Optimal Portfolio Diversification Under Cardinality Constraint

Öz

Portfolio selection is an important selection process in economy and finance. The classic modern portfolio theory is a model that focuses on portfolio return and risk in the light of historical data that is assumed to be normally distributed in portfolio selection problem. However, the past return series of stocks are not normally distributed frequently in real life, and it is meaningful to add skewness and kurtosis to the portfolio model. The entropy function that provides the natural diversity is included in the model in order to add future uncertainty in the model and prevent the accumulation of certain stocks encountered in portfolio selection based on higher order moments. In the study, the model, which has become a np-hard problem with the addition of cardinality constraint limiting the number of stocks that can be found in the portfolio, has been solved by particle swarm optimization. From the assets in the sample dataset, models were set for different scenarios and the effectiveness of the proposed entropy function for selection process, in diversification was discussed.

Nicelik Kısıtı Altında Optimal Portföy Çeşitlendirme

Öz

Portföy seçimi ekonomi ve finans alanında önem verilen bir seçim sürecidir. Klasik modern portföy teorisi portföy seçim probleminde normal dağıldığı varsayılan tarihsel veriler ışığında portföy getiri ve riskine odaklanan bir modeldir. Öte yandan hisse senetlerinin geçmiş dönem getiri serileri gerçek hayatta çoğunlukla normal dağılmamakta, çarpıklık ve basıklığın modele eklenmesi anlamlı olmaktadır. Yüksek dereceden momentler ile portföy optimizasyonunda karşılaşılan belirli hisse senetlerine yığılmayı önlemek ve gelecek belirsizliği modele dahil etmek için doğal çeşitlilik sağlayan entropi fonksiyonu modele eklenmektedir. Çalışmada, portföyde bulunabilecek hisse senedi sayısını kısıtlayan nicelik kısıtı eklenmesi ile np-zor hale gelen model, parçacık sürü optimizasyonu ile çözülmüştür. Örnek veri setinde bulunan hisse senetlerinden, farklı senaryolar için modeller kurulmuş ve seçim süreci için önerilmiş olan entropi fonksiyonunun çeşitlendirmede etkinliği tartışılmıştır.

Anahtar Kelimeler

• Nicelik Kısıtlı Portföy Optimizasyonu,Yüksek Momentler,Portföy Çeşitlendirme

Kaynakça

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