Robust covariance estimators for mean-variance portfolio optimization with transaction lots

This study presents an improvement to the mean-variance portfolio optimization model, by considering both the
integer transaction lots and a robust estimator of the covariance matrices. Four robust estimators were tested,
namely the Minimum Covariance Determinant, the S, the MM, and the Orthogonalized Gnanadesikan–Kettenring
estimator. These integer optimization problems were solved using genetic algorithms. We introduce the lot
turnover measure, a modified portfolio turnover, and the Robust Sharpe Ratio as the measure of portfolio
performance. Based on the simulation studies and the empirical results, this study shows that the robust estimators
outperform the classical MLE when data contain outliers and when the lots have moderate sizes, e.g. 500
shares or less per lot.