# Robust Bayesian allocation

## Attilio Meucci

#### Abstract

ABSTRACT

Using the Bayesian posterior distribution of market parameters we define selfadjusting 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.