Portfolio selection in a multi-moment setting: A simple Monte-Carlo-FDH algorithm

This paper proposes a non-parametric efficiency measurement approach for the static portfolio 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 distance (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 optimization approaches suggested so far. This new approach is much faster, more robust to reach the optimum and more flexible 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. It appears that our approach is much more performant than the numerical optimization techniques, both in terms of computing time, but also in terms of robustness, avoiding the pitfall of local numerical optima.