AN APPLICATION ON PORTFOLIO OPTIMIZATION WITH FUZZY PROGRAMMING

Year 2020, Issue: 38, 197 - 209, 29.01.2020

Nuri Avşarlıgil

https://doi.org/10.30794/pausbed.554863

Cited By: 1

Abstract

The purpose of this study is to investigate the
availability of fuzzy models in the portfolio preference phase for financial
investors. For this purpose, in establishing the portfolios that investors will
use to invest in the financial resources of the investors, they will try to
obtain high returns through the Fuzzy Verdegay method, using past price
changes. An optimal portfolio decision was made by using 10 index data traded
in Borsa Istanbul. The average return and maximum return thresholds are
determined using the historical values of the Indices. When an investment
decision is taken by investors, the Verdegay fuzzy model, which is one of the
optimization techniques used for portfolio selection in the literature,
performs optimal weighting according to the objective function among the mixed
strategies. After the weighting process, the success of the result to be
reached in the last part of the study was discussed through retrospective
tests.

Keywords

Optimal Portfolio, Fuzzy Programming, Verdegay Model

BULANIK PROGRAMLAMAYLA PORTFÖY OPTİMİZASYONU ÜZERİNE BİR UYGULAMA

Abstract

Bu çalışmanın amacı, finansal yatırımcılar için
portföy tercihi aşamasında bulanık modellerin kullanılabilirliğini
araştırmaktır. Bu amaçla, yatırımcıların ellerinde bulunan finansal kaynakları
yatırıma dönüştürmek için kullanacakları portföylerin oluşturulmasında, geçmiş
fiyat değişimlerinden yararlanılarak, Bulanık Verdegay yöntemi aracılığıyla
yüksek getiri elde etmeye çalışılacaktır. 
Borsa İstanbul’da işlem gören, 10 adet endeks verisi kullanılarak,
optimal portföy kararı verilmeye çalışılmıştır. Endekslerin geçmiş değerleri
kullanılarak, ortalama getiri ve maksimum getiri eşik değerleri belirlenmiştir.
Yatırımcılar tarafından bir yatırım kararı alınırken, literatürde portföy
seçimi için kullanılan optimizasyon tekniklerinden bir tanesi olan Verdegay
bulanık modeli, karma stratejiler arasından amaç fonksiyonuna göre optimal
ağırlıklandırma işlemi yapmaktadır. Yapılan ağırlıklandırma işlemi sonrası,
çalışmanın son bölümünde ulaşılacak sonucun başarısı geriye dönük testler
aracılığıyla tartışılmıştır.

Keywords

Optimal Portföy, Bulanık Programlama, Verdegay Modeli

References

• Ammar, Elsaid El (2008), “On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem” Information Sciences,178, 468–484.
• Ammar, Elsaid El, Khalifa, Hamdeen Abdulwahid (2003), “Fuzzy portfolio optimization: A quadratic programming approach”, Chaos, Solutions & Fractals, 18, 1045–1054
• Aslantaş, Cem (2008), Portföy yönetiminde fuzzy yaklaşımı, Marmara Üniversitesi Sosyal Bilimler Enstitüsü, Yüksek Lisans Tezi, İstanbul, Türkiye
• Atan, Sibel (2012), “0-1 Tamsayılı Programlama İle Portföy Seçim Modeli ve İmkb–30 Endeksinde Bir Uygulama”, e-Journal of New World Sciences Academy, Volume: 7, Number: 2, 74-86
• Bertsimas, Dimitris, Pachamanova, Dessislava (2008), “Robust multi period portfolio management in the presence of transaction costs”, Computers and Operations Research, 35, 3–17
• Chen, Zhiping (2005), “Multiperiod consumption and portfolio decisions under the multivariate GARCH model with transaction costs and CVaR-based risk control”, ORSpectr,27, pp. 603–632
• Elton, Edwin, Gruber, Matthias (1997), “Modern Portfolio Theory, 1959 to date”, Journal of Banking & Finance, 21, pp: 1743 – 1759
• Ertuğrul, İrfan, Tuş, Ayşegül (2007), “Interactive fuzzy linear programming and an application at a textile firm”, Fuzzy Optimal Decision Making, 6(1)
• Fang, Ling Lu, Ji Xian Xiao, Xin Chun Wang (2010), “A new algorithm for solving fuzzy linear programming”, 2010 Second International Conference on Computer Modeling and Simulation, Çin, 125-127
• Geyer, Alois, Hanke, Michael , Weissensteiner, Alex (2009), “A stochastic programming approach for multiperiod portfolio optimization”, Computer Management Science, V:6, 187–208
• Gupta, Pankaj, Mehlawat, Mukesh Kumar,Saxena Anand (2008), “Asset portfolio optimization using fuzzy mathematical programming”, Information Sciences, 178, 1734–1755
• Gülgör, Gonca (2010), “İmkb 30 endeksinde klasik ve bulanık analitik hiyerarşi süreci ile portföy seçimi ve performanslarının karşılaştırılması”, Osmangazi Üniversitesi Sosyal Bilimler Enstitüsü, Yüksek Lisans Tezi, Eskişehir, Türkiye
• Hansen, Bjerna (1996), “Fuzzy Logic and Linear Programming Find Optimal Solutions for Meteorological Problems”, Term Paper for Fuzzy Coursa at Technical University of Nova Scotia
• Ince, Hüseyin, Trafalis, Theodore B. (2006), “Kernel methods for short-term portfolio management”, Expert Systems with Applications, 30, 535–542
• Inuiguchi, Masahiro, Sakawa, Masatoshi, (1998), “Robust optimization under softness in a fuzzy linear programming problem”, International Journal of Approximate Reasoning, 21-34
• Karadayı, Turgay (2007), Bulanık doğrusal programlama kullanılarak yapısal sistemlerin boyutlandırılması, Fırat Üniversitesi Fen Bilimleri Enstitüsü, yüksek lisans tezi
• Keskenler, Mustafa Furkan,” Bulanık Mantığın Tarihi Gelişimi”, Takvim-i Vekayi, Cilt: 5 No: 1 2017, Sayfa: 1-10
• Kocadağlı, Ozan, Keskin, Rıdvan (2015), “A novel portfolio selection model based on fuzzy goal programming with different im portance and priorities”, Expert Systems with Applications 42/20,6898-6912
• Konno, Hiroshi, Yamazaki, Hiroaki (1991), “Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market”, Management Science, 37, 519–531
• Lai, Young-Jou, Hwang, Ching-Lai (1992a), Fuzzy Mathematical Programming: Methods And Application,. Berlin: Springer-Verlag
• Lai, Young-Jou, Hwang, Ching-Lai (1992b), “A new approach to some possibilistic linear programming problem”, Fuzzy Sets and Systems, 49, 121-133
• Li, Duan, Wan-Lung Ng (2000), “Optimal dynamic portfolio selection: multiperiod mean–variance formulation” Mathematical Finance, 10/3, 387–406
• Momen, Omid , Esfahanipour, Akbar, Seifi, Abbas (2017), “A robust behavioral portfolio selection: model with investor attitudes and biases”, Operational Research, 2/1–20
• Negoita, Constantin Virgil (1981), Fuzzy systems, Tunbridge Wells, Abacus Pres
• Özkan, Şule (2005), Lineer Programlama, Nobel Yayın Dağıtım, 1. Basım, Ankara
• Pelitli, Dilek (2007), Portföy analizinde bulanık mantık yaklaşımı ve uygulama örneği, Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü, Yüksek Lisans Tezi, Denizli, Türkiye
• Rubio, Angel, Jose, Bermúdez, Ernesto, Vercher (2007), “Comparative Analysis Of Forecasting Portfolio Returns Using Soft Computing Technologies”, Advances in Intelligent Systems Research, vol.89, pp.617–623.
• Sadjadi, Seyed-Jafar, Seyedhosseini, Seyed Muhammad, Hassanlou, Khadijeh (2011) “Fuzzy multi period portfolio selection with different rates for borrowing and lending”, Applied Soft Computing, 11, 3821– 3826
• Song, Qiang, Brad Chissom (1993), “Forecasting enrollments with fuzzy time series – part I”, Fuzzy Sets Systems, 54/1–9
• Song, Qiang, Brad Chissom (1994),”Forecasting enrollments with fuzzy time series – part II”, Fuzzy Sets Systems, 62, 1–8
• Sun, Wei (2016), “Portfolio selection strategies with investor psychology and behavior under fuzzy random environment”, 8th International Symposium on Computational Intelligence and Design (ISCID), 208–211
• Tiryaki, Fatma, Ahlatcioglu, Beyza (2009), “Fuzzy portfolio selection using fuzzy analytic hierarchy process”, Information Sciences, 179, 53–69
• Tsaur, Ruey-Chyn (2013), “Fuzzy portfolio model with different investor risk attitudes”, European Journal of Operational Research, 227/2, 385–390
• Tüfekçi, Ömer Kürşad, Avşarlıgil Nuri, “Optimal Portföy Kuramı ve Oyun Teorisi Yaklaşımı: BIST’ta Bir İnceleme”, Journal of Strategic Research in Social Science, Cilt:2, Sayı:4, 2016, 41-64
• Verdegay, Jose Luis (1984), "A dual approach to solve the fuzzy linear programming problem", Fuzzy Sets and Systems 14, 131-141
• Wang, Dingwei (1997),“An Inexact Approach For Linear Programming Problems With Fuzzy Objective And Resources”, Fuzzy Sets and Systems, 89(1), 61-68
• Wang, Zhen, Liu, Sanyang (2013),”Multi-period mean–variance portfolio selection with fixed and proportional transaction costs”, Journal of Industrial & Management Optimization, 9/3, 643–657
• Werners, Brigitte (1987), “An interactive fuzzy programming system”, Fuzzy Sets and Systems, Vol. 23, 131-147
• Zadeh, Lotfi (1999), “Fuzzy sets as a basis for a theory of possibility”, Fuzzy Sets and Systems, 100, 9–34
• Zhang, Wei-Guo, Liu, Yong-Jun, Xu, Wei-Jun (2012), “A possibilistic mean semivariance-entropy model for multi-period portfolio selection with transaction costs”, European Journal of Operational Research,222/2, 341–349
• Zhou, Jiandong, Xiang Li, Witold Pedrycz (2016), “Mean-semi-entropy models of fuzzy portfolio selection”, IEEE Transactions on Fuzzy Systems, 99, 1-1
• Zhou, Rongxi , Yang, Zebin , Yu, Mei, Ralescu, Dan (2015), “A portfolio optimization model based on information entropy and fuzzy time series”, Fuzzy Optimization and Decision Making 14/381–397
• Zhu, Shu-Shang, Li, Duan, Wang, Shou-Yang (2004),”Risk control over bankruptcy in dynamic portfolio selection: A generalized mean–variance formulation”, IEEE Transactions on Automatic Control, 49/3, 447–457
• Zımmermann, Hans-Jürgen (1987), Fuzzy Sets, Decision Making, And Expert Systems , Kluwer Academic Publishers, Boston
• Zimmermann, Hans-Jürgen (1974),”Optimization in fuzzy environment”, XXI International TIMS and 46th ORSA Conference, San Juan, Puerto Rico