International Journal of Nonlinear Analysis and Applications

Designing and explaining a portfolio optimization model using the cuckoo optimization algorithm

Document Type : Research Paper

Authors

1 Department of Financial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

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

Abstract

Choosing the right portfolio is a crucial goal for investors. Two key factors to consider when selecting a portfolio are return and portfolio risk. This problem can be written as a mathematical programming equation and can be solved quickly. For instance, some investors choose stocks based on past performance, while others consider factors like liquidity when making their selections. Additionally, fundamental and technical analysis are often used in stock and portfolio selection. However, the strategies and methods used to select stocks and portfolios can vary depending on the current market conditions and the investor's level of knowledge. This article focuses on designing and explaining a portfolio optimization model using the cuckoo optimization algorithm. Results show that the best value of the utility function increases as the number of iterations increases. The growth value of the best value of the utility function is higher in the initial iterations and gradually decreases until it reaches zero, indicating that the algorithm has converged to the optimal solution. This research fills a gap in the study of investment portfolio optimization using nested optimization models. Additionally, the study finds that shares selected from industries with better performance make up a higher proportion of the portfolio.

Keywords

[1] H. Babazadeh and A. Esfahanipour, A novel multi period mean-VaR portfolio optimisation model considering practical constraints and transaction cost, J. Comput. Appl. Math. 361 (2019), 313–342.
[2] A. Bacevic, N. Vilimonovic, I. Dabic, J. Petrovic, D. Damnjanovi´c and D. Dzamic, Variable neighborhood search heuristic for nonconvex portfolio optimisation, Eng. Econ. 64 (2019), no. 3, 254–274.
[3] Y. Chen, A. Zhou, and S. Das, Utilising dependence among variables in evolutionary algorithms for mixed-integer programming: A case study on multi-objective constrained portfolio optimisation, Swarm Evolut. Comput. 66 (2021), 100928.
[4] A.M. Daryani, M.M. Omran and A. Makui, A novel heuristic, based on a new robustness concept, for multiobjective project portfolio optimisation, Comput. Ind. Eng. 139 (2020), 106187.
[5] K. Erwin and A. Engelbrecht, Improved set-based particle swarm optimisation for portfolio optimisation, IEEE Symp. Ser. Comput. Intell. (SSCI), IEEE, 2020, pp. 1573–1580.
[6] M. Feshari and R. Nazari, Portfolio optimisation in selected Tehran stock exchange companies (symbiotic organisms search and memetic algorithms), Region. Sci. Inquiry 10 (2018), no. 1, 149–160.
[7] C. John, Complete neighbourhood search heuristic algorithm for portfolio optimization, Tanzania J. Eng. Technol. 40 (2021), no. 2, 97–104.
[8] C. John, High speed hill climbing algorithm for portfolio optimization, Tanzania J. Sci. 47 (2021), no. 3, 1236–1242.
[9] C.B. Kalayci, O. Ertenlice and M.A. Akbay, A comprehensive review of deterministic models and applications for mean-variance portfolio optimisation, Expert Syst. Appl. 125 (2019), 345–368.
[10] A.T. Khan, X. Cao, I. Brajevic, P.S. Stanimirovic, V.N. Katsikis and S. Li, Non-linear activated beetle antennae search: A novel technique for non-convex tax-aware portfolio optimisation problem, Expert Syst. Appl. 197 (2022),  116631.
[11] R. Kizys, A.A. Juan, B. Sawik and L. Calvet, A biased-randomised iterated local search algorithm for rich portfolio optimisation, Appl. Sci. 9 (2019), no. 17,  3509.
[12] H. Markowitz, The utility of wealth, J. Political Econ. 60 (1952), no. 2, 151–158.
[13] H.M. Markowitz, Foundations of portfolio theory, J. Finance 46 (1991), no. 2, 469–477.
[14] N.B. Mazraeh, A. Daneshvar and F.R. Roodposhti, Stock portfolio optimization using a combined approach of multi objective grey wolf optimizer and machine learning preselection methods, Comput. Intell. Neurosci. 2022 (2022).
[15] J.C. Mba, E. Pindza and U. Koumba, A differential evolution copula-based approach for a multi-period cryptocurrency portfolio optimisation, Financ. Markets Portfolio Manag. 32 (2018), no. 4, 399–418.
[16] B.A. Mercangoz, Particle swarm algorithm: An application on portfolio optimisation, Metaheuristic approaches to portfolio optimisation, IGI Global, 2019, pp. 27–59.
[17] D.A. Milhomem and M.J.P. Dantas, Analysis of new approaches used in portfolio optimisation: a systematic literature review, Production 30 (2020).
[18] N.S.M. Mussafi and Z. Ismail, A review on Shariah stock portfolio optimization, DLSU Bus. Econ. Rev. 31 (2021), no. 1, 142–157.
[19] M.J. Naik and A.L. Albuquerque, Hybrid optimisation search-based ensemble model for portfolio optimisation and return prediction in business investment, Progress Artif. Intell. 11 (2022), no. 4, 315–331.
[20] R. Rajabioun, Cuckoo optimisation algorithm, Appl. Soft Comput. 11 (2011), no. 8, 5508–5518.
[21] D. Venturelli and A. Kondratyev, Reverse quantum annealing approach to portfolio optimisation problems, Quantum Machine Intell. 1 (2019), no. 1, 17–30.
[22] J. Wang, A novel firefly algorithm for portfolio optimisation problem, IAENG Int. J. Appl. Math. 49 (2019), no. 1, 1–6.
[23] Z. Wang, X. Zhang, Z. Zhang and D. Sheng, Credit portfolio optimisation: A multi-objective genetic algorithm approach, Borsa Istanbul Rev. 22 (2022), no. 1, 69–76.
[24] I. Yaman and T.E. Dalkılı，c, A hybrid approach to cardinality constraint portfolio selection problem based on nonlinear neural network and genetic algorithm, Expert Syst. Appl. 169 (2021), 114517.
[25] M. Zanjirdar, Overview of portfolio optimisation models, Adv. Math. finance Appl. 5 (2020), no. 4, 419–435.
International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 10
October 2024
Pages 33-50
  • Receive Date: 02 February 2023
  • Revise Date: 19 June 2023
  • Accept Date: 27 June 2023