Portfolio optimization using gray wolf algorithm and modified Markowitz model based on CO-GARCH modeling

محورهای موضوعی : Financial Accounting

Fahime Jahanian ¹ (Department of Accounting, Tabriz Branch, Islamic Azad University, Tabriz, Iran)
Ahmad Mohammadi ² (Department of Accounting, Tabriz Branch, Islamic Azad University, Tabriz, Iran)
seyyed ali paytakhti oskooe ³ (Department of Economics, Tabriz Branch, Islamic Azad University, Tabriz, Iran)
Aliasghar Mottaghi ⁴ (Department of Accounting, Tabriz Branch, Islamic Azad University, Tabriz, Iran)

تاریخ دریافت : 1401/06/05 تاریخ پذیرش : 1401/08/01 تاریخ انتشار : 1402/09/10

کلید واژه: gray wolf algorithm, Markowitz model, Portfolio optimization, CO-GARCH,

چکیده مقاله :

Portfolio optimization which means choosing the right stocks based on the highest return and lowest risk, is one of the most effective steps in making optimal investment decisions. Deciding which stock is in a better position compared to other stocks and deserves to be selected and placed in one's investment portfolio and how to allocate capital between these stocks, are complex issues. Theoretically, the issue of choosing a portfolio in the case of minimizing risk in the case of fixed returns can be solved by using mathematical formulas and through a quadratic equation; but in practice and in the real world, due to the large number of choices in capital markets, the mathematical approach used to solve this model, requires extensive calculations and planning. Considering that the behavior of the stock market does not follow a linear pattern, the common linear methods cannot be used and useful in describing this behavior. In this research, portfolio optimization using the gray wolf algorithm and the Markowitz model based on CO-GARCH modeling has been investigated. The statistical population of the current research included the information of 698 companies from the companies admitted to the Tehran Stock Exchange for the period of 2011 to 2020. First, the optimal investment model is presented based on the gray wolf algorithm, and After extracting the optimal model, the efficiency of the gray wolf algorithm is compared with the Markowitz model based on CO-GARCH modeling.

چکیده انگلیسی:

Portfolio optimization which means choosing the right stocks based on the highest return and lowest risk, is one of the most effective steps in making optimal investment decisions. Deciding which stock is in a better position compared to other stocks and deserves to be selected and placed in one's investment portfolio and how to allocate capital between these stocks, are complex issues. Theoretically, the issue of choosing a portfolio in the case of minimizing risk in the case of fixed returns can be solved by using mathematical formulas and through a quadratic equation; but in practice and in the real world, due to the large number of choices in capital markets, the mathematical approach used to solve this model, requires extensive calculations and planning. Considering that the behavior of the stock market does not follow a linear pattern, the common linear methods cannot be used and useful in describing this behavior. In this research, portfolio optimization using the gray wolf algorithm and the Markowitz model based on CO-GARCH modeling has been investigated. The statistical population of the current research included the information of 698 companies from the companies admitted to the Tehran Stock Exchange for the period of 2011 to 2020. First, the optimal investment model is presented based on the gray wolf algorithm, and After extracting the optimal model, the efficiency of the gray wolf algorithm is compared with the Markowitz model based on CO-GARCH modeling.

منابع و مأخذ:

[1] Ebrahimi, S.B, Jirofti, A., Abdi, M., Optimizing the investment portfolio under the fuzzy credit theory using the average-value model under conditional risk. Financial knowledge of securities analysis, 2017; 11(37): 17-27.
[2] Pour Ahmadi, Z., Najafi, A.A., Dynamic optimization of the investment portfolio according to the cost of financial engineering transactions and securities management, 2014: 22(6): 146-127.
[3] Dedekhani H., Hojjati Estani S., Presenting a multi-objective planning model for stock selection considering fuzzy value-at-risk: fuzzy credit theory approach. Financial Engineering and Securities Management, 2015; 8(32): 239-268.
[4] Ramoz, N., Akbari Aghamshahdi, Z., Atef Dost, A., Choosing the optimal portfolio using consensus planning model in Tehran Stock Exchange. Financial Management Strategy, 2019; 8(1): 57-74.
[5] Ramtinnia, S., Atrachyi, R., Stock portfolio optimizer using differential evolution algorithm and conditional risk value approach. Knowledge of analysis. Securities, 2017; 11(40): 25-36.
[6] Seifourib Z., Amarib M., Investigation of combined refrigeration systems with microturbine and absorption chiller, scientific and research journal of energy management, 2013; 2(3).
[7] Rostami, M.R., Behzadi, A., Higher order moments in stock portfolio optimization in fuzzy environment, Journal of Financial Engineering and Securities Management, 2014; 24: 41-61.
[8] Rezaei, As, Falahati, A., and Sohaili, K., Stock portfolio optimization using three-objective particle aggregation algorithm. Quarterly Journal of Applied Economic Theories, 2017; 5(4): 31-52.
[9] Humaifar, S., and Roghnian, E., The use of sustainable optimization patterns and ideal planning in the problem of choosing a multi-period investment portfolio, Financial Engineering and Securities Management, 2015; (28) 2: 157-163.
[10] Shiri Kahri, A., Dedekhani, H., Khalili, K., Saeedi, P., Comparative study of multi-period multi-objective portfolio optimization model in fuzzy credit environment with different risk criteria. Financial Management Strategy, 2016; 5(3): 1-26.
[11] Shahmohammadi, Mohsen, Emami Meibdi, Lili, Zare Mehrjardi, Yahya, Presentation of a hybrid intelligent algorithm based on the mean-variance-skewness fuzzy model for portfolio selection, International Journal of Industrial Engineering and Production Management, 2018; 23: 458-448.
[12] Kazemi Mian Gaskeri, M., Yakideh, K., Qolizadeh, M.H., Optimizing the stock portfolio (using the value-at-risk model on cross-functionality), Financial Management Strategy, 2016; 5(2): 159-183.
[13] Anagnostopoulos, K. & Mamanis, G. Multiobjective evolutionary lgorithms for complex portfolio optimization problems. Springer-Verlag, 2009; 8(3): 259-279.
[14] Bellman,R.E., & Zadeh, L. A., Decision-making in a fuzzy environment. Management science, 1970; 17(4): 141.
[15] Bhattacharyya, R., Hossain, S. A., & Kar, S., Fuzzy cross-entropy, mean, variance, skewness models for portfolio selection. Journal of King Saud University-Computer and Information Sciences, 2014; 26(1): 79-87.
[16] Beni G, Wang J, Swarm intelligence in cellular robotic systems. In: Dario P, Sandini G, Aebischer P (eds) Robots and biological systems: towards a new bionics? Springer, Berlin, Heidelberg, 1993; 703–712.
[17] Bridgewater: the all weather story. https ://www.bridg ewate r.com/resou rces/all-weath er-story .pdf. Accessed Mar 2019.
[18] Cai L, Jin Y, Qi Q, Xu X, a comprehensive study on smart beta strategies in the a-share market. Appl Econ 2018; 50(55): 6024– 6033. doi: 10.1080/00036 846.2018.14891 13.

[19] Cesarone, F., Tardella, F., Equal risk bounding is better than risk parity for portfolio selection. J Glob Pptimiz, 2017; 68(2):439–461. doi: 10.1007/s1089 8-016-0477-6 (The Journal of Computational Finance, 1)

[20] Choueifaty Y, Coignard Y, Toward maximum diversification. J Portfolio Manag, 2008; 35(1):40–51. doi: 10.3905/ JPM.2008.35.1.40 (Cited by 102)

[21] Choueifaty Y, Froidure T, Reynier J, Properties of the most diversified portfolio. J Investment Strateg, doi: 10.2139/ssrn.18954 59.

[22] Chang, T, G., Yang, S, C., Chang, K.G., Portfolio optimization problem different risk measure using genetic algorithm, Expert system with application, 2009; 36: 10529-10537.

[23] Chen, L. H., Huang, L., Portfolio optimization of equity mutual funds with fuzzy return rates and risks. Expert Systems with Applications, 2009; 36(2): 3720-3727.

[24] Chen, L., Pan, H., Selection of stocks using constrained fuzzy AHP and PROMETHEE. Advances in information Sciences and Service Sciences (AISS), 2013; 5(15): 97- 103

[25] Connor, G., Active portfolio management: a quantitative approach to providing superior returns and controlling risk. Rev Financ Stud, 2000; 13(4): 1153–1156

[26] Davey, K., Building algorithmic trading systems a trader’s journey from data mining to Monte Carlo simulation to live trading, 2014.

[27] Deb, K., Agrawal, S., Pratap, A., Meyarivan, T., A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture notes in computer science, 2000; 1917: 849-858.

[28] Dubois, D., Prade, H., The mean value of a fuzzy number. Fuzzy sets and systems, 1987; 24(3): 279-300.

[29] Dubois, D., Prade, H., possibility theory: Approach to computerized processing of uncertainty, plennm 1988; 4.

[30] Enea, M., Piazza, T. Project selection by constrained fuzzy AHP.Fuzzy Optimization and Decision Making, 2004; 3(1): 39-62.

[31] Fang, Y., Lai, K. K., Wang, S. Y., Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research, 2006; 175(2): 879- 893.
[32] Giove, S., Funari, S., Nardelli, C., An interval portfolio selection problem based on regret function. European Journal of Operational Research, 2006; 170(1): 253-264.

[33] Gupta, P., Inuiguchi, M., Mehlawat, M. K., Mittal, G., Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints.Information Sciences, 2013; 229: 1-17.

[34] Gupta, P., Mehlawat, M. K., Inuiguchi, M., Chandra, S., Fuzzy Portfolio Optimization. Springer-Verlag, Berlin. 2014.

[35] Hao, f. f., Liu, Y. K., Mean-variance model for portfolio selection whit fuzzy random return. Journal of Applied Mathematics and Computing, 2009; 30(1-2): 9-38.

[36] Hasuike, T., Katagiri, H., Ishii, H., Portfolio selection problems with random fuzzy variable returns. In Fuzzy Systems Conference, 2007, FUZZ-IEEE 2007. IEEE International, 1-6, IEEE.

[37] Heilpern, S., The expected value of a fuzzy number. Fuzzy sets and Systems, 1992, 47(1), 81-86.

[38] Jana, P., Roy, T. K., Mazumder, S. K., Multi-objective possibilistic model for portfolio selection with transaction cost. Journal of Computational and Applied Mathematics, 2009; 228(1): 188-196.

[39] Kamdem, J. S., Deffo, C. T., Fono, L. A., Moments and semi-moments for fuzzy portfolio selection. Insurance: Mathematics and Economics, 2012; 51(3): 517-530

[40] Kiris, S., Ustun, o., Fuzzy MCDM Approach of Stocks Evaluation and Portfolio Selection, 24th Mini EURo International Conefernce, Izmir, Turkey, 2010; 23-26:.330-336.

[41] Kung, J. Y., Chuang, T. N., Ky, C. M., A fuzzy MCDM method to select the best company based on financial report analysis. InFuzzy Systems (FUZZ), 2011 IEEE International Conference on (2011;2013-2017)

[42] Kwakernaak, H., Fuzzy random Variables-I. Definitions and theorems. Information Sciences, 1978; 15(1):1-29.

[43] Lai, K. K., Wang, S. Y., Xu, J. P., Zhu, S. S., Fang, Y., A class of linear interval programming problems and its application to portfolio selection. IEEE Transactions on Fuzzy Systems, 2002;10(6): 698-704.

[44] Li, J., Xu, J. A novel portfolio selection model in a hybrid uncertain environment. Omega, 2009; 37(2): 439-449.

[45] Li, X., Qin, Z., Kar, S., Mean-variance-skewness model for portfolio selection with fuzzy returns. European Journal of Operational Research, 2010; 202(1): 239-247

[46] Wiley Trading, Hoboken Gupton G, Finger C, Bhatia M., CreditMetrics technical document. J.P. Morgan & Co., New York Investopedia: www.inves toped ia.com (2019). www.inves toped ia.com, www.inves toped ia.com

[47] Markowitz, H., Portfolio selection. J Finance, 1952; 7(1):77–91. Doi:10.1111/j.1540-6261.1952.tb015 25.x

[48] Marshall, C., Isolating the systematic and unsystematic components of a single stock’s (or portfolio’s) standard deviation. Appl Econ, 2015; 47(1):1–11. doi:10.1080/00036 846.2014.95965 2 (Cited By 3)

[49] Mirjalili, S., Mirjalili, S., Lewis, A., Grey wolf optimizer. Adv Eng Softw, 2014; 69:46–61. doi:10.1016/j.adven gsoft .2013.12.007

[50] Olorunda, O., Engelbrecht, A., Measuring exploration/exploitation in particle swarms using swarm diversity, 2008: 1128–1134. doi:10.1109/CEC.2008.46309 38 (cited by 104).

[51] Pun, C. S., Time-consistent mean-variance portfolio selection with only risky assets. Economic Modelling, 2018; 75: 281-292.

[52] Rubin, A., Segal, D., The effects of economic growth on income inequality in the US. Journal of Macroeconomics, 2015; 45: 258-273.

[53] Rezaei, S., Vaez-Ghasemi, M., A new Method for Sustainable Portfolio Selection with DEA, TOPSIS and MIP in Stock exchange, 2020.

[54] Seltzer, M., Forbes, forbes magazine. www.forbe s.com/sites /forbe sfina nceco uncil /2018/01/11/premi um-finan ce-risks -andconsi derat ions/. Accessed Mar 2019

[55] Sharpe, W., The sharpe ratio. J Portfolio Manag 1994; 21:1.

[56] Sharpe, W.F., Budgeting and monitoring pension fund risk. Financ Anal J .2002; 58(5):74–86.

[57] S. PGlobal: Us stock index s and p 100 official site 2019.

[58] Stuart, A., Markowitz, H.M., Portfolio selection: efficient diversification of investments. 1959, OR 10:4.

[59] Stoilov, T., Stoilova, K., Vladimirov, M., Explicit Value at Risk Goal Function in Bi-Level Portfolio Problem for Financial Sustainability. Sustainability, 2021,13(4): 2315.

[60] Sinha, N., 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, Palgrave Macmillan, London 2005; 369-383.

[61] Teiletche, J., Roncalli, T., Maillard, S., The properties of equally-weighted risk contributions portfolios. In: IDEAS Working Paper Series from RePEc, 2010.

[62] Shaolin, M., Jiangfeng. W., Zhequan, Y., Yiping, D., Bingheng, L., Thermodynamic analysis of a new combined cooling, heat and power system driven by solid oxide fuel cell based on ammonia–water mixture, Journal of Power Sources, 2011; 196: 8463– 8471, doi: 10.1016/j.jpowsour.2011.06.008

[63] Xu, D., Ren, J., Dong, L., Yang, Y., Portfolio selection of renewable energy-powered desalination systems with sustainability perspective: A novel MADM-based framework under data uncertainties. Journal of Cleaner Production, 2020; 275:124114. doi: 10.1016/j.jclepro.2020.124114

[64] Wang, J., He, F., Shi, X., Numerical solution of a general interval quadratic programming model for portfolio selection. PloS one, 2019, 14(3), e0212913, doi: 10.1371/journal.pone.0212913

[65] Wan P, Alpha and risk factors. Wiley, 2015. doi: 10.1002/97811 19057 871.ch11.

[66] Zhu, S.S., Li, D., Sun, X., Portfolio selection with marginal risk control. J Computat Finance, 2010. doi: 10.21314 / JCF.2010.213.

[67] Zhou, F., Wang, X., Goh, M., Zhou, L., He, Y., Supplier portfolio of key outsourcing parts selection using a two-stage decision making framework for Chinese domestic auto-maker. Computers & Industrial Engineering, 2019; 128: 559-575. doi: 10.1016/j.cie.2018.12.014