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

A scoring function is described as 'strictly consistent' for the 99% quantile. What does this property guarantee?

Strict consistency means the expected score is uniquely minimized by reporting the true 99% quantile of the loss distribution. A forecaster cannot improve the expected score by shading the forecast up or down, so the score properly rewards accurate VaR.

  1. AThe expected score is minimized uniquely by reporting the true 99% quantile of the loss distributionCorrect
  2. BThe score is always zero when the model has no exceedances
  3. CThe score is minimized by reporting the largest possible VaR
  4. DThe score is independent of the realized losses

Explanation

Strict consistency means that, in expectation, the score is uniquely minimized when the forecaster reports the true quantile, so honest forecasting is optimal. Reporting very large values is penalized by the under-side weight, and the score clearly depends on realized losses.

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