Since 1998, U.S. commercial banks with significant trading activities have been required to hold capital against their defined market risk exposure. Under the "internal models" approach embodied in the current regulatory guidelines, the capital charges are a function of banks' own value-at-risk (VaR) estimates. VaR estimates are simply forecasts of the maximum portfolio loss that could occur over a given holding period with a specified confidence level. Clearly, the accuracy of these VaR estimates is of concern to both banks and their regulators. ; To date, two hypothesis-testing methods for evaluating VaR estimates have been proposed, namely, the binomial and the interval forecast methods. For these tests, the null hypothesis is that the VaR estimates in question exhibit a specified property that is characteristic of accurate VaR estimates. As shown in a simulation exercise, these tests generally have low power and are thus prone to misclassifying inaccurate VaR estimates as "acceptably accurate." ; An alternative evaluation method, based on regulatory loss functions, is proposed. Magnitude loss functions that assign quadratic numerical scores when observed portfolio losses exceed VaR estimates are shown to be particularly useful. Simulation results indicate that the loss function evaluation method is capable of distinguishing between VaR estimates generated by accurate and alternative VaR models. The additional information provided by this method as well as its flexibility with respect to the specification of the loss function make a reasonable case for its use in the regulatory evaluation of VaR estimates.
