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

Authors: Michael Schyns

Addresses: QuantOM, HEC-Management School, University of Liege, Bd. du Rectorat 7(B31), Liege 4000, Belgium

Abstract: 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.

Keywords: combinatorial optimisation; robustness; Markowitz model; beta computation; MCD estimator; minimum covariance determinant; stocks; stock portfolios; optimisation heuristics; operational research.

DOI: 10.1504/IJOR.2010.035520

International Journal of Operational Research, 2010 Vol.9 No.3, pp.258 - 271

Published online: 30 Sep 2010 *

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