The portfolio optimization with simulated annealing algorithm: An application of Borsa Istanbul

Abstract

One of the key concepts in finance is Markowitz’s constrained mean-variance model, the number of assets to be included in the portfolio is restricted. The solution of this generalized problem, which belongs to the quadratic and integer programming problem class, as the number of dimensions increases, is difficult to obtain with standard methods. In this study, the simulated annealing (SA) algorithm, which is one of the local search-based meta-heuristic methods, was preferred. The developed SA algorithm was applied to the Hang-Seng benchmark data set, and the results were compared with pioneering studies. According to the experimental results, upon the performance of the algorithm was found to be sufficient, the SA algorithm was applied for the Borsa Istanbul 30 index. The results of the experiments based on the Markowitz mean-variance model demonstrate that, while more assets must be maintained at lower risk levels to converge an unconstrained efficient frontier and the number of assets needed to do so decreases as risk rises

Keywords

• Portfolio optimization
• markowitz mean-variance model
• simulated annealing
• heuristic optimization

Tavlama benzetim algoritmasıyla portföy optimizasyonu: Borsa İstanbul uygulaması

Abstract

Finans alanının önemli konularından Markowitz’in kısıtlı ortalama-varyans modelinde, portföye dahil edilecek varlık sayısı sınırlandırılır. Kuadratik ve tamsayılı programlama problem sınıfına ait genelleştirilmiş bu problemin, boyut sayısının artmasıyla çözümünün standart yöntemlerle elde edilmesi zordur. Bu çalışmada yerel arama tabanlı meta-sezgisel yöntemlerden olan tavlama benzetim (TB) algoritması tercih edilmiş, geliştirilen TB algoritması Hang-Seng benchmark veri setine uygulanmış, sonuçlar öncü çalışmalarla kıyaslanmıştır. Markowitz kısıtlı ortalama-varyans modeline dayanarak elde edilen kısıtsız etkin sınıra yaklaşabilmek için, düşük risk düzeyinde varlık sayısının daha fazla, yüksek risk seviyesinde varlık sayısının daha az olması gerektiği sonucuna ulaşılmıştır.

Keywords

• Portföy optimizasyonu
• markowitz ortalama-varyans modeli
• tavlama benzetim
• sezgisel optimizasyon.

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