A metaheuristic multi-criteria optimisation approach to portfolio selection

Portfolio selection is concerned with selecting from of a universe of assets the ones in which one wishes to invest and the amount of the investment. Several criteria can be used for portfolio selection, and the resulting approaches can be classified as being either active or passive. The two approaches are thought to be mutually exclusive, but some authors have suggested combining them in a unified framework. In this work, we define a multi-criteria optimisation problem in which the two types of approaches are combined, and we introduce a hybrid metaheuristic that combines local search and quadratic programming to obtain an approximation of the Pareto set. We experimentally analyse this approach on benchmarks from two different instance classes: these classes refer to the same indexes, but they use two different return representations. Results show that this metaheuristic can be effectively used to solve multi-criteria portfolio selection problems. Furthermore, with an experiment on a set of instances coming from a different financial scenario, we show that the results obtained by our metaheuristic are robust with respect to the return representation used.