  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.
