Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfall

Marie Kratz, Yen Hsiao Lok, Alexander John McNeil

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Under the Fundamental Review of the Trading Book, capital charges are based on the coherent Expected Shortfall (ES) risk measure, which is sensitive to tail risk. We argue that backtesting of the forecasting models used to derive ES can be based on a multinomial test of Value-at-Risk (VaR) exceptions at several levels. Using simulation experiments with heavy-tailed distributions and GARCH volatility models, we design a statistical procedure to show that at least four VaR levels are required to obtain tests for misspecified trading book models that are more powerful than single-level (or even two-level) binomial exception tests. A traffic-light system for model approval is proposed and illustrated with three real-data examples spanning the 2008 financial crisis.
Original languageEnglish
Article numberJBF-D-16-01251R1
Pages (from-to)393-407
Number of pages15
JournalJournal of Banking and Finance
Early online date13 Jan 2018
Publication statusE-pub ahead of print - 13 Jan 2018

Bibliographical note

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.


  • Backtesting
  • Banking regulation
  • Expected shortfall
  • Financial risk management
  • Statistical test
  • Value-at-Risk

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