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Empirical implementation of a quantitative reverse stress test for defaultable fixed-income instruments with macroeconomic factors and principal components

This paper provides a quantitative reverse stress test approach that takes macroeconomic risk factors into account. We use principal component analysis to describe the movements of the term structure of risk-free interest rates, which, in combination with a latent systematic risk factor and an economic indicator, serve as risk factors that drive the obligors’ asset returns. The sensitivities of the asset returns towards these risk factors are estimated empirically and the univariate and multivariate distribution of the risk factors is analyzed. The proposed reverse stress test evaluates the whole risk factor space and finds those scenarios that exactly lead to a presumed loss. In the last step the most plausible of these scenarios is determined and discussed. The results show that the found reverse stress test scenarios are particularly reasonable for the assumed bank portfolio. However, the results also show that reverse stress tests are exposed to considerable model and estimation risk which makes numerous robustness checks necessary.