Risk adjusted performance measures of hedge funds: A third-order likelihood-based approach

The rapid growth of hedge fund industry since the early 1990's requires an improved understanding of the risk-adjusted returns and the risk exposure properties of hedge funds. This dissertation studies the risk-adjusted return behavior of hedge funds while control various issues peculiar to hedge fund studies, in particular, the small sample problem. Due to its relative short history, opaque operations, and the lack of performance reporting standard, hedge funds have severe small sample problem. As many commonly used parametric statistic inference methods rely on the first-order asymptotic theory, the small sample problem has significant draw back when apply these parametric statistic inference methods on hedge fund studies.;In this dissertation, we provide a brief history of the hedge fund industry and explain why the standard statistical methodologies for analyzing mutual funds are not applicable for analyzing hedge funds. Then we examine the recent development of the third-order likelihood-based methods. In particular, the Barndorff-Nielsen's R* formula and the Lugannani and Rice method are reviewed. A simulation study illustrates the supreme accuracy of these two methods especially when the sample size is small. These statistical methods are then applied to study the performance persistence of hedge fund returns. Moreover, they are also applied to obtain confidence intervals of the Sharpe ratio, a risk-adjusted return measure for a fund, in a hedge fund database. Numerical examples showed the proposed methods and the standard methods can give very different results when the sample size is small. Theoretically, the proposed methods have third-order accuracy and the standard methods have only first-order accuracy. All the numerical computations are implemented by SAS.