Value-at-Risk: The Effect of Autoregression in a Quantile Process

Value-at-Risk (VaR) is an institutional measure of risk favored by financial regulators. VaR may be interpreted as a quantile of future portfolio values conditional on the information available, where the most common quantile used is 95%. Here we demonstrate Conditional Autoregressive Value at Risk, first introduced by Engle, Manganelli (2001). CAViaR suggests that negative/positive returns are not i.i.d., and that there is significant autocorrelation. The model is tested using data from 1986- 1999 and 1999-2009 for GM, IBM, XOM, SPX, and then validated via the dynamic quantile test. Results suggest that the tails (upper/lower quantile) of a distribution of returns behave differently than the core.