Monitoring Value-at-Risk and Expected Shortfall Forecasts

This paper introduces formal monitoring procedures as a risk-management tool. Continuously monitoring risk forecasts allows practitioners to swiftly review and update their forecasting procedures as soon as forecasts turn inadequate. Similarly, regulators may take timely action in case reported risk forecasts become poor. Extant (one-shot) backtests require, however, that all data are available prior to testing and are not informative of when inadequacies might have occurred. To monitor value-at-risk and expected shortfall forecasts “online”—that is, as new observations become available—we construct sequential testing procedures. We derive the exact finite-sample distributions of the proposed procedures and discuss the suitability of asymptotic approximations. Simulations demonstrate good behavior of our exact procedures in finite samples. An empirical application to major stock indices during the COVID-19 pandemic illustrates the economic benefits of our monitoring approach. This paper was accepted by Agostino Capponi, finance. Funding: Y. Hoga gratefully acknowledges support of the German Research Foundation [Grant HO 6305/1-1]. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2022.4460 .