Heuristic for finding the efficient frontier in cardinality constrained portfolio optimisation
Résumé
In this paper we consider the problem of finding the efficient frontier with the mean-variance portfolio optimisation model. The classical portfolio optimisation problem is a quadratic convex programming model that can be numerically solved with great efficiency. However, in practice, it is necessary to consider other characteristics of portfolio performances, such as, for instance, transaction costs, restriction of number of holding assets and transaction roundlot restrictions which make the problem NP-hard. We consider here the cardinality constrained portfolio problem that limits a portfolio to have a specified number of assets. To solve the problem, first we propose an exact approach consisting in using a commercially available software with a branch-and-bound procedure based on a continuous relaxation of the problem. Second, in order to solve realistic size problems in a reasonable computing time we propose an efficient heuristic algorithm based on fixation of variables which uses the solution of the continuous relaxation. Computational results and comparisons are presented for five data sets involving up to 225 assets.
Keywords : Portfolio Optimisation, Mean-Variance Model, Efficient Frontier, Branch and Bound, Heuristic, Experiments.