Markowitz-based cardinality constrained portfolio selection using Asexual Reproduction Optimization (ARO)

The Markowitz-based portfolio selection turns to an NP-hard problem when considering cardinality constraints. In this case, existing exact solutions like quadratic programming may not be efficient to solve the problem. This work presents ARO, a model free metaheuristic algorithm inspired by the asexual reproduction, in order to solve the portfolio optimization problem including cardinality constraint to ensure the investment in a given number of different assets and bounding constraint to limit the proportions of fund invested in each asset. We show that ARO results in better quality solutions in comparison with some of the well-known metaheuristics stated in the literature. To validate our proposed algorithm, we measured the deviation of obtained results from the standard efficient frontier. We report our computational results on a set of publicly available benchmark test problems relating to five main market indices containing 31, 85, 89, 98, and 225 assets. The experimental results indicate that ARO outperforms GA, TS, SA, and PSO in most of test problems. In terms of the obtained error, by using ARO, the average error of the aforementioned test problems is reduced by approximately 20 percent of the minimum average error calculated for the above-mentioned algorithms.