On the optimality of hedge fund investment strategies: A Bayesian skew t distribution model

Abstract

This paper presents a forward looking model for selection of hedge fund investment strategies. Given excess skewness observed in hedge funds’ return distributions, we assume that the historical returns have a skew student t distribution. We implement a Bayesian framework to derive the parameters of the posterior return distribution. The predictive return distribution is easily obtained once the posterior parameters are estimated by assuming that the unknown future expected returns are equal to the posterior distribution multiplied by the likelihood of the unknown future expected returns conditional on available posterior parameters. We derive the predictive mean, predictive variance and predictive skewness from the predictive distribution after twenty-one thousand simulations, and solve a multi-objective portfolio selection problem using a data set of monthly returns of investment strategy indices published by the Hedge Fund Research group. Our results show that the methodology presented in this paper provides the highest rate of return (16.79%) with a risk of 2.62% compared to the mean-variance method, which provides 0.8% rate of return with 1.41% risk, respectively. Key words: Predictive distribution, skew t distribution, posterior distribution, prior distribution, MCMC simulations, Gibbs sampler.