| Abstract [eng] |
Risk estimation of equity portfolio is still very important issue nowadays. In order to complete risk evaluation, reliable portfolio has to be constructed, which reflects empirical characteristics. In this thesis ARMA(1,1)-GARCH(1,1) model with fat-tailed innovations was chosen for modelling portfolio returns. This decision was determined by following characteristics: serial dependence of returns, heavy-tailed returns, conditional heteroskedasticity. In order to get more robust model, problem of reduction of portfolio dimension had been solved. For this purpose principal component analysis was performed in order to identify factors with the highest variability. Identifying dependency structure between portfolio equities and modeling this structure is another important issue. According to the empirical evidence, which says that returns are asymmetrically dependent (dependency between the lower quantiles is higher than the upper), asymmetric Student‘s t-distribution was employed in order to model such dependence structure. After dependence structure was captured and each factor approximated with ARMA-GARCH, equity portfolio model was obtained, which reflected empirical characteristics. This approach allowed us to generate future scenarios. Further, estimation of portfolio weights, which maximized performance and risk ratios, had been performed. With different modeling assumptions, the best characteristics of the portfolio has been obtained by optimizing Sharpe and MAD measures. |
