Mutual fund performance evaluation methodology and local false discovery rate approach

The history of applying statistical simultaneous inference methods to a financial problem of mutual fund performance evaluation is very short. A major problem in applying simultaneous inference methods is the non-trivial dependence among the utilized test statistics. When the number of tests is large, the explicit modeling of dependence structure becomes difficult. As a result, assumptions that are too restrictive are made, which can substantially bias the inference. In addition, the initial performance evaluation model itself can be misspecified and thus distort the results. For instance, the recent study of Barras, Scaillet and Wermers (2008) utilizes a multiple inference procedure with oversimplifying assumptions and, therefore, is prone to both sources of bias. Another under-investigated issue is the statistical power in a typical mutual fund study. The study of Kothari and Warner (2001) makes some progress but their research is not based on real mutual fund data. This paper catches up with the recent developments in Statistics by applying a state-of-the-art “empirical null hypothesis” concept combined with the” local false discovery rate” method, developed by Efron in 2001-2007. That offers a viable alternative to the explicit modeling of high-dimensional dependence structure. In addition, the findings of Efron suggest that the new procedure may account for the performance evaluation model misspecification. The new method also provides informative power measures and an elegant way of comparing the performance of mutual fund subgroups. A comprehensive investigation is performed for about 1900 actively managed US equity mutual funds observed monthly between 1993 and 2007. The results provide a significant extension to the findings of Barras et al. whose method can be seen as a restricted version of the method in this study. It is shown that the version of Barras et al. has both statistically and practically significant bias. We conclude that, unfortunately, Barras et al. are too optimistic about the performance of US mutual funds. In addition, a detailed power analysis reveals that a typical mutual fund study with monthly dataset and multifactor performance evaluation model has a very low power. Even when outperformers are present in the sample, it usually requires too many years of data to single them out