An econometric model of serial correlation and illiquidity in hedge fund returns

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Abstract

The returns to hedge funds and other alternative investments are often highly serially correlated. In this paper, we explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure and smoothed returns. We propose an econometric model of return smoothing and develop estimators for the smoothing profile as well as a smoothing-adjusted Sharpe ratio. For a sample of 908 hedge funds drawn from the TASS database, we show that our estimated smoothing coefficients vary considerably across hedge-fund style categories and may be a useful proxy for quantifying illiquidity exposure.

Introduction

One of the fastest growing sectors of the financial services industry is the hedge fund or alternative investments sector. Long the province of foundations, family offices, and high net-worth investors, hedge funds are now attracting major institutional investors such as large state and corporate pension funds and university endowments. Efforts are underway to make hedge fund investments available to individual investors through more traditional mutual-fund investment vehicles. One of the main reasons for such interest is the performance characteristics of hedge funds. Often known as high-octane investments, many hedge funds have yielded double-digit returns to their investors and, in some cases, in a fashion that seems uncorrelated with general market swings and with relatively low volatility. Most hedge funds accomplish this by maintaining both long and short positions in securities (hence the term “hedge fund”) which, in principle, gives investors an opportunity to profit from both positive and negative information while, at the same time, providing some degree of market neutrality because of the simultaneous long and short positions.

However, several recent empirical studies have challenged these characterizations of hedge fund returns, arguing that the standard methods of assessing their risks and rewards are misleading. For example, Asness et al. (2001) show in some cases where hedge funds purport to be market neutral, i.e., funds with relatively small market betas, including both contemporaneous and lagged market returns as regressors and summing the coefficients yields significantly higher market exposure. Moreover, in deriving statistical estimators for Sharpe ratios of a sample of mutual and hedge funds, Lo (2002) shows that the correct method for computing annual Sharpe ratios based on monthly means and standard deviations can yield point estimates that differ from the naive Sharpe ratio estimator by as much as 70%.

These empirical properties have potentially significant implications for assessing the risks and expected returns of hedge fund investments. We can trace them to a single common source of significant serial correlation in their returns.

This is surprising because serial correlation is often (though incorrectly) associated with market inefficiencies, implying a violation of the Random Walk Hypothesis and the presence of predictability in returns. This seems inconsistent with the popular belief that the hedge fund industry attracts the best and the brightest fund managers in the financial services sector. In particular, if a fund manager's returns are predictable, the implication is that the manager's investment policy is not optimal. If the manager's returns next month can be reliably forecasted as positive, the fund manager should increase positions this month to take advantage of this forecast, and vice versa for the opposite forecast. By taking advantage of such predictability, the fund manager will eventually eliminate it, along the lines of Samuelson's (1965) original “proof that properly anticipated prices fluctuate randomly.” Given the outsize financial incentives of hedge fund managers to produce profitable investment strategies, the existence of significant unexploited sources of predictability seems unlikely.

In this paper, we argue that in most cases, serial correlation in hedge fund returns is not due to unexploited profit opportunities, but is more likely the result of illiquid securities that are contained in the fund. For example, these illiquid securities can include securities that are not actively traded and for which market prices are not always readily available. In such cases, the reported returns of funds containing illiquid securities will appear to be smoother than true economic returns (returns that fully reflect all available market information concerning those securities) and this, in turn, will impart a downward bias on the estimated return variance and yield positive serial return correlation.

The prospect of spurious serial correlation and biased sample moments in reported returns is not new. Such effects are available in the literature on “nonsynchronous trading”, which refers to security prices recorded at different times but which are erroneously treated as if they were recorded simultaneously. For example, the daily prices of financial securities quoted in the Wall Street Journal are usually “closing” prices, prices at which the last transaction in each of those securities occurred on the previous business day. If the last transaction in security A occurs at 2:00pm and the last transaction in security B occurs at 4:00pm, then included in B's closing price is information not available when A's closing price was set. This can create spurious serial correlation in asset returns since economy-wide shocks will be reflected first in the prices of the most frequently traded securities, with less frequently traded stocks responding with a lag. Even when there is no statistical relation between securities A and B, their reported returns will appear to be serially correlated and cross-correlated simply because we have mistakenly assumed that they are measured simultaneously. One of the first to recognize the potential impact of nonsynchronous price quotes was Fisher (1966). Since then more explicit models of nontrading have been developed by Atchison et al. (1987), Dimson (1979), Shanken (1987), Cohen 1978, Cohen 1979, Cohen 1983a, Cohen 1983b, Cohen 1986, Kadlec and Patterson (1999), Lo and MacKinlay 1988, Lo and MacKinlay 1990, and Scholes and Williams (1977). Campbell et al. (1997, Chapter 3) provide a more detailed review of this literature.

However, this literature focuses exclusively on equity market-microstructure effects as the sources of nonsynchronicity (closing prices that are set at different times, or prices that are stale) where the temporal displacement is on the order of minutes, hours, or, in extreme cases, several days. For such applications, Lo and MacKinlay 1988, Lo and MacKinlay 1990 and Kadlec and Patterson (1999) show that nonsynchronous trading cannot explain all of the serial correlation in weekly returns of equal- and value-weighted portfolios of US equities during the past three decades.

In the context of hedge funds, we argue in this paper that serial correlation is the outcome of illiquidity exposure, and while nonsynchronous trading could be one symptom or by-product of illiquidity, it is not the only aspect of illiquidity that affects hedge fund returns. Even if prices are sampled synchronously, they can still yield highly serially correlated returns if the securities are not actively traded. In fact, for most hedge funds, returns are computed on a monthly basis, hence the pricing or mark-to-market of a fund's securities typically occurs synchronously on the last day of the month. Therefore, although our formal econometric model of illiquidity is similar to those in the nonsynchronous trading literature, the motivation is considerably broader, including linear extrapolation of prices for thinly traded securities, the use of smoothed broker–dealer quotes, trading restrictions arising from control positions and other regulatory requirements, and, in some cases, deliberate performance-smoothing behavior. Thus, the corresponding interpretations of our parameter estimates must be modified accordingly.

Regardless of the particular mechanism by which hedge fund returns are smoothed and serial correlation is induced, the common theme and underlying driver is illiquidity exposure, and although we argue that the sources of serial correlation are spurious for most hedge funds, nevertheless, the economic impact of serial correlation can be quite real. For example, spurious serial correlation yields misleading performance statistics such as volatility, Sharpe ratio, correlation, and market-beta estimates. Such statistics are commonly used by investors to determine whether or not they will invest in a fund, how much capital to allocate to a fund, what kinds of risk exposures they are bearing, and when to redeem their investments. Moreover, spurious serial correlation can lead to wealth transfers between new, existing, and departing investors, in much the same way that using stale prices for individual securities to compute mutual-fund net-asset-values can lead to wealth transfers between buy-and-hold investors and day-traders (see, for example, Boudoukh et al., 2002).

In this paper, we develop an explicit econometric model of smoothed returns and derive its implications for common performance statistics such as the mean, standard deviation, and Sharpe ratio. We find that the induced serial correlation and impact on the Sharpe ratio can be quite significant even for mild forms of smoothing. We estimate the model using historical hedge fund returns from the TASS Database, and show how to infer the true risk exposures of a smoothed fund for a given smoothing profile. Our empirical findings are quite intuitive. Funds with the highest serial correlation tend to be the more illiquid funds (e.g., emerging market debt, fixed income arbitrage, etc.), and after correcting for the effects of smoothed returns, some of the most successful types of funds tend to have considerably less attractive performance characteristics.

Before describing our econometric model of smoothed returns, we provide a brief literature review in Section 2 and then consider other potential sources of serial correlation in hedge fund returns in Section 3. We show that these other alternatives (time-varying expected returns, time-varying leverage, and incentive fees with high-water marks) are unlikely to generate the magnitudes of serial correlation observed in the data. We develop a model of smoothed returns in Section 4. We then derive its implications for serial correlation in observed returns, and we propose several methods for estimating the smoothing profile and smoothing-adjusted Sharpe ratios in Section 5. We apply these methods to a data set of 908 hedge funds spanning the period from November 1977 to January 2001 and summarize our findings in Section 6. We conclude in Section 7.

Section snippets

Literature review

Thanks to the availability of hedge-fund returns data from sources such as AltVest, Hedge Fund Research (HFR), Managed Account Reports (MAR), and TASS, a number of empirical studies of hedge funds are available. For example, Ackermann et al. (1999), Agarwal and Naik 2000b, Agarwal and Naik 2000c, Edwards and Caglayan (2001), Fung and Hsieh 1999, Fung and Hsieh 2000, Fung and Hsieh 2001, Kao (2002), and Liang 1999, Liang 2000, Liang 2001 provide comprehensive empirical studies of historical

Other sources of serial correlation

Before turning to our econometric model of smoothed returns in Section 4, we first consider four other potential sources of serial correlation in asset returns: (1) market inefficiencies; (2) time-varying expected returns; (3) time-varying leverage; and (4) incentive fees with high water marks.

Perhaps the most common explanation (at least among industry professionals and certain academics) for the presence of serial correlation in asset returns is a violation of the Efficient Markets

An econometric model of smoothed returns

Having shown in Section 3 that other possible sources of serial correlation in hedge-fund returns are hard-pressed to yield empirically plausible levels of autocorrelation, we now turn to illiquidity and smoothed returns, which are the main focus of this study. Although illiquidity and smoothed returns are two distinct phenomena, it is important to consider them in tandem because one facilitates the other. For actively traded securities, both theory and empirical evidence suggest that in the

Estimation of smoothing profiles and Sharpe ratios

Although the smoothing profiles described in Section 4.2 can all be easily estimated from the sample moments of fund returns, e.g., means, variances, and autocorrelations, we wish to estimate more general forms of smoothing. Therefore, in this section we propose two estimation procedures (maximum likelihood and linear regression) that place fewer restrictions on a fund's smoothing profile than the three examples in Section 4.2. In Section 5.1 we review the steps for maximum likelihood

Empirical analysis

For our empirical analysis, we use the TASS database of hedge funds which consists of monthly returns and accompanying information for 2,439 hedge funds (as of January 2001) from November 1977 to January 2001 (http://www.tassresearch.com). The database is divided into two parts: “Live” and “Graveyard” funds. Hedge funds that belong to the Live database are considered active as of January 1, 2001. Once a hedge fund decides not to report its performance, is liquidated, restructured, or merged

Conclusions

Although there are several potential explanations for serial correlation in asset returns, we argue in this paper that the serial correlation present in the returns of hedge funds is due primarily to illiquidity and smoothed returns. Using a simple econometric model in which observed returns are a finite moving-average of unobserved economic returns, we generate empirically realistic levels of serial correlation for historical hedge-fund returns while, at the same time, explaining the findings

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  • Cited by (0)

    This research was supported by the MIT Laboratory for Financial Engineering. We thank Cliff Asness, David Geltner, Jacob Goldfield, Stephanie Hogue, Stephen Jupp, S.P. Kothari, Bob Merton, Myron Scholes, Bill Schwert, Jonathan Spring, Andre Stern, Svetlana Sussman, a referee, and seminar participants at Harvard, the MIT Finance Student Lunch Group, Morgan Stanley, and the 2001 Fall Q Group Conference for many stimulating discussions and comments.

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    Present address: Eugene M. Isenberg School of Management, University of Massachusetts, Amherst, 121 Presidents Drive, Amherst, MA 01003, USA.

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