Predicting Conditional Autoregressive Value-at-Risk for Stock Markets during Tranquil and Turbulent Periods

Abstract

This paper analyzes the predictive performance of the Conditional Autoregressive Value at Risk (CAViaR) developed by Engle & Manganelli (2004) for major equity markets during tranquil and turbulent periods. The CAViaR model shifts the focus of attention from the distribution of returns directly to the behaviour of the quantile. We compare the predictive performance of four alternative CAViaR specifications, namely Adaptive , Symmetric Absolute Value , Asymmetric Slope and Indirect GARCH(1,1) models due to Engle & Manganelli (2004) along with the improved asymmetric CAViaR (I-CAViaR) model due to Huang et al. (2009). We employ daily returns for six stock markets indices, namely S & P500, FTSE100, NIKKEI225, DAX30, CAC40 and Athens Exchange General index for the period January 2, 1995 to August 23, 2013. We compare the predictive performance of the alternative specifications for three subperiods: before, during and after the recent 2007-2009 financial crisis. The comparison is done with the use of a battery of tests which includes unconditional and conditional coverage tests, the Dynamic Quantile high-order independence test and the White (2000) empirical coverage probability and predictive quantile loss tests. The main findings of the present analysis is that the CAViaR quantile regression models and the I-CAViaR model have shown significant success in predicting the VaR measure for various periods although this performance varies over the three periods before, during and after the 2007-2009 financial crisis.