یک الگوی اقتصاد سنجی همبستگی زنجیره ای و عدم نقدینگی در بازده صندوق های تامینی

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.

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 View the MathML source and the last transaction in security B occurs at View the MathML source, 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 and Cohen 1986, Kadlec and Patterson (1999), Lo and MacKinlay 1988 and 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 and 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.

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 of Asness et al. (2001) regarding the significance of lagged market returns in market-model regressions for hedge funds. Although our moving-average specification is similar to some of the early models of nonsynchronous trading, our motivation is quite different and is meant to cover a broader set of factors that give rise to serial correlation and smoothed returns, even in the presence of synchronously recorded prices. Maximum likelihood estimates of our smoothing model for the returns of 908 hedge funds in the TASS Hedge Fund database yield empirically plausible estimates of smoothing coefficients and suggest that simple time-series measures such as our smoothing index serve as useful proxies for a hedge fund's illiquidity risk exposure. In some cases, our econometric model may also be useful for flagging possible cases of deliberate performance-smoothing behavior, although additional information will need to be gathered before any firm conclusions regarding such behavior can be made. Regardless of the sources of serial correlation, illiquidity exposure is the main implication and this has potentially important consequences for both managers and investors. Therefore, we also develop a set of tools for quantifying the degree of smoothing in the data and adjusting for smoothed returns in computing performance statistics such as means, variances, market betas, and Sharpe ratios, and derive their asymptotic distributions using continuous-record asymptotics that can better accommodate the small sample sizes of most hedge-fund datasets. Our empirical results suggest several applications for our econometric model of illiquidity and smoothed returns. Despite the general consistency of our empirical results with common intuition regarding the levels of illiquidity among the various hedge-fund investment styles, the variation in estimated smoothing coefficients within each category indicates that there are better ways of categorizing hedge funds. Given the importance of liquidity for the typical hedge-fund investor, it may be appropriate to subdivide each style category into “liquidity tranches” defined by our smoothing index. This may prove to be especially useful in identifying and avoiding the potential wealth transfers between new and existing investors that can occur from the opportunistic timing of hedge-fund investments and redemptions. Alternatively, our smoothing parameter estimates may be used to compute illiquidity exposure measures for portfolios of hedge funds or fund of funds, which may serve as the basis for a more systematic approach to managing portfolios that include alternative investments. Although we focus on hedge funds in this paper, our analysis may be applied to other investments and asset classes, e.g., real estate, venture capital, private equity, art and other collectibles, and other assets for which illiquidity and smoothed returns are even more problematic, and where the estimation of smoothing profiles can be particularly useful for providing investors with risk transparency. More generally, our econometric model may be applied to a number of other contexts in which there is a gap between reported results and economic realities. For example, recent events surrounding the collapse of Enron and other cases of corporate accounting irregularities have created renewed concerns about “earnings management”, in which certain corporations are alleged to have abused accounting conventions so as to smooth earnings, presumably to give the appearance of stability and consistent growth. Beneish (2001) and Healy and Wahlen (1999) provide reviews of the extensive literature on earnings management. The impact of such smoothing can sometimes be “undone” using an econometric model such as ours. There are a number of outstanding issues regarding our analysis of illiquidity and smoothed returns that warrant further study. Perhaps the most pressing issue is whether the proximate source of smoothing is inadvertent or deliberate. Our linear regression model with contemporaneous and lagged common factors can serve as the starting point for distinguishing between systematic illiquidity versus idiosyncratic smoothing behavior. However, this issue is likely to require additional information about each fund along the lines of Chandar and Bricker's (2002) study, e.g., the size of the fund, the types of the securities in which the fund invests, the accounting conventions used to mark the portfolio, the organization's compensation structure, and other operational aspects of the fund. With these additional pieces of information, we can construct more relevant common factors for our linear-regression framework, or relate the cross-sectional variation in smoothing coefficients to assets under management, security type, fee structure, and other characteristics, yielding a more complete picture of the sources of smoothed returns. It may also be fruitful to view the hedge-fund industry from a broader perspective, one that acknowledges the inherent capacity constraints of certain types of strategies as well as the time lags involved in shifting assets from one type to another. Because of the inevitable cross-sectional differences in the performance of hedge-fund styles, assets often flow in loosely coordinated fashion from one style to another, albeit under various institutional restrictions such as calendar-specific periods of liquidity, tiered redemption schedules, redemption fees, and other frictions. The interactions between asset flows and institutional rigidities (especially over time) sometimes cause statistical side-effects that include periodicities in performance and volatility, time-varying correlations, structural breaks, and under certain conditions, serial correlation. The dynamics of the hedge-fund industry are likely to be quite different than that of more traditional investment products, hence the “ecological framework” of Niederhoffer (1998, Chapter 15), Farmer (1998), and Farmer and Lo (1999), or the system dynamics approach of Getmansky and Lo (2004) might be more conducive paradigms for addressing these issues. Finally, from the hedge-fund investor's perspective, a natural extension of our analysis is to model illiquidity directly and quantify the illiquidity premium associated with each hedge-fund investment style, perhaps in a linear-factor framework such as Chordia 2000, Chordia 2001 and Chordia 2002 and Pastor and Stambaugh (2003). Whether such factor models can forecast liquidity crises like August 1998, or show that there are systematic illiquidity factors that are common to categories of hedge funds, are open questions that are particularly important in the context of hedge-fund investments. We plan to address these and other related questions in our ongoing research.