Portfolio Optimization Based on Semi Variance and Another Perspective of Value at Risk Using NSGA II, MOACO, and MOABC Algorithms

Advances in Mathematical Finance and Applications

مقاله 7، دوره 7، شماره 1، فروردین 2022، صفحه 99-115   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/amfa.2020.1907264.1479

نویسندگان

Reza Aghamohammadi¹؛ Reza Tehrani^{* 2}؛ Abbas Raad³

¹PhD Student of Industrial Management - financial, Faculty of Management, Islamic Azad University, North Tehran Branch, Tehran, Iran

²Management and Insurance Group, Faculty of Management, Tehran University, Tehran, Iran

³Industrial Management and information technology Group, Faculty of management and accounting, Shahid Beheshti University, Tehran, Iran

چکیده

This study examines the criterion of value at risk from another perspective and presents a new type of mean-value at Risk model. To solve the portfolio optimization problem in Tehran Stock Exchange, we use NSGA II, MOACO, and MOABC algorithms and then compare the mean-pVaR model with the mean-SV model. Given that, finding the best answer is very important in meta-heuristic methods, we use the concept of dominance in the discussion of multi-objective optimization to find the best answers and show that, at low iterations, the performance of the NSGA II algorithm is better than the MOABC and MOACO algorithms in solving the portfolio optimization problem. As the iteration increases, the performance of the algorithms improves, but the rate of improvement is not the same, in a way, the performance of the MOABC algorithm is better than that of the NSGA II and MOACO algorithms. Then, to compare the performance of the “mean-percentage of Value at Risk” model and the “mean-semi variance” model, we examine both models in the standard mean-variance model and show that the mean-pVaR model, compared to the mean-SV model, Has better performance in stock portfolio optimization.

کلیدواژه‌ها

Semi Variance؛ Value at Risk؛ NSGA II Algorithm؛ MOACO Algorithm؛ MOABC Algorithm

مراجع

[1] Azar, A., Mӧmeni. M., Statistics and Its Application in Management (Statistical Analysis), The Organization for Researching and Composing University Textbooks in the Humanities (SAMT), Tehran, Iran, 2000, 2. (in Persian).

[2] Bacanin, N., Tuba, M., Artificial bee colony (ABC) algorithm for constrained optimization improved with genetic operators, Studies in Informatics and Control, 2012, 21(2), P.137-146, Doi:10.24846/v21i2y201203.

[3] Chang, T.J., Yang, S.C., Chang, K.J., Portfolio optimization problems in different risk measures using genetic algorithm, Expert Systems with Applications, 2009, 36(7), P.10529–10537, Doi:10.1016/j.eswa.2009.02.062.

[4] Chen, W., Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem, Physica A Statistical Mechanics and its Applications, 2015, 429(C), P. 125-139 , Doi:10.1016/j.physa.2015.02.060.

[5] Chen, W., Yang, Y., Ma, H., Sun, M., Application of artificial bee  colony algorithm to portfolio adjustment problem with transaction costs. Journal of Applied Mathematics, 2014, 2014(6), Doi:10.1155/2014/192868. 

[6] Davoodi, S.M., Sadri, A., Compare Meta-Heuristic Algorithms on Optimal Model of Multi Period Portfolio Based on the Value at Risk. JOURNAL OF SECURITIES EXCHANGE, 2018, 11(41), P. 121-152, Doi:10.22034/JSE.2018.11125, (in Persian).

[7] Deb, K., Agrawal, S., Pratap, A., Meyarivan, T., A fast elitist nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II, Paper presented at International Conference on Parallel Problem Solving from Nature (PPSN-VI), 2000, P. 849-858.

[8] Deb, K., Multi-objective optimization using evolutionary algorithms, Wiley, United States, 2001.

[9] DeMiguel, V., Mei, X., Nogales, F.J., Multiperiod portfolio optimization with multiple risky assets and general transaction costs, Journal of Banking & Finance, 2016, 69(C), P. 108-120. Doi: 10.1016/j.jbankfin.2016.04.002.

[10] Dorigo, M., Maniezzo, V., Colorni, A., Ant System: Optimization by a colony of cooperating agents, IEEE Transactions on Systems, Man, and Cybernetics Society, 1996, 26(1), P.29–41, Doi:10.1109/3477.484436.

[11] Dorigo, M., Maniezzo, V., Colorni, A., Positive feedback as a search strategy. Tech. Rep. P.91-016, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1991b.

[12] Dorigo, M., Stützle, T., Ant Colony Optimization. MIT Press, Cambridge, MA, 2004   

[13] Eslami Bidgoli, G., Tayebi Sani, E.,  A novel Meta-Heuristic method for solving an extended Markowitz Mean–Variance portfolio selection model, Journal of Investment knowledge, 2014, 3(10), P. 101-122, Print ISSN: 2322-5777, (in Persian).    

[14] Fallahshams, M., Abdollahi, A., Moghadassi, M.,  Examining the Performance of Different Risk Criteria in Portfolio Selection and Optimization, Using the Ant Colony Algorithm In companies Listed at the Tehran Stock Exchange, Journal of Financial Management Strategy, 2013, 1(2),  Doi:10.22051/JFM.2014.960, (in Persian).            

[15] Fobuzi, F., Modigliani, F., Ferry, M., Translated by Tabrizi, A., Fundamentals of Markets and Financial Institutions, Pishboard Publishing, Tehran, Iran, 1997, (In Persian).     

[16] Fotros, M.H., Miri, I., Miria, A., Comparison of Portfolio Optimization for Investors at Different Levels of Investors' Risk Aversion in Tehran Stock Exchange with Meta-Heuristic Algorithms, Advances in Mathematical Finance & Applications, (2020), 5(1), P.  1-10, Doi:10.22034/AMFA.2019.1870129.1235.

[17] Garkaz, M., Abbasi, A., Moghaddasi, M., Portfolio Selection and Optimization Using Genetic Algorithm Based on Different Definitions of Risk, Journal of Industrial Management, Faculty of Humanities, Azad University of Sanandaj, 2010, 5(11), P.21-34, (In Persian).           

[18] Goldenberg, D.E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Professional, New York, United States, 1989, Doi:10.5860/choice.27-0936.      

[19] https://breakingdownfinance.com/ /finance-topics/risk-management/market-risk/value-at-risk/.   

[20] Karaboga, D., Akay, B., A comparative study of Artificial Bee Colony algorithm, Applied Mathematics and Computation, 2009, 214(1), P. 108-132. Doi: 10.1016/j.amc.2009.03.090.      

[21] Larsen, N., Mausser, H., Uryasev, S., Algorithms for optimization of value-at-risk, Financial Engineering, E-commerce and Supply Chain. Kluwer Academic Publishers, United States, 2002, 70.       

[22] López-Ibáñez, M., Stützle, T., An experimental analysis of design choices of multi-objective ant colony optimization algorithms, Springer Science + Business Media, Swarm Intelligence, 2012, 6(C),  P.207–232, Doi:10.1007/s11721-012-0070-7.          

[23] López-Ibáñez, M., Stützle, T., The Automatic Design of Multi-Objective Ant Colony Optimization Algorithms. IEEE Transactions on Evolutionary Computation, 2012, 16(6), P.861–875, Doi:10.1109/TEVC.2011.2182651.     

[24] Macedo, L.L., Godinh, P., Alves M.J., Mean-Semivariance Portfolio Optimization with Multiobjective Evolutionary Algorithms and Technical Analysis Rules, Expert Systems with Applications,  2017, 79(C), P. 33-43, Doi:10.1016/j.eswa.2017.02.033.         

[25] Mansini, R., Ogrycsak, W., Speranza, M.G., Twenty years of linear programming based portfolio optimization, European Journal of Operational Research, 2014, 234(2), P. 518-535, Doi: 10.1016/j.ejor.2013.08.035.      

[26] Markowitz, H.M., Portfolio selection, Journal of Finance, 1952, 7(1), P. 77-91. Doi:10.2307/2975974      

[27] Metaxiotis, K., Liagkouras, K., Multiobjective evolutionary algorithms for portfolio management: a comprehensive literature review, Expert Systems with Applications, 2012,  39(14), P. 11685-11698, Doi:10.1016/j.eswa.2012.04.053.            

[28] Mishra, S.K., Panda, G., Meher S., Multi objective Particle Swarm Optimization approach to portfolio optimization, Paper present at World congress on nature and biologically inspired computing, 2009, Doi:10.1109/NABIC.2009.5393659.           

[29] Mohammadi, E., Mohammadi, E., Ramtin Nia, Sh., Portfolio Optimization by Using the Symbiotic Organisms Search, Financial Research, 2016, 18(2), P. 369-390, Doi:10.22059/JFR.2016.61597, (In Persian).               

[30] Mӧmeni, M., Ghayoumi, A. F., Statistical Analysis with SPSS, Gang Shayegan Publication, Tehran, Iran, 2015, (in Persian).           

[31] Ni, H., Wang, Y., Stock index tracking by Pareto efficient genetic algorithm. Applied Soft Computing Journal, 2013, 13(12), P.4519–4535, Doi:10.1016/j.asoc.2013.08.012.       

[32] Paryabi, A., Salemi, Z., Stock Price Forecasting with Combined Data by Bee Colony Algorithm, Paper present at First National Conference on Economics, Management and Accounting, 2016, (In Persian).           

[33] Qasemi, J., Sarveh, F., A Review on the Application of Meta-Heuristic Algorithms in Financial Matters, Business Reviews, 2018, 96, P. 56-77, (In Persian).             

[34] Raei, R., Saeedi, A., Fundamentals of Financial Engineering and Risk Management, The Organization for Researching and Composing University Textbooks in the Humanities (SAMT), Tehran, Iran, 2017, (in Persian).

[35] Rahmani, M., Khalili Eraqi, M., Nikoomaram, H., Portfolio Optimization by Means of Meta Heuristic Algorithms, Advances in mathematical finance & applications, 2019, 4(4), P. 83-97.

 Doi:10.22034/amfa.2019.579510.1144.        

[36] Rom, B.M., Ferguson, K.W., Post-Modern Portfolio Theory Comes of Age. Journal of Investing, Winter, Reprinted Fall, 1994, 3(3), P. 349- 364, Doi:10.3905/joi.3.3.11.        

[37] Sharpe, W. F., Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 1964, 19, P.425–442, Doi:10.2307/2977928.           

[38] Sinaei, H., Zamani, S., Deciding to Select Portfolio, Comparing Genetic and Bee Algorithms, Journal of Executive Management, 2014, 6(11), P. 83-102, Print ISSN:2008-6237, (in Persian).       

[39] Tehrani R., Management Financial, Negah Danesh Publications, Tehran, Iran, 2014, (in Persian).             

[40] Tuba, M., Pelevic, B., Bacanin N., Artificial Bee Colony (ABC) Algorithm for Portfolio Optimization Problem. Recent Researches in Medicine, Biology and Bioscience, 2013, ISBN: 978-960-474-326-1.     

[41] Zanjirdar M., Overviwe of Portfolio Optimization Models, Advance in mathematical finance, 2020, 5(4), P. 419-435, Doi:10.22034/amfa.2020.1897346.1407.        

[42] Zou, W., Zhu, Y., Chen, H., Zhang B., Solving Multi objective Optimization Problems Using Artificial Bee Colony Algorithm, Discrete Dynamics in Nature and Society, 2011, 2011(2), Doi:10.1155/2011/569784.