The Effect of Probability and Uncertainty Models on Hedge Fund Performance Analysis

Abstract

This paper implements two types of framework to investigate the outperformance, selectivity and market timing skills in hedge funds: uncertainty and probability. Using the uncertainty framework, the paper develops an uncertain fuzzy credibility regression model in the form of a linear and quadratic CAPM in order to estimate these performance skills. Using the probability framework the paper implements frequentist and Bayesian CAPMs (linear and quadratic) to estimate the same performance skills. We consider a data set of monthly investment style indices published by Hedge Fund Research group. The data set extends from January 1995 to June 2010. We divide this sample period into four overlapping sub-sample periods that contain different market trends. Using the probability framework, our results show that bounded rationality triggers inefficiencies in the market that fund managers can utilise to outperform the market. This market outperformance is due to selectivity and market timing skill during periods of economic recovery only. We admit that these results contradict the rational expectations model. However, with the uncertainty framework this effect disappears on behalf of the rational expectations model and the efficient market hypothesis. This disappearance may be a result of the increased amount of high frequency trading witnessed recently that has made market inefficiencies, which are the main source of hedge fund performance, rarer.

Keywords: selectivity skill, market timing skill, fuzzy regression, chi-square test, quadratic CAPM, membership functions, uncertainty distribution, market efficiency, Bayesian quadratic CAPM, priors, posteriors, beliefs

JEL Classification: C11, C15, C46, G23, G14