Применение методов кластеризации для формирования оптимального инвестиционного портфеля на российском фондовом рынке

Финансовый журнал. 2026. Т. 18. № 4. С. 45–63.

Lysenok N., Маркова Ю. Е.

The article discusses the application of clustering methods to form an optimal investment portfolio
that allows the investor to achieve an effective risk-reward ratio. Three popular clustering methods,
K-Means, MeanShift, and DBSCAN, are examined. The article focuses on the DBSCAN clustering method
and highlights its advantages over other clustering methods in the context of financial data analysis.
DBSCAN is particularly useful for identifying clusters of arbitrary shapes, being resistant to noise
and eliminating the need to pre-define the number of clusters. The article presents a comprehensive
approach to forming an optimal portfolio. The first step involves preparing the data and clustering it
based on historical data on returns, volatility, and correlations using a programming language. The
second stage involves further ranking by assigning integral scores that take into account a variety of
criteria and allow for the identification of the stocks most attractive for investment within each selected
cluster. After completing these stages, an optimal portfolio is formed with the highest Sharpe ratio,
Sortino ratio, and other metrics that outperform the weighted average portfolio and the MOEX index.
To validate the results, Monte Carlo simulations are used to assess the portfolio’s resilience in various
market scenarios, including periods of volatility and crises. The study fills a gap in the study of the
application of clustering methods for optimizing an investment portfolio, proposing a practical algorithm
that can be adapted for individual and institutional investors. The findings highlight the potential of
applying clustering methods to form an optimal investment portfolio.

Keywords: фондовый рынок, метод Монте-Карло, коэффициент Шарпа, stock market, Sharpe ratio, clustering methods, методы кластеризации, optimal investment portfolios, The Monte Carlo method, оптимальный инвестиционный портфель