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

A bank backtests its 97.5% one-day ES model using a joint approach in which ES is treated as elicitable together with VaR. Which description of this result is most accurate?

The pair of VaR and ES at the same confidence level is jointly elicitable, so a single scoring function can evaluate both forecasts together. This allows comparative backtesting of ES through its link with VaR, without needing a normal distribution or a special confidence level.

  1. AThe pair (VaR, ES) is jointly elicitable, so a scoring function can evaluate both forecasts togetherCorrect
  2. BES becomes elicitable once the confidence level is raised above 99%
  3. CJoint elicitability applies only to VaR forecasts at two different confidence levels
  4. DThe pair is jointly elicitable only if losses are independent and identically normal

Explanation

Research shows that although ES alone is not elicitable, the pair (VaR, ES) at the same level is jointly elicitable. This gives a scoring function that can compare the two forecasts together. It does not depend on a particular confidence level or on normality.

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