When working with portfolio optimization, we encounter problems with the proper way of representing the risk measure and choosing the suitable optimization method. These problems are even more prominent in times of economic recession, such as the global COVID pandemic, when the markets are extremely volatile. The aim of the thesis is to describe the main approaches to the modelling of the market risk using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models family. Day-to-da... show full abstractWhen working with portfolio optimization, we encounter problems with the proper way of representing the risk measure and choosing the suitable optimization method. These problems are even more prominent in times of economic recession, such as the global COVID pandemic, when the markets are extremely volatile. The aim of the thesis is to describe the main approaches to the modelling of the market risk using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models family. Day-to-day dynamic portfolio optimization approaches are subsequently utilized, and adaptations of Markowitz Model and Mean-ES model are compared. Adaptations of Markowitz model are based on replacing the diagonal of the covariance matrix of the considered assets with differently estimated various risk measures such as volatility, or Expected Shortfall (ES), estimated with GARCH and Exponential GARCH (EGARCH) models. Comparison of the individual approaches is based on their returns during the first half-year of the global COVID pandemic, for a suitably selected portfolio. The difference between approaches using Markowitz model showed to be only minor. Therefore it can not be deduced that one approach is better than the other, it can be only assumed that it is better to utilize ES, rather than volatility, as a risk measure during the economic recession. However, the best approach to portfolio optimization during the economic recession was seemed to be Mean-ES where there was an immense difference in return. |