Revisions of modern portfolio theory optimization model

Abstract

Among others, fluctuations in market sentiment cause step changes of correlations of financial instrument prices. This phenomenon of the correlations’ destabilization, which was markedly highlighted during the recent financial crisis, reduces the efficiency of the traditional approach to the market risk diversification based on the Markowitz Optimal Portfolio Selection Model. The original Markowitz optimization model represents a convex quadratic programming problem. Almost any efforts to its reformulation involving the above-mentioned facts lead to the loss of a positive semi-definiteness of the matrix occurring in the model’s structure. This leads to a non-convex programming problem whose solution is generally problematic. By refinement of the merits of the original model, we get into trouble with its computational, formal aspect. Therefore, it is necessary to find a way to the reconvexification of the reformulated model. Main objective of the paper is to propose a convex representation of the reformulated model.