Posterior Inference for Portfolio Weights

Abstract

We investigate estimation uncertainty in portfolio weights through their posterior distributions in a Bayesian regression framework. While we derive analytical posterior results for shrinkage variants of the global minimum variance portfolio (GMVP), the main advantage of our novel approach is the direct specification of the prior on the optimal portfolio weights whereas modeling the asset return distribution explicitly is avoided. We show how to incorporate economic views about the asset returns in our framework as a shrinkage target and how to account for the investor’s uncertainty about these views through a hierarchical set-up. In a series of empirical experiments we explore the effect of estimation errors on the performance of the optimal portfolio and propose various practical trading strategies derived from the posterior information on the optimal portfolio weights that are highly beneficial to the investor.