Optimization of Stock Portfolio Selection in Iran Capital Market Using Meta-heuristic Algorithms

Document Type : Research Paper


1 Department of Industrial Engineering, Kurdestan University, Kurdestan, Iran

2 Department of Finance, Esfarayen Branch, Islamic Azad University, Esfarayen, Iran


The purpose of this study is to optimize the portfolio in companies listed on the Iran capital market (Tehran Stock Exchange and Iran Farabours) as a multi-objective optimization problem. The first objective function includes risk minimization and the second objective function includes return maximization. The limitations of the model include the limitation of selecting companies individually as well as the limitation of budget. In order to solve the problem, two genetic metaheuristic algorithms and a gray wolf have been developed, which are analyzed using numerical examples taken from 491 companies listed on the Tehran Stock Exchange and the Iran Farabours market from April 26, 2016 to December 21, 2022 were subjected to numerical analysis.
According to the numerical results, it can be seen that the gray wolf algorithm has a higher efficiency than the genetic algorithm in all examples. It is noteworthy, however, that in none of the numerical examples did the percentage of unwarranted responses in the algorithm improvement procedure exceed 10.2%. Also, the percentage improvement of the gray wolf algorithm compared to the genetic algorithm is reported to be between 3 and 11%.


Main Subjects

  1. Benita, F., López-Ramos, F., & Nasini, S. (2019). A bi-level programming approach for global investment strategies with financial intermediation. European Journal of Operational Research, 274(1), 375-390.‏
  2. Bilbao-Terol, A., Jiménez-López, M., Arenas-Parra, M., & Rodríguez-Uría, M. (2018). Fuzzy multi-criteria support for sustainable and social responsible investments: the case of investors with loss aversion. In The Mathematics of the Uncertain (pp. 555-564). Springer, Cham.‏
  3. Bozorg-Haddad, O. (Ed.). (2018). Advanced optimization by nature-inspired algorithms (Vol. 720). Singapore: Springer.‏
  4. Castilho, D., Gama, J., Mundim, L. R., & de Carvalho, A. C. (2019, June). Improving portfolio optimization using weighted link prediction in dynamic stock networks. In International Conference on Computational Science (pp. 340-353). Springer, Cham.‏
  5. Cesarone, F., Scozzari, A., & Tardella, F. (2020). An optimization–diversification approach to portfolio selection. Journal of Global Optimization, 76(2), 245-265.‏
  6. Chen, X., Kelley, C. T., Xu, F., & Zhang, Z. (2018). A smoothing direct search method for Monte Carlo-based bound constrained composite nonsmooth optimization. SIAM Journal on Scientific Computing, 40(4), A2174-A2199.‏
  7. Doaei, M., Davarpanah, S. H., & Sabzi, M. Z. (2017). ANN-DEA approach of corporate diversification and efficiency in bursa Malaysia. Advances in Mathematical Finance and Applications, 2(1), 9-20.‏
  8. Doaei, M., Mirzaei, S. A., & Rafigh, M. (2021). Hybrid multilayer perceptron neural network with grey wolf optimization for predicting stock market index. Advances in Mathematical Finance and Applications, 6(4), 1-21.‏
  9. Farughi, H., Dolatabadiaa, M., Moradi, V., Karbasi, V., & Mostafayi, S. (2017). Minimizing the number of tool switches in flexible manufacturing cells subject to tools reliability using genetic algorithm. Journal of Industrial and Systems Engineering, 10(special issue on Quality Control and Reliability), 17-33.‏
  10. Farughi, H., Tavana, M., Mostafayi, S., & Santos Arteaga, F. J. (2020). A novel optimization model for designing compact, balanced, and contiguous healthcare districts. Journal of the Operational Research Society, 71(11), 1740-1759.‏
  11. Rahiminezhad Galankashi, M., Mokhatab Rafiei, F., & Ghezelbash, M. (2020). Portfolio selection: a fuzzy-ANP approach. Financial Innovation, 6(1), 1-34.‏
  12. Garcia, F., González-Bueno, J., Oliver, J., & Tamošiūnienė, R. (2019). A credibilistic mean-semivariance-PER portfolio selection model for Latin America. Journal of Business Economics and Management, 20(2), 225-243.‏
  13. González-Díaz, J., González-Rodríguez, B., Leal, M., & Puerto, J. (2021). Global optimization for bilevel portfolio design: Economic insights from the Dow Jones index. Omega, 102, 102353.‏
  14. Guo, S., & Ching, W. K. (2021). High-order Markov-switching portfolio selection with capital gain tax. Expert Systems with Applications, 165, 113915.‏
  15. Hadavandi, E., Mostafayi, S., & Soltani, P. (2018). A Grey Wolf Optimizer-based neural network coupled with response surface method for modeling the strength of siro-spun yarn in spinning mills. Applied Soft Computing, 72, 1-13.‏
  16. Jing, K., Xu, F., & Li, X. (2022). A bi‐level programming framework for identifying optimal parameters in portfolio selection. International Transactions in Operational Research, 29(1), 87-112.‏
  17. Kalashnikov, V. V., Kalashnykova, N. I., & Leal-Coronado, M. A. (2017). Solution of the portfolio optimization model as a bilevel programming problem. Bulletin of the Cherkasy Bohdan Khmelnytsky National University. Economic Sciences, (1).‏
  18. Kellner, F., & Utz, S. (2019). Sustainability in supplier selection and order allocation: Combining integer variables with Markowitz portfolio theory. Journal of cleaner production, 214, 462-474.‏
  19. Kobayashi, K., Takano, Y., & Nakata, K. (2020). Bilevel Cutting-plane Algorithm for Solving Cardinality-constrained Mean-CVaR Portfolio Optimization Problems. arXiv preprint arXiv:2005.12797.‏
  20. Liagkouras, K. (2019). A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem. Knowledge-Based Systems, 163, 186-203.‏
  21. Majumdar, S., & Partridge, M. D. (2009). Impact of economic growth on income inequality: A regional perspective (No. 319-2016-9872).‏
  22. Masmoudi, M., & Ben Abdelaziz, F. (2017). A chance constrained recourse approach for the portfolio selection problem. Annals of Operations Research, 251(1), 243-254.‏
  23. Majumdar, S., & Partridge, M. D. (2009). Impact of economic growth on income inequality: A regional perspective (No. 319-2016-9872).‏
  24. Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.‏
  25. Oikonomou, I., Platanakis, E., & Sutcliffe, C. (2018). Socially responsible investment portfolios: Does the optimization process matter?. The British Accounting Review, 50(4), 379-401.‏
  26. Pesaran, H., & Shin, Y. (1999). An autoregressive distributed lag modelling approach to cointegration “chapter 11. In Econometrics and Economic Theory in the 20th Century: The Ragnar Frisch Centennial Symposium. Cambridge University Press Cambridge.‏
  27. Pesaran, M. H., Shin, Y., & Smith, R. J. (1996). Testing for the'Existence of a Long-run Relationship' (No. 9622). Faculty of Economics, University of Cambridge.‏
  28. Pesaran, M. H., & Smith, R. P. (2014). Signs of impact effects in time series regression models. Economics Letters, 122(2), 150-153.‏
  29. Pun, C. S. (2018). Time-consistent mean-variance portfolio selection with only risky assets. Economic Modelling, 75, 281-292.‏
  30. Quaranta, A. G., & Zaffaroni, A. (2008). Robust optimization of conditional value at risk and portfolio selection. Journal of Banking & Finance, 32(10), 2046-2056.‏
  31. Raza, S. A., & Shah, N. (2017). Tourism growth and income inequality: does Kuznets Curve hypothesis exist in top tourist arrival countries. Asia Pacific Journal of Tourism Research, 22(8), 874-884.‏
  32. Rubin, A., & Segal, D. (2015). The effects of economic growth on income inequality in the US. Journal of Macroeconomics, 45, 258-273.‏
  33. Rezaei, S., & Vaez-Ghasemi, M. (2020). A new Method for Sustainable Portfolio Selection with DEA, TOPSIS and MIP in Stock exchange.‏
  34. Stoilov, T., Stoilova, K., & Vladimirov, M. (2021). Explicit Value at Risk Goal Function in Bi-Level Portfolio Problem for Financial Sustainability. Sustainability, 13(4), 2315.‏
  35. Sinha, N. (2005). Growth, Inequality and Structural Adjustment: An Empirical Interpretation of the S-Curve for the Indian Economy. In Economic Growth, Economic Performance and Welfare in South Asia (pp. 369-383). Palgrave Macmillan, London.‏
  36. Tribble, R. (1996). The Kuznets-Lewis process within the context of race and class in the US economy. International Advances in Economic Research, 2(2), 151-164.‏
  37. Vickers, N. J. (2017). Animal communication: when i’m calling you, will you answer too?. Current biology, 27(14), R713-R715.
  38. Vuković, M., Pivac, S., & Babić, Z. (2020). Comparative analysis of stock selection using a hybrid MCDM approach and modern portfolio theory. Croatian Review of Economic, Business and Social Statistics, 6(2), 58-68.‏
  39. Wang, J., He, F., & Shi, X. (2019). Numerical solution of a general interval quadratic programming model for portfolio selection. PloS one, 14(3), e0212913.‏
  40. Xu, D., Ren, J., Dong, L., & Yang, Y. (2020). Portfolio selection of renewable energy-powered desalination systems with sustainability perspective: A novel MADM-based framework under data uncertainties. Journal of Cleaner Production, 275, 124114.‏
  41. Yoshino, N., Taghizadeh-Hesary, F., & Otsuka, M. (2021). Covid-19 and optimal portfolio selection for investment in sustainable development goals. Finance research letters, 38, 101695.‏‏
  42. Zhou, F., Wang, X., Goh, M., Zhou, L., & He, Y. (2019). Supplier portfolio of key outsourcing parts selection using a two-stage decision making framework for Chinese domestic auto-maker. Computers & Industrial Engineering, 128, 559-575.