Selecting The Optimal Multi-Period Stock Portfolio with Different Time Horizons in the Credibility Theory Framework

الموضوعات :

Younes Nozarpour ¹ (Department of Financial Orientation, Dehaghan Branch, Islamic Azad University, Dehaghan, Iran)
Sayyed Mohammad Reza Davoodi ² (Department of Management, Dehaghan Branch, Islamic Azad University, Dehaghan, Iran)
Mahdi Fadaee ³ (Department of Economics, Payame Noor University, Iran)

تاريخ الإرسال : 24 الجمعة , رجب, 1443 تاريخ التأكيد : 09 الأربعاء , ذو القعدة, 1443 تاريخ الإصدار : 13 السبت , ذو الحجة, 1444

الکلمات المفتاحية: different time horizons, Portfolio, credibility theory, Multi-period, fuzzy variables,

ملخص المقالة :

After closing, the multi-period portfolio can be corrected and revised at regular intervals. The philosophy behind using multi-period portfolio models is that investors often have a multi-period view of future changes in assets, which can be the result of technical and fundamental analysis or statistical model analysis. In conventional multi-period portfolio models, it is assumed that the forecast and correction time horizons are the same for all assets. However, one asset may be forecasted over a one-month horizon while another may be forecasted over a two-month horizon, and both may be revised in the future. The purpose of this study is to present a multi-period portfolio model in which assets have different time horizons for corrections or an asset may not be traded for the first few periods and then enter the correction stage. In this model, fuzzy variables defined in a credibility space are used to describe the return, and the credibility measure controls the risk. The model's objective function is to maximize the portfolio's ultimate wealth, and a constraint is used to control portfolio risk, in which the validity of the portfolio's ultimate wealth below a certain threshold is controlled at a certain level of confidence. A combination of particle swarm optimization and simulation is used to find the best solution. Finally, using a numerical example, the model is implemented on a portfolio with 6 assets and 4 monthly time steps on the Tehran Stock Exchange.

المصادر:

[1] Ansari, H., Behzadi, A., Imam Doust, M., Selection of fuzzy stock portfolio using hybrid intelligent algorithm taking into account undesirable risk, Investment Knowledge, 1398, 8(30), P.329-354.

[2] Carlsson, C., Fullér, R., On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, 2001, 122(2), P.315–326.

[3] Farrokh, M., Fuzzy stock portfolio selection with simultaneous review of undesirable returns and risk, Recent Research in Decision Making, 2021, 6(2), P.1-18.

[4] Guo, S.N., Yu, L. A., Skewness of fuzzy numbers and its applications in portfolio selection, IEEE Transactions on Fuzzy Systems, 2015, 23(6), P.2135–2143. Doi: 10.1109/TFUZZ.2015.2404340.

[5] Guo, S.N., Yu, L.A., Kar, S., Fuzzy multi-period portfolio selection with different investment horizons, European Journal of Operational Research, 2016, 254(3), P.1-10. Doi: 10.1016/j.ejor.2016.04.055.

[6] Gupta, P., Mehlawat, M.K., Yadav. D., Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models, Soft Comput, 2020, 24, P.11931–11956. Doi: 10.1007/s00500-019-04639-3.

[7] Huang, X.X., Mean-entropy models for fuzzy portfolio selection, IEEE Transaction on Fuzzy Systems, 2008, 16(4), P.1096–1101. Doi: 10.1109/TFUZZ.2008.924200.

[8] Kar, S., Bhattacharyya, R., 2011, Possibilistic mean-variance-skewness portfolio selection models, International Journal of Operations Research, 8, P.44–56.

[9] Li, X., Credibilistic programming, New York: Springer, 2013.

[10] Li, X., Shou, B. Y., Qin, Z. F., An expected regret minimization portfolio selection model, European Journal of Operational Research, 2012, 218(2), P.484–492. Doi: 10.1016/j.ejor.2011.11.015.

[11] Li, X., Wang, Y., Yan, Q., Zhao, X., Uncertain mean-variance model for dynamic project portfolio selection problem with divisibility, Fuzzy optimization and decision making, 2019, 18(1), P.37-56.

[12] Liu, B., Uncertainty Theory, second ed., Springer-Verlag, Berlin, 2007.

[13] Liu, B., Liu, Y. K., Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 2002, 10(4), P.445–450. Doi: 10.1109/TFUZZ.2002.800692.

[14] Liu, Y. J., Zhang, W. G., Multiperiod fuzzy portfolio selection optimization model based on possibility theory. International Journal of Information Technology and Decision Making, 2019, 17(03), P.941-968.

[15] Liu, Y. J., Zhang, W. G., A multi-period fuzzy portfolio optimization model with minimum transaction lots. European Journal of Operational Research, 2015, 242, P.933-941. Doi: 10.1016/j.ejor.2014.10.061.

[16] Liu, Y. J., Zhang, W. G., Xu, W. J., Fuzzy multi-period portfolio selection optimization models using multiple criteria. Automatica, 2012, 48(12), P.3042–3053. Doi: 10.1016/j.automatica.2012.08.036.

[17] Markowitz, H., Portfolio selection. Journal of Finance,1952, 3, P.77–91. Doi: 10.2307/2975974

[18] Nouri, M., Mohammadi, O., Fuzzy Multi-Period Portfolio Optimization: Capital-Risk-Liquidity Model, 16th International Conference on Industrial Engineering, Tehran. 2019. (in Persian)

[19] Izadikhah, M., A Fuzzy Goal Programming Based Procedure for Machine Tool Selection, 2015, 28(1), P. 361-372, Doi: 10.3233/IFS-141311

[20] Oprisor, R., Kwon, R., Multi-period portfolio optimization with investor views under regime switching, Journal of Risk and Financial Management, 2020, 14(1), 3.

[21] Peykani, P., Nouri, M., Eshghi, F., A novel mathematical approach for fuzzy multi-period multi-objective portfolio optimization problem under uncertain environment and practical constraints, Journal of fuzzy extension and application, 2021, 2(3), P.191-203.

[22] Qin, Z. F., Kar, S., Mean-variance-skewness model for portfolio selection with fuzzy returns, European Journal of Operational Research, 2010, 202(1), P.239-247. Doi: 10.1016/j.camwa.2010.10.039.

[23] Qin, Z. F., Li, X., Ji, X. Y., Portfolio selection based on fuzzy cross-entrop, Journal of Computational and Applied Mathematics, 2009, 228, P.139–149. Doi: 10.1016/j.cam.2008.09.010.

[24] Rezaei, B., Mohammadi, S., Rastegar, B., Multi-period portfolio optimization using risk-based measurement in the framework of GJR GARCH-EVT-copula method, the first national conference on optimization of production and service systems, 2020.

[25] Shiri Ghahi, A., Dideh Khani, H., Khalili Damghani, K., Saidi Comparative study of multi-objective multi-period portfolio optimization model in fuzzy credit environment with different risk criteria, Financial management strategy, 2017, 5(3), P.1-26. (in Persian).

[26] Vercher, E., Bermudez, J. D., Portfolio optimization using a credibility mean-absolute semi-deviation model, Expert Systems with Applications, 2015, 42, P.7121-7131.

[26] Xue, L., Di, H., Zhao, X., Zhang, Z., Uncertain portfolio selection with mental accounts and realistic constraints, Journal of computational and applied mathematics, 2019, 346, P.42-52.

[27] Yong-Jun L., Zhang. W-G., Fuzzy multi-period portfolio selection model with time-varying loss aversion, Journal of the Operational Research Society, 2020, 14, P.1-15. Doi: 10.1080/01605682.2019.1705191.

[28] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems,1978, 1, P.3–28.

 Doi: 10.1016/S0165-0114(99)80004-9.

[29] Zhang, B., Peng, J., Li, S., Uncertain programming models for portfolio selection with uncertain returns, International journal of systems science, 2015, 46(14), P.2510-2519.

[30] Zhang, W. G., Nie, Z. K., On possibilistic variance of fuzzy numbers, Lecture Notes in Artificial Intelligence, 2003, 2639, P.398–402.

[31] Zhang, W. G., Zhang, X. L., Xiao, W. L., Portfolio selection under possibilistic mean-variance utility and a SMO algorithm, European Journal of Operational Research, 2009, 197(2), P.693-700.

[32] Zhu, Y., Uncertain optimal control with application to a portfolio selection model, Cybernetics and systems: an international journal, 2010, 41(7), P.535-547.

[35] Zamani, S., Zanjirdar, M., Lalbar, A., The effect of information disclosure on market reaction with meta-analysis approach, Advances in Mathematical Finance and Applications, 2022, 7(3), P. 629-644.

Doi: 10.22034/amfa.2021.1937478.1625

 

[36] Zanjirdar, M., Overview of Portfolio Optimization Models, Advances in Mathematical Finance and Applications, 2020. 5(4), P.419-435. Doi: 10.22034/amfa.2020.674941.

 

[37] Zanjirdar, M., Kasbi, P., Madahi, Z., Investigating the effect of adjusted DuPont ratio and its components
on investor & quot; s decisions in short and long term, Management Science Letters, 2014, 4(3), P.591-596.
Doi: 10.5267/j.msl.2014.1.003