Mean-Variance Portfolio Optimization : Challenging the role of traditional covariance estimation

Abstract: Ever since its introduction in 1952, the Mean-Variance (MV) portfolio selection theory has remained a centerpiece within the realm of e_cient asset allocation. However, in scienti_c circles, the theory has stirred controversy. A strand of criticism has emerged that points to the phenomenon that Mean-Variance Optimization su_ers from the severe drawback of estimation errors contained in the expected return vector and the covariance matrix, resulting in portfolios that may signi_cantly deviate from the true optimal portfolio. While a substantial amount of e_ort has been devoted to estimating the expected return vector in this context, much less is written about the covariance matrix input. In recent times, however, research that points to the importance of the covariance matrix in MV optimization has emerged. As a result, there has been a growing interest whether MV optimization can be enhanced by improving the estimate of the covariance matrix. Hence, this thesis was set forth by the purpose to investigate whether nancial practitioners and institutions can allocate portfolios consisting of assets in a more e_cient manner by changing the covariance matrix input in mean-variance optimization. In the quest of chieving this purpose, an out-of-sample analysis of MV optimized portfolios was performed, where the performance of ve prominent covariance matrix estimators were compared, holding all other things equal in the MV optimization. The optimization was performed under realistic investment constraints, taking incurred transaction costs into account, and for an investment asset universe ranging from equity to bonds. The empirical _ndings in this study suggest one dominant estimator: the covariance matrix estimator implied by the Gerber Statistic (GS). Speci_cally, by using this covariance matrix estimator in lieu of the traditional sample covariance matrix, the MV optimization rendered more e_cient portfolios in terms of higher Sharpe ratios, higher risk-adjusted returns and lower maximum drawdowns. The outperformance was protruding during recessionary times. This suggests that an investor that employs traditional MVO in quantitative asset allocation can improve their asset picking abilities by changing to the, in theory, more robust GS  ovariance matrix estimator in times of volatile nancial markets.