Robust Bayesian Allocation

Abstract

Using the Bayesian posterior distribution of the market parameters we define self-adjusting uncertainty regions for the robust mean-variance problem. Under a normal-inverse-Wishart conjugate assumption for the market, the ensuing robust Bayesian mean-variance optimal portfolios are shrunk by the aversion to estimation risk toward the global minimum variance portfolio.

After discussing the theory, we test robust Bayesian allocations in a simulation study and in an application to the management of sectors of the S&P 500.

Fully commented code is available for download

Keywords: estimation risk, Bayesian estimation, MCMC, robust optimization, location-dispersion ellipsoid, classical equivalent, shrinkage, global minimum variance portfolio, equally-weighted portfolio, quantitative portfolio management

JEL Classification: C1, G11