FORMATION AND OPTIMIZATION OF VARIOUS PORTFOLIOS MODELS ON THE VaR INDICATOR BASIS

Abstract

This article describes a formation of various portfolios models based on H. Markovitz portfolio theory. The portfolios which can include instruments with fixed profitability and common stock are considered. As a risk measure VaR indicator is used. In the research historical data on the stock prices included in the Dow30 market index were used. The profitability of all shares was analyzed in the period from 01.09.2015 to 01.09.2016 on one day basis. Companies included in the surveyed portfolios were selected using factor analysis method. They are considered as a portfolio consisting of a uniform distribution of shares and optimization portfolios. In these optimization models maximization of portfolio efficiency at the set risk level and risk minimization at the set level of efficiency can act as criterion functions. In some optimization tasks efficiencies of risky assets are calculated considering market changes. For portfolios of different profitability, the optimal curves "Profitability-Risk" are constructed. Comparison of the results is providing. Portfolios consisting of shares of various companies are explored. Depending on the investor's attitude to risk, appropriate portfolios can be chosen. Numerical results of effective assets distribution within the portfolio for various optimization problems statements are shown.

Keywords

• portfolio
• risk
• VaR
• asset
• optimization.