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

A risk analyst notes that Value-at-Risk (VaR) can be backtested directly by counting exceedances, but Expected Shortfall (ES) cannot be backtested the same way. In the literature on forecast evaluation, which property of VaR makes it directly comparable across competing models using a scoring function, while ES on its own lacks this property?

VaR is elicitable: a scoring function, the quantile loss, is minimized in expectation by the true quantile, so competing forecasts can be ranked. ES alone is not elicitable, so no such function exists for it by itself, though ES is elicitable jointly with VaR.

  1. AVaR is elicitable, meaning a scoring function exists whose expected value is minimized by the true VaR, whereas ES alone is not elicitableCorrect
  2. BVaR is coherent, whereas ES is not subadditive
  3. CVaR is always larger than ES at the same confidence level
  4. DVaR depends only on the mean of the return distribution, whereas ES depends on the variance

Explanation

A risk measure is elicitable if some scoring function is minimized in expectation by the true value. VaR (a quantile) is elicitable via the quantile (pinball) loss, but ES on its own is not. The coherence option is wrong because ES is subadditive and coherent, and VaR is the one that can fail subadditivity.

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