Bayesian Portfolio Selection with Gaussian Mixture Returns

Markowitz portfolio selection is challenged by huge implementation barriers. This paper addresses the parameter uncertainty and deviation from normality in a Bayesian framework. The non-normal asset returns are modeled as finite Gaussian mixtures. Gibbs sampler is employed to obtain draws from the posterior predictive distribution of asset returns. Optimal portfolio weights are then constructed so as to maximize agents’ expected utility. Simple experiment suggests that our Bayesian portfolio selection procedure performs exceedingly well.