Hybrid Approaches and Dimensionality Reduction for Portfolio Selection with Cardinality Constraints

A novel memetic algorithm that combines evolutionary algorithms, quadratic programming, and specially devised pruning heuristics is proposed for the selection of cardinality-constrained optimal portfolios. The framework used is the standard Markowitz mean-variance formulation for portfolio optimization with constraints of practical interest, such as minimum and maximum investments per asset and/or on groups of assets. Imposing limits on the number of different assets that can be included in the investment transforms portfolio selection into an NP-complete mixed-integer quadratic optimization problem that is difficult to solve by standard methods. An implementation of the algorithm that employs a genetic algorithm with a set representation, an appropriately defined mutation operator and Random Assortment Recombination for crossover (RAR-GA) is compared with implementations using Simulated Annealing (SA) and various Estimation of Distribution Algorithms (EDAs). An empirical investigation of the performance of the portfolios selected with these different methods using financial data shows that RAR-GA and SA are superior to the implementations with EDAs in terms of both accuracy and efficiency. The use of pruning heuristics that effectively reduce the dimensionality of the problem by identifying and eliminating from the universe of investment assets that are not expected to appear in the optimal portfolio leads to significant improvements in performance and makes EDAs competitive with RAR-GA and SA.