Back-Testing of Expected Shortfall: Main Challenges and Methodologies

Abstract

In a context of an ever-changing regulatory environment over the last years, Banks have witnessed the draft and publication of several regulatory guidelines and requirements in order to frame and structure their internal Risk Management. Among these guidelines, one has been specifically designed for the risk measurement of market activities. In January 2016, the Basel Committee on Banking Supervision (BCBS) published the Fundamental Review of the Trading Book (FRTB). Amid the multiple evolutions discussed in this paper, the BCBS presents the technical context in which the potential loss estimation has changed from a Value-at-Risk (VaR) computation to an Expected Shortfall (ES) evaluation. The many advantages of an ES measure are not to be demonstrated, however this measure is also known for its major drawback: its difficulty to be back-tested. Therefore, after recalling the context around the VaR and ES models, this white paper will review ES back-testing findings and insights along many methodologies; these have either been drawn from the latest publications or have been developed by the Global Research & Analytics (GRA) team of Chappuis Halder & Co. As a conclusion, it has been observed that the existing methods rely on strong assumptions and that they may lead to inconsistent results. The developed methodologies proposed in this paper also show that even though the ES97.5% metric is close to a VaR99,9% metric, it is not as easily back-tested as a VaR metric; this is mostly due to the non-elicitability of the ES measure.