Share Restrictions and Asset Pricing: Evidence from the Hedge Fund Industry

Transcription

1 Share Restrictions and Asset Pricing: Evidence from the Hedge Fund Industry by George O. Aragon November, 2004 JOB MARKET PAPER Abstract This paper finds a positive, concave relation between the returns and share restrictions of private investment funds, and shows that previously documented positive alphas can be interpreted as compensation for holding illiquid fund shares. The annual returns on funds with lockup provisions are approximately 4% higher than those for non-lockup funds, and the alphas of funds with the most liquid shares are either negative or insignificant. This paper also finds a positive association between share restrictions and illiquidity in fund assets, suggesting that funds facing high redemption costs use restrictions to screen for investors with low-liquidity needs. The results are consistent with previous theories which posit that liquidity is priced, and that less liquid assets are held by investors with longer investment horizons. JEL classification: G11; G12 Keywords: Liquidity; transactions costs; Hedge Funds; Lockups I am grateful for the early and continued support of my committee-wayne Ferson (chair), Pierluigi Balduzzi, Alan Marcus, and Jeff Pontiff; for the helpful comments and suggestions of Geert Bekaert, Roger Edelen, and seminar participants at the JFE/Oregon Conference on Delegated Portfolio Management, 2003 FMA Doctoral Student Consortium, and Boston College Brown Bag Workshop; for data provided by Hedge- Fund.net and Vikas Agarwal and Narayan Naik. Financial support from the Foundation for Managed Derivatives Research is gratefully acknowledged. Finance Department, The Wallace E. Carroll School of Management, Boston College, Chestnut Hill, MA Tel.: ; fax: ; aragong@bc.edu.

2 Because of the limitation on redemption rights and the fact that interests in the Fund are not tradeable, an investment in the Fund is a relatively illiquid investment and involves a high degree of risk. -Offering memorandum of a hedge fund company 1. Introduction In a seminal article, Amihud and Mendelson (1986) develop a model in which assets differ in transactions costs and investors have different holding periods. In equilibrium, financial markets exhibit a clientele effect, where longer-horizon investors hold less liquid assets, and the relation between expected returns and transactions costs is positive and concave. 1 Subsequently, a number of empirical studies have tested the relation between asset returns and liquidity. These articles have considered a variety of liquidity proxies, and focus mainly on the markets for publicly-traded debt and equity. 2 We provide a direct empirical test of the relation between asset returns and transactions costs, by considering share restrictions of private investment funds (hereafter, hedge funds). Focusing on transactions costs in this manner provides a number of important advantages. In principle, share restrictions do not contain measurement error, since they are directly observable from the fund s limited partnership agreement. This is to be contrasted with comparatively noisy liquidity proxies such as bid-ask spread, trading volume, or the estimated parameters of microstructure models obtained from high-frequency data. The hedge fund industry provides an ideal environment in which to examine liquidity issues. Since hedge funds may hold illiquid assets and face few limitations on the liquidity of their share agreements, we expect significant variation in transactions costs across funds. In contrast, mutual funds only charge investors a redemption, or, exit fee, up to 8.5%. Moreover, while a substantial literature has addressed the performance of investment funds, very little is known about the role of investor heterogeneity in the market for investment 1 Research on the pricing of liquidity goes back at least to Keynes (1936), who defines a liquidity premium as, the amount which [people] are willing to pay for the potential convenience or security given by this power of disposal (p.226). See, also, Mayers (1973,1976), Levy (1978), and Constantinides (1986). 2 See, e.g., Amihud and Mendelson (1991), Kamara (1994), Brennan and Subrahmanyam (1996), Brennan, et al. (1998), Datar, et al. (1998), and Amihud (2002). 1

3 fund shares. We investigate the possibility of a clientele effect, where longer-term investors hold shares with greater restrictions. 3 This analysis also has implications for recent studies suggesting that, in aggregate, hedge funds generate positive, after-fee excess returns, or, alphas. 4 The positive alphas are interpreted as evidence of superior ability, possessed by the most talented portfolio managers, to systematically identify and profit from mispricing in one or many securities markets. However, it is unclear why superior managerial skill implies higher after-fee performance, because better managers can simply charge higher fees. Moreover, much of the conventional analysis has ignored the fact that a typical hedge fund share is a relatively illiquid asset. 5 Share restrictions raise an important question for the interpretation of hedge fund performance: Do hedge fund alphas represent ability, or simply a liquidity premium? Using monthly data from , we document a positive, concave relationship between a fund s excess returns and its redemption notice period and minimum investment size. We also show that, in aggregate, the difference in excess returns on lockup versus non-lockup funds, or, the lockup premium, is about 4% per annum. This lockup premium is almost always positive across hedge fund style groups, though its magnitude exhibits variation across styles. The positive, concave relation between returns and share restrictions suggests that a clientele effect exists in the market for hedge fund shares. Consistent with Amihud and Mendelson (1986) (hereafter, AM), less liquid shares provide higher returns, and are held by investors with longer investment horizons. Strikingly, after controlling for lockup, notice period, and minimum investment size, previously positive alphas are indistinguishable from zero. In fact, estimated fund alphas of the most liquid shares are either negative or insignificant. This provides an interesting complement to Edelen s (1999) analysis of mutual funds, which shows that negative alphas reflect an indirect cost or, liquidity discount, due to liquidity-motivated trading of fund 3 Recently, Johnson (2004) studies mutual funds, and finds that short-term investors can impose significant liquidity costs on long-term investors within the same fund. 4 See, e.g., Ackermann et al. (1999), Liang (1999), Agarwal and Naik (2000), Harri and Brorsen (2002), and Kazemi and Schneeweis (2003) for evidence of positive hedge fund alphas. 5 See Krishnan and Nelken (2003) and, Nice Hedges, but Beware of Thorns, (BusinessWeek Online, December 27, 1999), for evidence of practitioner concern about share restrictions. Also, Asness, et al. (2001) and Getmansky, et al. (2003) examine the effects of illiquidity exposure on reported returns; and Aragon (2003) shows that a hedge fund s market timing ability is correlated with the illiquidity exposure of the fund s portfolio. 2

4 investors. In contrast, we argue that the positive alphas of hedge funds represent a liquidity premium due to trading restrictions imposed on investors. 6 Other authors have examined measures of transactions costs in contexts that are related to hedge fund share restrictions. For example, Ippolito (1989) documents that annual market-adjusted returns of load-type mutual funds are approximately 3.5% higher than that of no-load funds, and Ackermann, et al. (1998) and Liang (1999) document a positive relationship between aggregate-level hedge fund returns and lockup provisions. 7 However, these authors neither focus on the effects of share restrictions on returns nor provide a direct test of the AM theory. We also provide the first analysis of the cross-sectional variation in hedge fund share liquidity; that is, Why do some funds impose restrictions on their investors, while other funds do not? Previous work builds on the AM model, and theorizes that share restrictions allow funds to screen for investors with low-liquidity needs, which is beneficial when share redemptions are costly. Chordia (1996) and Nanda, et al. (2000) examine mutual funds, and model redemption costs as the costs of trading the non-cash components of the fund s portfolio. Thus, exit fees, or, the formation of load funds, are more common among managers that hold illiquid assets. More recently, Lerner and Schoar (2003) model redemption costs as a lemons problem. They argue that a short-term investor is more likely to force the fund to raise additional capital from outsiders, who cannot determine whether this activity is due to an insider s liquidity shock, or an insider s informed opinion that the fund is bad. Thus, share restrictions are more common among younger funds, where the lemons problem is most severe. 8 Using cross-sectional data on hedge fund characteristics, we provide empirical support for the investor-screening theories of Chordia (1996) and Lerner and Schoar (2003). Specifically, lockups are more common among younger funds, and funds which hold more illiquid assets. We make a distinction between a portfolio s average illiquidity level versus its liquidity 6 In his concluding remarks, Edelen (1999) notes,...[hedge funds] might be expected to outperform as a result of this [liquidity] restriction (p.465). 7 Elton et al. (1993) and Gruber (1996) argue that Ippolito s result is due to load funds greater exposure to small stocks, which we control for in the present study. Also, see Ljungqvist and Richardson (2003), who document that illiquid private equity stakes generate excess returns of 5-8% per annum. 8 Empirically, Chordia (1996) finds some evidence that load mutual funds hold a larger fraction of small stocks than no-load funds, while Lerner and Schoar (2003) find, consistent with the predictions of their model, transfer restrictions in private equity shares are more common among young funds. 3

5 risk-the covariance of portfolio returns with innovations in market liquidity. We consider the return-based smoothing model of Getmansky, Lo, and Makarov (2003), and find that lockups are positively related to the level of infrequent trading in a fund s holdings. However, lockups are uncorrelated with a fund s exposure to liquidity risk, where market liquidity is defined in the sense of either Pastor and Stambaugh (2003) or Amihud (2002). Since illiquid assets are associated with high transactions costs, this result highlights the relation between the liquidity of a fund s portfolio and its shares, and the mechanism through which fund managers compensate investors for bearing share restrictions: An investor in a fund which holds an illiquid asset captures at least part of the asset s illiquidity premium as compensation for the illiquidity of the fund. The remainder of the paper is organized as follows: Section 2 discusses hedge fund share restrictions, the data, and summary statistics; Section 3 presents our main results on the relation between share restrictions and returns; Section 4 addresses robustness; Section 5 studies the relation between lockup provisions and fund characteristics; and Section 6 concludes. 2. Hedge Fund Share Restrictions 2.1. Share Restrictions and transactions costs A typical hedge fund is organized as a limited partnership, the terms and conditions of which are outlined in the limited partnership agreement. This agreement is intended to provide material information about the fund to prospective investors, including the fund s fee structure and redemption policy. The redemption policy often involves either a lockup provision and/or a redemption notice period. A lockup provision requires that all initial monies allocated to the fund may not be withdrawn before the end of a pre-specified duration, or, lockup period. 9 The redemption notice period is the amount of time the investor is required to provide notice before redeeming his shares. Both of these restrictions contrast with the liquidity of mutual funds which, on any business day, are legally required by the Investment Company Act to satisfy an investor s share redemption request. 9 The effective lockup period may be longer, since some funds satisfy redemptions only at the end of the calendar year. For example, if the initial investment in January, 2002, is subject to a one-year lockup, then the earliest fund redemption may be at December, 2003, and the effective lockup is two years. 4

6 Hedge fund share restrictions differ from most measures of transactions costs considered in previous studies. Instead of dollar transactions costs such as bid-ask spreads, lockups and notice periods impose time-dependent rules against share redemption. However, lockup provisions and notice periods may also be interpreted as exit fees, for the duration of the lockup and notice period, which are sufficiently high to preclude an investor from selling the fund s shares. As in the case of bid-ask spreads, the marginal impact of these costs becomes smaller for longer-horizon investors, since these costs are discounted over a larger investment horizon. Consequently, our predictions are the same as those of the AM theory: the relation between returns and share restrictions is positive and concave. Theoretical work on the relation between share restrictions and returns is provided by the growing literature on restricted ( letter ) stock. Restricted stock is analogous to a lockup provision, since the holder is subject to a minimum holding period. Longstaff (2001) and Kahl, et al. (2003) model the effects of restricted stock on an investor s optimal portfolio and consumption policies, and show that the implied value of restricted stock can range from 50-90% of its market value. 10 Empirically, Wruck (1989) documents that a 2-year restricted stock sells at an average discount of 15% below unrestricted stocks, while in Silber s (1991) sample the discount on restricted stock is about 35%. 11 Lippman and McCall (1986) consider a time delay between a sell order and its execution, and argue that this case provides a useful definition of liquidity, since illiquid assets are commonly viewed as those which cannot be immediately traded without cost. Koren and Szeidl (2002) examine the impact of time delays on portfolio and consumption policies of an investor subject to random liquidity shocks. They show that the effects of execution delays can be significant, and increase with the size and intensity of liquidity shocks, as well as the length of the time delay. Taken together, this evidence suggests that lockups and notice periods can have significant effects on investors utility and, ceteris paribus, illiquid hedge fund shares should offer higher rates of return. 10 See, also, Longstaff (1995) and Henderson and Hobson (2001). Longstaff (2001) examines the impact of an upper bound on the number of shares which can be sold per trading period, and shows that the liquidity discount can range from 1-25%, depending upon the investor s trading horizon, the trading bounds, and the volatility of the illiquid asset s return volatility. 11 However, Hertzell and Smith (1993) argue that this discount is not entirely due to a lack of marketability, but also reflects the costs borne by outside investors in assessing firm value during a private placement. 5

7 2.2. Data The main database used in our study consists of share characteristics and historical returns of individual hedge funds. These data were provided by TASS Tremont Ltd.-a leading hedge fund data vendor. The raw sample includes 3,354 funds, of which 2,068 were live as of January, The remaining 1,286 funds are considered defunct. Defunct funds have ceased reporting to TASS, but may not have ceased operations. Each fund reports a monthly time series of returns, calculated net of fees. Each fund also reports a single, updated snapshot of it s organizational characteristics, including the fund s liquidity and fee structure. Characteristics of a defunct fund are those disclosed in the fund s final report to TASS. 12 The sample period covers January 1994 through December Although some funds report returns well before 1994, these observations introduce a survivorship bias, since data on defunct funds were not collected until Additional funds were dropped if either they (i.) do not report returns net of fees; (ii.) do not report returns on a monthly (versus quarterly) basis; or (iii.) do not report returns in US dollars. Most of these criteria are consistent with those used by CSFB/Tremont in the construction of its hedge fund indices. The final sample includes 2,871 funds, of which 491 have lockup provisions. We do not consider a fund s lockup period directly since, as shown in Table I, lockup periods are clustered around one year across funds, and exhibit little variability. Instead, for each fund we generate the dummy variable dlock, which takes the value of unity if the fund reports a lockup period. The variables min and notice denote the minimum initial investment size (reported in $ millions) and the fund s redemption notice period (reported in days), respectively. In Section 5, we consider other fund variables in a probit analysis of our dlock variable. The variable size is a fund s monthly reported estimated asset value. 14 A fund s age in a 12 Section 4 addresses a number of potential biases related to most hedge fund databases, including TASS. These include self-selection, survivorship, backfilling, delisting, and a previously unexamined endogeneity issue due to observing fund characteristics only at the end of the sample period. To address the endogeneity issue, we study a smaller, proprietary sample of hedge fund data that have been hand-collected from HedgeFund.net-a hedge fund placement agent. These data will be discussed in Section Incidentally, for this reason major hedge fund indices do not report returns before A significant fraction (27%) of funds do not report estimated assets. These funds were dropped whenever the size variable is used for estimation. 6

8 given month is the number of months from its first observation date in TASS. 15 In some cases, age may be misleading because many funds are managed by the same management company. For example, it is common for a management company to create a new fund when the existing fund has reached its legal capacity for number of limited partners. 16 Thus, it may be important to ensure that a spinoff fund of a well-established management company is not classified as young. To address this issue we define a fund s effective age at date t (eage) as the number of months between t and the earliest of the first observation dates across all funds within the same management company. The variable hfvol is defined as the sample standard deviation of the fund s monthly return over its sample period, in excess of the return on a value-weighted index of hedge funds within the same style group. These indices are maintained by CSFB/Tremont and appear in the TASS database. We consider excess returns to normalize fund-level variation across different time periods, since the intersection of calendar date observations across many funds is small. However, the qualitative results are unchanged when vol is defined as either the standard deviation of either the fund s monthly returns or returns in excess of a value-weighted portfolio of NYSE/AMEX/NASDAQ stocks. Section 5 examines the relationship between share restrictions and the liquidity of fund holdings, including both the average liquidity level and liquidity risk. Our liquidity level proxy s are two-fold. First, liq is a subjectively-determined dummy variable, and equals unity if the fund s primary focus suggests relatively liquid holdings. We set liq = 1 if the fund strategy is either Dedicated Short Bias (SB), Equity Market Neutral (EN), Global Macro (GM), Long/Short Equity Hedge (LS), or Managed Futures (MF). The remainder are defined as illiquid strategies. These include Convertible Arbitrage (CA), Emerging Markets (EM), Event Driven (ED), Fixed Income Arbitrage (FA), Fund of Funds (FF), and Other (OT). The construction of liq follows Asness, Krail, and Liew (2001, hereafter AKL), who show that the returns on funds for which liq = 0 (the illiquid group) are more likely to have significant lagged betas in a market model regression. AKL argue that illiquid assets 15 The age variable includes pre-1994 and backfilled observations-observations which precede the fund s addition to TASS. The consideration of these observations is intended to capture the idea that, while the return observations may be biased, they are still informative about manager ability. Also, these observations proxy for the degree of non-return-based information production; e.g., whether the manager provides timely reports to investors. 16 This distinction seems important for investors, since the offering documents of spinoff funds often advertise the performance history of the parent. 7

9 are not actively traded and, thus, suffer from stale price bias. Thus, current fund returns are often explained by past realizations of a systematic news factor. The liq variable suffers from three major limitations. First, since liq is a binary variable, it ignores a potentially rich degree of variability in the cross-section of portfolio liquidity. Second, liq assumes that liquidity exposure is homogenous within style groups. This is unrealistic, since there is no reason why, say, the Fixed Income Arbitrage group does not include funds that invest in (illiquid) corporate issues as well as funds that invest in (liquid) interest rate derivative products. Third, the liq sorting relies upon a single declaration of the fund s self-reported style group, rather than a time series of reported returns. To address these issues, we also consider the return-based, smoothing model developed by Getmansky, Lo, and Makarov (2003, hereafter GLM). GLM formalize the intuition of AKL by making a distinction between a fund s reported and economic returns. They assume that the reported returns of illiquid portfolios only partially reflect contemporaneous economic returns, but that economic returns are eventually, fully incorporated into reported returns. Specifically, the fund s reported return in period t (Rt o ) satisfies, Rt o = θ 0 R t + θ 1 R t θ k R t k (1) θ j [0, 1], j = 0, 1,, k (2) 1 = θ 0 + θ θ k (3) where R t is the fund s economic return in period t. The parameters θ j are interpreted as the speed at which information is reflected into reported returns. For example, in the following analysis we focus on θ 0 -the fraction of a fund s economic return that is contemporaneously reflected in its reported return. Thus, a larger θ 0 is interpreted as a relatively liquid portfolio. 17 The parameters in (1) are estimated by maximum likelihood, assuming that de-meaned economic returns are mean-zero, normal random variables. We also consider pre-1994 observations to estimate these parameters, since we have no reason to believe that survivorship bias is correlated with estimates of a fund s illiquidity exposure. Each fund must have at least 17 The GLM measure builds on the earlier work of Scholes and Williams (1977) and Dimson (1979), who study infrequent trading in publicly-traded equities. GLM refer to their measure as a smoothing parameters, since reported returns of illiquid portfolios have less volatility than true, economic returns. As we discuss in Sections 3 and 4, our asset-pricing tests control for return-smoothing by considering a lagged market model, using long-horizon returns, and directly including the smoothing parameter in our estimation. 8

10 24 return observations to be included in the analysis. 18 Following GLM, the estimates are obtained without imposing the restriction (2), since unrestricted estimates provide a specification check for the smoothing model. However, we also report stronger, yet qualitatively unchanged results from using the restricted estimates. We estimate liquidity risk-the covariance of fund returns with innovations to stock market liquidity-at the fund-level, by regressing fund returns on innovations to market liquidity. 19 As a matter of robustness, we consider two different proxies for market liquidity. These proxies are conceptually distinct, although both are averages of individual stock-level liquidity measures, and are constructed from daily stock return and volume data using CRSP. First, we follow Pastor and Stambaugh (2003) and consider a measure based upon volume-related return reversals. 20 The second measure, considered by Amihud (2002) equals the absolute return divided by its volume. This measure is intended to proxy for the price impact of a given order flow. Finally, the performance analysis in this study considers linear, multi-factor models, that include the returns from holding a wide range of buy-and-hold and option-based indices. The use of several buy-and-hold indices is intended to capture the broad spectrum of markets in which hedge funds invest, while the option-based indices are intended to capture the dynamic strategies employed by these funds. The buy-and-hold indices consist of the value-weighted return on the NYSE/AMEX/NASDAQ reported by the CRSP Stock File Indices, and the payoffs on hypothetical long-short spreads constructed by sorting stocks according to market capitalization (SMB), book-to-market ratio (HML), and past returns (UMD), respectively. 21 We also consider the MSCI World excluding US equity index, a set of Merrill Lynch aggregate bond indices (US Government, US Corporate, and US High Yield), the Federal Reserve Bank Competitiveness-Weighted 18 GLM require at least 60 observations of monthly returns. The trade-off between efficiency and sample size is more important here since, as discussed in Section 5, fund age is expected to be correlated with lockup choice. 19 See Appendix for details on our estimates of a fund s liquidity risk. 20 This measure was originally motivated by Grossman and Miller (1988) and Campbell, Grossman, and Wang (1993). The intuition is that volume-related trades are more likely to be noise, or, informationless trading. Volume-related sell (buy) trades force the market to bear more (less) risk. Therefore, negative (positive) returns are reversed since expected returns are higher (lower). The magnitude of the reversal depends on the thinness, or, illiquidity, of the stock s market. 21 These data were taken from Ken French s website. 9

11 Dollar index, and the Goldman Sachs Commodity index. The option-based indices represent the monthly returns from holding either out-of-the-money or at-the-money, call or put options on the S&P 500. The options have one-month maturity, and are bought (sold) at the beginning (end) of each month. Returns from the option strategies are calculated using price data from The Institute for Financial Markets. Agarwal and Naik (2003) show that these indices capture much of the dynamic market exposure of many important hedge fund style groups. 22 Excess returns are generated by subtracting the 30-day Treasury Bill return, reported by the CRSP Fama Risk Free Rate File. This file contains nominal 1 and 3-month risk-free rates implied by U.S. Treasury Bills, and are based upon the bid/ask average price Summary Statistics of Fund Characteristics Tables I and II present summary statistics of the share restrictions across funds. For example, Panel A of Table I presents the distribution of the lockup period across the total sample, and shows that approximately 17% of all funds impose a lockup. Although the lockup period ranges from 1 month to 7.5 years, it is heavily clustered around 1 year. Panel B shows that the frequency of lockups varies considerably across hedge fund styles. For example, 28% (of 945) Long/Short funds have lockups, compared to only 1% (of 342) of the Managed Futures category. Panels A and B of Table II present the distribution of min and notice, respectively, across fund styles. For most fund categories, the majority of funds report minimum investments between $100, ,000. However, most Funds of Funds, Global Macro, and Managed Futures have min between 0 and.1, while most Fixed Income Arbitrage funds have min between.1 and.5. Panel B shows that most notice periods range between 0 and 30 days. Table III presents summary statistics for various fund characteristics, conditional on dlock. The median age (size) is lower (higher) for lockup funds; specifically, the median non-lockup (lockup) fund has 50 (33) monthly observations, and a median size of 17 (26) million dollars of net assets. While eage raises the level of age, the qualitative results under either age definition do not change. Lockup funds also have a lower frequency of leverage use (.63 versus.70), suggesting that lockups are more important for funds which do not 22 See Agarwal and Naik (2003) for a detailed discussion of the option-based indices. 23 In only a few cases, bills were not available and notes were used. Thus, we do not expect our results to be affected by a note/bill liquidity premium, as documented by Amihud and Mendelson (1991) and Kamara (1994). 10

12 use leverage to satisfy unexpected share redemptions. Finally, both the incentive if ee and management fees mf ee are similar between lockup and non-lockup funds. On average, the management fee of these two types of funds is 1%, and the incentive fee is 17% and 19%, respectively. This suggests that any performance differences between funds with and without lockups are due to higher before-fee returns. Summary statistics of the point estimates of parameter θ 0 from the GLM smoothing model are presented in Table IV. The variables ˆθ 0 and ˆθ 0 denote the unrestricted and restricted estimates, respectively, of θ 0. Results are computed separately by dlock. From the original set of 2871 funds, 664 were dropped because they did not have at least 24 return observations. For the unrestricted estimates, an additional 73 (10 lockup) funds are dropped for which ˆθ 0 < 5 or ˆθ 0 > 5. These observations are considered to be those for which the smoothing model is not well-specified. 24 The first set of columns (total) indicates that, despite imposing a less stringent data requirement (24 versus 60 observations) and using a larger sample period, the results are qualitatively the same as those obtained by GLM. Specifically, a greater concentration of ˆθ 0 between.7 and.85 for CA, EM, ED, FA, and FF categories. While these results are consistent with the broad intuition of the AKL measure, they provide a considerably richer analysis. Table IV breaks down the GLM statistics by dlock at the style-level and shows that, for most groups, the average ˆθ 0 and ˆθ 0 are lower for the lockup group. Table IV also suggests that the difference in illiquidity exposure between lockup and non-lockup groups can be substantial for some styles. For example, the Emerging Markets lockup group has an average ˆθ 0 of.77, compared to.86 for the non-lockup group. That is, on average, an additional 9% of a fund s economic return is contemporaneously reflected in the reported return of non-lockup EM funds versus lockup EM funds. This evidence suggests that the negative relationship between lockup choice and GLM smoothing parameters is generally robust across groups. These results contrast with those obtained for the dummy variable liq which, from Table III, indicate that the proportion of non-lockup funds with liquid portfolios (55%) falls below that of lockup funds (63%). Table IV also summarizes, at the aggregate and style-level, the liquidity risk estimates by dlock. For both the Amihud (2002) and Pastor and Stambaugh (2003) measures, we 24 No clear relation exists between violations of this condition and reported style category. However, as a fraction of total funds within the same style group, the OT group leads the way with 7.8%, followed by 6.7% of the GM group; no funds were dropped from the CA and SB groups. 11

13 find that lockup funds do not have greater exposure to liquidity risk. For example, the average ˆβ am and ˆβ ps for lockup funds is.01, compared to.03 and.04 for non-lockup funds, respectively. This relation holds generally at the style-level. 3. Results We consider three alternative regression methodologies to test the relation between fund performance and share restrictions: Aggregate and style-level time series regressions using lockup portfolios; aggregate and style-level pooled panel data regressions; and fund-level time series regressions, followed by a single cross-sectional regression Models We consider four non-nested models to control for other sources of risk in the estimates of performance. The models are intended to control for differentials in risk and other stylespecific characteristics across funds, and to compare both style and fund-level returns to a portfolio that is a mixture of both passive and dynamic benchmarks and a risk-free asset that has the same exposure as the fund. It is generally unclear, ex-ante, which model best describes the systematic risk of hedge funds, so the consideration of four non-nested is taken as a matter of robustness. However, since the focus of the analysis concerns the marginal impact of share restrictions on returns, as opposed to the level of returns, we only need to assume that any omitted variable bias is uncorrelated with a fund s use of share restrictions. A fund s returns are assumed to be linearly related to the returns on a set of traded portfolios, and can be described, in general, as r i,t = α i + k β i,k I k,t + ɛ i,t (4) where r i,t denotes the return on fund i, in excess of the 1-month risk-free interest rate; I k,t is the monthly excess return on the k th traded portfolio during month t; and β i,k is the sensitivity of the excess return on the i th fund to the excess return on the k th index. The first model-the lagged market model (LMM)-includes both contemporaneous and lagged observations on the value-weighted market index as benchmarks. This specification is intended to account for variation in the market returns, as well as the impact of nonsynchronous trading, or, stale prices, on reported fund returns, due to the fund s holding of 12

14 illiquid assets. Asness, et al. (2001) show that the inclusion of lagged market observations increases the explanatory power for hedge fund returns, and shows that the increase is larger for funds which are more likely to hold illiquid assets. 25 The second model (FF4) controls for variation in the market return, as well as payoffs to size, value, and momentum strategies. The third model (Options) includes the market index as well as the option-based indices as benchmarks. This specification is intended to capture the dynamic exposure of hedge fund portfolios to market risk. As discussed earlier, Agarwal and Naik (2003) document that the option-based indices explain a significant fraction of hedge fund return variation. The use of dynamic benchmarks is also motivated by Fung and Hsieh (2001), who document that the returns on straddle positions explain part of the return variation in hedge funds. 26 The fourth model (Base) includes the US and MSCI excluding US market indices, the three Merrill Lynch bond indices, the Federal Reserve Dollar Index, and the Goldman Sachs Commodity Index. This model is intended to account for the static exposure of hedge funds to multiple asset classes, due to their broad investment mandates Lockup Portfolios The sample is initially sorted into two groups, according to the fund s updated lockup variable. Portfolios are equally-weighted and re-balanced monthly. We define the lockup premium as the difference between the portfolios excess returns (α dlock=1 -α dlock=0 ). Table VI reports the annualized, model-specific estimated intercepts of (4). 28 The results suggest that, in aggregate, lockups imply a significant, positive liquidity premium, and is estimated at approximately 7.5% per annum. This result is consistent with the hypothesis that more restricted shares offer higher returns. Table VI also reports the results from sorting the funds into 18 equally-weighted portfolios, according to the fund s style and lockup choice. The results show a positive lockup 25 GLM show that the LMM is a special case of their smoothing model, when a fund s economic returns are determined by a linear, single factor model. 26 More recently, Ferson, Kisgen,and Henry (2004) show how a stochastic discount factor methodology may avoid estimation problems associated with dynamic trading. 27 Section 4.5 considers a conditional model, where a fund s market beta may change over time in response to publicly available information. The results are qualitatively similar to our unconditional models. 28 We also test whether the addition of the lagged market returns in the LMM significantly changes explained variance. The F-test results are roughly consistent with previous results that lagged betas are important for style groups which, according to the AKL liq measure, involve exposure to illiquid assets. 13

15 premium across styles. In fact, the coefficient is positive and significant for all groups except SB and groups with almost no proportion of funds having lockups (EM) and funds with no definitive focus (OT). Moreover, the statistical significance and magnitude of the lockup premium is generally robust across the four models. Note that the magnitude of the lockup premium varies across styles. For example, CA investors receive a lockup premium of approximately 3% per annum, while EN and LS investors receive approximately 7 and 8%, respectively. Table VII reports results from analogous tests using value-weighted portfolios. The lockup premium is less substantial for value-weighted portfolios. For example, the aggregate lockup premium drops to between 4 and 5% per annum, depending on the model, while the coefficient on the ED group becomes insignificant. The difference between the equal and value-weighted portfolios is most likely due to the positive correlation (.17) between fund size and age, and evidence that the lockup premium on younger funds is larger. Section 4 discusses this issue further Multivariate Analysis of Share Restrictions This subsection considers style-level, pooled least squares regressions to examine the individual impact of lockup and other share restrictions on performance. While a pooled regression methodology exhausts the full sample of returns data, it is limited by the set of restrictions it imposes on factor exposures across funds. Models relating returns with asset attributes may be mis-specified if variation in the attribute proxies for variation in the asset s exposure to factor risk. Due to our assertion that share restrictions do not vary with time, this concern is limited to a possible cross-sectional relation between share restrictions and factor betas. 29 We conduct the pooled regression analysis while allowing factor exposures to depend linearly on share restrictions. Specifically, r i,t = α + k β ik I k,t + γ 0 dlock i + γ 1 min i + γ 2 notice i + ɛ i,t, (5a) β ik = b 0k + b 1k dlock i + b 2k min i + b 3k notice i (5b) 29 See Ferson and Harvey (1998, 1999). However, to the extent that our factor model is correct, the portfolio analysis of Section 3.2 and the following two-pass approach are immune from this critique, because factor exposures are estimated at the portfolio and fund-level, respectively. Also, our assertion that share restrictions do not vary with time is supported by the evidence in Section

16 for all i within a given style group, where r i,t denotes the return on portfolio i, in excess of the 1-month risk-free interest rate, and I k,t denotes the excess return on the k th traded portfolio. The variables dlock, min, and notice correspond to the lockup dummy, minimum investment size (in $ millions), and redemption notice period (in 30-day units). For each fund i, we observe a single observation of these variables, measured at the end of the sample period. 30 Table VIII reports the results from the pooled least squares regression using the complete hedge fund sample. Standard errors are heteroscedasticity-consistent and account for contemporaneous, cross-correlation in returns. For each style group and factor model, the first column (α U ) displays the intercept from estimating (5) while excluding the share restriction variables. This measure of performance can be viewed as an unconditional alpha, in the sense that it does not control for the illiquidity imposed on investors through share restrictions. Consistent with the portfolio results as well as previous research, the unconditional alphas are positive and statistically significant. 31 At the aggregate-level, estimated alphas range between 4-6%, depending on the model. Results from style-level results are similar, with almost all styles (except EM and FF) generating significant, positive excess returns. 32 Table VIII also displays, adjacent to the α U column, the results from including the share restrictions into the pooled regression. 33 Consistent with the portfolio results, the estimated lockup premium is, in aggregate, approximately 6-7.5% per annum. Minimum investment (min) and notice period (notice) are also positive and statistically significant. While the economic impact of min is relatively small (50bp per annum increase in returns per $1 million dollar increase), a 30-day notice period is associated with an additional return of 2% per annum. At the style-level, the relative impact of different share restrictions varies across groups. Lockups are positive and significant in all but 4 groups (CA, SB, EM, and OT). 30 We do not allow for fund-level fixed effects (i.e., α i ) because some funds have too few observations. The two-pass approach considered in the following section estimates fund-level α s and β s, but requires at least 24 return observations for a fund to be included. 31 See, e.g., Ackermann, et al. (1999), Liang (1999), and Liang (2003). 32 The failure to identify significant, positive unconditional alphas for the FOF group is consistent with the results of Brown, et al. (2003), who show that FOF s underperform relative to other hedge fund style groups. They argue that this is due to the double layer of incentive fees faced by FOF investors. In the following, we show that the relative under-performance of FOF s is robust to variation in the use of share restrictions. 33 We conduct an F test of whether, within a style, the coefficients (b 1, b 2, b 3 ) in equation (5b) are jointly zero. Except for the EN, FA, and FF style groups, this hypothesis is consistently rejected across models. 15

17 The impact of notice periods is also positive and significant in all but 4 groups (SB, EM, EN, OT). 34 The α column displays the liquidity-adjusted alphas, which are the excess fund returns after controlling for risk and share liquidity. Alternatively, these alphas can be interpreted as estimates of risk-adjusted returns on funds which impose no share restrictions on investors. Strikingly, the aggregate-level alphas, while still positive, are now 3-3.5% lower and insignificant; that is, the positive unconditional alphas cannot be distinguished from compensation for holding restricted shares. Observe also that this result is consistent at the style-level; that is, of the 7 style groups for which the unconditional alphas are positive and significant, 4 groups have liquidity-adjusted alphas that are either negative or insignificant. The remaining style groups-ca EN, and LS-appear to generate smaller, positive alphas for investors, even after controlling for share liquidity. 35 The large differences between unconditional and liquidity-adjusted alphas suggests that share restrictions are important control variables for hedge fund performance studies. While the above results suggest that returns are higher for funds with less liquid shares, the AM theory implies that the relationship between returns and transactions costs is also concave. We test the linearity of the return/share restrictions relation by including quadratic variables (min 2 and notice 2 ) into (5). The results are presented in Table VIII. 36 Accounting for the non-linear relation between returns and liquidity decreases the level of estimated performance. Specifically, aggregate-level estimates of alpha are either negative or insignificant, and the alphas of EN and LS are now insignificantly different from zero. However, the CA group does generate statistically significant excess returns after controlling for restrictions. Table VIII shows that the coefficient estimates for both (min 2 and notice 2 ) are negative and statistically significant. This results holds generally at the style-level; that is, the relationship between returns and share restrictions is positive and concave for 6 of the 9 styles. This evidence is consistent with a clientele effect in the market for hedge fund shares: Less liquid hedge fund shares are held by investors with longer investment horizons. 34 Since lockup use and notice period are positively correlated, this provides an explanation for the significance of lockups on CA returns in the portfolio approach. 35 Still, the estimated liquidity-adjusted alphas of the CA EN, and LS groups are substantially (approximately 2.5%, 2.5% and 4.5% per annum, respectively) lower than the unconditional alphas. 36 We also sort funds into mutually-exclusive portfolios by lockup periods of 0, less than 12, 12, and more than 12 months. Point estimates for the mean annual returns are 6, 12.3, 15, and 15.7%, respectively. Not surprisingly, statistical significance is weak, due to the lack of variation in non-zero lockup periods. 16

18 3.4. Two-pass Approach While the pooled regression approach exhausts the time-variation of fund returns and characteristics in the full sample of hedge funds, it imposes restrictions (5b) on individual fund loadings on the factor indices within a style group. This section considers a two-pass approach, which allows for heterogenous factor loadings at the fund level. This analysis is performed in two steps: first, fund-level alphas are estimated using (4). The total number of estimated alphas equals 2135, since we drop 641 funds because they do not have at least 24 monthly observations, 95 funds because they do not report either minimum investment size or fees, and an additional 2 funds with outlying returns. 37 The second step involves the following cross-sectional regression of estimated alphas (ˆα) on fund characteristics: ˆα i = a + b 1 dlock i + b 2 min i + b 3 notice i + b 4 min 2 i + b 5 notice 2 i + e in (6) The coefficients b 1, b 2, and b 3 are intended to estimate the degree to which a fund s liquidity characteristics contribute to excess returns. More precisely, they may be interpreted in the context of Fama-Macbeth cross-sectional regression coefficients, as liquidity premia on liquidity factors. The coefficients, b 4 and b 5, provide a test of whether the return/share restriction relation is linear. 38 Panel A of Figure 1 shows the histogram of the 2135 fund unconditional alphas from the lagged market model (LMM). The distribution of alphas is relatively symmetric, and centered around 4.71% per year. Panel B shows that, consistent with previous studies, the factor models do a relatively poor job of explaining the variation in hedge fund returns, since for the majority of funds the R 2 lies below 40%; the mean R 2 is about 20%. 39 The results from the cross-sectional regression (6) are reported in Table IX. Similar to the pooled regression results, the estimated annual excess return is, in aggregate, approximately 5%, and statistically significant. This result is also consistent with the conclusions of earlier research that hedge funds generate positive alphas. After controlling for share restrictions, however, the excess returns drop approximately 5%, and the estimated lockup premium in the simple regression is 7% per year. Also, notice periods and minimum investment 37 Including the 2 outlying funds does not change the qualitative results. 38 We have also run monthly cross-sectional regressions of fund excess returns on share restrictions, after estimating fund betas using the full sample period. We then calculate the premium for a share restriction as the time-series mean of its coefficient estimates. This approach yields qualitatively similar results. 39 See, e.g., Fung and Hsieh (1997a, 2001). Results from the other models are similar: The mean R 2 for the FF4, Options, and Base models are 25%, 19%, and 23%. 17

19 have a significant, positive relation with excess returns. Specifically, a fund with a 30- day notice period provides an additional 5% annual return, while a $1 million minimum investment implies a 1% increase in excess returns. These results are consistent with the pooled regression results, and the prediction that other forms of share restrictions affect expected returns. More strikingly, the excess returns of funds without share restrictions, or, liquidity-adjusted alphas are either negative or insignificant, across almost all models. 40 Panel B of Figure 1 shows the histogram of the alphas for the LMM model, after subtracting the estimated share restriction premia from the unconditional alphas. The distribution shifts considerably to the left, and is now centered at -.71% per annum. Table IX also presents evidence in support of a concave relationship between returns and share restrictions. The coefficient on the quadratic variables (min 2 and notice 2 ) are negative and significant. As in the pooled regression analysis results, this evidence is consistent with AM result of a clientele effect, whereby investors with lower-liquidity needs hold less liquid shares. 4. Robustness Previous research argues that hedge fund returns are subject to a number of biases, including self-selection (Fung and Hsieh (1997a, 1997b, 2000)), survivorship (Ackermann, et al. (1999), Brown, et al. (1995), and Brown, et al. (1999)), and de-listing and backfilling (Baquero, et al. (2003) and Posthuma and van der Sluis (2003)). In this section we address these biases, and a heretofore unexamined endogeneity bias, due to the fact that fund characteristics are measured only at the end of the sample period. We also consider a conditional performance model to examine whether our earlier results withstand a possible correlation between share restrictions and the use of dynamic strategies based upon public information. Finally, we examine whether our results are due to a possible correlation between share restrictions and the use of leverage Self-Selection A selection bias may result from the fact that reporting to a database is voluntary. In fact, funds are only required to provide audited financial statements to fund investors, on an 40 While the Base model estimates a 2% excess return after controlling for share restrictions, the following section shows this result to be driven by backfilled data. 18