Bayesian Portfolio Selection: An Empirical Analysis of the S&P 500 Index 1970–1996

Abstract

In this article we present a technique for implementing large-scale optimal portfolio selection. We use high-frequency daily data to capture valuable statistical information in asset returns. We describe several statistical issues involved in quantitative approaches to portfolio selection. Our methodology applies to large-scale portfolio-selection problems in which the number of possible holdings is large relative to the estimation period provided by historical data. We illustrate our approach on an equity database that consists of stocks from the Standard and Poor's index, and we compare our portfolios to this benchmark index. Our methodology differs from the usual quadratic programming approach to portfolio selection in three ways: (1) We employ informative priors on the expected returns and variance-covariance matrices, (2) we use daily data for estimation purposes, with upper and lower holding limits for individual securities, and (3) we use a dynamic asset-allocation approach that is based on reestimating and then rebalancing the portfolio weights on a prespecified time window. The key inputs to the optimization process are the predictive distributions of expected returns and the predictive variance-covariance matrix. We describe the statistical issues involved in modeling these inputs for high-dimensional portfolio problems in which our data frequency is daily. In our application, we find that our optimal portfolio outperforms the underlying benchmark.