Robust stress testing

In recent years, stress testing has become an important component of financial and macro-prudential regulation. Despite the general consensus that such testing has been useful in many dimensions, the techniques of stress testing are still being honed and debated. This paper contributes to this debate in proposing the use of robust forecasting analysis to identify and construct adverse scenarios that are naturally interpretable as stress tests. These scenarios emerge from a particular pessimistic twist to a benchmark forecasting model, referred to as a ?worst case distribution?. This offers regulators a method of identifying vulnerabilities, even while acknowledging that their models are misspecified in possibly unknown ways. We first carry out our analysis in the familiar Linear-Quadratic framework of Hansen and Sargent (2008), based on an estimated VAR for the economy and linear regressions of bank performance on the state of the economy. We note, however, that the worst case so constructed features undesirable properties for our purpose in that it distorts moments that we would prefer were left undistorted. In response, we formulate a finite horizon robust forecasting problem in which the worst case distribution is required to respect certain moment conditions. In this framework, we are able to allow for rich nonlinearities in the benchmark process and more general loss functions than in the L-Q setup, thereby bringing our approach closer to applied use.