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

A risk manager compares two competing 99% VaR models using a quantile (pinball) scoring function applied to realised losses over a long sample. Model A has a lower average score than Model B. Assuming lower scores are better, what is the most appropriate conclusion?

Model A is better. VaR is elicitable, so the quantile scoring function is consistent for it, and a lower average score means better VaR forecasts in expectation. Higher scores indicate worse forecasts, and ranking does not require zero exceedances.

  1. AModel A provides better VaR forecasts in terms of that scoring functionCorrect
  2. BModel B is better because the higher score shows greater conservatism
  3. CNeither can be ranked, because VaR is not elicitable
  4. DThe scores can rank models only if both have zero exceedances

Explanation

Because VaR is elicitable, the quantile scoring function is consistent, so a lower average score indicates a better forecast in expectation. Higher scores are worse, not more conservative in a favourable sense. Zero exceedances are not required.

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