Robust estimation of the covariance matrix for the optimal selection of investment portfolios

Abstract

The selection of portfolios under the Media-Variance (M-V) model work bad when it is exposed to the presence of atypical data that generate error estimation of the parameters In order to minimize this estimation error, we investigate new robust methodologies and their financial performance in terms off the ratio Sharpe, of the turnover index and of the variance. The estimation of the covariance matrix parameter is done with three different robust methods that seek to minimize the instability generated by atypical data, the first is the great contribution of this research, which consists in shrinking the covariance matrix with a cut-out to the mean, the second and third methods are chi-square cut-outs in the distance of Mahalanobis and Minimum Determinant of the Covariance Matrix (MCD) respectively.