The evolving beta-liquidity relationship of hedge funds

Author’s Accepted Manuscript The Evolving Beta-Liquidity Relationship of Hedge Funds Arjen Siegmann, Denitsa Stefanova

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S0927-5398(17)30031-2 http://dx.doi.org/10.1016/j.jempfin.2017.04.002 EMPFIN972

To appear in: Journal of Empirical Finance Received date: 7 November 2016 Revised date: 24 March 2017 Accepted date: 9 April 2017 Cite this article as: Arjen Siegmann and Denitsa Stefanova, The Evolving BetaLiquidity Relationship of Hedge Funds, Journal of Empirical Finance, http://dx.doi.org/10.1016/j.jempfin.2017.04.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The Evolving Beta-Liquidity Relationship of Hedge Funds Arjen Siegmanna1, Denitsa Stefanovab2* a

b

Vrije Universiteit Amsterdam, Faculty of Economics and Business, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands

Luxembourg School of Finance, Université du Luxembourg, 4, rue Albert Borschette, L-1246 Luxembourg [email protected] [email protected] *Corresponding author.

Abstract Hedge funds are known to have liquidity-timing capability, but this might be conditional on aggregate market conditions. To test this, we analyze changes in the relation between hedge funds’ stock market exposure and aggregate stock market liquidity. Employing an optimal changepoint approach, we find that equity-oriented hedge funds display a significant shift in liquidity-timing behavior after the major market microstructure changes in the year 2000. The shift is from a negative relation between market beta and liquidity towards a positive relation. We rule out a mechanistic explanation of the results by computing the returns to several familiar risk arbitrage strategies, finding in them no evidence of a similar shift in liquidity timing. Keywords: hedge funds, market timing, liquidity timing, changepoint regression, dynamic strategies JEL-Classifications: G14, G18, G23

1 Introduction Hedge funds seem to be able to time general market trends and risk factors. Market timing behavior is observed from their early exit from the technology bubble as well as quickly changing exposures to market risk factors (see Brunnermeier and Nagel (2004) and Patton and Ramadorai (2013). Dynamic trading strategies employed by hedge funds potentially get reflected 

We thank André Lucas, Albert Menkveld, Bernd Schwaab, Joop Huij, Yufeng Han, Paulo Maio, Redouane Elkamhi, Dale Rosenthal, seminar participants at the CFR Research Seminar at Cologne, the 14th Conference of the Swiss Society for Financial Market Research (SGF), International Paris Finance Meeting 2011, Montreal Mathematical Finance Days 2012, FMA Europe 2012 meeting, Luxembourg School of Finance and an anonymous referee for useful comments and suggestions. A previous version of this paper circulated as ‘Market Liquidity and Exposure of Hedge Funds’. 1 2

Tel.: +31 20 598 6581; fax +31-20 598 6020. Tel.: +352 46 66 44 5589; fax +352 46 66 44 35589.

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in option-like returns, pointing towards certain timing behavior (see Fung and Hsieh (1997). Chen and Liang (2007) find evidence of a market and volatility timing ability of hedge funds (self-described as ‘market-timers’) that tends to decrease their market presence in times of high volatility. This timing behavior is well documented and has implications for hedge fund investors as well as other financial market participants. A risk factor that is of particular importance to hedge funds is liquidity. Hedge funds can earn the liquidity premium by tilting their investment portfolio towards stocks that are less liquid. Or they earn from dynamic and statistical arbitrage strategies, which need market liquidity to be executed profitably. The two types of strategies have a different relationship with aggregate liquidity. Until now, only Cao et al. (2013) find evidence for a relationship of hedge fund returns with aggregate liquidity— and for one type only: hedge funds tune their market presence to states of high market liquidity, with the best timers having the best performance. This paper analyzes the evidence for alternative relations between hedge fund market presence and aggregate liquidity. There is ample reason to believe that the liquidity-timing behavior of hedge funds could reveal itself in different ways than the one documented in Cao et al. (2003). For example, hedge funds are known to exploit liquidity-based long-short strategies, which implies an increased market presence when liquidity becomes scarce. This is the opposite effect of Cao et al. (2013). Moreover, if one or the other mechanism prevails at a certain point in time, we would find a structural break in the market presence of hedge funds related to market liquidity (i.e. in their liquidity-timing behavior). That is the subject of our empirical investigation. We hypothesize that the direction of the liquidity-timing behavior of hedge funds is a function of market conditions. Market-wide liquidity has been found to be a priced factor (see Pastor and Stambaugh 2003 and Acharya and Pedersen 2005), and constitutes an important element of market circumstances. While stock market liquidity has improved considerably over recent decades, there is a well-documented trend of a diminishing liquidity premium. Ben-Rephael et al. (2015) find that the effect of improved liquidity on the characteristic liquidity premium (i.e. the premium associated with the transaction costs of trading in a security) has been that of a large and significant decline. Related to that finding, Ben-David et al. (2012) document that trading on the liquidity premium has become less profitable over time, and selling activity during market declines has become more prominent. See also Cella et al. (2013) for similar evidence on shortterm traders in general. Likewise, we predict that the role of hedge funds as liquidity providers has declined, which could be visible in their liquidity-timing behavior becoming more prominent on the stock market. The declining liquidity premium is likely caused by changes in market structure. For example, Chordia et al. (2014) identify distinct regimes in market efficiency related to the exogenous decreases in market liquidity that were caused by consecutive reductions in the minimum tick

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size.3 Exogenous liquidity events also have a bearing on the ability of hedge funds to supply liquidity. For example, Jylhä et al. (2014) document that the advent of automated quote dissemination (autoquote) at the NYSE has changed the speed with which hedge funds provide liquidity, in that it takes longer to enter and exit their liquidity providing trades. Also, Hendershott et al. (2011) find large increases in liquidity due to the arrival of algorithmic trading. To the extent that liquidity supply is manifested in increased market presence in times of low liquidity, such exogenous liquidity shocks are likely to impact the ability of hedge funds to time liquidity. Our prediction is that, due to technological change, market-making activities of hedge funds have become less profitable, which has led to the skills of hedge funds in that area becoming less important. Activities in algorithmic trading that make use of highly liquid securities have become more prominent, and liquidity-timing behavior has changed accordingly, towards a market presence that is highest when liquidity is high. In order to uncover a structural break in the liquidity-timing behavior of hedge funds without pre-specifying the breakpoint, we propose an optimal changepoint model for the stock market exposure of hedge funds. The model allows for breaks in the linear relation between hedge fund market betas and the level of aggregate market liquidity. It nests models that use contemporaneous conditioning information to detect evidence of timing ability (see, for example, Busse (1999), Chen and Liang (2007) and Cao et al. (2013) and adds the potential for structural changes in that timing behavior via an optimal changepoint. In particular, the model pinpoints the optimal time when the interaction between market risk exposure and aggregate stock market liquidity changes. To account for potential effects of volatility or market timing, we also estimate an extended model that allows for breaks in the volatility timing behavior of hedge funds. Our results provide strong evidence of structural breaks in the liquidity-timing behavior of hedge funds, thereby supporting our hypothesis. Equity-oriented hedge funds from the Long/Short Equity Hedge and Equity Market Neutral style categories and Funds of Funds (which together constitute about 75% of the Lipper TASS database) show a consistent pattern in their betaliquidity relation, with a significant break in the direction of this relation in the year 2000. Before the breakpoint, the market exposures of equity-oriented hedge funds generally increase when aggregate market liquidity decreases, which confirms that hedge funds indeed have the role of liquidity suppliers. The market exposures of Funds of Funds are relatively insensitive to liquidity conditions in that period. After the breakpoint, we find the opposite effect of increased market exposure in times of improved market liquidity. This finding holds across most style categories. The location of the breakpoint in 2000 that our model identifies coincides with the institutional changes of tick size decimalization4 and disclosure of execution quality5 that took place at that 3

The minimum tick size on the New York Stock Exchange (NYSE) was reduced from $1/8 to $1/16 in 1997; it was reduced further to one cent in 2001. 4 The conversion to decimal pricing on the NYSE was phased in throughout the year 2000 and was completed in January 2001. The reduction of the minimum tick size to one cent was introduced in April 2001 for NASDAQ.

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time. The increase in transparency following the changes in disclosure rules has led to more competition between exchanges, with the result that execution quality in U.S. equities has improved dramatically (see Zhao and Chung (2007) and O'Hara and Ye (2011). Moreover, after the decimalization, the liquidity of the U.S. stock market increased across all commonly used determinants of liquidity (see Schapiro (2010) and Chordia et al. (2011), and both the average trade size and trading costs decreased sharply (see Bessembinder (2003), Gibson et al. (2003), Chakravarty et al. (2005) and Bacidore et al. (2003).6 Our findings suggest that, following the exogenous change in liquidity conditions induced by these major changes in market microstructure, hedge funds have altered the way in which they adjust market exposures to the state of liquidity. Besides equity-oriented hedge funds, funds in the style categories Event Driven, Global Macro and Multi Strategy also experienced a shift in their market exposure. However, the breakpoint is primarily located in September 1998, the month in which the hedge fund LTCM failed. At an individual fund level, the turning point for these funds is primarily located in the period 20072008. Both 1998 and 2007-2008 are characterized by stock market volatility spikes that coincide with liquidity dry-ups. The literature suggests that the economic value of a market timer is the greatest when the volatility of the market return is high (see Merton 1981). In line with this observation, we demonstrate that hedge funds that are not primarily oriented toward U.S. equity have become more inclined to time liquidity during episodes of high volatility of market liquidity. Given that the trading carried out by hedge funds can itself affect market liquidity, we perform similar analyses for small funds that are unlikely to have a substantial market impact. Our findings remain robust to this investigation. Also, the breakpoints in liquidity timing are robust to other specifications of the market index, to the choice of hedge fund portfolio and liquidity measure, or to the inclusion of a second changepoint in the regression specification. The result holds for hedge funds that do not use leverage or that are not prone to changing market exposures when liquidity conditions deteriorate due to funding constraints. For the breakpoints in 2000, our results are not caused by a composition effect, as the results are similar when only using hedge funds that exist in 1998. Our findings remain robust to allowing for either market timing via an indicator variable for bull/bear market conditions or volatility timing. To rule out mechanistic explanations of the breakpoints, we compute the returns to several dynamic trading strategies that hedge funds may employ: momentum trading, a long/short 5

By virtue of Act 11Ac1-5, adopted in November 2000 and later redesignated as rule 605, by the U.S. Securities and Exchange Commission (SEC). Under Rule 605, any exchanges on which U.S. stocks are traded are required to publish a monthly report of execution quality on a per-stock basis. 6 Further, reductions in the minimum price increment could potentially limit the incentives to providing liquidity and lead to a reduction in liquidity supply (see Harris (1997), Goldstein and Kavajecz (2000) and Jones and Lipson (2001) for evidence on prior tick size reductions, and Gibson et al. 2003 for the impact of the 2000-2001 decimalization).

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liquidity strategy, pairs trading and a reversal strategy. We find that only the momentum strategy has a similar breakpoint; conditioning on funds that load on momentum does not, however, explain the existence of the breakpoints. This paper contributes to the literature in several ways. First, we confirm the importance of aggregate liquidity conditions for hedge fund investment behavior, as in Cao et al. (2013) and Sadka (2010). Second, we show how the methodology of detecting breakpoints in hedge fund returns, as introduced by Bollen and Whaley (2009), can be used successfully to pinpoint periods of changing behavior that coincide with systemic events in the market. Finally, our results are related to the systematic linkages between hedge funds and the financial system, as in Adrian and Brunnermeier (2011) and Billio et al. (2012). The institutional changes that have facilitated automated trading have affected the dynamics of hedge fund beta and liquidity. This has implications for researchers and practitioners who estimate dynamic risk exposures of hedge funds. The paper proceeds as follows. Section 2 introduces the model for testing for changepoints in hedge fund returns. Section 3 describes the data. Section 4 presents the main results. Section 5 analyzes four dynamic trading strategies that might underlie the changepoints. Section 6 provides robustness analyses. Section 7 concludes.

2 Detecting Structural Breaks in Hedge Fund Exposures Consider the following linear specification for hedge fund returns and risk factors with a timevarying beta for the stock market return : ∑ where

∑

is the hedge fund portfolio return in month ,

(1) the return on the market,

a set of

risk factors and an error term. is the time-varying market beta, are the lagged market betas and , , are the exposures to the other six hedge fund risk factors of Fung and Hsieh (2004), and an innovation in liquidity to account for priced liquidity risk. The Fung and Hsieh factors, which include linear and option-like factors, are given by a size factor, the monthly change in 10-year Treasury yields, the change in the yield spread between a 10-year Treasury bond and Moody’s Baa bonds, as well as three trend-following factors represented by the return of a portfolio of lookback options straddles on bond, currency and commodity futures. Unless noted otherwise, the market return is the return on the S&P 500 stock index. Our focus is now on the relation between the stock market beta and aggregate liquidity. Considering aggregate liquidity as an information variable is suggested by several sources in the literature. Regarding expected returns, Amihud (2002) and Acharya and Pedersen (2005) find that in the cross-section of U.S. stocks, the conditional expected return is inversely related to liquidity. Bekaert et al. (2007) find a similar result for emerging markets. Jones (2002) finds a 5

relation between the annual stock market return and the previous year’s bid-ask spread and turnover. We model the time-variation in as being linearly dependent on market liquidity and market volatility , while allowing for a break in the relation between beta and liquidity. By including volatility, we account for any volatility timing ability of hedge funds. We allow for a change in the relation between beta and liquidity via changepoints within the optimal changepoint regression framework of Andrews et al. (1996). Changepoint regressions for capturing time-varying hedge fund risk exposures have been previously used in the literature (see Bollen and Whaley (2009) and Patton and Ramadorai (2013)). Our setting is different in that we model variations in market betas via observable variables, while allowing for a structural change in the interaction between those variables and the risk exposure. Thus, we can uncover the economic mechanism behind the dynamic of market betas, linking it to liquidity-timing behavior. Specifically, with possible changepoints, the model for becomes ∑ where

(

{

})

(2)

is the liquidity variable,

is market volatility,

{ }

is the indicator function for

event and is the optimal location in time of the -th changepoint. The formulation in Equation (2) allows for separate responses of to liquidity, before and after the changepoint. The parameter measures the change in the sensitivity of beta to liquidity after changepoint . In the case of the S&P 500, the liquidity variable is an aggregate measure of the liquidity of the S&P 500 stocks. Whenever we use other stock market aggregates, the liquidity variable is computed as the aggregate liquidity for the respective market. In our baseline specification we use one changepoint . Section 4.6 tests for two changepoints; using more than two improves the fit of the model but leads to losses in economic interpretation and significance. An alternative would be to estimate a stochastic (latent) process for beta, but this leads to less powerful tests, given the short time-span of individual hedge funds; see Bollen and Whaley (2009). Substituting Equation (2) into (1), we obtain the following partial structural change model for a single changepoint : ( ∑

{

})

∑ (3)

Our specification in (3) nests the case of constant risk exposures (obtained by setting the parameters , and to zero), as well as the model of time-varying betas and constant liquidity interaction (for which ), considered in Cao et al. (2013). Compared to Cao et al., we are interested in patterns of changes in the beta-liquidity relation, while they explore whether hedge funds with a positive beta-liquidity relation have better performance. 6

The optimal changepoint is the one that maximizes the fit (i.e. the change-date that minimizes the sum of squared errors). The details on determining the significance of a changepoint are provided in Appendix A. Extreme liquidity conditions have occurred together with high volatility and low returns— e.g. during market crashes. This could bias our results towards finding a liquidity-timing effect or breakpoint where it may actually be a volatility-timing effect, for example. We control for this by estimating an extended model that allows for breaks in the beta-volatility relation as well. In addition, we control for the effect of bear markets by augmenting the specification for the dynamics of the market beta with a dummy variable , a bear market indicator that is one if the cumulative market return in the 12 preceding months is negative. The specification is as follows: (

{

})

(

})

{

.

(4)

Using Equation (4) for the evolution of leads to a structural change model for changepoints in the interaction terms for volatility and liquidity simultaneously at a breakpoint as follows: ( ∑

{

})

(

{

})

∑

(5)

We measure market liquidity using the Amihud (2002) ILLIQ, which measures stock market illiquidity as the average daily ratio of absolute stock return to dollar volume. This can be seen as the average price impact of a given dollar volume of a transaction. Among daily proxies, the ILLIQ is the most strongly correlated measure with intra-day measures of the price impact of trading (see Goyenko et al. (2009), De Jong and Driessen (2012), Hasbrouck (2009) and Korajczyk and Sadka (2008). To obtain an aggregate ILLIQ measure, we take the average ILLIQ across all stocks for each month, weighted by market capitalization: ∑

(6)

where is the number of stocks in month , is the market capitalization at the end of month and is the market cap at the beginning of the sample period. is the ILLIQ measure for stock in month and is estimated as ∑ where

(7)

denotes the number of trading days in month ,

day of month , and

denotes the return on stock in the

denotes the dollar trading volume for stock in the

day of month

.

7

The illiquidity variable picks up predictable changes in liquidity, such as changes in tick size and time trends in liquidity. To correct for this, we follow Hameed et al. (2010) and adjust ILLIQ for predicted changes in liquidity. This boils down to regressing on (i) tick-change dummies to capture the tick change from 1/8 to 1/16 on June 24, 1997 (ii) the change from 1/16 to the decimal system on January 29, 2001, and (iii) two time-trend variables equal to the difference between the current year and the years 1994 and 1997, respectively, or the first year when the stock is included in the S&P 500 index (if that is later than 1994 or 1997). The adjusted ILLIQ is denoted as and is used side-by-side with the unadjusted ILLIQ measure in most of our analyses. To mitigate a possible problem of outliers (small stocks that have extremely low volumes in one or more days), Acharya and Pedersen (2005) propose a capped version of ILLIQ. Our results remain qualitatively similar when we use this measure to proxy for aggregate market illiquidity.

3 Data For the hedge fund returns we use monthly returns and asset values of individual hedge funds from the Lipper TASS database, as provided by Thomson Reuters. The database contains both live and graveyard funds; it starts retaining dead funds only after 1994, however, and data from earlier periods are subject to survivorship bias (see Fung and Hsieh (2002). We thus follow the conventional approach in the hedge fund literature and start our sample period from January 1994. Our data end in December 2013. We apply the following filter to the individual funds. We discard funds that either do not report on a monthly basis or have less than 24 consecutive months of data. We convert the assets of non-USD funds to U.S. Dollars, using the exchange rate at the end of the month. We include only funds that report net-of-fee returns on a monthly basis and consider only funds with average Assets under Management of $10 million or more. We exclude hedge funds that have no exposure to the U.S. stock market, and those classified as either Fixed Income Arbitrage or Managed Futures. Also, because few hedge funds are classified as Equity Market Neutral, we combine Long/Short Equity Hedge and Equity Market Neutral into one category ("Long/Short Equity"). Table 1 summarizes the descriptive statistics of the monthly hedge fund returns in our sample. It contains a total of 11,008 hedge funds divided over eight style classifications. The most populous styles are Long/Short Equity Hedge and Equity Market Neutral (3,389 funds) and Fund-of-funds (4,696 funds). They jointly account for roughly 75% of the sample.

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For stock market index returns we use the monthly total return on the S&P 500 (large cap), S&P 400 (mid cap), and S&P 600 (small cap), as provided by Datastream. The risk factors used in the changepoint regressions are the seven factors from Fung and Hsieh (2004), as provided on the website of David Hsieh, augmented with contemporaneous AR(2) residuals of the Amihud’s (2002) ILLIQ measure. These include a size factor, the monthly change in 10-year Treasury yields, the change in the yield spread between a 10-year Treasury bond and Moody’s Baa bonds, as well as three trend-following factors represented by the return of a portfolio of lookback straddles on bond, currency and commodity futures. For the volatility measure we take the CBOE VIX index, which is commonly used to capture volatility timing (see Chen and Liang (2007)). Table 2 has the summary statistics of the market factors, liquidity measures and FungHsieh hedge fund risk factors.

Panel B of Table 2 gives the summary statistics of the liquidity measures. For the construction of ILLIQ we use individual stock returns from the Center for Research in Security Prices (CRSP). To construct the monthly ILLIQ measure for each stock, we use daily data (returns, volume and market capitalization) for the constituents of each of the S&P indices (small cap S&P 600, mid cap S&P 400 and large cap S&P 500) for the 1994-2013 period. To obtain a market-wide illiquidity measure for each index, we take the mean of the individual ILLIQ measures across all stocks that constitute the index in a given month, scaled by the market capitalization of the index portfolio.

4 Results We estimate hedge fund market betas and the potential changepoints in the interaction term of market beta and liquidity. Unless noted otherwise, the S&P 500 serves as the market index, and the monthly aggregate of Amihud’s ILLIQ measure is the aggregate liquidity measure using the stocks in the S&P 500, computed as outlined in Section 2.

4.1

Dynamics of Hedge Fund Beta without Changepoint

To obtain a benchmark model for the dynamics of the stock market beta of hedge funds, we start with a model without changepoints. So, we allow for market liquidity to impact hedge fund beta, but assume that this relation is fixed over time. This is similar to Cao et al. (2013), and provides a natural test of liquidity timing. We regress value-weighted hedge fund portfolio returns on the market return and three interaction terms with the market using ILLIQ, volatility, and a bear market indicator, respectively. For the measurement of volatility we use implied volatility of option prices (i.e., the 9

CBOE VIX index). The benefit of using VIX is that it captures both realized volatility as well as (changes in) investor sentiment. The bear market indicator is one if the cumulative market return in the 12 preceding months is negative, and zero otherwise. The Fung-Hsieh risk factors are included as controls. Our main analysis focuses on three hedge fund styles. Two styles are self-reported: Fund-offunds and Long/Short Equity Hedge. The third style is a portfolio with hedge funds that do not have a U.S.-equity focus. This gives us an angle on whether the absence of this focus also precludes an exposure to stock market liquidity. The results are in Table 3.

All three portfolio styles show a positive loading on the market return. We find a positive market beta even for the portfolio of hedge funds that are not equity-oriented (bottom row). There, the loading on the market return is 0.30 and significant. Regarding liquidity timing, we find that the interaction term of the market return and ILLIQ is positive and significant for the portfolio with Long/Short Equity hedge funds. This is consistent with the findings of Cao et al. (2013). Some styles show dynamics of beta associated with changes in VIX. For Long/Short Equity hedge funds, the relation is negative, which is to be expected for investors who are net long. A bear market is associated with a lower market beta, indicative of hedge funds moving out of stocks in bad times. In all, Table 3 gives us a clear indication that liquidity timing is strongly significant for Long/Short Equity hedge funds, and generally absent for Fund-of-funds and hedge funds specializing in non-U.S. equity. The latter two styles could still employ timing strategies, however, when accounting for a changepoint in the relation between market beta and liquidity. We turn now to explore this possibility.

4.2

A Single Changepoint

We estimate the partial structural change model for a single changepoint, as given in Equation (3), with value-weighted portfolio returns of hedge funds. Table 4 reports the coefficient estimates for our three hedge fund portfolio styles. Panel A uses the uncorrected aggregate ILLIQ measure; panel B uses the ILLIQ measure that is corrected for predictable changes in liquidity, as in Hameed et al. (2010)7. We control for the interaction of the VIX measure times the market return, in order to capture the impact of liquidity crises that accompany spikes in the VIX, or the effect of volatility timing by hedge funds.

7

Note that correcting for predictable changes in liquidity is not necessarily the better approach, as we are just as much interested in changes in liquidity timing that could be caused by these changes.

10

Table 4 has several observations worthy of note. First, in the penultimate column, all style portfolios show a significant changepoint in the beta-liquidity relation. Changepoint dates tend to cluster around two specific years (1998 and 2000) and are all significant at the 90% level. Moreover, the loadings on the changepoint are significant for all styles. These results suggest a structural variability in the exposure of hedge funds to the market, which is explained by aggregate liquidity. The loadings on the interaction with VIX are only insignificant for Long/Short Equity, which is similar to the effect found for mutual funds (see Busse (1999). The coefficient estimates for the changepoint are negative and significant for all styles. The negative coefficient implies an inverse relation between market beta and illiquidity, after the date of the changepoint. This type of relationship (high beta if illiquidity is low) is consistent with the findings of Cao et al. (2013), who refer to this as liquidity timing. Their interpretation is that liquidity timing is a signal of manager skill. Hedge fund managers are aware of the risk of withdrawals in times of low market liquidity, and adjust their market presence accordingly. But timing this is difficult, and only the best managers succeed, so that liquidity timing is associated with superior performance. In contrast to Cao et al. (2013), the results in Table 3 show that the liquidity-timing behavior of hedge funds has undergone change, and that styles that do not show liquidity timing in the full sample still show liquidity timing after the breakpoint. Regarding the changepoint years, September 1998 is the month of the LTCM crisis. LTCM was a Global Macro hedge fund (not included in our sample), and hedge funds of that style are among those featuring non-U.S. equity. The changepoint approach captures changes in liquiditytiming behavior of hedge funds occurring after the LTCM crisis. Equity-oriented hedge funds display a significant change in their liquidity-timing behavior in the year 2000. Before the breakpoint, funds in the Long/Short Equity Hedge and Equity Market Neutral style categories demonstrate an increase in their market exposure when aggregate market liquidity decreases, which confirms their playing the role of liquidity suppliers. After the breakpoint, however, their behavior is widely consistent with liquidity timing. The years 2000 and 2001 are well known for the institutional changes that took place. In addition, the literature documents a drastic change in liquidity conditions following the changes. This offers a potential explanation for the significant changes in the beta-liquidity relation of hedge funds that we document in that period. The first institutional change is the mandatory disclosure of execution quality, by virtue of Act 11Ac1-5, adopted in November 2000 and later redesignated as SEC Rule 605, by the U.S. Securities and Exchange Commission (SEC). Under Rule 605, any exchanges on which U.S. stocks are traded are required to publish a monthly report of execution quality on a per-stock basis. The introduction of the rule was a response to increased market fragmentation: the rise of electronic trading together with increased numbers of trading venues meant that consumers and traders could not be sure that their trades were executed at the best available price. In some markets, 50% of trades were executed at better 11

prices than the public quotes (see Securities and Exchanges Commission (2000). Several studies suggest that the rule had its intended effect: The increase in transparency led to more competition between exchanges, and the execution quality in U.S. equities improved dramatically in the years after the introduction of the rule (see Zhao and Chung (2007) and O'Hara and Ye (2011). The second institutional change is the decimalization of quotes, which involves the reduction of the minimum tick size from $1/16 to one cent, which was gradually introduced throughout 2000 and was finalized in January 2001 for the New York Stock Exchange (NYSE) and in April 2001 for NASDAQ. As a result, the liquidity of the U.S. stock market has increased across all commonly used determinants of liquidity; see Schapiro (2010) and Chordia et al. (2011). The average trade size and trading costs decreased sharply after 2001 (see Bessembinder (2003), Gibson et al. (2003), Chakravarty et al. (2005) and Bacidore et al. (2003). Doubts remain about whether this has benefited small stocks to the same extent as large stocks (see Hendershott et al. (2011) and Brennan et al. (2012). Ronen and Weaver (2001) find a significant reduction in volatility after AMEX’s May 1997 tick-size reduction. Chakravarty et al. (2004) find an initial increase in volatility after decimalization in 2001 but a decline over the longer term. Our findings suggest that, following the shift in aggregate liquidity conditions implied by the above major changes in market microstructure, equity-oriented hedge funds have altered their investment behavior in a way to adjust market exposures to the state of liquidity. Our model identifies an optimal changepoint in liquidity timing for these funds within the period of exogenous changes in liquidity. We discuss the robustness checks in Section 6. Overall, our findings link the market microstructure changes in the year 2000 to equity-oriented hedge funds tilting their investment behavior towards liquidity timing. To gauge the relative importance of the estimated changepoint dates in the time series, we also report the evolution of the exp-F statistic used to test for the significance of the changepoint; see Appendix A. Figure 1 has the resulting F-statistic of the changepoint, reported separately for hedge funds taken from Long/Short Equity (panel A) and from Fund-of-funds (panel B).

For Long/Short Equity funds, the F-statistic spikes in the period between 2000 and 2001, attaining its maximum value in the year 2000. A minor peak in the F-statistic occurs towards the end of 2008. For Fund-of-funds, the peak occurs in the period 2000-2001. In addition, there is another peak in the F-statistic (of about half the size of the one in 2001) in 1998, and a minor one towards the end of 2008. The peak in 2008 is not surprising, given the period of the recent financial crisis. Further results below put a second breakpoint for Fund-of-Funds one month after the failure of Lehman Brothers, and the existing literature points to the dramatic impact that this event had on stock markets and hedge funds simultaneously; see Aragon and Strahan (2011). This supports the changepoint methodology in that it is picking up meaningful dates for structural changes in hedge fund dynamics. 12

The single period with a peak in the F-statistic for Long/Short Equity suggests that the model with just one changepoint captures an important shift in the beta-liquidity relation of hedge funds and their liquidity timing behavior. Specifically, hedge fund betas have become increasingly related to market liquidity after the break. Fund managers have thus become more inclined to time liquidity. We have discussed the need for an extended model that allows for breaks in the beta-volatility relation as well, in Equation (5). Table 5 has the results.

Table 5 shows that the location of the changepoints is either in January or September 2000, as in our baseline specification. Also, the coefficients for the changepoint term in ILLIQ are negative and significant for both the basic ILLIQ measure and the adjusted ILLIQ. For the changepoint term in VIX, none of the coefficients is significant at the changepoint dates. Thus, our results indicate changes in the beta-liquidity relation of hedge funds and not coincident changes in the beta-volatility relation. To test for the impact of market timing, we further control for the effect of bear markets by including a dummy variable in the specification for the market beta. It is a bear market indicator that takes the value of one if the cumulative market return in the 12 preceding months is negative. Results on the location and direction of the structural change in liquidity timing remain robust to the state of the market effect. Finally, there is evidence that hedge funds smooth returns, either on purpose or passively, through the illiquidity of some of their assets, such as real estate investments (see Getmansky et al. (2004). Correcting for the possible smoothing of returns does not change our results.

4.3

Conditioning on Stock Market Segments

The horizons of investors might be different for small and large stocks. Also, there is evidence that most illiquid stocks are also the stocks with the smallest market capitalization; see Acharya and Pedersen (2005). To test whether our results are confined to a segment of hedge funds and/or market indices of particular size, we condition our sample of hedge funds on the exposure to small-, medium- and large-sized stock indices. We determine the relevant index for each fund by applying the AIC information criterion from a multivariate regression of individual hedge fund returns on the Fung and Hsieh (1997) seven-factor model, augmented with contemporaneous AR(2) residuals of the Amihud’s (2002) ILLIQ measure, computed on the respective indices. Then we perform a similar set of regressions as in Table 3, but this time with the ILLIQ computed for the respective index (i.e., for the portfolio of hedge funds selected on the S&P 400 Midcap index, we use the ILLIQ measure computed based on the constituents of the S&P 400 as well). It turns out that 39% of hedge funds have the S&P 500 as the appropriate market index.

13

For 43% of funds, the S&P 400 is selected. The remainder, 18%, has the S&P 600 as market index. The regression results are in Table 6.

Table 6 shows that the coefficient for the interaction term, , remains negative and { } significant for most styles. The changepoint dates are similar to those in Table 4.

4.4

Changepoints for Individual Hedge Funds

To gain further insight into potential shifts in the liquidity-timing ability of hedge fund managers, we estimate the changepoint regression for individual funds. We only take hedge funds within the Long/Short Equity Hedge and Equity Market Neutral style categories with at least 36 months of return data. If hedge funds have a significant changepoint, we record the year of the changepoint. Table 7 reports the outcomes in terms of the frequency of optimal changepoints per calendar year.

The years in which the most changepoints in liquidity timing occur are 2000 and 2009, with respectively 13% and up to 16% of hedge funds within the LSEH/EMN category having an optimal changepoint in those years. For the 2000 breakpoint, the average and cross-sectional tstatistics point consistently at a significant negative sign for the interaction term of market beta and liquidity after the breakpoint. In other years, there are similar negative coefficients, but for a far lower fraction of hedge funds.8 In line with the portfolio results, Long/Short Equity hedge and Fund-of-funds account for the majority of hedge funds that show a structural change in their liquidity-timing behavior around the year 2000.9 The most popular breakpoint for individual funds is in 2008, when 26% of all funds with a changepoint show a significant shift in liquidity timing. The failure of Lehman Brothers in 2008 led to market turmoil, which is reflected in the observed changepoint. This is also the year in which most funds in the style categories Event-driven, Global macro and Multistrategy display a significant change in their market timing behavior. In line with the literature on the economic value of a market timer (see Merton 1981), we find that individual hedge funds, especially those not primarily oriented toward U.S. equity, become more inclined to time liquidity right after 2008, a period of high volatility of market liquidity.

8

Note that in interpreting the results in Table 7 we must take into account that individual fund returns give a much noisier measurement of systematic risk factors, so that these results are best interpreted as being indicative of a pattern that we found in a more robust way in the previous subsection. 9 About 9% of the Funds-of-funds with a changepoint show a structural change in their liquidity-timing behavior in the year 2000.

14

The frequency of optimal changepoints per style is illustrated in Figure 2.10

Figure 2 illustrates the results for Long/Short Equity and Funds of Funds, with changepoints clustering around the years 2000 and 2008. Figure A1 in the Supplementary Appendix has changepoint frequencies for hedge funds from styles that are not predominantly equity-oriented. There, a peak around the year 2000 is absent, which supports the notion that the equity orientation of hedge funds is a determining factor of the changepoint results that we document. The results for separate styles in the supplementary appendix suffer from measurement noise. Nevertheless, the liquidity-timing behavior of convertible arbitrage funds is worth noting. Funds in this style category exploit mispricing of convertible bonds and employ delta-neutral trading strategies, typically short-selling the underlying equity. Dynamic hedging prompts convertible arbitrageurs to buy the stock after a decrease in the firm’s stock price and to increase their short position after a stock price increase. Trading against the aggregate market demand essentially renders them liquidity providers (see Choi, Getmansky and Tookes 2009 for an analysis of convertible arbitrageurs and stock market liquidity). The positive coefficient of the interaction term between market return and illiquidity that we document corroborates that evidence. The breakpoints for convertible arbitrage funds (mostly 2005 and 2008) are specific to this style category and correspond to periods of large redemptions from investors.11

4.5

Conditioning on Hedge Fund Characteristics

Our results might be driven by a subset of hedge funds that use leverage or are exposed to investor withdrawals, since they might be faced with forced liquidations after a liquidity event. To analyze whether this affects our results, we re-estimate our model for portfolios of hedge funds that are less likely to be affected by the above-mentioned constraints. For brevity, we restrict the analysis to portfolios of hedge funds from Long/Short Equity and Fund-of-funds. We form value-weighted portfolios using hedge funds that (1) do not employ leverage, (2) have a low redemption frequency, (3) have redemption notice periods of 60 days or more, (4) have lockup periods of more than three months, and (5) have a below-median fund-flow volatility, as computed in Sirri and Tufano (1998). The results, with the prevalence of each statistic, are in Table 8.

10

See also Figure A1 in the Supplementary Appendix for frequencies of optimal changepoint years for several nonequity styles. 11 Thanks for an anonymous referee for pointing us to this point. See Mitchell et al. (2007) for a discussion on investor redemptions in 2005.

15

Table 8 shows significant change dates for all five portfolios, all located in the year 2000. The reversal in the beta-liquidity relationship remains strongly significant, even when hedge funds are less likely to be impacted by external funding constraints.

4.6

Extension to Two Changepoints

Our results for a single changepoint, and especially the distribution of the F-statistics in Figure 1 suggest that a single changepoint captures a significant change in the dynamics of hedge funds’ market exposure. However, individual fund results for the style categories Long/Short Equity and Fund-of-funds suggest that there may be more than one relevant changepoint in timing liquidity. Thus, we extend our baseline model to a specification with two changepoints ( and ). We estimate a model with the following dynamics of market beta: (

{

}

{

})

(

{

})

.

(8)

We report coefficient estimates and breakpoint dates for Long/Short Equity funds and Fund-offunds in Table 9.

For Long/Short Equity, the changepoints are very close together, spaced within two months (i.e., Feb-00 and Mar-00). This shows that the value-added of an extra changepoint is minimal. Moreover, it confirms the prevalence of single changepoints around the year 2000. For Fund-offunds, the model with volatility timing finds optimal changepoints in September 2000 and November 2008. The reported results are consistent with the peaks in the F-statistic that we observed for the portfolio results in Figure 1, as well as the evidence on individual funds in Figure 2 (Panel A).

5 Changepoints in Dynamic Strategies The relation between hedge fund betas and liquidity could be due to a specific trading strategy or to systematic exposure that is common among hedge funds and that was particularly affected by the institutional changes in 2000 and 2001, or (for some funds), the onset of the financial crisis in 2008. Thus, we analyze four dynamic strategies which might have a similar beta-liquidity relation that we observe for hedge funds: (i) a liquidity trading strategy, (ii) pairs trading, (iii) momentum and (iii) a reversal strategy. Appendix B has the details on the construction of each strategy. For each strategy, we compute the monthly returns and estimate the changepoint model for the strategy return. The results are in Table 10.

Table 10 shows that for each strategy, the exposure to the market is limited. Only pairs trading has a small but significant exposure of 0.05, and an exposure to the interaction term 16

of -0.18. The interaction term with a changepoint is significant for all strategies, but only negative for the Momentum strategy, equal to -3.15. Based on the F-test for significance of the changepoint date, the changepoint for the momentum strategy is significant and located in December 2000. For each strategy, we sort hedge funds into loading and non-loading portfolios, based on whether their exposure to the strategy return is statistically significant. We then test for a changepoint in their liquidity-timing behavior. The results are in Table 11, with a separate panel for each dynamic strategy.

Across all panels in Table 11, the panel for Momentum (Panel C) has the most hedge funds loading on that strategy: 23% of Long/Short Equity funds and 43% of Fund-of-Funds. For Long/Short Equity, the breakpoint is at April 2000 with a coefficient on the interaction term with changepoint of -1.05. The portfolio of non-loading funds has a coefficient -0.59 with a changepoint in April 2000. The findings for both subsets of funds are qualitatively similar, which does not suggest that Momentum explains the occurrence of the changepoint. The other panels (A, B and D) have the results for portfolios sorted on the other three strategies, but only a small fraction of hedge funds have a significant loading on the strategy returns. Likewise, the split between loading/non-loading funds does not lead to large shifts in the changepoint results. Controlling for market timing by including the bear-market indicator in the regression leads to similar results for Momentum.12 Overall, dynamic strategies do not seem to explain the changepoint found for hedge funds in their dynamics of market beta. Momentum has a similar changepoint, but the prevalence of this strategy among hedge funds cannot explain the structural change in their liquidity-timing behavior.

6 Robustness Our results might be affected by reporting biases that are known to exist in hedge fund data. The most prominent of these is backfill bias, which is the problem that early observations of any hedge fund in a database result from selective attrition: funds with unimpressive results do not enter the database, or wait until they have a string of relatively good results to offer as a return history (see Fung and Hsieh (2009) and Aiken et al. (2013). To correct for this, we exclude observations before the month in which the fund was added to the database, using the field “Date added” that is provided by Lipper/TASS. The results remain qualitatively similar.

12

Results are available upon request.

17

Another concern is that the break that we find is actually an indication of new ‘types’ of hedge funds that sprung up after 2002, to exploit the investment opportunities that arise because of changes in market structure and aggregate liquidity conditions. To rule out the possibility that our results are caused by a composition effect, we undertake a separate analysis on a sample of hedge funds that existed in 1998. The analysis with the selected sample of funds leads to results that are similar to the ones obtained when using the full sample. We also analyzed the robustness of the results when using the Pastor-Stambaugh liquidity measure, conditioning on small funds, or funds that have changepoints in their beta and have found similar results (available upon request).

7 Conclusion Employing a changepoint methodology, we find optimal changepoints in the beta-liquidity relation of hedge funds. The breakpoints are located in periods featuring either market turmoil or structural changes such as the LTCM crisis, the introduction of automated trading and the financial crisis of 2008. During these times, subsets of hedge funds change the way in which market exposures are related to market liquidity. Our results resonate with recent research on the liquidity-timing ability of hedge funds. We corroborate the ability of hedge funds to shift in and out of the stock market in expectation of improved liquidity, but our results suggest that this is a phenomenon that, for Long/Short Equity hedge funds, is only observed after 2000. In earlier years, the evidence points to investment behavior that profits from episodes of illiquidity, aimed at earning the liquidity premium. An analysis of dynamic strategies does not resolve the question of the deeper cause of the changepoints. The changepoint for a momentum strategy comes closest to the observed changepoint for hedge funds, but momentum-sorted portfolios of hedge funds do not differ significantly in changepoint outcomes. Our results hold important lessons for researchers and practitioners that estimate hedge fund exposures with a dynamic model or embedded timing behavior. Even when evidence for this behavior is found, the behavior is not necessarily constant and seems to change with the investment opportunity set. Changes in market structure, in particular, can change the observed dynamic risk exposures of hedge funds completely. An important question remains: to what extent can the time-variation in the ability of hedge funds to time market liquidity impact the dynamics of market prices? For example, when hedge funds are providing liquidity, some well-known stock return anomalies may exhibit weaker patterns. We leave this question for future research. 18

Appendix A: Significance Testing of Changepoints We start from partial structural change model for a single changepoint (

{

})

∑

:

∑ (A1)

The optimal changepoint is the one that maximizes the fit (i.e. the change date that renders the minimum sum of squared errors). To test for the significance of the changepoint, we compute the -statistic of Andrews et al. (1996) for each candidate date and its corresponding leastsquares parameter estimates: [

]

(A2)

where is the sum of squared errors of an estimated constant parameter model (obtained by setting ), corresponds to the changepoint regression for time , denotes the sample size, and equals the number of factors in the changepoint regression plus one. We calculate the following two limiting cases of the exponential -statistic of Andrews et al. (1996) that direct power against alternatives of small and large parameter changes, respectively: ∑ ∑

(

)

,

(A3)

where is a weighting function. We equally weigh the -statistics and obtain the critical values using a bootstrap procedure (see Bollen and Whaley (2009) and Patton and Ramadorai (2013). First, a constant parameter model is estimated under the null of no changepoint (i.e. with ) in (A1). Second, we bootstrap samples of hedge fund returns of length by re-sampling the residuals and adding them to the fitted return estimates from the constant parameter model. To account for autocorrelation, we follow Politis and Romano (1994) and Patton and Ramadorai (2013) by drawing the residuals in blocks of random size and starting points. The block lengths are drawn from a geometric distribution, with an average block length of 3. For each bootstrapped sample we estimate the changepoint model (A1) and calculate the and the statistic in (A3). We simulate and estimate 1000 sets of hedge fund returns and set the th 90 percentile of the distribution of a test statistic as the critical value at 10%. A changepoint parameter shift is significant if the test statistic exceeds that critical level.

19

Appendix B: Dynamic Trading Strategies Trading on Liquidity We replicate the liquidity trading strategy in Ben-Rephael et al. (2015). Within each size tercile, stocks are sorted within five portfolios, based on their previous-year illiquidity, as measured by Amihud’s (2002) ILLIQ measure. The Long/Short liquidity portfolio per size-tercile consists of a long position in the least liquid quintile and a short position in the most liquid quintile. Pairs trading We generate pairs trading-returns along the lines of Gatev et al. (2006) as follows: At the beginning of each month, we rank pairs of stocks from the NYSE-Amex-NASDAQ universe based on the sum of squared deviations of the normalized price indices over the past 12 months (the formation period). Only stocks with a full price history over the formation period are considered. This list of pairs is monitored during a period of six months (trading period) to detect a widening between prices of more than two standard deviations. The day after such an event, the pair is 'opened' by going one dollar short in the higher-priced stock and one dollar long in the lower-priced stock. A pair is closed once the prices cross or at the end of a six-month trading period. The return on a pair is computed as the reinvested payoffs during the trading interval. A pair can open and close several times during the trading period. Given that we take a six-month trading period, it is assumed that six strategies (managers) are operating simultaneously, in overlapping (six-month) periods. We follow Engelberg et al. (2009) in that we also consider a strategy that closes out pairs that do not converge after ten days. Momentum trading The return on momentum is the return on a portfolio with a long position in past winners and a short position in past losers; see Jegadeesh and Titman (1993). To obtain the return on momentum we take the monthly return of the Up-Minus-Down (UMD) factor from Kenneth French’s website. Reversal trading We take the monthly Short-Term Reversal Factor from Kenneth French’s website, which is the return on a portfolio strategy where the weights are determined by the inverse of the previousmonth excess return over the market. It is a contrarian strategy, in that it buys past losers and sells past winners.

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20

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Sirri, E. R. and P. Tufano (1998). Costly search and mutual fund flows. Journal of Finance 53(5), pp. 1589-1622. Zhao, X. and K. H. Chung (2007). Information disclosure and market quality: The effect of sec rule 605 on trading costs. Journal of Financial and Quantitative Analysis 42(3), pp. 657.

30

25

20

15

10

5

0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Panel A: Long/Short Equity funds

23

45 40 35 30 25 20 15 10 5 0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Panel B: Fund-of-funds Figure 1: F-statistics of a changepoint in hedge fund portfolio returns This figure shows the exp-F-statistics calculated following Equation (A.2) for the optimal changepoint model in Equation (3). Plotted are the F-statistics for the whole permissible range of date changes for value-weighted portfolios of Long-Short Equity Hedge (LSEH) and Equity Market Neutral (EMN) hedge funds (Panel A), as well as Fund-of-funds (Panel B), with the following specification for the dynamics of the market beta: (

{

})

,

where is Amihud’s (2002) measure of stock market illiquidity in month t, adjusted for predictable changes in illiquidity following Hameed et al. (2010), is the stock market return volatility as proxied by the CBOE VIX index and is the changepoint. is the return of the S&P 500 index.

24

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Long/Short Equity

Fund-of-funds

Figure 2: Fund-specific Changepoints for Long/Short Equity and Fund-of-funds Frequencies of optimal changepoint years as a percentage of the total number of hedge funds with a significant changepoint per style. The changepoints are estimated for the returns of individual hedge funds from the Long/Short Equity and the Fund-of-funds style categories. Time-varying market betas evolve according to the following specification: (

{

})

,

where is Amihud’s (2002) measure of stock market illiquidity in month t , adjusted for predictable changes in illiquidity following Hameed et al. (2010), and is the changepoint. is obtained based on the constituents of the most appropriate market index variable per fund (S&P 500 Large cap, the S&P 400 Midcap or the S&P 600 Small cap-index) on the basis of the AIC criterion from a multivariate regression of individual hedge fund returns on the Fung and Hsieh (1997) seven-factor model, augmented with contemporaneous AR(2) residuals of the Amihud illiquidity measure. The sample period is from January 1994 to December 2013.

25

Table 1. Summary statistics of hedge fund portfolios The table presents summary statistics of value-weighted returns of portfolios of hedge funds grouped by style classification. The sample period is from January 1994 to December 2013. N Long/Short Equity Hedge and Equity Market Neutral Convertible Arbitrage Dedicated Short Bias Emerging Markets Event-Driven Global Macro Multi-Strategy Fund-of-Funds

Mean

Median

STD

Skewness

Kurtosis

Min

Max

3,389

0.70

0.83

2.39

0.47

6.96

-8.82

12.82

231 47 732 647 469 797 4,696

0.50 -0.06 0.68 0.65 0.67 0.67 0.34

0.70 -0.46 1.09 0.86 0.53 0.67 0.46

1.78 4.21 4.04 1.45 2.94 2.73 1.62

-3.12 0.79 -0.65 -1.45 0.15 0.05 -0.43

24.83 5.35 7.20 7.64 7.66 7.17 6.00

-12.80 -8.45 -21.20 -7.03 -13.94 -10.03 -5.91

5.84 21.92 15.57 4.19 12.82 12.73 6.68

Table 2. Market factors and liquidity measures The table presents summary statistics of the risk factors and the liquidity measures. Panel A summarizes the returns of the market factors, S&P 500, S&P 400 and the S&P 600 index. Panel B reports the descriptives of the monthly Amihud illiquidity measure (ILLIQ), the Pástor-Stambaugh liquidity measure and their innovations from an AR(2) model based on S&P 500, S&P 400 or S&P 600 constituents. It also reports the descriptives of ILLIQ residuals from regressing the ILLIQ variable on two tick change dummies to capture the tick change from 1/8 to 1/16 on June 24, 1997 and the change from 1/16 to the decimal system on January 29, 2001, as well as two time-trend variables equal to the difference between the current year and the year 1994 (1997) or the first year when the stock is included in the S&P 500 index, whichever is later, following Hameed et al. (2010). Panel C summarizes the Fung-Hsieh risk factors. Apart from the market return, they include a size factor (SMB), monthly change in the 10-year Treasury constant maturity yield, monthly change in the Moody's Baa yield less 10-year Treasury constant maturity yield, and three trend-following factors: PFTSBD (bond), PFTSFX (currency), and PFTSCOM (commodity). The sample period is from January 1994 to December 2013. Mean Median STD Skewness Kurtosis Min Max Panel A: Market factors S&P 500

0.44

0.93

4.39

-0.68

4.04

-17.00

10.77

S&P 400

0.74

1.11

5.07

-0.65

4.94

-21.89

14.74

S&P 600

0.71

1.31

5.43

-0.58

4.49

-20.30

17.30

Amihud ILLIQ (S&P 500)

0.29

0.21

0.15

0.40

1.62

0.09

0.65

Amihud ILLIQ (S&P 400)

0.33

0.22

0.19

0.57

1.87

0.11

0.76

Panel B: Liquidity measures

Amihud ILLIQ (S&P 600)

0.41

0.30

0.22

0.56

1.94

0.13

1.01

Amihud ILLIQ innovations (S&P 500)

0.000

-0.003

0.03

0.81

5.88

-0.09

0.14

Amihud ILLIQ innovations (S&P 400)

0.00

-0.004

0.05

1.22

7.98

-0.12

0.24

Amihud ILLIQ innovations (S&P 600)

0.00

-0.01

0.06

0.68

6.50

-0.22

0.28

Amihud ILLIQ residuals (S&P 500) Pástor-Stambaugh liquidity (S&P 500) Pástor-Stambaugh liquidity innovations (S&P 500)

0.45

0.43

0.07

0.83

2.95

0.33

0.68

-0.002

-0.002

0.004

0.12

10.54

-0.02

0.02

0.000

0.001

0.004

0.75

12.93

-0.02

0.02

26

Panel C: Fung-Hsieh risk factors Small minus big (SMB) Yield change Change in default spread

0.21

-0.09

3.45

0.87

11.34

-16.40

22.02

-0.01

-0.03

0.23

-0.21

4.56

-1.11

0.65

0.00

-0.01

0.12

1.56

23.95

-0.63

0.94

PTFSBD

-0.01

-0.04

0.15

1.38

5.47

-0.27

0.69

PTFSFX

-0.01

-0.05

0.19

1.36

5.64

-0.30

0.90

PTFSCOM

-0.01

-0.03

0.14

1.13

4.97

-0.25

0.65

0.21

-0.09

3.45

0.87

11.34

-16.40

22.02

Table 3. Market beta dynamics for Hedge Fund Portfolios This table reports parameter estimates of the dynamic beta specification of value-weighted portfolios of hedge funds, using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: , where is Amihud’s (2002) measure of stock market illiquidity in month t, is the stock market return volatility as proxied by the CBOE VIX index and is a bear market indicator equal to 1 if the cumulative market return in the 12 preceding months is negative. is the return of the S&P 500 index. Only hedge funds with more than 24 monthly observations are included. Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. The sample period is from January 1994 to December 2013. Long/Short Equity and Market Neutral

Fund-of-funds

Funds that are not U.S.-equity oriented

0.34***

(6.57)

0.62***

(4.64)

-0.0069***

(-4.44)

0.40***

(8.14)

0.76***

(5.81)

-0.0083***

(-5.53)

0.17***

(2.83)

0.25

(1.55)

-0.0024

(-1.26)

0.32***

(5.41)

-0.06

(-0.34)

0.0019

(0.97)

0.30***

(5.00)

-0.25

(-1.44)

-0.0023

(-1.44)

0.32***

(6.17)

-0.02

(-0.15)

-0.0035**

(-2.27)

0.72 -0.09**

(-2.30)

0.77

0.48 -0.25***

(-5.39)

0.59

0.45 -0.01

(-0.31)

0.48

Table 4. Changepoint in Liquidity Timing for Hedge Fund Portfolios This table reports the changepoint estimation results for value-weighted portfolios of hedge funds, using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: ( , { }) where is Amihud’s (2002) measure of stock market illiquidity in month t (Panel A), or its residual obtained from from regressing the ILLIQ variable on predicted changes in liquidity, following Hameed et al. (2010) (Panel B). is the return of the S&P 500 index. is the stock market return volatility as proxied by the CBOE VIX index and is the changepoint. Only hedge funds with more than 24 monthly observations are included. Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. We test for significance of the changepoint for a given portfolio using a parametric bootstrap. Changepoint significance is given for the 90% level of the exp-F statistic. The sample period is from January 1994 to December 2013. {

Changepoint date

}

Panel A: ILLIQ

Long/Short Equity

0.44***

(8.67)

0.54***

(4.21)

-0.64***

(-4.76)

Fund-of-funds

0.29***

(5.95)

0.04

(0.31)

-0.82***

(-7.89)

-0.0055*** 0.0002

(-3.45)

Jan-00*

0.75

(0.12)

Sep-00*

0.55

27

Funds that are not U.S.equity oriented

0.33***

(6.12)

Long/Short Equity

0.47***

(4.02)

Fund-of-funds

0.60***

Funds that are not U.S.equity oriented

0.52***

-0.14

(-1.18)

-0.36**

(-2.61)

-0.0016

(-1.01)

Sep-98*

0.48

0.45*

(1.68)

-0.57***

(-5.96)

-0.0054***

(-2.89)

Jan-00*

0.75

(5.23)

-0.62**

(-2.21)

-0.62***

(-7.79)

0.0025

(1.04)

Sep-00*

0.55

(3.72)

-0.55*

(-1.77)

-0.22**

(-2.23)

-0.0003

(-0.14)

Sep-98

0.48

Panel B: Residual ILLIQ

Table 5. Controlling for Volatility Timing This table has the changepoint estimation results for value-weighted portfolios of hedge funds, using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: ( ( , { }) { }) where is Amihud’s (2002) measure of stock market illiquidity in month t (Panel A), or its residual obtained from regressing the ILLIQ variable on predictable changes in liquidity (Panel B). is the stock market return volatility as proxied by the CBOE VIX index and is the changepoint. is the return of the S&P 500 index. LSEH/EMN denotes the portfolio with hedge funds from Long-Short Equity Hedge (LSEH) and Equity Market Neutral (EMN). We consider only hedge funds with more than 24 monthly observations. Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. Changepoint significance is given for the 90% level of the exp-F statistic. The sample period is from January 1994 to December 2013. Long/Short Equity (2) (1)

Fund-of-funds (3) (4)

Panel A: ILLIQ 0.39*** (6.22) 0.39

{

}

1.04***

(2.95)

(5.94)

0.10

0.11

(3.14)

(0.31)

(0.30)

-0.67**

-0.78**

-1.11***

-0.0029

0.0005 (0.13)

(-2.03) -0.0127*** (-3.01) 0.0044 (0.94)

(-2.37) 0.0020 (0.54) 0.0005 (0.10)

-0.0263

2

R

(-3.11) -0.0021 (-0.44) 0.0038 (0.71) -0.0838*

(-0.57)

Changepoint

0.41***

-0.68**

(-1.00) }

(7.62)

0.22***

(1.58)

(-2.42)

{

0.45***

(-1.71)

Sep-00*

Jan-00

Sep-00*

Sep-00*

0.71

0.77

0.53

0.63

0.37***

0.31**

0.50***

0.75***

Panel B:Residual

(2.92) 0.54 (1.37)

(2.52) 1.42*** (3.15)

(3.77)

(5.32)

-0.48

-0.57

(-1.33)

(-1.46)

28

{

-0.56**

}

-0.90***

(-2.09)

(-2.74)

-0.0051

-0.0172***

(-1.27) {

(-3.34)

0.0018

}

0.0082

(0.39)

(1.51)

-0.66** (-2.43) 0.0033 (0.92) 0.0014 (0.29)

-0.0201

(-2.91) -0.0005 (-0.12) 0.0050 (1.02) -0.1036**

(-0.44)

Changepoint

-0.85***

(-2.00)

Jan-00*

Jan-00*

Sep-00*

Sep-00*

0.71

0.77

0.53

0.63

2

R

Table 6. Small-, Mid- and Large-cap ILLIQ This table reports the changepoint estimation results for hedge fund portfolios, using liquidity measures for small-, mid- and large-cap market indices. We estimate a changepoint model of the returns of value-weighted portfolios of hedge funds, using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: ( , { }) where is Amihud’s (2002) measure of stock market illiquidity in month based on the constituents of the S&P 500, the S&P 400 or the S&P 600 index in that month, is the stock market return volatility as proxied by the CBOE VIX index and is the changepoint month. is the index-return of the S&P 500, the S&P 400 or the S&P 600 index, respectively. Funds are further sorted into portfolios according to the most appropriate market index variable (S&P 500 Large cap, the S&P 400 Midcap or the S&P 600 Small cap-index) on the basis of the AIC criterion from a multivariate regression of individual hedge fund returns on the Fung and Hsieh (1997) seven-factor model, augmented with contemporaneous AR(2) residuals of the Amihud illiquidity measure. We consider only hedge funds with more than 24 monthly observations. Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. We test for significance of the changepoint for a given portfolio using a parametric bootstrap. Changepoint significance is given for the 90% level of the exp-F statistic. The sample period is from January 1994 to December 2013.

{

Market index: S&P 500 (39 %) Long/Short Equity Fund-of-funds Funds that are not U.S.-equity oriented Market index: S&P 400 Midcap (43 %) Long/Short Equity Fund-of-funds Funds that are not U.S.-equity oriented Market index: S&P 600 Smallcap (18 %) Long/Short Equity Fund-of-funds Funds that are not U.S.-equity oriented

Changepoint date

}

0.47*** 0.44*** 0.40***

(8.71) (7.17) (6.89)

0.81*** -0.08 -0.37***

(6.08) (-0.53) (-2.65)

0.46*** 1.07*** 1.10***

(-3.40) (-7.73) (-4.75)

-0.0094*** 0.0001 -0.0013

(-6.04) (0.05) (-1.08)

Jan-00* Sep-00* Nov-08*

0.77 0.60 0.51

0.41*** 0.23*** 0.27***

(7.96) (6.02) (7.14)

0.11 0.01 -0.21**

(1.23) (0.12) (-2.13)

0.83*** 0.51*** 0.54***

(-5.83) (-5.15) (-5.60)

-0.0006 0.0004 0.0016

(-0.42) (0.34) (1.15)

Apr-01* Sep-00* Feb-01*

0.68 0.56 0.52

0.42*** 0.09* 0.32***

(9.31) (1.81) (4.53)

0.11 -0.15* -0.42**

(1.47) (-1.90) (-2.27)

0.49*** -0.42** 0.43***

(-7.48) (-4.40) (-2.10)

-0.0023 0.0031*** 0.0014

(-1.40) (2.64) (0.70)

Apr-00* Nov-08* Sep-02

0.26 0.21 0.23

Table 7. Changepoint Estimation for Individual Hedge Funds This table reports the changepoint estimation results for individual hedge funds from the Long-Short Equity Hedge (LSEH) and Equity Market Neutral (EMN) style categories. We estimate the changepoint model given by Equation (3) on the returns of

29

individual hedge funds, where is Amihud’s (2002) measure of stock market illiquidity in month t , adjusted for predictable changes in illiquidity following Hameed et al. (2010), and is the changepoint. is the market return. Both and are obtained based on the most appropriate market index variable (S&P 500 Large cap, the S&P 400 Midcap or the S&P 600 Small cap-index) on the basis of the AIC criterion from a multivariate regression of individual hedge fund returns on the Fung and Hsieh (1997) seven-factor model, augmented with contemporaneous AR(2) residuals of the Amihud’s illiquidity measure. Reported are the percentages of individual funds with a significant changepoint in years 1998 through 2012 along with the corresponding parameter estimates of the dynamic beta specification according to the exp-F statistic at a 90% significance level with critical values obtained using a parametric bootstrap. The sample period is from January 1994 to December 2013. Changepoint year

199 8

199 9

200 0

200 1

200 2

200 3

200 4

200 5

200 6

200 7

200 8

200 9

201 0

201 1

201 2

% of funds with a changepoint

3.1 %

3.1 %

13.1 %

8.1 %

6.4 %

6.8 %

3.1 %

2.8 %

6.7 %

7.8 %

15.9 %

9.3 %

3.6 %

4.3 %

3.6 %

2.69

0.67 0.37 1.34

0.07

0.10

1.14 0.02

0.43

1.35

0.62 0.68 2.25

0.02

0.26

0.60 0.74 1.94

0.36

0.09

0.62 0.22 1.38

0.06

0.31

0.22 0.85 0.74

0.21

0.59

0.46 2.14 1.78

0.54 1.90 4.33

0.03 0.87 0.15

0.19 0.58 0.71

0.04 1.16 0.13

0.34 1.35 1.81

0.43 1.27 2.09

0.05 0.58 0.32

Average t-statistic

0.14

Cross-sectional t-statistic

0.93

}

2.39

Average t-statistic

1.72

Cross-sectional t-statistic

0.92

{

0.20

0.67 0.63 1.33 0.37 1.73 1.24

0.86 0.55 0.78

0.16 0.14 0.49

0.61 0.21 1.60

0.70 1.29 2.27

0.10 0.30 0.34

0.21 0.63 0.86

0.12 1.00 0.31

0.02 0.76 0.09

Table 8. Selecting on Hedge Fund Characteristics This table reports the changepoint estimation results for hedge fund portfolios composed of hedge funds with characteristics that are most likely to influence the results. The results are the estimation, using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: ( , { }) where is Amihud’s (2002) measure of stock market illiquidity in month t, is the stock market return volatility as proxied by the CBOE VIX index and is the changepoint. is the return of the S&P 500 index. Value-weighted portfolios are formed using hedge funds that (1) do not employ leverage, (2) have low redemption frequency, (3) have redemption notice periods of 60 days or more, (4) have lock-up periods of more than three months, or (5) have below-median fund-flow volatility, computed as in Sirri and Tufano (1998). Panel A has the results for value-weighted portfolios of Long-Short Equity Hedge (LSEH) and Equity Market Neutral (EMN) hedge funds. Panel B reports results for portfolios of funds-of-funds. Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. We test for significance of the changepoint for a given portfolio using a parametric bootstrap. Changepoint significance is given for the 90% level of the exp-F statistic. The sample period is from January 1994 to December 2013. Not using leverage

(1) Panel A: Long/Short Equity [% of funds] [42%] 0.41***

{

}

0.44*** -0.80*** 0.0040**

Low redemption frequency (quarterly and above) (2) [37%] 0.44***

(9.47) (3.99) (-8.07) (-2.60)

0.67*** -0.58*** 0.0049**

Long redemption notice period (60 days or more) (3) [16%] 0.38***

(8.29) (4.61) (-4.61) (-2.25)

0.17 -0.47** -0.0025

(5.29) (1.14) (-2.52) (-1.05)

Long lock-up periods (more than three months) (4)

Low (below median) fund flow volatility

[26%] 0.59***

[44%] 0.35***

0.07 -0.70*** -0.0023

(8.62) (0.40) (-5.10) (-0.97)

(5)

0.10 -0.61*** 0.0035**

(10.25 ) (1.19) (-7.35) (-2.82)

30

Changepoint R2

Sep-00* 0.76

Jan-00* 0.77

Panel B: Fund-of-funds [% of funds] [63%]

{

}

Changepoint R2

0.28*** 0.12 -0.91*** 0.00 Sep-00* 0.57

(5.75) (0.91) (-8.43) (0.15)

[29%] 0.24*** -0.06 -0.79*** 0.00 Sep-00* 0.57

Sep-00 0.60

(5.04) (-0.44) (-7.73) (0.98)

[25%] 0.25*** 0.12 -0.77*** 0.00 Sep-00* 0.61

* Apr-00* 0.65

Sep-00* 0.73

(5.88) (0.96) (-8.66) (0.25)

[9%] 0.28*** -0.12 -0.68*** 0.00 Sep-00* 0.59

(6.19) (-0.96) (-7.44) (0.49)

[44%] 0.22*** -0.08 -0.51*** 0.00 Sep-00* 0.55

(5.86) (-0.77) (-6.93) (0.18)

Table 9. A Model with Two Changepoints This table reports the changepoint estimation results for value-weighted portfolios of hedge funds, using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: ( , { } { }) where is Amihud’s (2002) measure of stock market illiquidity in month t (Panel A), or its residual obtained from from regressing the ILLIQ variable on predictable changes in liquidity (Panel B). is the return of the S&P 500 index. is the stock market return volatility as proxied by the CBOE VIX index and and are two changepoints. The portfolio of PFE funds consists of funds with Primary Focus on Equities. LSEH/EMN denotes the portfolio with hedge funds from LongShort Equity Hedge (LSEH) and Equity Market Neutral (EMN). We consider only hedge funds with more than 24 monthly observations. Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. We test for significance of the changepoint for a given portfolio using a parametric bootstrap. Changepoint significance is given for the 90% level of the exp-F statistic for joint significance of the two changepoints. The sample period is from January 1994 to December 2013. Long/Short Equity

Fund-of-funds (3) (4)

(1)

(2)

0.31***

0.45***

0.47***

0.41***

(5.48)

(9.77)

(5.73)

(6.14)

0.48***

0.53***

-0.30

-0.33*

Panel A: ILLIQ

{

{

}

}

(3.35)

(4.31)

(-1.60)

(-1.76)

-7.03***

-7.12***

-0.93***

-0.98***

(-10.61)

(-11.19)

(-8.80)

(-8.29)

-0.67***

-0.58***

-2.01***

-2.11***

(-4.60)

(-4.71)

(-5.26)

(-5.46)

-0.0058***

0.0030*

(-3.97)

(1.86)

Changepoint

Feb-00*

Feb-00*

Sep-00*

Sep-00*

Changepoint

Mar-00*

Mar-00*

Dec-08*

Nov-08*

0.76

0.77

0.57

0.57

0.50***

0.47***

0.44***

0.77***

(4.03)

(4.46)

(3.01)

(5.26)

2

R

Panel B: Residual

0.10

0.45*

-0.22

-1.02***

(0.43)

(1.80)

(-0.78)

(-2.86)

31

{

{

-5.92***

}

}

-5.97***

-0.64***

-0.62***

(-10.91)

(-11.56)

(-7.84)

(-7.86)

-0.62***

-0.52***

-0.43***

-0.90***

(-5.95)

(-3.04)

(-6.06)

(-6.14)

-0.0058***

0.0043*

(-3.32)

(1.85)

Changepoint

Feb-00*

Feb-00*

Sep-00*

Sep-00*

Changepoint

Mar-00*

Mar-00*

Dec-03*

Nov-08*

0.76

0.78

0.56

0.56

R2

Table 10: Characteristics of Candidate Dynamic Strategies for Hedge Funds This table reports the changepoint estimation results for four dynamic strategies. The pairs trading strategy is that of Gatev et al. (2006), Momentum and Short-term Reversal are obtained from Kenneth French’s website, and the Liquidity strategy is that of Ben Rephael et al. (2010), based on large-cap stocks. We estimate a changepoint regression as given by Equation (3), using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: ( { }) where is Amihud’s (2002) measure of stock market illiquidity in month t, is the stock market return volatility as proxied by the CBOE VIX index, and is the changepoint. is the return of the S&P 500 index. Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. We test for significance of the changepoint for a given portfolio using a parametric bootstrap. Changepoint significance is given for the 90% level of the exp-F statistic. The sample period is from January 1994 to December 2013.

{

}

Changepoint R2

Liquidity

Pairs trading

Momentum

Reversal

-0.04 (-1.50) 0.03 (0.48) 0.24*** (3.61) 0.0003 (0.33)

0.05*** (2.67) -0.18*** (-3.95) 0.13*** (2.75) -0.0005 (-1.02)

0.09 (0.36) 0.11 (0.16) -3.15*** (-4.29) -0.0009 (-0.10)

-0.37* (-1.80) 0.89* (1.74) 4.14*** (3.81) 0.0092** (2.03)

Apr-00* 0.13

Aug-97 0.10

Dec-00* 0.34

Jun-10* 0.21

Table 11. Sorting hedge fund returns on the loading on the dynamic strategies This table reports the changepoint estimation results for the returns of value-weighted portfolios of hedge funds that load or not on four dynamic strategies. The pairs trading strategy is that of Gatev et al. (2006), Momentum and Short-term Reversal are obtained from Kenneth French’s website, and the Liquidity strategy is that of Ben Rephael et al. (2010), based on large-cap stocks. Whether funds belong to the loading or non-loading portfolio for a given strategy is determined from a multivariate regression of individual hedge fund returns on the S&P 500 market index return and the return of the dynamic strategy. We estimate a changepoint regression as given by Equation (3), using the Fung and Hsieh (1997) seven-factor model and the following specification for the dynamics of the stock market beta: ( { }) where is Amihud’s (2002) ILLIQ measure of stock market illiquidity in month t, is the stock market return volatility as proxied by the CBOE VIX index and is the changepoint. is the return of the S&P 500 index. For each strategy, we report the percentage of loading funds, the coefficient of the interaction term, and the changepoint date. The portfolio of PFE funds contains hedge funds with primary focus on equities, and LSEH/EMN denotes the portfolio with hedge funds from Long-Short

32

Equity Hedge (LSEH) and Equity Market Neutral (EMN). Newey-West corrected t-values are given between parentheses. *,** and *** denote significance at the 90%, 95% and 99% levels, respectively. We test for significance of the changepoint for a given portfolio using a parametric bootstrap. Changepoint significance is given for the 90% level of the exp-F statistic. The sample period is from January 1994 to December 2013. If the number of loading funds is too small to make a full time series, the cell is left blank.

Panel A: Liquidity Loading funds Pe rc. Long/Short Equity

2%

Fund-offunds

1%

{

3.6 5** *

Panel B: Pairs trading Non-loading Loading funds funds

Non-loading funds

}

Chg pt.

(7.05)

Sep02*

{

}

Chg pt.

P er c.

Pe rc. Long/Short Equity

23 %

Fund-offunds

43 %

{

1.0 5** * 0.8 7** *

}

Chg pt.

{

Chg pt.

}

0.64** *

(4.76)

Jan00*

4 %

1.13* **

(6.07 )

Nov00*

0.64* **

(4.7 6)

Jan00*

0.82** *

(7.89)

Sep00*

2 %

1.03* **

(5.63 )

Oct00*

0.82* **

(7.8 7)

Sep00*

Panel C: Momentum Loading funds

{

Panel D: Reversal Non-loading Loading funds funds

Non-loading funds Chg pt.

P er c.

{

0.95* **

}

Chg pt.

(4.88)

Jan00*

0.59** *

(5.47)

Apr00*

5 %

(8.20)

Sep00*

0.76** *

(6.45)

Sep00*

1 %

{

}

}

Chg pt.

(3.0 8)

Feb00*

{

Chg pt.

}

0.68* **

(5.0 2)

Jan00*

0.82* **

(7.9 0)

Sep00*

Highlights



An optimal changepoint approach to study the liquidity timing ability of hedge funds



Document a shift in liquidity timing related to market microstructure changes in 2000



Funds’ability to change market exposure in expectation of improved liquidity observed after 2000



In earlier years, funds’ investment behavior consistent with earning the liquidity premium



Common dynamic strategies do not mechanically explain the change in the beta-liquidity relation

33