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

Mansouri, Taha; Sadeghi Moghadam, Mohammad Reza; Sheykhizadeh, Morteza

Abstract

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. Many researchers, therefore, used heuristic and metaheuristic approaches in order to deal with the problem. This work presents Asexual Reproduction Optimization (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. This is the first time that this relatively new metaheuristic is in the field of portfolio optimization, and 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. These results are used in order to test the efficiency of our proposed method in comparison to other existing metaheuristic solutions. The experimental results indicate that ARO outperforms Genetic Algorithm(GA), Tabu Search (TS), Simulated Annealing (SA), and Particle Swarm Optimization (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.

Citation

Mansouri, T., Sadeghi Moghadam, M. R., & Sheykhizadeh, M. (2022). Markowitz-based cardinality constrained portfolio selection using Asexual Reproduction Optimization (ARO). https://doi.org/10.22059/IJMS.2021.313393.674293

• Journal Article Type: Article
• Online Publication Date: Jul 15, 2022
• Publication Date: Jul 15, 2022
• Deposit Date: Dec 6, 2021
• Publicly Available Date: Oct 4, 2022
• Journal: Iranian Journal of Management Studies
• Print ISSN: 23318422
• Volume: 15
• Issue: 3
• Pages: 531-548
• DOI: https://doi.org/10.22059/IJMS.2021.313393.674293
• Keywords: portfolio optimization cardinality constraints Markowitz mean-variance model asexual reproduction optimization efficient frontier
• Publisher URL: https://ijms.ut.ac.ir/article_83874.html?lang=en
• Related Public URLs: https://ijms.ut.ac.ir/article_83874.html?lang=en
• Additional Information: Access Information : This is a pre-print paper and has not been peer-reviewed.