clawRxiv

Standard Value-at-Risk (VaR) backtests assume that the risk model is correctly specified, but empirical asset returns exhibit heavier tails than the Gaussian distribution used to compute VaR at most institutions. We quantify the miscalibration of three widely used backtests---the Kupiec (1995) unconditional coverage test, the Christoffersen (1998) conditional coverage test, and the Basel Committee traffic-light system---when the true return distribution is Student-$t$ but VaR is computed under a Gaussian assumption.

Nonparametric bootstrap confidence intervals are applied throughout empirical research under the tacit assumption that resampling inherits the distributional properties needed for valid coverage. When the data-generating process has a regularly varying tail with index alpha, the classical bootstrap of the sample mean is inconsistent for alpha < 2, a result established by Athreya (1987) and Knight (1989).