Construction of a Sparse Covariance Matrix Based on Statistical Data Analysis and Its Use in Choosing an Optimal Portfolio of Securities

Purpose of the study. The aim of the study is to develop a new method for finding an optimal portfolio of securities based on suboptimization using a sparse covariance matrix, and to create a program based on it to automate the procedure for selecting an investment strategy.

Materials and methods. The paper presents one of the possible formalizations of a two-criterion investment problem – setting the problem for the maximum expected portfolio yield with an upper limit on the standard deviation. At the same time, the calculation of the standard deviation of a portfolio with a sparse matrix of covariances of financial instruments’ yields is justified. A solution to a two-criterion problem based on the use of the Karush-Kuhn-Tucker optimality conditions is given. All necessary primary calculations and studies are performed in Microsoft Excel; the functions of the Python programming language are used for automation and implementation of the graphical interface.

Results. The analysis of the methods used to make investment decisions was carried out and the use of each of them for specific stock market data was justified. To automate analytical approaches to finding the optimal investment strategy with full, partial and absent correlation dependence, a program and a graphical interface were created using the Python programming language libraries. The software product was tested on the example of the investment process with real data of the Russian stock market. The initial data in this study were quotes of shares of Russian companies for the period from 01.01.2019 to 31.12.2021, taken from the Yahoo Finance website. The choice of each of the shares was based on the results of the fundamental and technical analysis.

Conclusion. As a result of the conducted research, it was established that the proposed method of finding the optimal strategy using a sparse covariance matrix is a suitable tool for an active investment strategy. The technical implementation of the proposed method - the use of the Python programming language to create a graphical interface – allows automating the process of constructing an investment strategy.

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