Application of GARCH-Copula Model in Portfolio Optimization

Abstract

Although the cornerstone of modern portfolio theory was set by Markowitz in 1952, the portfolio optimization problem is a never-ending research topic for both academics and practitioners. In this problem the future prediction of time series evolution plays an important role. However, it is rarely addressed in research. In the paper we analyze the applicability of the GARCH-copula model. To be more concrete we assume the investor maximizing Sharpe ratio while the future evolution of the time series is simulated by means of the AR(1)-GARCH(1,1) model using the copula modelling approach. The bootstrapping technique is applied as a benchmark. From the empirical results we found out that the GARCH-copula model provides better forecasts of future financial time series evolution than the bootstrapping method. Assuming the investor is maximizing the Sharpe ratio, both the final wealth increases and maximum drawdown decreases when we apply the GARCH-copula model compared to the application of bootstrapping technique.