Portfolio optimization with estimation errors—A robust linear regression approach

Covariance and precision matrices of asset returns are unknown in practice and must be estimated in minimum variance portfolio optimizations. Although a variety of estimators have been proposed that give better out-of-sample performance than the sample covariance matrix, they nevertheless contain estimation error of the type that is most likely to disrupt the optimizer. In this study, we propose a robust optimization framework to tackle the estimation error issue. Rather than the sample covariance matrix, as is the case with the existing approaches, our framework focuses on the row sums of estimates of the precision matrix, which can greatly minimize the number of unknown parameters. A robust linear regression framework is developed to tackle the estimate error by first rewriting the portfolio optimization as a least-squares regression model. Furthermore, our results on both simulated and empirical data reveal that the suggested robust portfolios are more stable and perform better out-of-sample than existing estimators in general.