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

- Similar pages