An Empirical Bayes Approach to Efficient Portfolio Selection

When portfolio optimization is implemented using the historical characteristics of security returns, estimation error can degrade the desirable properties of the investment portfolio that is selected. Given the problem of estimation risk, it is natural to formulate rules of portfolio selection within a Bayesian framework. In this framework, portfolio selection is based on maximization of expected utility conditioned on the predictive distribution of security returns. Most researchers have addressed the problem of estimation risk by asserting a noninformative diffuse prior that reduces the detrimental effect of estimation risk, but does not directly reduce estimation error. Portfolio performance can be improved by specifying an informative prior that reduces estimation error. An informative prior that all securities have identical expected returns, variances, and pairwise correlation coefficients is asserted. This informative prior reduces estimation error by drawing the posterior estimates of each security's expected return, variance, and pairwise correlation coefficients toward the average return, average variance, and average correlation coefficient, respectively, of all the securities in the population. The amount that each of these parameters is drawn toward its grand mean depends upon the degree to which the sample is consistent with the informative prior. This empirical Bayes method is shown to select portfolios whose performance is superior to that achieved, given the assumption of a noninformative prior or by using classical sample estimates.