Portfolio optimization considering cardinality constraints and based on various risk factors using the differential evolution algorithm

As the main achievement of the modern portfolio theory, portfolio diversifica-tion based on risk and return has attracted the attention of many researchers. The Markowitz mean-variance problem is a convex quadratic problem turned into a mixed-integer quadratic programming problem when incorporating car-dinality constraints. Due to the high number of stocks in a market, this problem becomes an NP-hard problem. In this paper, a metaheuristic approach is pro-posed to solve the portfolio optimization problem with cardinality constraints using the differential evolution algorithm, while it is also intended to improve the solutions generated by the algorithm developed. In addition, variance, val-ue-at-risk, and conditional value-at-risk are assessed as risk measures. Candi-date models are solved for 50 top stocks introduced by the Tehran Stock Ex-change by considering the cardinality constraints of not more than five stocks within the portfolio and 24 trading periods. Finally, the obtained results are compared with the results of genetic algorithm. The results show that the pro-posed method has reached the optimal solution in a shorter time.