عنوان مقاله [English]
The selection of an appropriate portfolio of assets to invest is the major concern for fund management companies as well as individual investors. The attractiveness of a security to an investor is not only based on its arithmetic mean of return, but the standard deviation of the assets return and its correlation with other securities return in the portfolio play an important role in the selection process as well. Having defined risk as the standard deviation of the portfolios return, the decision to be made is to select a subset of assets (with their corresponding weights) out of a given set of assets in such a way that the constructed portfolio yields the minimum amount of risk for a given level of return. The solution for this problem, also known as the standard Markowitz portfolio selection problem, can be determined using his proposed Critical Line method. However, the computational complexity increases when the total number of available assets is high and/or other realistic constraints are included into the problem.This paper presents a novel heuristic method for solving an extended Markowitz mean-variance portfolio selection model. The extended model includes four sets of constraints: bounds-on-holdings, cardinality, minimum transaction lots, and sector (or market/class) capitalization constraints. The generalized model is classified as a quadratic mixed-integer programming model necessitating the use of efficient heuristics to find the solution. Some heuristic methods based on Genetic Algorithm, Simulated Annealing, Tabu Search and Neural Networks have been reported in the literatures. In this paper, we propose a novel heuristic based on Particle Swarm Optimization method. The approach is based on two parts integrated to each other: one that selects M securities out of N available securities (satisfying the cardinality constraints) and the other part that seeks best positive integer investment weights, for the M selected securities.The proposed approach is illustrated and compared with Genetic Algorithm subject to four performance criteria commonly used in literature. The criteria are the best variance among the risks obtained from the algorithm runs, the mean portfolio variance found, the standard deviation of obtained variances, and the mean run time. The computational results show that the proposed approach outperforms Genetic Algorithm and can effectively solve large-scale problems.