Portfolio Selection in a Multi-Input Multi-Output Setting: a Simple Monte-Carlo-FDH Algorithm

This paper proposes a nonparametric efficiency measurement approach for the static portfo- lio selection problem in a general inputs-outputs space, where inputs can include variance and kurtosis and outputs can include mean and skewness. Our work is in the vein of Briec, Kerstens and Jokung (2007) and Jurzenko, Maillet and Merlin (2006) who develop a directional dis- tance (shortage function) approach to evaluate the performance of portfolios in Mean-Variance- Skewness and in Mean-Variance-Skewness-Kurtosis spaces. Our approach use the Free Disposal Hull (FDH) estimator to derive an algorithm avoiding the heavy and non-robust numerical op- timization approaches suggested so far. This new approach is much faster, more robust to reach the optimum and more exible since it can be extended to more general situations. We illustrate the algorithm with a data set on the French CAC 40 already used in the literature, to compare our method with the numerical optimization approaches.