An empirical Bayesian approach to stein-optimal covariance matrix estimation

Abstract

This paper proposes a conjugate Bayesian regression model to estimate the covariance matrix of a large number of securities. Characterizing the return generating process with an unrestricted factor model, prior beliefs impose structure while preserving estimator consistency. This framework accommodates economically-motivated prior beliefs and nests shrinkage covariance matrix estimators, providing a common model for their interpretation. Minimizing posterior finite-sample square error delivers a fully-automated covariance matrix estimator with beliefs that become diffuse as the sample grows relative to the dimension of the problem. In application, this Stein-optimal posterior covariance matrix performs well in a large set of simulation experiments.

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