Markowitz'in ortalama-varyans portföy optimizasyon modeli için metasezgisel yöntemlerin değerlendirilmesi ve karşılaştırılması

Abstract

Portföy seçimi, tatmin edici bir yatırım getirisi elde etmek için birden fazla varlık içeren portföyler arasından bir varlık kombinasyonu seçme sürecidir. Markowitz (1952) tarafından önerilen ortalama varyans modeli, portföy seçim problemi için yaygın olarak kullanılmaktadır. Portföydeki varlıkları minimum risk ve maksimum getiriye dayalı olarak seçen bir karesel programlama modelidir. Karesel programlama probleminin çözümü için genellikle klasik optimizasyon algoritmaları kullanılmaktadır. Son yıllarda, portföy seçim problemlerinin çözümü için klasik optimizasyon tekniklerine ek olarak metasezgisel optimizasyon algoritmaları kullanılmaktadır. Metasezgisel yöntemler, kesin çözüm yöntemleri ile makul bir sürede çözülemeyen karmaşık optimizasyon problemlerini çözmek için tasarlanmış algoritmalardır. Farklı alanlar için çeşitli metasezgisel algoritmalar geliştirilmektedir. Bu çalışmada Aralık 2016 - Aralık 2017 tarihleri arasında BİST30 endeksinde işlem gören 30 hisse senedinin günlük kapanış fiyatlarından elde edilen veri seti kullanılmıştır. Optimal portföy oluşturmak için Markowitz'in ortalama varyans modeli ele alınmıştır. Optimal portföyü belirlemek için çoğunlukla metasezgisel yöntemlerden, Parçacık Sürüsü Optimizasyonu ve Diferansiyel Evrim ve Yapay Arı Kolonisi uygulanmıştır. Bu yöntemlerin performansları, risk değerleri yani portföy varyansları dikkate alınarak karşılaştırılmıştır.

Keywords

• Yapay arı kolonisi
• Diferansiyel evrim
• Metasezgiseller
• Parçacık Sürü Optimizasyonu
• Portföy optimizasyonu
• Karesel programlama

Evaluation and comparison of metaheuristic methods for Markowitz’s mean-variance portfolio optimization model

Abstract

 Portfolio selection is the process of selecting a combination of assets among portfolios containing multiple assets to achieve a satisfactory return on investment. Mean-variance model proposed by Markowitz (1952) has been extensively used for portfolio selection problem. It is a quadratic programming model based on the minimum risk and maximum return by choosing assets in the portfolio. Generally, classical optimization algorithms have been used for solving the quadratic programming problem. Recently, metaheuristic optimization algorithms have been used in addition to classical optimization techniques for solving portfolio selection problems. Metaheuristic methods are designed to solve complex optimization problems that cannot be solved in a reasonable time with the definitive solution methods. Various metaheuristic methods have been developed for different areas. In this study, BIST30 index data set obtained from daily closing prices of 30 stocks between December 2016 - December 2017 was used. Markowitz’s mean-variance model is considered to constitute an optimal portfolio. , Particle Swarm Optimization, Differential Evolution, and Artificial Bee Colony which are mostly used metaheuristic methods, are applied to determine an optimal portfolio. Performances of these methods are compared by considering risk values, i.e. portfolio variances.  

Keywords

• Artificial Bee Colony
• Differential Evolution
• Metaheuristics
• Particle Swarm Optimization
• Portfolio Optimization
• Quadratic programming

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