Preprint B90/2016
Robust Multivariate Estimates of Location and Scatter Applied to the Optimum Portfolio Selection Problem
Claudio Cardoso Flores
Keywords: Robust Estimation | portfolio optimization | Multivariate Robust Estimators

The optimum portfolio selection is at the core of utility maximization problems and, accordingly, it has been extensively investigated during the past decades. Nowadays, although there are various methodologies available to portfolio managers, the most widely adopted one still relies on the traditional mean-variance approach, mainly because of its mathematical tractability. However, it is well known that mean-variance optimum portfolios can be heavily distorted due to the non-robustness of the classical mean and covariance estimates (e.g. sample mean and covariance matrix of asset returns). Under this approach, optimum portfolios may be composed by counterintuitive and/or extreme asset weights, may be unstable and sensitive to new information, and may perform poorly out of the sample. Practical consequences are: excessive transaction costs due to rebalancing policies and lack of adherence with investors views. In this work we address this issue replacing the sample classical estimates of location and scatter as inputs in the portfolio problem by their robust counterparts. We propose the use of the high breakdown point, affine equivariant MVE, MCD, S and Stahel-Donoho estimators and compare the performance and stability of respective portfolios. By dynamically determining breakdown points for the robust estimators and by employing a semi-parametric bootstrapping procedure, in order to formally address hypotheses tests, we find that robust portfolios present higher stability than the classical non robust one and relative performance conditioned to the level of transaction costs in a financial market, possibly rewarding in less developed economies. Also, results prove to be robust both to the change of the analyzed portfolio and to modifications in the portfolio optimization restrictions. We find that ?? portfolios present the best stability profile and, accordingly, the best relative performance as well.