Decomposition of portfolio VaR and expected shortfall based on multivariate Copula simulation

Portfolio risk-adjusted performance measurement involves the calculation of the risk contribution for each asset it contains. This paper uses multivariate Copula functions to model the dependence structure among the assets in a portfolio, then, based on a simulation, decomposes the portfolio VaR and Expected Shortfall. The research shows this simulation approach provides a way to test if the risk contributions of various assets are significantly different, and also displays results insusceptible to confidence level and risk measures. Furthermore, with this approach, the risk contribution calculated using Expected Shortfall is more robust, and its estimation error can be reduced by increasing the simulation sample size. For the equally-weighted portfolios of five Shanghai industrial stock indices, empirical evidence shows that the Real Estate Index has the largest risk contribution of the whole portfolio.