Estimation of Optimal Investment Portfolio Using Value at Risk (VaR) and Expected Shortfall (ES) Models: GARCH-EVT-Copula Approach

In this paper, an optimal investment portfolio including securities of four sectors: financial, chemical, pharmaceutical and automotive is estimated. Various types of Copula models are used to study the structure of asset co-dependency. Different types of GARCH models are used to explain volatility of asset returns, and Extreme Value theory is used to model the tails of the distribution. Also, expected shortfall model is used to calculate asset portfolio risk. The results of this research show that securities of chemical sector have the highest weight in optimal investment model. Also, in order to achieve higher returns (and of course, with higher risk tolerance), we can increase the weight of the pharmaceutical sector in the asset portfolio. The automotive sector does not have a significant weight in any of investment portfolios due to high level of fluctuations. The results of the Sharpe test also showed that two types of Copula models, Frank and Gumbel, were more effective in diversifying investment portfolios.