New Hesitant Fuzzy Portfolio Optimization Model and Application in Türkiye

Öz

Traditional portfolio theory is designed to find optimum investment rates for a set of stocks and other financial assets based on quantitative data such as returns and risks. However, the relationship between return and risk is an important theory and investors who want to increase their returns may have to bear large risk rates. These data may not always be known clearly and cause uncertainty. In this case, instead of working with exact data, there was a need to develop new models created with the help of fuzzy theory. In this study, hesitant fuzzy theory, which is an extended extension of fuzzy theory, is discussed and a new unsteady fuzzy mathematical model is developed for portfolio optimization. The model is based on finding the maximum value of fuzzy return if the fuzzy risk is minimized. This model was used and interpreted to determine portfolio options by taking the daily closing values of the stocks listed in Borsa Istanbul 50 (BIST 50) in Türkiye.

Anahtar Kelimeler

• Portfolio optimization
• Hesitant fuzzy theory
• Hesitant fuzzy mathematical programming

Yeni Kararsız Bulanık Portföy Optimizasyonu Modeli ve Türkiye Uygulaması

Öz

Geleneksel portföy teorisi bir dizi hisse senedi ve diğer finansal varlıkların getiri ve riskler gibi niceliksel verilere bağlı olarak optimum yatırım oranlarının bulunması üzerine tasarlanmıştır. Ancak getiri ve risk arasındaki ilişki önemli bir kuram olup getirisini yükseltmek isteyen yatırımcı büyük risk oranlarına katlanmak zorunda kalabilir. Bu veriler her zaman net olarak bilinmeyebilir ve belirsizliğe sebep olurlar. Bu durumda kesin verilerle çalışmak yerine bulanık teorinin yardımıyla oluşturulan yeni modellerin gelişmesine ihtiyaç duyulmuştur. Bu çalışmada bulanık teorinin genişletilmiş bir uzantısı olan kararsız bulanık teori ele alınmış ve portföy optimizasyonu için yeni bir karasız bulanık matematiksel model geliştirilmiştir. Model bulanık riskin enküçüklenmesi halinde bulanık getirinin en büyük değerinin bulunması üzerine kurulmuştur. Bu model Türkiye’de Borsa İstanbul 50 (BIST 50)’da yer alan hisse senetlerinin günlük kapanış değerleri alınarak portföy seçeneklerinin belirlenmesi amacıyla kullanılmış ve yorumlanmıştır.

Anahtar Kelimeler

• Portföy optimizasyonu
• Kararsız bulanık teori
• Karasız bulanık matematiksel programlama

Kaynakça

1. Ammar EE. 2007. On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem. Inf Sci, 178(2): 468-484.
2. Atanassov KT. 1986. Intuitionistic fuzzy sets. Fuzzy Sets Syst, 20(1): 87–96.
3. Chen N, Xu Z, Xia M. 2013a. Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model, 37(4): 2197-2211.
4. Chen N, Xu Z, Xia M. 2013b. Interval-valued hesitant preference relations and their applications to group decision making. Knowl Based Syst, 37: 528–540.
5. Chen L, Peng J, Zhang B, Rosyida I. 2017. Diversified models for portfolio selection based on uncertain semivariance. Int J Syst Sci, 48(3): 637–648.
6. Fang Y, Lai KK, Wang SY. 2006. Portfolio rebalancing model with transaction costs based on fuzzy decision theory. Eur J Oper Res, 175: 879–893.
7. Farhadinia B. 2016. Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting. Knowl Based Syst, 93: 135–144.
8. Hao Z, Xu Z, Zhao H, Su Z. 2017. Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowl Based Syst, 127: 16–28.

9. Huang X. 2011. Mean-risk model for uncertain portfolio selection. Fuzzy Optimization and Decision Making, 10 (1): 71–89.
10. Huang X, Qiao L. 2012. A risk index model for multi-period uncertain portfolio selection. Inf Sci, 217: 108–116.
11. Kerstens K, Mounir A, Van de Woestyne I. 2011. Geometric representation of the mean–variance–skewness portfolio frontier based upon the shortage function. Eur J Oper Res, 210(1): 81-94.
12. Kim WC, Fabozzi FJ, Cheridito P, Fox C. 2014. Controlling portfolio skewness and kurtosis without directly optimizing third and fourth moments. Econ Lett, 122(2): 154-158.
13. Konno H, Yamazaki H. 1991. Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manage Sci, 37(5): 519-531.
14. Konno H, Waki H, Yuuki A. 2002. Portfolio optimization under lower partial risk measures. Asia-Pacific Financial Markets, 9: 127-140.
15. Lai YJ, Hwang CL, Lai YJ, Hwang CL. 1992. Fuzzy mathematical programming. Springer, Berlin, Heidelberg, pp: 74-186.
16. Li J, Xu J. 2013. Multi-objective portfolio selection model with fuzzy random returns and a compromise approach-based genetic algorithm. Inf Sci, 220: 507-521.
17. Li X, Wang Y, Yan Q, Zhao X. 2019. Uncertain mean-variance model for dynamic project portfolio selection problem with divisibility. Fuzzy Optimiz Decis Making, 18: 37-56.
18. Liao H, Xu Z. 2015. Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making. Soft Comput, 19(9): 2551–2564.
19. Lin C, Tan B, Hsieh PJ. 2005. Application of the fuzzy weighted average in strategic portfolio management. Decis Sci, 36: 489–511.
20. Lintner J. 1965. Security prices risk and maximal gains from diversification. J Finance, 20(4): 587-615.
21. Markowitz HM. 1952. Portfolio selection. J Finance, 7(1): 77–91.
22. Markowitz H. 1959. Portfolio Selection: Efficient Diversification of Investments. New York: Wiley, pp: 245.
23. Mossin J. 1966. Equilibrium in a capital asset market. Econometrica, 34(4): 768-783.
24. Ning Y, Yan L, Xie Y. 2013. Mean-TVaR model for portfolio selection with uncertain returns. Inter Inform Instit Inform, 16(2): 977-985.
25. Parra MA, Terol AB, Urı´a MVR. 2001. A fuzzy goal programming approach to portfolio selection. Eur J Oper Res, 133: 287–297.
26. Ranjbar M, Effati S, Kamyad AV. 2018. T-operators in hesitant fuzzy sets and their applications to fuzzy rule-based classifier. Appl Soft Comput, 62: 423–440.
27. Rodríguez RM, Martínez L, Herrera F. 2012. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst, 20(1): 109–119.
28. Rodriguez RM, Xu ZS, Martinez L. 2018. Hesitant fuzzy information for information fusion in decision making. Inf Fusion, 42: 62–63.
29. Sharpe FW. 1964. Capital asset prices: A Theory of market equilibrium under conditions of risk. J Finance, 19: 425-442.
30. Torra V, Narukawa Y. 2009. On hesitant fuzzy sets and decision. In: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, pp: 1378–1382.
31. Torra V. 2010. Hesitant fuzzy sets. Int J Intell Syst, 25(6): 529–539.
32. Wan SP, Qin YL, Dong JY. 2017. A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees. Knowl Based Syst, 138: 232-248.
33. Watada J. 1997. Fuzzy portfolio selection and its applications to decision making. Tatra Mount Math Public, 13: 219–248.
34. Xia M, Xu Z. 2011. Hesitant fuzzy information aggregation in decision making. Int J Approx Reason, 52(3): 395-407.
35. Xu Z, Xia M. 2011. On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst, 26(5): 410-425.
36. Yadav S, Kumar A, Mehlawat MK, Gupta P, Charles V. 2023. A multi-objective sustainable financial portfolio selection approach under an intuitionistic fuzzy framework. Inf Sci, 646: 119379.
37. Zadeh LA. 1965. Fuzzy sets. Inf Comput, 8(3): 338–353.
38. Zeng W, Xi Y, Yin Q, Guo P. 2021. Weighted dual hesitant fuzzy set and its application in group decision making. Neurocomputing, 458: 714–726.
39. Zhu B, Xu Z, Xia M. 2012. Dual hesitant fuzzy sets. J Appl Math, 2012(1): 1–13.