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

A bank's VaR model passes a standard 99% exceedance-count test over 250 days, with 2 exceedances. A PIT backtest of the same model, however, rejects uniformity because the PIT histogram shows a pronounced excess of values between 0.01 and 0.05 relative to 0.04 expected frequency, and the middle is normal. Which conclusion is best supported?

The PIT test uses the whole forecast distribution, so it can reveal misspecification between the 95% and 99% levels that a 99% exceedance count misses. The excess mass in the 1%-5% band shows losses in that region are underestimated, even though the 99% VaR looks adequate.

  1. AThe model understates losses beyond the 95% level but within the 99% quantile, a weakness the 99% exceedance count cannot detectCorrect
  2. BThe exceedance test is wrong and the model must understate the 99% VaR
  3. CThe PIT test is invalid because it uses the whole distribution rather than one quantile
  4. DThe model overstates risk at all quantiles because few exceedances occurred

Explanation

Exceedance tests only look at the single 99% quantile, so losses in the 1%-5% tail region are invisible to them. Excess PIT mass between 0.01 and 0.05 means losses in that band occur more often than forecast, so the lower tail is understated short of the 99% VaR. Few exceedances at 99% do not imply a correct tail elsewhere.

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