Quantitative Risk Assessment Methods for Optimal Portfolios: Examination of the Russian Stock Market

This paper assesses the effectiveness of various methods for evaluating optimal portfolios Value at Risk on the Russian stock market. In particular, the paper provides an overview of existing methods of portfolio optimization, as well as recommendations for their use. The research part of the work consists of two parts. The first part is devoted to portfolio optimization of first-tier shares on the Moscow Exchange. Stock weights are obtained by maximizing the Sharpe ratio, relative to the yield of the IMOEX index. As the object of optimization, we take the returns of stocks and indices predicted by the ARMA model. The order of the ARMA model is obtained by minimizing the AIC criterion. This operation was repeated for 5 years (2015-2020). As a result, it was found that the methodology proposed in this study works more effectively than the market investing if there is no increase in market volatility. The second part of the study is devoted to finding the most effective way to evaluate Value at Risk. The study showed that the Delta-normal method, using the volatility predicted by the GARCH model with a minimum AIC criterion, is the most preferred method for calculating the Value at Risk.