Метод дихотомической кластеризации и оптимальный портфель

Abstract

The problem of optimal portfolio finding is considered in the paper. Many papers are devoted to the solving of this problem in various its formulations, that is why the problem is relevant. For the solving of the problem the methods of robust optimization and machine learning are used, namely, the splitting of the sample of the random asset returns into clusters and subsequent construction of an ellipsoid in each cluster. The method of maximal likelihood is used for dividing on two clusters, the method of dichotomous clustering is used for dividing on several clusters. The sample average and the sample covariance matrix are used for the constructing of the ellipsoid; the radius is calculated based on the assumption that the sample elements have a normal distribution. The example of calculating the optimal portfolio is given. It uses the real values of the return vectors. In this case part of the sample is used to calculate the sample means and the sample covariance matrices of the clusters, the rest part of the sample is used for verification of the portfolio. The tables show the dependence of the optimal portfolio return on the model parameter and on the number of clusters (ellipsoids). The comparing of results is considered; there are cases in which there is an increase in the income of the investor.