Portfolio Optimization Problem with Multivariate Heavy-tailed and Asymmetric Distribution of Financial Assets Return (an Example from the Russian Stock Market)

Over the years, models based on normal distribution assumptions were considered appropriate for portfolio choice purposes. However, the financial crisis of 2008 showed that such models are over-simplified, which leads to huge losses for many investors. The main purpose of this study is to identify whether using more complex models considering non-Gaussian features are justified in terms of getting more profit than models based on the ”normality” assumptions under the conditions of the Russian stock market. We provide empirical evidence that univariate return distributions of stocks (components of our portfolio) demonstrates a wide range of ”non-normal” features: heavy tails, conditional heteroskedasticity, volatility clustering. It is important to mention that the dependence structure between assets is non-linear: there are pairs of stocks that exhibit tail dependence. For portfolio construction purposes we evaluate multivariate ARMAX-GARCHX-EVT-Vine-Copula models to deal with all mentioned above properties. We compare the out-of-sample performance of two modeled portfolios based on maximized Sharpe and Sortino ratios with a benchmark based on the normal distribution. We find that the modeled portfolios capture non-Gaussian features of distributions and generate more profit due to better risk hedging, and also they outperform the average market.