Dependence modeling and portfolio risk estimation using GARCH-copula approach

Abstract

Past studies have shown that linear correlation measure may result in misleading interpretations and implications of dependency when financial variables are involved. The copula approach can be adopted as an alternative for measuring dependence as it provides the solution to fat tail problems in multivariate cases which arises from the probability of large or extreme co-movements. Due to limited studies on copulas using Islamic financial data, this study set outs to obtain a clear picture on the dependence between Islamic and conventional stock markets in Malaysia. Firstly, we model the dependence between Islamic and conventional returns data using the copula-ARMA-GARCH models with normal and non-normal error distributions, and secondly, we evaluate the portfolios of Islamic and conventional indices using recent risk measures. This paper shows that, by using the copula approach for measuring the dependency between two financial variables while maintaining their true nature as described by the ARMA-GARCH models, meaningful interpretation can be made about the association of the financial variables which reflects the real association between markets. Furthermore, this study proposes a set of procedures on how portfolio risks can be estimated using VaR based on the ARMA(p,q)-GARCH(1,1)-t-copula models including backtesting via simulation.