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

Advances in Mathematical Finance and Applications

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 شهریور 1401   

نوع مقاله: َApplied-Research Paper

شناسه دیجیتال (DOI): 10.22034/amfa.2022.1950768.1688

نویسندگان

mehrzad minooei^{* 1}؛ behnaz ghadimi²؛ Gholamreza Zomorodian³؛ Mirfeiz Fallahshams⁴

¹Department of Industrial Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

²Department of Financial Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

³Department of Business Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

⁴Associate Professor, Department of Business Management, Central Tehran Branch , Islamic Azad University, Tehran, Iran

چکیده

Abstract
As the main achievement of the modern portfolio theory, portfolio diversification 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 cardinality 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 proposed 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, value-at-risk, and conditional value-at-risk are assessed as risk measures. Candidate models are solved for 50 top stocks introduced by the Tehran Stock Exchange 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 proposed method has reached the optimal solution in a shorter time.

کلیدواژه‌ها

Portfolio optimization؛ Cardinality constraint؛ Differential evolution algorithm؛ Value-at-risk؛ Conditional value-at-risk