PORTFOLIO OPTIMIZATION BASED ON HIGHER ORDER MOMENTS AND FUZZY ENTROPY

Year 2018, 18. EYI Special Issue, 415 - 432, 18.01.2018

Osman Pala , Mehmet Aksaraylı

https://doi.org/10.18092/ulikidince.351487

Abstract

The effectiveness of the mean variance model, which is
based on the assumption that the historical returns are normally distributed,
falls when the series of stock returns do not follow a normal distribution. In order to increase the efficiency of the
model and to cover the properties of the return series’ distribution better,
higher order moments are added to the model. Mean variance model and its
variants are often facing another problem, corner solutions that models often
produce. Entropy function is used to prevent accumulation in
certain stocks and to increase natural diversity. Entropy functions, however,
can be far from the decision maker's point of view and can also produce results
that dominate other objective functions. In the study, a new mean-variance-skewness-kurtosis-fuzzy entropy
portfolio selection model with a new defined fuzzy entropy has been proposed to
overcome the problems mentioned and experiments was performed on two real data
sets to show the effectiveness of the proposed model with using various
portfolio objectives and preferences of decision makers. Entropy and fuzzy entropy
are compared in basis of portfolio models which have higher moments. Results
present that proposed fuzzy entropy approach is better-suited especially with
higher-moment portfolio models.

Keywords

Portfolio optimization, higher order moments, entropy, fuzzy entropy

YÜKSEK DERECEDEN MOMENTLER VE BULANIK ENTROPİYE DAYALI PORTFÖY OPTİMİZASYONU

Abstract

Tarihsel
getirilerin normal dağıldığı varsayımına dayanan ortalama varyans modelinin
etkinliği, hisse senetleri getiri serileri normal dağılım göstermediğinde
düşmektedir. Modelin etkinliğini artırmak ve getiri serilerinin dağılışını daha
iyi modele aktarabilmek için yüksek dereceden momentler modele eklenmektedir.
Ortalama varyans modeli ve varyantlarının bir başka karşılaştığı problem ise
modellerin sıklıkla ürettiği köşe çözümlerdir. Belirli hisse senetlerine
yığılmayı önlemek ve doğal çeşitliliği artırmak için entropi fonksiyonu
kullanılmaktadır. Fakat entropi fonksiyonları karar vericinin bakış açısından
uzak ve diğer amaç fonksiyonlarına baskınlık kuran sonuçlar üretebilmektedir.
Çalışmada, değinilen sorunları aşmak için yeni bir bulanık entropi
tanımlanmış,  yeni bir ortalama-varyans-çarpıklık-basıklık-bulanık
entropi portföy seçim modeli önerilmiş ve önerilen modelin etkililiğini
göstermek için, iki gerçek veri seti üzerindeki deneyler, çeşitli portföy
hedefleri ve karar vericilerin tercihleri kullanılarak gerçekleştirilmiştir.
Entropi ve bulanık entropi, amaç fonksiyonu olarak yüksek momentleri içeren
portföy modelleri açısından karşılaştırılmıştır. Bulgular, önerilen bulanık
entropi yaklaşımının, özellikle yüksek dereceden momentli portföy modelleri
için daha uygun olduğunu göstermektedir.

Keywords

portföy optimizasyonu, yüksek dereceden momentler, entropi, bulanık entropi

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