Portfolio risks of bivariate financial returns using copula-VaR approach: A case study on Malaysia and U.S. stock markets

The recent financial turmoil which causes the financial markets to react in a non- linear way has led to a renewed interest in the modeling of portfolio dependence and risk. Risk can be measured by the traditional VaR measures such as normal VaR and historical simulation. However, it is challenging to estimate the portfolio VaR via parametric methods because of the complexity of modeling the joint mul- tivariate distribution of the assets in the portfolio. Copula model is an alternative method that is able to account for the joint multivariate distribution. The purpose of this study is to evaluate the risks of equally and mixed weighted portfolios of the SP500 and KLCI returns using the VaR based copula (copula-VaR) approach. Comparisons between the copula-VaR estimates with the traditional VaR measures were also conducted. This study reveals that the marginal distribution of the SP500 and KLCI return series can be modeled by the ARMA-GARCH models, while the dependence structure between both indices can be described by the Clayton copula. The backtesting results indicate that the copula-VaR provide better estimates of the portfolio risks compared to the normal VaR and historical simulation. Our study also found that the VaR models produce a more accurate risk estimates when a less volatile asset has a higher investment fraction in the portfolio