Bayesian Shrinkage of Portfolio Weights

Abstract

We propose a novel regression approach for optimizing portfolios by means of Bayesian regularization techniques. In particular, we represent the weight deviations of the global minimum variance portfolio from a reference portfolio (e.g. the naive 1/N portfolio) as coefficients of a linear regression and shrink them towards zero through Bayesian shrinkage priors. By doing so, we aim to robustify the portfolios against estimation risk. Modeling the optimal portfolio weights through Bayesian priors avoids estimating the moments of the asset return distribution and substantially reduces the dimensionality of the estimation problem. We compare the proposed Bayesian shrinkage strategies to popular frequentist approaches and find that the former show better out-of-sample performance based on various performance criteria. They also turn out to be particularly attractive for high-dimensional portfolios.

Keywords: Bayesian regression, estimation risk, global minimum variance portfolio, shrinkage

JEL Classification: C11, C58, G11