FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models
A risk team backtests daily 99% VaR forecasts from two models over 250 days. Both models record exactly 2 exceedances, so a simple exceedance count cannot separate them. Which feature of a quantile (pinball) scoring function allows it to rank the two models anyway?
The quantile scoring function uses the size of the deviation between the realized loss and the VaR forecast, with asymmetric weights tied to the confidence level. Models with equal exceedance counts can thus receive different scores, whereas a pure exceedance count ignores magnitudes and cannot discriminate between them.
- AIt penalizes each day according to the size of the gap between the realized loss and the VaR forecast, with asymmetric weightsCorrect
- BIt counts only the number of days on which the loss exceeds VaR and ignores magnitudes
- CIt rewards models that produce the highest VaR forecasts regardless of realized losses
- DIt tests whether exceedances are independent over consecutive days
Explanation
The quantile scoring function assigns a loss that depends on the distance between the realized outcome and the forecast quantile, weighting the two sides asymmetrically (by alpha and 1-alpha). Two models with equal exceedance counts will therefore usually differ in score. Counting exceedances ignores magnitudes, and independence testing is a different exercise.
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