International diversification and dependence structure of equity portfolios during market crashes: the Archimedean copula approach

This paper analyzes the effect of the recent market crash on the international diversification of equity portfolios from the perspective of dependence structure. We use the generalized Pareto distribution to fit the left and the right tail of each return distribution in order to evaluate the upside and the downside risk measures separately after removing both autocorrelation and heteroscedasticity in the historical returns. We thereafter build a multivariate generalized Pareto distribution and draw one million simulated returns for each time series using three Archimedean copulas – Gumbel, Clayton and Frank. Using the data from emerging and developed countries; we find that the Clayton copula exhibits strong left tail dependence structure with higher Sharpe ratio and relatively weak right tail dependence after the subprime crisis. We also find that the Clayton copula is ultimately useful in modelling the left tail dependence structure in bear markets only. In addition; our empirical results show that both the Gumbel and Frank copulas produce the same magnitude of Sharpe ratio in bull and bear markets. The Frank copula is found to be useful in modelling returns with strong positive or negative dependence; while the Gumbel copula is found to be useful in modelling the upper tail of the return distribution in bull markets only.