Risk of Portfolio with Simulated Returns Based on Copula Model

The commonly used tool for measuring risk of a portfolio with equally weighted stocks is variance-covariance method. Under extreme circumstances, this method leads to significant underestimation of actual risk due to its multivariate normality assumption of the joint distribution of stocks. The purpose of this research is to compare the actual risk of portfolio with the simulated risk of portfolio in which the joint distribution of two return series is predetermined. The data used is daily stock prices from the ASEAN market for the period January 2000 to December 2012. The copula approach is applied to capture the time varying dependence among the return series. The results shows that the chosen copula families are not suitable to present the dependence structures of each bivariate returns. Exception for the Philippines-Thailand pair where by t copula distribution appears to be the appropriate choice to depict its dependence. Assuming that the t copula distribution is the joint distribution of each paired series, simulated returns is generated and value-at-risk (VaR) is then applied to evaluate the risk of each portfolio consisting of two simulated return series. The VaR estimates was found to be symmetrical due to the simulation of returns via elliptical copula-GARCH approach. By comparison, it is found that the actual risks are underestimated for all pairs of portfolios except for Philippines-Thailand. This study was able to show that disregard of the non-normal dependence structure of two series will result underestimation of actual risk of the portfolio.