Bayes-Stein Estimation for Portfolio Analysis

TLDR

Portfolio analysis suffers from uncertainty in parameter estimates, rendering the classical sample mean inadmissible and leading to suboptimal investor utility under a loss function based on simultaneous estimation of normal means. The study proposes a simple empirical Bayes estimator aimed at outperforming the classical sample mean in portfolio selection. The authors develop an empirical Bayes estimator that shrinks individual return estimates toward a common mean to reduce estimation error. Simulation results demonstrate that the Bayes–Stein estimator yields significant gains in portfolio selection compared to the sample mean.

Abstract

In portfolio analysis, uncertainty about parameter values leads to suboptimal portfolio choices. The resulting loss in the investor's utility is a function of the particular estimator chosen for expected returns. So, this is a problem of simultaneous estimation of normal means under a well-specified loss function. In this situation, as Stein has shown, the classical sample mean is inadmissible. This paper presents a simple empirical Bayes estimator that should outperform the sample mean in the context of a portfolio. Simulation analysis shows that these Bayes-Stein estimators provide significant gains in portfolio selection problems.