An Econometric Analysis of Serial Correlation and Illiquidity in Hedge-Fund Returns¶
Motivation(s)¶
Hedge funds are attracting major institutional investors (e.g. pension funds, university endowments) due to their relatively low volatility double-digit returns that seems uncorrelated with general market swings. Several recent empirical studies have argued that the standard methods of assessing their risks and rewards are misleading.
The spurious serial correlation and biased sample moments in the reported asset returns has been attributed, albeit inadequately, to nonsynchronous trading, which refers to the erroneous treatment of security prices as if they were recorded at the same time. Information generated at date \(t\) may not be fully impounded into prices until several periods later. The shortcoming of that literature stems from its focus on equity market microstructure effects (e.g. closing prices, stale prices) as the sources of non-synchronicity where the temporal displacement is typically on the order of minutes, hours, or several days.
Proposed Solution(s)¶
The authors argue that serial correlation in hedge fund returns is the outcome of illiquidity exposure. These illiquid securities can include securities that are either not actively traded or lacking readily available market prices. Since they can induce highly serially correlated returns even if prices are sampled synchronously, nonsynchronous trading is not the only aspect of illiquidity that affects hedge fund returns, which are computed synchronously on the last day of each month.
The authors propose an explicit econometric model of smoothed returns and derive its implications for common performance statistics such as the mean, standard deviation, and Sharpe ratio. Although their model of illiquidity is similar to those in the nonsynchronous trading literature, they claim that their proposal handles 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 deliberate performance-smoothing behavior. Their model could take up to \(k + 1\) periods, from the time the information is generated, before the observed returns fully reflect the information driving the fund’s performance. They argue this is reasonable for hedge funds because even the most illiquid securities will trade eventually, and when that occurs, all of the cumulative information affecting that security will be fully impounded into its transaction price. Hence the parameter \(k\) should be selected to match the fund’s type of illiquidity of the fund.
Evaluation(s)¶
The authors estimate the smoothing profiles (e.g. uniform weights, sum-of-years, geometric) and sharpe ratios via maximum likelihood and linear regression with the additional assumption of a linear single-factor model. The historical hedge fund returns were extracted from the TASS database. Their model is able to generate empirically realistic levels of serial correlation for historical hedge fund returns. Furthermore, the empirically estimated smoothing profiles imply lagged beta coefficients that are consistent with the existing literature’s lagged beta estimates.
The authors addressed outstanding arguments in favor of other sources as possible explanations for serial correlation through Monte Carlo simulations of the most basic models. Each of the following models had very little explanatory power (i.e. small first-order autocorrelations coefficients) unless implausible parameter values are used:
Two-state Markov model of time-varying expected returns,
time-varying leverage model with a VaR constraint,
and net-of-fee returns under an incentive fee with a high water mark.
The authors assert their model can serve as the starting point for distinguishing between systematic illiquidity versus idiosyncratic smoothing behavior. More information about each fund (e.g. size, composition, accounting convention, compensation structure) are needed to yield a more complete picture.
Future Direction(s)¶
Could data mining uncover deliberate performance smoothing of illiquid securities by hedge fund managers?
How do style factors influence the proposed model?
Question(s)¶
Why is performance persistence even used as an indicator?
How are the specification checks any different compared to the usual construction of a model for a specific domain?
Why are market betas and Sharpe ratios still used despite being so easily manipulated?
How practical is the Herfindahl index?
Analysis¶
Serial correlation in hedge fund returns is due primarly to illiquidity and smoothed returns. Even though it is important to understand the sources of serial correlation, the authors should have presented more concisely. There was too much information, so it was difficult to grasp the core concepts.
The analysis of simple models to refute other possible sources of serial correlation is quite clever. Unfortunately, the main empirical analysis focused too much on statistical significance. Nevertheless, their proofs and derivations are helpful for deriving new models.
References
- GLM04
Mila Getmansky, Andrew W Lo, and Igor Makarov. An econometric model of serial correlation and illiquidity in hedge fund returns. Journal of Financial Economics, 74(3):529–609, 2004.