Measuring Portfolio Value at Risk

Abstract: On estimating portfolio Value at Risk, the application of traditional univariate VaR models is limited. Under specific circumstance, the VaR estimation could be inadequate. Facing the financial crises and increasing uncertainty in financial markets, effective multivariate VaR models have become crucial. This paper gives an overview of various multivariate VaR models. The main aim is to compare the one day out-of-sample predictive performances of different models, including basic multivariate VaR models, volatility weighted multivariate VaR models and copula-based multivariate VaR models. Performance is evaluated in terms of Christoffersen test, quadratic probability score and root mean squared error. The findings show that basic multivariate VaR models such as multivariate normal VaR model and multivariate t VaR model behave poorly and fail to generate reliable VaR estimations. By contrast, volatility weighted multivariate VaR models and copula-based multivariate VaR models show notable improvements in the predictive performance.