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

A validation analyst wants to backtest ES and VaR forecasts together using a single strictly consistent scoring function. Which feature of the (VaR, ES) pair makes this possible?

The pair of VaR and ES is jointly elicitable, meaning a scoring function exists whose expected value is minimized by the true VaR and ES together. This permits comparing joint forecasts, even though ES alone has no such scoring function.

  1. AThe pair is jointly elicitable, so a scoring function exists that the true VaR and ES pair minimizes in expectationCorrect
  2. BES is elicitable on its own when VaR is assumed normally distributed
  3. CVaR is not elicitable but ES is, so scoring uses ES only
  4. DThe pair is elicitable only if the exceedance count equals the expected count

Explanation

Fissler and Ziegel showed that VaR and ES together are jointly elicitable, allowing consistent joint scoring functions. Option B and C misstate elicitability, since VaR is elicitable and ES alone is not. Exceedance counts are unrelated to elicitability.

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