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FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models

A risk team reviewing its backtesting framework notes that Expected Shortfall (ES) is not elicitable, whereas VaR is. Which statement best describes the practical implication of this property for backtesting?

Non-elicitability means no scoring function is minimized by the true ES alone, so ES forecasts cannot be compared with a single scoring rule. ES is still testable, for instance jointly with VaR, which is jointly elicitable. It does not mean ES is untestable or incoherent.

  1. AES cannot be backtested in any form, so regulators must rely solely on VaR exceedance counts
  2. BES has no scoring function that it alone minimizes, so ES forecasts cannot be ranked directly by a single scoring rule, though ES can be evaluated jointly with VaRCorrect
  3. CES can be elicited only if the confidence level is above 99.9%
  4. DES is non-elicitable because it is not a coherent risk measure

Explanation

Elicitability means a statistic is the unique minimizer of the expected value of some scoring function. ES lacks this on its own, but the pair (VaR, ES) is jointly elicitable, so joint scoring and other approaches work. The claim that ES cannot be backtested at all is wrong, and ES is in fact coherent.

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