Kümeleme Tabanlı Portföy Optimizasyonu: BIST100 Üzerine Ampirik Bir Analiz

Öz

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.

Anahtar Kelimeler

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

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

1. Arı, Emin S- Özköse, H.- Doğan, A. - Calp, M. H. (2016).“İstanbul Borsası’nda işlem gören firmaların finansal performanslarının kümeleme analizi ile değerlendirilmesi”. Bilişim Teknolojileri Dergisi, 9(1), 33-39.
2. Arı, G.- Sarıoğlu, S. E. (2021) “Fama french beş faktör varlık fiyatlama modelinin borsa İstanbul’da 2006–2018 dönemi için geçerliliğinin test edilmesi”. Sosyal Ekonomik Araştırmalar Dergisi, 21(2), 114-131.
3. Arthur, D.- Sergei, V. (2006). K-means++: The advantages of careful seeding. Stanford, 2006.
4. Asawa, Y. S. (2022). “Modern machine learning solutions for portfolio selection”. IEEE Engineering Management Review, 50(1), 94-112.
5. Black, F.- Litterman, R. ( 1992 ). “Global portfolio optimization”. Financial Analysts Journal, 48 (5), 28-43. Bnouachir, N.- Mkhadri, A. (2021). “Efficient cluster-based portfolio optimization”. Communications in Statistics-Simulation and Computation, 50(11), 3241-3255.
6. Chen, R. - Wang, S. - Zhu, Z. - Yu, J. - Dang, C. (2023). “Credit ratings of Chinese online loan platforms based on factor scores and K-means clustering algorithm”. Journal of Management Science and Engineering, 8(3), 287-304.
7. Cheong, D.- Kim, Young M. - Byun, Hyun W. - Oh, Kyong J. - Kim, Tae Y. (2017). Using genetic algorithm to support clustering-based portfolio optimization by investor information. Applied Soft Computing, 61, 593-602.
8. Çolak, Z. (2025). “Derin öğrenme modelleri ile hisse senedi fiyat tahmini: lstm, gru, rnn, mlp modellerinin karşılaştırmalı analizi”. Yönetim Bilimleri Dergisi, 23(56), 1250-1286.

9. Dai, Z. - Chang, X. (2021). Predicting stock return with economic constraint: can interquartile range truncate the outliers?. Mathematical Problems in Engineering, 2021(1), 1-12.
10. Durak, İ.- Çömlekçi, İ. (2021). “BIST100 endeksinde yer alan firmaların COVID-19 öncesi ve COVID-19 dönemi finansal verilerine göre sınıflandırılması: Bir hiyerarşik kümeleme analizi uygulaması”. Yaşar Üniversitesi E-Dergisi, 16(64), 1657-1681.
11. Dziuba, P.- Glukhova, D. - Shtogrin, K. (2022). “Risk, return and international portfolio diversification: k-means clustering data”. Baltic Journal of Economic Studies, 8(3), 53-64.
12. Esmalifalak, H.- Ajirlou, Ali I. - Behrouz, Sahar P. - Esmalifalak, M. (2015). (Dis) integration levels across global stock markets: A multidimensional scaling and cluster analysis. Expert Systems with Applications, 42(2015), 8393-8402.
13. Faheem, M. A.- Aslam, M. - Kakolu, S. (2022). “Artificial intelligence in investment portfolio optimization: a comparative study of machine learning algorithms”. International Journal of Science and Research Archive, 6(1), 335-342.
14. Gazel, S.- Akel, V. (2018). “Borsa İstanbul’da sektör sınıflandırmasının kümeleme analizi ile belirlenmesi”. Muhasebe ve Finansman Dergisi, 77, 147-164.
15. Gotardelo, D.- Goliatt, L. (2024). Multi-objective optimization of portfolio selection involving non-convex attributes in an anti-fragile perspective. Evolving Systems, 15(3), 703-715.
16. Gubu, La - Rosadi, D.- Abdurakhman, A. (2019, December). Classical portfolio selection with cluster analysis: Comparison between hierarchical complete linkage and ward algorithm. In Proceedings of International Conference on Mathematics and its Applications, Yogyakarta, Indonesia. https://doi.org/10.1063 /1.5139174.
17. Gunjan, A.- Bhattacharyya, S. (2023). “A brief review of portfolio optimization techniques”. Artificial Intelligence Review, 56(5), 3847-3886.
18. Han, J. - Pei, J - Tong, H. (2022). Data mining: concepts and techniques. Burlington, USA: Morgan kaufmann.
19. Han, J.- Ge, Z. (2020). Effect of dimensionality reduction on stock selection with cluster analysis in different market situations. Expert Systems with Applications, 147, 113226.
20. Ikotun, A. - Habyarimana, F.- Ezugwu, A. (2025). Benchmarking validity indices for evolutionary K-means clustering performance. Scientific Reports, 15(1), 21842.
21. Januzaj, Y.- Beqiri, E. - Luma, A. (2023). “Determining the optimal number of clusters using silhouette score as a data mining technique”. International Journal of Online & Biomedical Engineering, 19(4). 174-182.
22. Karaatlı, M.- Yıldız, E. (2021). “Mevduat bankaların finansal yapılarının kümeleme analizi ile incelenmesi”. Business & Management Studies: An International Journal, 9(1), 1-17.
23. Korzeniewski, J. (2018). Efficient stock portfolio construction by means of clustering. Acta Universitatis Lodziensis. Folia Oeconomica, 1(333), 85-92.
24. Lemieux, V.- Rahmdel, P. S.- Walker, R.- Wong, W.- Flood, M. (2014). Clustering techniques and their effect on portfolio formation and risk analysis”. In Proceedings of the International Workshop on Data Science for Macro-Modeling (1-6).
25. León, D.- Aragón, A. - Sandoval, J. - Hernández, G. - Arévalo, A. - Niño, J. (2017). Clustering algorithms for risk-adjusted portfolio construction. Procedia Computer Science, 108, 1334-1343.
26. Markowitz, Harry (1952). “Portfolio selection”. Journal Finance, 7 (1), 77–91.
27. Markowitz, H. (1959). Portfolio selection efficient diversification of investments. New Haven, CT, USA: Yale Univ. Press.
28. Massahi, M.- “Mahootchi, M.- Khamseh, A. A. (2020). Development of an efficient cluster-based portfolio optimization model under realistic market conditions”. Empirical Economics, 59(5), 2423-2442.
29. Michaud, R. O. (1989). “The Markowitz optimization enigma: Is ‘optimized’ optimal?. Financial Analysts Journal, 45 (1), 31–42.
30. Mohammed, M.- Khan, M.B., - Bashier, Eihab B. M. (2016). Machine learning: algorithms and applications. Crc Press.
31. Morteza, H.- Jameii, S. M. - Sohrabi, M. K. (2023). “An improved learning automata based multi-objective whale optimization approach for multi-objective portfolio optimization in financial markets”. Expert Systems with Applications, 224, 119970.
32. Nanda, S. R - Mahanty, B. - Tiwari, M. K. (2010). “Clustering Indian stock market data for portfolio management”. Expert Systems with Applications, 37(12), 8793-8798.
33. Ndikum, P.- Ndikum, S. (2024). “”Advancing ınvestment frontiers: Industry-grade deep reinforcement learning for portfolio optimization”. arXiv preprint arXiv:2403.07916. https://doi.org/10.48550/arXiv.2403.07916
34. Nourahmadi, M.- Sadeqi, H. (2023). “Portfolio diversification based on clustering analysis”. Iranian Journal of Accounting, Auditing and Finance, 7(3), 1-16.
35. Ogbuabor, G.- Ugwoke, F. N. (2018). “Clustering algorithm for a healthcare dataset using silhouette score value”. International Journal of Computer Science & Information Technology, 10(2), 27-37.
36. Özkan, M.- Boran, L. (2014). “Veri madenciliğinin finansal kararlarda kullanımı”. Çankırı Karatekin Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 4(1), 59-82.
37. Park, K. V. (2025). “Optimizing portfolio performance through clustering and sharpe ratio-based optimization: A comparative backtesting approach”, arXiv preprint arXiv:2501.12074, https://arxiv.org/abs/2501.12074
38. Rajabinasab, B. - Asghari, O. (2019). Geometallurgical domaining by cluster analysis: Iron ore deposit case study. Natural Resources Research, 28(3), 665-684.
39. Rodrigues, L.- Rodrigues, L. (2018). “Economic-financial performance of the Brazilian sugarcane energy industry: An empirical evaluation using financial ratio, cluster and discriminant analysis”. Biomass and bioenergy, 108, 289-296.
40. Rousseeuw, P. J. (1987). “Silhouettes: A graphical aid to the interpretation and validation of cluster analysis”. Journal of computational and applied mathematics, 20, 53-65.
41. Sancho, A. - Ribeiro, J. C. - Reis, M. S. - Martins, F. G. (2022). “Cluster analysis of crude oils with k-means based on their physicochemical properties”. Computers & Chemical Engineering, 157, 107633.
42. Sarker, Iqbal H. (2021). “Machine learning: Algorithms, real-world applications and research directions”. SN computer science, 2(3), 160.
43. Sass, J. - Thös, A. K. (2024). “Risk reduction and portfolio optimization using clustering methods”. Econometrics and Statistics, 32, 1-16.
44. Sharpe, W. F. (1963). “A simplified model for portfolio analysis”. Management Science, 9(2), 277–293.
45. Sharpe, W. F. (1966). “Mutual fund performance”. Journal of Business, 39(1), 119–138.
46. Shutaywi, M. - Kachouie, N. N. (2021). “Silhouette analysis for performance evaluation in machine learning with applications to clustering”. Entropy, 23, 759.
47. Steinley, D. - Brusco, M. J. (2008). A new variable weighting and selection procedure for k-means cluster analysis. Multivariate Behavioral Research, 43(1), 77–108.
48. Tekin, B. - Bastak, S. N. (2022).” Türkiye’de faaliyet gösteren bankaların kümeleme analizi ile karşılaştırmalı performans analizi”. Türk Sosyal Bilimler Araştırmaları Dergisi, 7(1), 55-76.
49. Tekin, B. - Temelli, F. (2021). “Firmaların kümeleme analizi ile finansal oranlar temelinde finansal başarılarının değerlendirilmesi: Borsa İstanbul örneği”. Journal of Emerging Economies and Policy, 6(1), 211-221.
50. Tekin, B. (2018). “Ward, k-ortalamalar ve iki adımlı kümeleme analizi yöntemleri ile finansal göstergeler temelinde hisse senedi tercihi”, Balıkesir Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 21(40), 401-436.
51. Tobin, J. (1958). “Liquidity preference as behavior towards risk”. Review Economic Studies, 25(2), 65–86.
52. Topaloğlu, F. (2024). “Saldırı tespit sistemlerinde k-means algoritması ve silhouette metriği ile optimum küme sayısının belirlenmesi”. Bilişim Teknolojileri Dergisi, 17(2), 71-79.
53. Zanjirdar, M. (2020). “Overview of portfolio optimization models”. Advances in Mathematical Finance and Applications, 5(4), 419-435. (www.kap.gov.tr, ( Erişim Tarihi: 02.05.2025) (www.investing.com.tr, (Erişim Tarihi: 15.05.2025) (www.finance.yahoo.com,)https://www.google.com/search?q=finance.yahoo.com%2C&oq=finance.yahoo.com%2C+&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIHCAEQABiABDIGCAIQABgeMgYIAxAAGB4yBggEEAAYHjIGCAUQABgeMgYIBhAAGB4yBggHEAAYHjIGCAgQABgeMgYICRAAGB7SAQkzNDc5ajBqMTWoAgiwAgHxBfB01MKkXzF3&sourceid=chrome&ie=UTF-8 (Erişim Tarihi: 16.05.2025)