With Domenico Mignacca and Gianluca Fusai.

We propose a unified analytical framework for reverse stress testing aimed at identifying the most statistically plausible configuration of risk factors associated with a prespecified portfolio loss.

The approach compresses the portfolio into a lower-dimensional system while preserving the covariance structure between the risk factors and portfolio returns, and interprets the problem through the geometry of plausibility regions.

Under elliptical distributions, we show that the optimal stress scenario lies along the direction determined by the portfolio’s factor exposures, regardless of whether the loss constraint is based on the mean, Value-at-Risk, or Expected Shortfall. Consequently, the multidimensional optimization problem reduces to a one-dimensional search for the Mahalanobis radius associated with the optimal scenario. The corresponding dual formulation yields a stress-efficiency frontier linking the plausibility budget to the maximum attainable loss.The framework is applied to monthly data using Gaussian, Student-t, symmetric Normal Inverse Gaussian, and non-parametric kernel density models. The empirical results show that heavy-tailed specifications assign greater severity to extreme scenarios, while the non-parametric benchmark identifies departures from elliptical dependence through changes in the direction and magnitude of the optimal stress scenario.

The framework combines analytical tractability with the ability to capture relevant features of the observed data, providing a transparent way to identify plausible stress scenarios and assess the impact of model assumptions on risk estimates.