For a given set of banks, how big can losses in bad economic or financial scenarios possibly get, and what are these bad scenarios? These are the two central questions of stress tests for banks and the banking system. Current stress tests select stress scenarios in a way which might leave aside many dangerous scenarios and thus create an illusion of safety; and which might consider highly implausible scenarios and thus trigger a false alarm. We show how to select scenarios systematically for a banking system in a context of multiple credit exposures. We demonstrate the application of our method in an example on the Spanish and Italian residential real estate exposures of European banks. Compared to the EBA 2016 stress test our method produces scenarios which are equally plausible as the EBA stress scenario but yield considerably worse system wide losses.

We present a new framework combining current methods of bank solvency stress tests with a model of fire sales. We apply the framework to the stress tests conducted by the European Banking Authority. Fire sales are described by an equilibrium model balancing leverage improvements and drops in security prices. Additional bank losses caused by fire sales are significant and go beyond the trivial fact that with fire sales we will get bigger losses. Ignoring potential fire sales effects may lead to a false sense of resilience by assuming that institutions, which are in fact fragile, are resilient.

Stress tests with handpicked scenarios might misrepresent risks either because dangerous scenarios are not considered or because the scenarios considered are too implausible. To overcome these two pitfalls we propose a systematic search for the worst case within a relative entropy ball of sufficiently plausible scenarios. For this purpose we use mixed scenarios, which are risk factor distributions rather than realisations. A Maximum Loss theorem explicitly gives the worst case distribution. The method is illustrated in a number of example applications: linear and quadratic portfolios, stressed default probabilities, stressed correlations, macroeconomic stress tests.

We propose a new method for analysing multi-period stress scenarios for portfolio credit risk more systematically than in current macro stress tests. The plausibility of a scenario is quantified by its distance from an average scenario. For a given level of plausibility, we search systematically for the most adverse scenario. This ensures that no plausible scenario will be missed. We show how this method can be applied to some models already in use by practitioners. While worst case search requires numerical optimisation we show that we can work with reasonably good linear approximations to the portfolio loss function. This makes systematic multi-period stress testing computationally efficient and easy to implement. Applying our approach to data from the Spanish loan register we show that, compared to standard stress test procedures, our method identifies more harmful scenarios that are equally plausible.

There is a tradition in the banking industry of dividing risk into market risk and credit risk. Both categories are treated independently in the calculation of risk capital. But many financial positions depend simultaneously on both market risk and credit risk factors. In this case, an approximation of the portfolio value function separating value changes into a pure market risk plus pure credit risk component can result not only in an overestimation, but also in an underestimation of risk. We discuss this compounding effect in the context of foreign currency loans and argue that a separate calculation of economic capital for market risk and for credit risk may significantly underestimate true risk.