Hybrid metaheuristics for portfolio selection problems

The portfolio selection problem consists in selecting a portfolio of assets that provides the investor a given expected return and minimizes the risk. In this work, we consider the mean-variance model, that takes the variance of the portfolio as measure of risk, plus three additional constraints: the cardinality constraint which limits the number of assets, the quantity constraint which fixes minimal and maximal shares of each individual one in the portfolio, and the preassignments that force some specific assets to be included in the portfolio. We devised a family of hybrid local search metaheuristics that incorporate as subcomponent a quadratic programming solver (QP) that implements the Goldfarb-Idnani dual algorithm for strictly convex quadratic programs. Local search works on the space of the assets that are selected for composing the portfolio (0/1 variables) and resorts to the QP for computing the best allocation of actual shares to the selected assets.