Developing an uncertain mean-chance model for portfolio optimization using forecasted returns

Subject Areas : Financial Knowledge of Securities Analysis

Hosein Didehkhani ¹ , Amir Shiri-ghehi ² , Behzad Miran ³

1 - Department of Industrial engineering, Islamic Azad University
2 - Department of financial Management, Aliabad katoul Branch, Islamic Azad University, Aliabad katoul, Iran
3 - Department of industrial engineering, Islamic azad university

Received: 1970-01-01 Accepted : 1970-01-01 Published : 1970-01-01

Keywords: Mean-chance model, uncertainty theory, portfolio optimization,

Abstract :

The purpose of this research is to present a portfolio optimization model within the framework of uncertainty theory. To estimate the return on assets, a prospective approach was used based on expert opinions. Also, a different risk-based approach based on uncertainty (chance model) was used to model risk. The theory used to model the uncertainty in model parameters is the uncertainty theory. The team of experts involved in this research was required to complete the required information on the projections used, including 30 managers of the portfolio of active investment funds in the Tehran Stock Exchange. In the end, to demonstrate the applicability, the model was designed in Tehran Stock Exchange and according to the nonlinear nature of the model, the hyper bacterial method of the genetic algorithm was used to solve it. Finally, by generating randomized portfolios and comparing them with the optimal portfolio for solving the model, we conclude that the optimized portfolio achieves a higher level of efficiency while delivering better performance.

References:

*      ابراهیمی, سیدبابک, جیرفتی, امیرسینا, عبدی, متین. (1397). بهینه‌سازی سبد سرمایه‌گذاری تحت نظریه اعتبار فازی با استفاده از مدل میانگین-ارزش در معرض ریسک مشروط. دانش مالی تحلیل اوراق بهادار, 11(37), 17-27.

*      -دیده خانی حسین ، حجتی استانی سعید. (1395). ارائه مدل برنامه ریزی چندهدفه جهت انتخاب سهام با در نظرگرفتن ارزش در معرض خطر فازی: رویکرد تئوری اعتبار فازی. مهندسی مالی و مدیریت اوراق بهادار, 8(32), 239-268.

*      رستمی‌، محمدرضا؛ کلانتری بنجار، محمود و بهزادی، عادل. (1394)، گشتاورهای مراتب بالاتر در بهینه سازی سبد سهام در محیط فازی، مجله مهندسی مالی و مدیریت اوراق بهادار، شماره 24 ، 61-41.

*      شیری قهی, امیر, دیده خانی, حسین, خلیلی, کاوه, سعیدی, پرویز. (1396). مطالعه تطبیقی مدل بهینه‌سازی پرتفوی چند دوره‌ای چندهدفه در محیط اعتبار فازی با معیارهای متفاوت ریسک. راهبرد مدیریت مالی, 5(3), 1-26.

*      DeMiguel, V., Mei, X.,  & Nogales, F. J. (2016). “Multiperiod portfolio optimization with multiple risky assets and general transaction costs”. Journal of Banking & Finance, 69, 108-120.

*      Liu, Y. J., & Zhang, W. G. (2015). “A multi-period fuzzy portfolio optimization model with minimum transaction lots”. European Journal of Operational Research, 242(3), 933-941.

*      Alexander G.J., & Baptista A.M. (2011). Portfolio selection with mental accounts and delegation. Journal of Banking & Finance, 35, 2637-2656.

*      Baptista A.M. (2012). Portfolio selection with mental accounts and background risk. Journal of

*      Ben-Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of operations research, 23(4), 769-805.

*      Bhattacharyya, R., Chatterjee, A., & Kar, S. (2013). Uncertainty theory based multiple objective mean-entropy-skewness stock portfolio selection model with transaction costs. Journal of Uncertainty Analysis and Applications, 1(1), 16.

*      Chunhachinda, P., Dandapani, K., Hamid, S., & Prakash, A. J. (1997). “Portfolio selection and skewness: Evidence from international stock markets”. Journal of Banking & Finance, 21(2), 143-167.

*      Cong, F., & Oosterlee, C. W. (2016). “Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation”. Journal of Economic Dynamics and Control, 64, 23-38.

*      Consigli, G. (2002). Tail estimation and mean–VaR portfolio selection in markets subject to financial instability. Journal of Banking & Finance, 26(7), 1355-1382.

*      Gao Y. (2012). Uncertain Models for Single Facility Location Problems on Networks. Applied Mathematical Modelling , 36, 2592-2599.

*      -Goldberg, David,(1989),genetic algorithms in search optimization and machine's learning. Addison-Wesly publishing

*      Grootveld, H., & Hallerbach, W. (1999). “Variance vs downside risk: Is there really that much difference?”. European Journal of operational research, 114(2), 304-319.

*      Guo, S., Yu, L., Li, X., & Kar, S. (2016). “Fuzzy multi-period portfolio selection with different investment horizons”. European Journal of Operational Research, 254(3), 1026-1035.

*      Huang X. (2011). Mean-risk model for uncertain portfolio selection. Fuzzy Optimization and

*      Huang X. (2012a). Mean-variance models for portfolio selection subject to experts’ estimations. Expert Systems with Applications, 39, 5887-5893.

*      Huang X. (2012b). A risk index model for portfolio selection with returns subject to experts’ evaluations. Fuzzy Optimization and Decision Making, 11, 451-463.

*      Huang, X. (2006). “Fuzzy chance-constrained portfolio selection. Applied mathematics and computation”, 177(2), 500-507.

*      Huang, X. (2008). “Mean-entropy models for fuzzy portfolio selection”. IEEE Transactions on Fuzzy Systems, 16(4), 1096-1101.

*      Huang, X. (2008). “Risk curve and fuzzy portfolio selection”. Computers & Mathematics with Applications, 55(6), 1102-1112.

*      Huang, X. (2010). Portfolio Analysis: From Probabilistic to Credibilistic and Uncertain Approaches. Berlin: Springer-Verlag, (Chapter 4).

*      Huang, X., Zhao, T. (2015), Mean-chance model for portfolio selection based on uncertain measure. Insurance: Mathematics and Economics (2014),  vol 59 pp  243-250

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

*      Katagiri, H., & Ishii, H. (1999). Fuzzy portfolio selection problem. In Systems, Man, and Cybernetics, 1999. IEEE SMC'99 Conference Proceedings. Vol. 3, pp. 973-978

*      Konno, H., & Yamazaki, H. (1991). “Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market”. Management science, 37(5), 519-531.

*      Liu, B. (2007). Uncertainty Theory. (2nd ed.). Berlin: Springer-Verlag

*      Liu, B. (2010). Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Berlin: Springer-Verlag,

*      Liu, Y. J., Zhang, W. G., & Xu, W. J. (2012). ‘Fuzzy multi-period portfolio selection optimization models using multiple criteria”. Automatica, 48(12), 3042-3053.‏

*      Liu, Y.-J., Zhang, W.-G., & Zhang, P. (2013). “A multi-period portfolio selection optimization model by using interval analysis”. Economic Modelling, 33, 113-119.

*      Liu, Y.-J., Zhang, W.-G., & Zhang, Q. (2016). “Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse”. Applied Soft Computing, 38, 890-906.

*      Markowitz, H., & Selection, P. (1959). “Efficient diversification of investments”. John Wiley and Sons, 12, 26-31.

*      -Markowitz, H., (1952), “Portfolio Selection”, Journal of Finance, 15, 77- 91.

*      Mehlawat, M. K. (2016). “Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels”. Information Sciences, 345, 9-26.

*      Qin, Z., & Kar, S. (2013). Single-period Inventory Problem under Uncertain Environment. Applied Mathematics and Computation, 219, 9630-9638.

*      Speranza, M. G.(1993). Linear programming models for portfolio optimization, J. Finance (14), 107–123.

*      Tsao, C.Y. (2010). Portfolio selection based on the mean-VaR efficient frontier. Quantitative Finance, 10, 931-945.

*      Vercher, E., & Bermúdez, J. D. (2015). “Portfolio optimization using a credibility mean-absolute semi-deviation model”. Expert Systems with Applications, 42(20), 7121-7131.

*      Watada, J. (1997). Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematical Publication, 13(4), 219-248.

*      Yao, H., Li, Z., & Li, D. (2016). “Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability”. European Journal of Operational Research, 252(3), 837-851.

*      Zhai, J., & Bai, M. (2018). Mean-variance model for portfolio optimization with background risk based on uncertainty theory. International Journal of General Systems, 47(3), 294-312.

*      Zhang Q., Huang X., & Tang L. (2011). Optimal multinational capital budgeting under uncertainty. Computers and Mathematics with Applications, 62, 4557-4567