New Hesitant Fuzzy Portfolio Optimization Model and Application in Türkiye

Abstract

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.

Keywords

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

Yeni Kararsız Bulanık Portföy Optimizasyonu Modeli ve Türkiye Uygulaması

Abstract

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.

Keywords

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

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