Multivariate Dependence Risk and Portfolio Selection: An Application to International Stock Portfolio

Abstract

This study analyses the risk dependence of international stock portfolio based on three risk metrics, namely, the portfolio expected return, CVaR, and the Sharp ratio. The portfolio is optimised under both multivariate GARCH models (DCC and GO-CARCH) and the copula approaches (Student t copula-GARCH-GEV and the D-vine pair copula- GARCH-GEV). Empirical application is performed on daily returns from four stock indices including ALSI, DAX, SHANGAI and SP500 over the period 1998-2010. Our findings suggest that copula based portfolio optimisation is more efficient than the multivariate GARCH alternatives. More importantly, the optimal stock portfolios are better characterised through D-vine pair copula-GARCH-GEV model than through the multivariate Student’s t copula-GARCH-GEV model. Understandably, these findings substantiate the ability of copula models to capture complex dependence behaviour from joint and multivariate distributions.

Keywords: Portfolio Optimisation, risk dependence, international stock, pair copula

JEL Classification: G11, G15