Kümeleme Tabanlı Portföy Optimizasyonu: BIST100 Üzerine Ampirik Bir Analiz

Abstract

Bu çalışmanın amacı, Borsa İstanbul 100 endeksinde işlem gören ve benzer getiri özelliklerine sahip hisselerden kümeleme tabanlı portföy oluşturmak ve bu portföyün performansını optimize etmektir. Çalışmada, 65 hissenin Ocak 2015–Nisan 2025 dönemine ait 124 aylık getirileri kullanılmıştır. Uç değerler IQR yöntemiyle temizlenmiş, getiriler Z-skor standardizasyonuna tabi tutulmuştur. Analizin birinci aşamasında, K-means yöntemiyle hisseler kümelenmiş ve optimum küme sayısı Silhouette skoruyla sekiz olarak belirlenmiştir. Her kümeden, en yüksek Sharpe oranı ve en düşük volatilite kriterleriyle belirlenen 15 hisseden portföy oluşturulmuştur. İkinci aşamada Sharpe oranını maksimize eden amaç fonksiyonu ve kısıtlar kullanılarak optimizasyon gerçekleştirilmiş ve yedi hisseye pozitif ağırlık atanmıştır. Eğitim dönemi için oluşan ağırlıklar test dönemine (Nisan 2023-Nisan 2025) uygulanmış ve portföy performansı BIST100 endeksi ile karşılaştırılmıştır. Test dönemi sonunda, kümeleme tabanlı portföyün kümülatif getirisi % 182,89 ve ortalama getirisi % 4,30, BIST100 endeksinin kümülatif getirisi % 91,67 ve ortalama getirisi % 3 olarak gerçekleşmiştir. Bu sonuçlar, kümeleme tabanlı portföy oluşturma yaklaşımının geleneksel optimizasyon yöntemleriyle birleştirilerek literatüre yeni bir perspektif sunabileceğini ve portföy performansını artırma potansiyeli taşıdığını göstermektedir.

Keywords

• Kümeleme Analizi
• K-Means
• Sharpe Oranı
• Portföy Optimizasyonu

Clustering-Based Portfolio Optimization: An Empirical Analysis on the BIST100

Abstract

The aim of this study is to construct a clustering-based portfolio composed of stocks traded on the Borsa Istanbul 100 Index that exhibit similar return characteristics, and to optimize the performance of this portfolio. The study uses the 124 month returns of 65 stocks for the period from January 2015 to April 2025. We identify and remove outliers from the dataset using the interquartile range (IQR) method. Following this, we standardize returns using Z-scores. The analysis comprises two stages. In the first stage, we cluster stocks using the K-means method. The optimal number of clusters is determined to be eight using the Silhouette score. From each cluster, a portfolio was constructed consisting of 15 stocks selected based on the criteria of the highest Sharpe ratio and the lowest volatility. In the second stage, optimization was performed using an objective function that maximizes the Sharpe ratio subject to relevant constraints, and positive weights were assigned to seven stocks. The weights obtained from the training period are applied to the test period (April 2023–April 2025), and the portfolio performance is compared with the BIST100 index. At the end of the test period, the clustering-based portfolio achieved a cumulative return of 182.89% and an average return of 4.30%, while the BIST 100 Index recorded a cumulative return of 91.67% and an average return of 3.00%. These results demonstrate that combining the cluster-based portfolio construction approach with traditional optimization methods provides a novel approach to the literature and may enhance portfolio performance.

Keywords

• Clustering Analysis
• K-Means
• Sharpe Ratio
• Portfolio Optimization

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