A robust heuristic for the optimal selection of a portfolio of stocks

This paper introduces a new optimisation heuristic for the robustification of critical inputs under consideration in many problems. It is shown that it allows to improve significantly the quality and the stability of the results for two classical financial problems, that is, the Markowitz' portfolio selection problem and the computation of the financial beta. Focus here is on the robust minimum covariance determinant (MCD) estimator which can easily be substituted to the classical estimators of location and scatter. By definition, the computation of this estimator gives rise to a combinatorial optimisation problem. We present a new heuristic, called ‘RelaxMCD’, which is based on a relaxation of the problem to the continuous space. The utility of this approach and the performance of our heuristic, with respect to other competitors, are illustrated through extensive simulations.