Применение математических методов для повышения эффективности управления инвестиционным портфелем

HSE Economic Journal. 2017. Vol. 21. No. 3. P. 451–481.

Nazarova V., Левичев И. П.

In recent years, the role of stock markets as the source of capital to fund increased significantly. Using investment portfolio enables companies to achieve maximum efficiency in the stock market, thereby reducing the risk of their operations and increase their profitability. The article deals with the effective management of the investment portfolio , including various types of assets . Through an integrated approach, combining the selection of assets with the help of fuzzy clustering, the Markowitz classical model and rebalancing, this problem was reduced to the problem of maximizing the Sharpe ratio at a given level of risk . The main result of research is mathematical model, which provides a significant increase of effectiveness of portfolio management  compared to conventional approaches. This paper proposes a modified algorithm for rebalancing over time, which allows to combine all the advantages of active management with a reduction in transaction costs. The choice of control method was carried out taking into account the investment horizon.

A comprehensive model for evaluating the effectiveness of management of the investment portfolio, having as target the function of profit maximization, and as constraints - the level of risk, and the constancy of the weighting factors increase the Sharpe ratio.

The most promising is the creation on the basis of algorithms developed special software that can be used by both private investors and managers of investment funds.

Keywords: инвестиционный портфель, коэффициент Шарпа, additive fuzzy clustering, Investment portfolio rebalancing model Markowitz, Sharpe ratio, efficient frontier, ребалансировка, модель Марковица, эффективная граница, нечеткая кластеризация