In light of the COVID 19 crisis, the Federal Reserve has carried out stress tests to assess if major banks have sufficient capital to ensure their viability should a new and perhaps unprecedented crisis emerge. The Fed argues that the scenarios underpinning these stress tests are severe but plausible, yet they have not offered any evidence or framework for measuring the plausibility of their scenarios. If the scenarios are indeed plausible, it makes sense for banks to retain enough capital to withstand their occurrence. If, however, the scenarios are not reasonably plausible, banks will have deployed capital less productively than they otherwise could have, thereby impairing credit expansion and economic growth. The authors apply a measure of statistical unusualness, called the Mahalanobis distance, to assess the plausibility of the Fed’s stress scenarios. A first pass of their analysis, based on conventional statistical assumptions, reveals that the Fed’s scenarios are not even remotely plausible. However, the authors offer two modifications to their initial analysis that increase the scenarios’ plausibility. First, they show how the Fed can minimally modify their scenarios to render them marginally plausible in a Gaussian world. And second, they show how to evaluate the plausibility of the Fed’s scenarios by replacing the theoretical world of normality with a distribution that is empirically grounded.