAB factors, i.e. the differences
between unleveraged and leveraged returns at time ,  is the level of TED
60
spread at time ,  is the level of VIX index at time ,  is aggregate past
one-month hedge fund flow and   is the traded liquidity factor at time  and
Δ is the 1-month change in the value of VIX index.
Following the study of Ang et al. (2011), VIX is used as a proxy for asset liquidity
and TED spread is a measure for funding liquidity. Also the traded liquidity factor of
Pastor & Stambaugh (2003) is used as a proxy for asset liquidity. With lower levels
of funding liquidity, i.e. the high levels of TED spread, it may be harder for hedge
funds to obtain requisite leverage. Hence, the return of leveraged share class may
decrease during those times, since the fund may not be able to keep the exposure of
leveraged share class at desired level. This is consistent with the finding of Frazzini
& Pedersen (2010) who conclude that with a high level of TED spread and
worsening funding liquidity, lenders tighten credit constraints and BAB returns
deteriorate consequently. Nevertheless, when fund is not being able to keep the
exposure at the level where it should be, during market downturns leveraged share
class may not lose value as much as it would, when its exposure would be higher.
Thus, the funding liquidity plays a double-edged role when studying its effect on the
BAB spread.
With the regression presented in equation (22), investigation of explaining power of
different macro variables is conducted. The purpose of this investigation is to
examine, whether these variables explain any of the movements in the spread
between unleveraged and leveraged hedge fund share classes, i.e. the BAB factor.
Also the robustness of these results is investigated. The estimation results of the
cross-sectional regression models are presented in Tables 12-15. The estimation is
conducted in the similar way as in previous subsection by testing one model at a time
and finally adding all the variables into a joint regression. In the first model, equalweighted return is regressed all alone to have a closer look into its statistical
properties and, whether the equal-weighted BAB return possesses any statistical
significance alone.
Results reported in Table 12 for the equal-weighted regression show that some of
macro variables are able to significantly explain changes in the BAB factor.
According to Ang et al. (2011) TED spread and VIX are very highly correlated, and
61
thus it is not surprising to find out the coefficient of VIX becoming insignificant in
joint regression [7]. Brunnermeier & Pedersen (2009) argue that when funding
liquidity is tight, measured here by TED spread, investors become unwilling to take
on positions. This leads to lower market liquidity and simultaneously increases
volatility. Statistical significance of aggregate hedge fund flow does not suffer when
it is added to joint regressions [7] and [8], since it does not have high correlations
with any other variables.15
However, the change in the level of VIX (∆VIX) is statistically significant also in
joint regression [8], as it is not that highly correlated with other variables. The largest
coefficient in magnitude is the aggregate hedge fund flow, which has also positive
sign in each model. For a 1 % increase in monthly aggregate hedge fund flow,
equally-weighted BAB spread increases by 0.04%, indicating that there is a positive
relation between contemporaneous aggregate hedge fund flow and the BAB return.
Table 12. Summary of all of the share classes.
Parameters
Intercept
Liq
[1]
[2]
[3]
Model
[4]
[5]
[6]
[7]
[8]
0.002
(5.89)
0.002
(5.92)
0.003
(4.13)
0.002
(4.42)
-0.004
(-0.68)
0.002
(6.23)
0.001
(0.54)
0.002
(0.25)
-0.01
(-1.32)
-0.01
(-1.53)
-0.005
(-0.73)
VIX
-0.0001
(-2.15)
TED
-0.00003
(-0.72)
-0.0008
(-1.12)
Flow
0.04
(5.02)
∆VIX
R2
-0.0003
(-0.43)
-0.0003
(-0.43)
0.03
(4.44)
0.03
(4.39)
-0.0001
(-3.06)
0.01
0.02
0.01
0.11
0.04
-0.0001
(-2.12)
0.12
0.13
Table presents summary statistics for 138 hedge fund groups, which are composed of 138 unleveraged and 154
leveraged share classes.  denotes the traded liquidity factor by Pastor & Stambaugh.  denotes the spread
between 3-month LIBOR and 3-month T-Bills called the TED spread.  denotes Chicago Board Options
Exchange Market Volatility Index, which is the level of implied volatility of S&P 500 index options. 
15
Correlation coefficients between variables used in regressions are presented in Appendix 1.
62
denotes the 1-month aggregate hedge fund flow.
 denotes the change in the level of VIX index from
2
month  − 1 to . R denotes the coefficient of determination for each model. -statistics are in parentheses.
What factors could possibly explain this positive relation? When hedge funds having
both unleveraged and leverage share class draw more capital inflows than outflows,
i.e. have net inflows, they may face unexpected difficulties. Money pouring into
unleveraged share class and invested in different assets would mean that leveraged
share class will have to increase its level of leverage in order to have the same
exposure to unleveraged share class as promised in fund prospectus. Now increasing
the amount of borrowed capital could raise costs affiliated with obtaining leverage.
This is congruent with the finding of Ang et al. (2011), who document that increase
in aggregate hedge fund flow simultaneously increases hedge fund leverage.
Therefore as more capital is raised, the funding costs for fund may rise and the BAB
spread to increase contemporaneously, since increased cost of obtaining leverage
may deteriorate the return of leveraged share class. To conclude, increase in
aggregate hedge fund flow introduces new problems for funds with leveraged share
classes, since obtaining returns matching the underlying unleveraged share class
becomes now more of an issue and makes the BAB factor to increase.
The positive sign of the coefficient of aggregate hedge fund flow operates to other
way around also. Decrease in the level of aggregate monthly hedge fund flow
indicates a decrease also in the level of BAB spread. If there exists a lockup period,
which has expired and investors are able to withdraw their capital, assuming short
notice and redemption periods, funds may be forced to liquidate their underlying
positions. Thus share classes with leverage may find their level of exposure being
below the desired level. Therefore, leveraged share classes may then behave more
like unleveraged share classes and produce returns that resemble more unleveraged
ones, since their exposure is not at the required level anymore.
Results for hedge fund share classes with at least 12 monthly return observations do
not differ dramatically from the ones reported in Table 12 and the results are
presented in Appendix 2.
63
In Tables 12-13, the signs of VIX and ∆VIX are unexpectedly negative. The BAB
spread would be expected to increase when the level of VIX index increases. Instead,
the coefficients of VIX and ∆VIX are negative and statistically significant. However,
these results can be explained with few factors. In financial markets, there may arise
different kinds of shock all of a sudden, which then in turn may correspond to surge
in the level of VIX index. According to Ang et al. (2011) when VIX increases, asset
prices drop. This may induce withdrawals from hedge funds in order to move capital
to safe havens to prevent the loss of capital. That simultaneously causes hedge funds
to liquidate some parts of the portfolio, i.e. to deleverage, to meet withdrawal
demands, which then decreases the available capital of hedge funds. This cycle may
increase the costs of obtaining leverage and may cut back funds from acquiring
leverage from different sources. Dai & Sundaresan (2011) argue that if the cost of
this involuntarily deleveraging is very high, continuation of fund’s operations is at
risk.
Table 13. Summary statistics of data without funds of hedge funds.
Model
Parameters
[1]
[2]
[3]
[4]
[5]
Intercept
Liq
0.002
(5.83)
0.002
(5.62)
0.004
(4.28)
0.002
(4.69)
-0.005
(-0.93)
[7]
[8]
0.002
(6.06)
0.001
(0.64)
0.0003
(0.38)
-0.01
(-1.04)
-0.01
(-1.28)
-0.003
(-0.34)
VIX
-0.0001
(-2.29)
TED
-0.00003
(-0.77)
-0.001
(-1.60)
Flow
0.04
(5.20)
∆VIX
R2
[6]
-0.0006
(-0.81)
-0.0006
(-0.86)
0.04
(4.51)
0.03
(4.44)
-0.0001
(-3.45)
0.00
0.02
0.01
0.13
0.05
-0.0001
(-2.36)
0.14
0.18
Table presents summary statistics for 112 hedge fund groups after removing funds of hedge funds.  denotes
the traded liquidity factor by Pastor & Stambaugh.  denotes the spread between 3-month LIBOR and 3month T-Bills called the TED spread.  denotes Chicago Board Options Exchange Market Volatility Index,
which is the level of implied volatility of S&P 500 index options.  denotes the 1-month aggregate hedge
fund flow.  denotes the change in the level of VIX index from month  − 1 to . R2 denotes the coefficient
of determination for each model. T-statistics are in parentheses.
64
Consequently, leveraged share classes may in this case resemble more their
unleveraged counterparts, since due to deleveraging their exposures do not equal
their targeted levels and what is promised in fund prospectuses. This is turn decreases
the BAB return. Our empirical results are consistent with the findings of Ang et al.
(2011), who concluded that when the level of VIX index increases, especially during
the recent financial crisis, hedge funds tend to deleverage. This deleveraging induces
leveraged share classes to become closer to their unleveraged pairs, consequently
making the BAB factor to narrow.
Aggregate hedge fund flow seems to predict the changes in the equal-weighted BAB
index throughout the whole sample period and for samples including all funds and
sample without funds of hedge funds. This is consistent with the findings of Wang &
Zheng (2008), who find positive and significant relation between quarterly aggregate
hedge fund flows and past aggregate hedge fund returns, as well as for
contemporaneous returns, using OLS and VAR methods in the period between 1994
and 2007 using TASS database. They purport that positive aggregate hedge fund
flows put pressure on underlying assets and consequently drive asset prices higher,
since investors steer capital into hedge funds following high stock market returns.
This positive relation between hedge fund flows and contemporaneous returns exists
only in the bull market and positive correlation between flows and past returns exists
only in the bear market. Finally, they find marginal evidence on a negative relation
between aggregate hedge fund flows and following period hedge fund returns
indicating that hedge fund investors are unable to successfully time hedge fund
returns.
Furthermore, findings of Goetzmann, Ingersoll & Ross (2003) support these results.
Their findings indicate price reversals and investors not being able to successfully
time hedge fund returns on multiple periods. Also Getmansky (2012) finds a concave
relation between past hedge fund performance and assets under management (AUM).
Since the BAB spread, i.e. the BAB return, is indeed a difference between returns of
different share classes, aggregate hedge fund flow can be considered as a valid and
significant parameter explaining greater returns generated by unleveraged than
leveraged share classes.
65
Results for funds of funds (FOFs) are reported in Table 14. One thing worth of
noticing are the reversals of signs of TED spread and ∆VIX. Those have changed to
positive in Table 14 compared to previous Tables 12 and 13. Now increase in TED
spread simultaneously increases the BAB return. This is consistent with our
hypothesis 2, that low funding liquidity increases the BAB factor. Worth of noticing
is also that the aggregate hedge fund flow does not possess any statistical
significance alone in the model, but merely when added to the joint regressions [7]
and [8]. Aggregate hedge fund flow may not that strong effect on funds of hedge
funds, since usually they are issued by investment banks, which have direct access to
borrowing facilities and they can be funded through banks’ own funds and credit
lines.
66
Table 14. Summary statistics of funds of hedge funds only.
Parameters
Intercept
Liq_Risk
[1]
[2]
[3]
Model
[4]
[5]
[6]
[7]
[8]
0.001
(2.68)
0.001
(2.85)
0.002
(1.65)
0.0003
(0.54)
0.00004
(0.06)
0.001
(2.63)
-0.001
(-0.45)
-0.002
(-1.93)
-0.01
(-1.07)
-0.01
(-0.93)
-0.01
(-1.27)
VIX
-0.00003
(-0.63)
TED
-0.00004
(-0.77)
0.001
(2.12)
Flow
0.02
(1.85)
∆VIX
R2
0.002
(2.68)
0.002
(2.42)
0.03
(2.22)
0.04
(3.06)
0.00001
(0.71)
0.01
0.01
0.03
0.03
0.01
0.0003
(1.18)
0.11
0.12
 denotes the traded liquidity factor by Pastor & Stambaugh.  denotes the spread between 3-month LIBOR and 3-month T-Bills called the TED spread.  denotes Chicago Board
Options Exchange Market Volatility Index, which is the level of implied volatility of S&P 500 index options.  denotes the 1-month aggregate hedge fund flow.  denotes the change in
the level of VIX index from month  − 1 to . Data includes 26 hedge fund groups. R2 denotes the coefficient of determination for each model. T-statistics are in parentheses.
67
Maybe the most important implication in Table 14 for FOFs is that the TED spread
has become statistically significant now. This can be due to small sample of FOFs
available, or TED spread playing more important role for FOFs than for traditional
hedge funds, which constitute the major part of the data used in this study. However,
for the sample of FOFs, we can conclude that the worsening of funding liquidity
induces the BAB factor to rise, as stated in hypothesis 2. FOFs are, as already
mentioned before, newly-found investment vehicles, thus gathering and inferring
data presents undesirable difficulties. There would be lot of room for further research
in the field concerning leveraged share classes of funds of hedge funds and factors
affecting to their returns.
From the model [1] in Tables 12-14 we can infer that the equal-weighted BAB return
has been statistically significant throughout the period for samples with and without
FOFs. This indicates that the BAB return is non-zero and it has also economic impact
for hedge fund investors.
4.3.1
Sub-period samples for equally-weighted BAB regression
As earlier in the fund-level regressions, we divide the sample into two sub-period
samples. The first sample consists of the period between December 1993 and
December 2002 and the second sub-period runs between January 2003 and June
2012. Like earlier in this chapter, sample running between December 1993 and
December 2002 includes none of the FOFs and funds have reported at least one full
year of return data. Thus sample in Table 15 entails all the share classes in that
period, and Table 14 represents the results of regression analysis for FOFs for the
second sub-period also. There are unleveraged 27 share classes in the first sub-period
indicating that 27 pairs from hedge fund share classes can be created. For the second
sub-period, there are 127 pairs of share classes with FOFs and 103 pairs without
FOFs, respectively.
As earlier in sample covering the full period, aggregate hedge fund flow has
statistical significance when considering variables in their separate models. When
considering the joint regressions [7] and [8], the traded liquidity risk factor becomes
68
statistically significant in both models; however its sign is negative. In model [8] all
of the variables are statistically significant at 95% confidence level. Also the sign of
the TED spread is now positive. TED spread becomes slightly statistically significant
in model [8], when taking VIX out of the model. This is in line with the finding of
Ang et al. (2011) that VIX and TED spread are highly correlated, thus affecting the
results of regression estimates. Levels of R2 are quite low in the first sub-period.
Results of Table 15 are consistent with our hypothesis 2 by indicating that low
funding liquidity simultaneously increases the BAB factor.
Table 15. Summary statistics of the first sub-period sample.
Model
Parameters
[1]
[2]
[3]
[4]
[5]
Intercept
Liq
0.003
(3.58)
0.003
(4.87)
0.003
(1.92)
0.004
(2.87)
0.001
(0.72)
[7]
[8]
0.002
(4.72)
0.004
(1.69)
0.003
(2.25)
-0.03
(-2.19)
-0.03
(2.52)
-0.03
(-1.88)
VIX
-0.00004
(-0.59)
TED
-0.00004
(-0.55)
0.002
(1.08)
Flow
0.03
(2.11)
∆VIX
R2
[6]
0.004
(1.84)
0.004
(2.04)
0.03
(2.35)
0.02
(2.39)
-0.0005
(-1.71)
0.03
0.01
0.01
0.04
0.03
-0.0001
(-2.18)
0.11
0.15
Data includes 27 pairs of hedge fund shares and covers the period from December 1993 to December 2002. 
denotes the traded liquidity factor by Pastor & Stambaugh.  denotes the spread between 3-month LIBOR and
3-month T-Bills called the TED spread.  denotes Chicago Board Options Exchange Market Volatility Index,
which is the level of implied volatility of S&P 500 index options.  denotes the 1-month aggregate hedge
fund flow. ∆ denotes the change in the level of VIX index from month  − 1 to . Table includes coefficients
for each variable and t-statistics in parentheses. R2 denotes the coefficient of determination for each model.
Table 16 presents results from regressions containing all of the funds between the
period from January 2003 and June 2012. This sample includes also FOFs, since first
return observations of FOFs start at the beginning of this period. Compared to Table
15, in which the change in the level of VIX, ∆, does not possess any statistical
significance in alone, it turns back to statistically significant for the second subperiod as it is in Table 12 for the entire sample period. For the second sub-period,
69
aggregate hedge fund flow has explained almost the third of the BAB return all
alone. Only notable distinction between all funds and funds with at least 1 year of
return data is that ΔVIX is not significant in joint regression [8] for all of the share
classes. Results for the sample consisting of funds with at least 12 monthly return
observations and for the sample not including funds of hedge funds are reported in
Appendix 2. They do not differ significantly from the results in Table 1616.
Table 16. Summary statistics of the second sub-period sample.
Model
Parameters
[1]
[2]
[3]
[4]
[5]
Intercept
Liq
0.003
(3.88)
0.003
(4.30)
0.003
(4.30)
0.002
(2.35)
-0.001
(-2.99)
[7]
[8]
0.001
(4.23)
-0.001
(-1.45)
-0.002
(-2.88)
0.004
(0.69)
0.004
(0.64)
-0.01
(-1.68)
VIX
-0.0001
(-2.93)
TED
-0.00002
(-0.60)
-0.001
(-0.91)
Flow
0.05
(7.49)
∆VIX
R2
[6]
-0.001
(-1.48)
-0.001
(-1.56)
0.05
(6.28)
0.05
(6.35)
-0.0005
(-3.15)
0.01
0.07
0.01
0.31
0.08
-0.0001
(-1.38)
0.31
0.33
Data includes all hedge fund share classes in the period and there are 127 pairs of share classes in total. Table
includes coefficients for each variable and t-statistics in parentheses. R2 denotes the coefficient of determination
for each model. Sample covers the period from January 2003 to June 2012.
When comparing the sub-period and whole period samples, we can find out that the
first sub-period supports more our hypothesis 2. For the second sub-period results
turn around and are similar to the whole period sample. As the quantity of data in the
first sub-period is quite low, the regressions estimates can be bit spurious. Thus,
when making inferences for the movements in the BAB factor, we favor the whole
period sample in Tables 12 and 13.
16
Table 18 presents results for share classes with at least 1 year of return observations. Only important
implication of Table 18 is that, the magnitude of R2 is much lower than those in Table 16. Same
applies for the sub-period sample of traditional hedge funds only.
70
5
CONCLUSION
By following the method of Frazzini & Pedersen (2011), this study investigates the
impact of embedded leverage on returns of hedge fund share classes with different
leverage coefficients, and the premium that investors are willing to pay to obtain it.
Investors’ desire for magnified returns and their inability to employ as much leverage
as desired induces them to invest in securities with embedded leverage without
violating their leverage constraints. Hedge funds have set up leveraged share classes
for qualified investors to have an access on levered returns. Hedge funds acquire this
leverage by either outside borrowing or by using securities with embedded leverage.
Even though hedge funds are only open to certain type of investors, there exist
investors belonging to that category, who are willing to pay a premium for assets
with embedded leverage. This premium responds with lower returns generated by
leveraged share classes compared to their unleveraged counterparts. Results of this
thesis are consistent with earlier studies of embedded leverage. Assets having highembedded leverage tend to produce lower returns relative to low-embedded leverage
assets as concluded in Frazzini & Pedersen (2010 & 2011).
Of the several empirical findings of this study, the first important contribution to
previous academic studies is that there actually exists a spread between the returns of
unleveraged and leveraged hedge fund share classes, area in which a void in the
research has existed. This return spread indicates that there is a negative relationship
between embedded leverage and the BAB returns. Embedded leverage deteriorates
the returns of leveraged hedge fund share classes and portfolios with higher
embedded leverage have lower mean returns. This study fills gaps in earlier research
and goes beyond by describing the parameters affecting to the level of the BAB
spread. Even though the BAB factor is not directly tradable, it has important
implications for hedge fund investors. Since this thesis also applies the combined and
extensive database of five different commercial hedge fund databases, the empirical
results are more comprehensive as some of the previous studies of hedge funds, and
mitigate some well-known biases in commercial hedge fund databases.
71
The second important contribution of this study is that the equally-weighted BAB
returns can be explained by some macroeconomic and risk variables. Empirical
findings for the changes in the level of the BAB spread in this study are consistent
with the findings of Ang et al. (2011) regarding their study of hedge fund leverage.
Economy-wide factors tend to have more predictive power to changes in the BAB
factor than fund-specific characteristics and the BAB factor mostly depends on the
aggregate state of financial markets. We find positive relationship between aggregate
hedge fund flow and BAB factor throughout the sample period. Aggregate flow is a
robust estimate and is capable of explaining the movements in the BAB factor.
Changes in asset and funding liquidity decreases the equally-weighted BAB return.
This may be partly explained by the fact that leveraged share classes de-lever their
exposures during low asset and funding liquidity, thus not maintaining exposures at
the targeted level constantly. Hence, investors in leveraged share classes may not
experience as poor results as would be expected as the BAB return decreases
simultaneously. Relating to our hypothesis 2, low funding liquidity, as measured by
TED spread, only increases the BAB factor for sample consisting of funds of hedge
funds.
Additionally, this study considers, whether the magnitude of the BAB factor is
affected by share restrictions or by serial correlation arising from illiquid portfolio
holdings. This study does not find significant relation between the BAB factor and
hedge fund illiquidity measured by different share restrictions imposed by hedge
funds. However, illiquidity of hedge funds appears in the form of serial correlation
between hedge fund returns. Findings of this thesis are congruent with those of
Getmansky et al. (2004). Empirical results indicate that the BAB returns are serially
correlated, but mainly with 2nd-lag coefficients only. These results could be also due
to multicollinearity and not indicate return smoothing of any kind. However, for the
sample consisting of funds of hedge funds only, positive and significant 1st-lag serial
correlation can be found. This contributes to the previous studies of funds of hedge
funds indicating that their returns yield positive serial correlation.
As a conclusion, embedded leverage in hedge fund share classes has important
implications. There exists a return difference between unleveraged and leveraged
share classes with the returns of leveraged share classes scaled with their level of
72
leverage being inferior to those of unleveraged share classes. Share restrictions
applied by hedge funds do not have significant effect on the magnitude of the BAB
factor. However, aggregate hedge fund flow, has positive relationship with the BAB
factor and is capable of explaining the magnitude of the BAB. Changes in asset and
funding liquidity have negative relation with the BAB factor. They affect hedge fund
leverage and cause leveraged share classes to de-lever. Thus, these actions have
direct effect on the level of the BAB factor.
73
REFERENCES
Acharya VV & Viswanathan S (2011). Leverage, moral hazard, and liquidity. The
Journal of Finance. 66(1), 99-138.
Ackermann C, McEnally R & Ravenscraft D (1999). The performance of hedge
funds: Risk, return and incentives. The Journal of Finance. 54(3), 833-874.
Adrian T & Shin HS (2010). Liquidity and leverage. Journal of Financial
Intermediation. 19(3), 418-437.
Agarwal V, Daniel ND & Naik NY (2009). Role of managerial incentives and
discretion in hedge fund performance. The Journal of Finance. 64(5), 2221-2256.
Agarwal V, Fos V & Jiang W (2013). Inferring reporting-related biases in hedge fund
databases from hedge fund equity holdings. Management Science. 59(6), 12711289.
Agarwal V & Naik NY (2004). Risks and portfolio decisions involving hedge funds.
The Review of Financial Studies. 17(1), 63-98.
Amin GS & Kat HM (2001). Welcome to the dark side: Hedge fund attrition and
survivorship bias over the period 1994-2001. Cass Business School Research
Paper. Available: http://ssrn.com/abstract=293828.
Ang A, Gorovyy S & van Inwegen GB (2011). Hedge fund leverage. Journal of
Financial Economics. 102(1), 102-126.
Ang A, Rhodes-Kopf M & Zhao R (2008). Do funds-of-funds deserve their fees-onfees? Journal of Investment Management 39, 1069-1095.
Aragon GO (2007). Share restrictions and asset pricing: Evidence from the hedge
fund industry. Journal of Financial Economics. 83(1), 33-58.
Asness C, Frazzini A & Pedersen LH (2012). Leverage aversion and risk parity.
Financial Analyst Journal. 68(1), 47-59.
Asness C, Krail R, Liew J (2001). Do hedge funds hedge? The Journal of Portfolio
Management. 28(1), 6-19.
Black F (1972). Capital market equilibrium with restricted borrowing. Journal of
Business. 45(3), 444-455.
Black F (1992). Beta and return. The Journal of Portfolio Management. 20, 8-18.
Black F, Jensen MC & Scholes M (1972). The capital asset pricing model: Some
empirical tests. In Jensen MC (ed.), Studies in the Theory of Capital Markets.
Praeger Publisher Inc.
74
Bollen N & Pool V (2009). Do hedge fund managers misreport returns? Evidence
from the pooled distribution. The Journal of Finance. 64(5), 2257-2288.
Breuer P (2002). Measuring off-balance-sheet leverage. Journal of Banking &
Finance. 26(3), 223-242.
Broadie M, Johannes M & Chernov M (2009). Understanding index option returns.
Review of Financial Studies. 22(11), 4493-4529.
Brown SJ, Goetzmann W & Liang B (2004). Fees on fees in funds of funds. Journal
of Investment Management. 2(4), 39-56.
Brunnermeier M & Pedersen LH (2009). Market liquidity and funding liquidity. The
Review of Financial Studies. 22(6). 2201-2238.
Buraschi A, Kosowski R & Sritrakul W (2013). Incentives and endogenous risk
taking: A structural view of hedge funds alphas. AFA 2012 Chicago Meetings
Paper. Available: http://ssrn.com/abstract=178599
Chandar N & Bricker R (2002). Incentives, discretion, and asset valuation in closedend mutual funds. Journal of Accounting Research. 40(4), 1037-1070.
Dai J & Sundaresan S (2010). Risk management framework for hedge funds: Role of
funding and redemption options on leverage. Working paper, Columbia
University.
Damodar G (2003). Basic Econometrics (4th ed.) McGraw-Hill.
Ding B, Getmansky M, Liang B & Wermers R (2009). Share restrictions and
investor
flows
in
the
hedge
fund
industry.
Available:
http://ssrn.com/abstract=891732.
Fostel A & Geanakoplos J (2008). Leverage cycles and anxious economy. The
American Economic Review. 98(4), 1211-1244.
Frazzini A & Pedersen LH (2010). Betting against beta. Working Paper, AQR Capital
Management, New York University and NBER.
Frazzini A & Pedersen LH (2011). Embedded leverage. Working Paper. AQR Capital
Management, New York University and NBER.
Fung W & Hsieh D (1997). Empirical characteristics of dynamic trading strategies:
The case of hedge funds. Review of Financial Studies. 10(2), 275-302.
Fung W & Hsieh D (2000). Performance characteristics of hedge funds and
commodity funds: Natural vs. spurious biases. Journal of Financial and
Quantitative Analysis. 35(3), 291-307.
75
Fung W & Hsieh D (2004). Hedge fund benchmarks: A risk-based approach.
Financial Analysts Journal. 60(5), 65-80.
Getmansky M, Lo AW & Makarov I (2004). An econometric model of serial
correlation and illiquidity in hedge fund returns. Journal of Financial Economics.
74(3), 529-609.
Getmansky M (2012). The life cycle of hedge funds: Fund flows, size, competition,
and performance. Quarterly Journal of Finance. 2(2) 1-53.
Goetzmann W, Ingersoll J & Ross S (2003). High water marks and hedge fund
management contracts. The Journal of Finance. 58(4), 1685-1718
Ibbotson RG, Chen P & Zhu KX (2011). The ABCs of hedge funds: Alphas, betas,
and costs. Financial Analyst Journal. 67(1), 15-25.
Jagannathan R, Malakhov A & Novikov D (2010). Do hot hands exist among hedge
fund managers? An empirical evaluation. The Journal of Finance. 65(1), 217-255.
Kat HM & Palaro H (2005). Who needs hedge funds? A copula-based approach to
hedge fund return replication. Alternative Investment Research Centre Working
Paper No. 27; Cass Business School Research Paper. Available:
http://ssrn.com/abstract=855424.
Kirschner S, Mayer EC & Kessler L (2006). The Investor’s Guide to Hedge Funds.
John Wiley and Sons.
Kosowski R, Naik NY & Teo M (2007). Do hedge funds deliver alpha? A bayesian
and bootstrap analysis. Journal of Financial Economics. 84(1), 229-264.
Lan Y, Wang N & Yang J (2013). The economics of hedge funds. Journal of Financial
Economics forthcoming.
Liang B (2000). Hedge funds: The living and the dead. Journal of Financial and
Quantitative Analysis. 35(3), 309-326.
Liang B & Park H (2007). Risk measures for hedge funds: a cross-sectional
approach. European Financial Management. 13(3), 333-370.
Liang B & Park H (2008). Share restrictions, liquidity premium and offshore hedge
funds. University of Massachusetts, Amherst Working Paper.
Lintner J (1965). The valuation of risk assets and the selection of risky investments
in stock portfolios and capital budgets. Review of Economics and Statistics. 47(1),
13-37.
Lo AW (2001). Risk management for hedge funds: Introduction and overview.
Financial Analyst Journal. 57, 16-33.
76
Lo AW (2005). Dynamics of hedge fund industry (2nd ed.). United States of America:
Research Foundation of CFA Institute.
McGuire P & Tsatsaronis K (2008). Estimating hedge fund leverage. BIS Working
Paper No. 260. Available: http://ssrn.com/abstract=1333617.
Mossin J (1966). Equilibrium in a capital asset market. Econometrica. 34(4), 768783.
Pastor L & Stambaugh RF (2003). Liquidity risk and expected stock returns. Journal
of Political Economy. 111(3). 642-685.
Posthuma N & Van der Sluis PJ (2003). A reality check on hedge fund returns.
Unpublished working paper. Available: http://ssrn.com/abstract=438840.
Schneeweis T, Martin GA, Kazemi HB & Karavas V (2005). The impact of leverage
on hedge fund risk and return. The Journal of Alternative Investments. 7(4), 1021.
Sharpe WF (1964). Capital asset prices: A theory of market equilibrium under
conditions of risk. Journal of Finance. 19(3), 425-442.
Stein J (2009). Sophisticated investors and market efficiency. The Journal of Finance.
64(4), 1517-1548.
Wang A & Zheng L (2008). Aggregate hedge fund flows and asset returns. Available:
http://ssrn.com/abstract=1081475.
77
APPENDIX 1
CORRELATION COEFFICIENTS
This appendix section provides detailed look into correlation coefficients between
variables used in cross-sectional regression analysis investigating hypothesis 2.
According to Ang et al. (2011) TED spread and VIX are highly correlated over some
periods, such as from 2007 to 2010, and as such may affect the results of regression
estimates. Since the main analysis period of this study is the period from 1993 to
2012, correlation coefficients are calculated for that period to find out, whether high
correlations are persistent throughout the whole sample period.
Correlation coefficients are presented in Table 17. Correlation between TED spread
and VIX has not been that high as proposed by Ang et al. (2011) for the whole
period. One interesting point worth of noticing is, that correlation between aggregate
hedge fund flow and other factors are quite low, which supports the empirical
findings of this study. Even when added to joint regressions, statistical properties of
aggregate hedge fund flow are not affected as much as are those of other variables.
Data period used in the study of Ang et al. (2011) is far shorter than in our study,
which could explain these deviations.
Table 17. Correlation coefficients of different macro and risk factors.
Factors
TED
VIX
FLOW
LIQ
TED
1.00
VIX
0.46
1.00
FLOW
-0.22
-0.24
1.00
LIQ
-0.18
-0.08
0.05
1.00
ΔVIX
0.17
0.38
-0.23
-0.13
ΔVIX
1.00
Table presents correlation coefficients of macro and risk factors used as variables in model presented in equation
(22). TED denotes the spread between 3-month LIBOR and 3-month T-Bills called the TED spread. VIX denotes
Chicago Board Options Exchange Market Volatility Index, which is the level of implied volatility of S&P 500
index options. FLOW denotes the 1-month aggregate hedge fund flow. LIQ denotes the traded liquidity factor of
Pastor & Stambaugh. ∆VIX denotes the change in the level of VIX index from month  − 1 to .
78
APPENDIX 2
ADDITIONAL EMPIRICAL RESULTS
Table 18 provides statistics for share classes with at least 1 year of return data for the
first sub-period in the fund-level regression. In comparison to tables provided in
section 4.2.1, in Table 18 redemption period becomes just slightly statistically
significant in model [4], but with very low coefficient of R2. However, in joint
regression model [7] it does not produce any statistical significance. Again 2nd-lag
autocorrelation coefficient is slightly significant, and one thing worth of noticing is
that coefficient is positive contrary to the whole period sample. Even though adding
2nd-lag autocorrelation coefficient increases the magnitude of R2, the level itself is
relatively low. Since data in Table 18 does not include any funds of hedge funds,
implications for the conventional hedge funds can be made.
Table 18. Summary of funds with at least 1 year of data for the second sub-period.
Model
Parameters
[1]
[2]
[3]
[4]
[5]
[6]
Intercept
Lockup
0.001
(2.95)
0.001
(2.57)
0.001
(1.71)
0.001
(1.65)
0.001
(2.87)
0.001
(1.34)
Notice
0.004
(0.89)
0.002
(0.34)
0.001
(1.97)
1st-lag corr
0.001
(1.28)
0.001
(0.52)
2nd-lag corr
0.01
0.001
(1.74)
0.001
(1.04)
Redemption
R2
0.001
(3.34)
[7]
0.01
0.02
0.00
0.001
(1.47)
0.002
(1.34)
0.004
(1.97)
0.004
(1.99)
0.05
0.07
Data includes 121 pairs of share classes Share restrictions parameters ,  and  measure
the redemption-, advance notice- and lockup periods in days. 1  −   denotes the 1st-lag autocorrelation
coefficient and  −   denotes 2nd-lag autocorrelation coefficient. T-statistics are in parentheses. R2
denotes the coefficient of determination for each model. Data covers the period between January 2003 and June
2012.
79
When considering the equally-weighted BAB regressions, results for the sample
consisting only of hedge fund share classes with at least 12 monthly return
observations do not differ dramatically from the table 11 presented earlier. Data
includes 121 pairs of hedge fund share classes. Aggregate hedge fund flow and
change in the level of VIX are still the most significant coefficients.
Results for the pure sample of traditional hedge fund share classes without FOFs for
the second sub-period are very similar when compared to Table 13 for the whole
period. Thus, results are not shown here. Aggregate hedge fund flow, VIX and the
change in VIX are still robust estimates explaining the movements in the equallyweighted BAB return. Intercept term is also statistically significant, indicating that
also for the sample without FOFs unleveraged share classes have outperformed
leveraged share classes.
Download PDF