Evaluating Covariance Forecasts Via Mean-Variance Portfolio Decisions

Abstract

This paper presents an empirical comparative study of di fferent covariance estimators. The Engle-Colacito test is used for an indirect evaluation of alternative out-of-sample covariance forecasts in a portfolio setting for varying sample sizes, short selling constraints and market conditions. Errors in the estimation of variances have a higher impact on realized portfolio variance than errors in the estimation of covariances. Bayesian shrinkage estimators and the orthogonal GARCH estimator of covariance matrices lead to signi ficantly lower realized portfolio volatility compared to benchmark estimators.