FRM Part II · FRM Exam Part II · Backtesting VaR
A bank backtests a 99% one-day VaR over 250 days. Assume exceptions are independent with probability 1% each. The bank has 5 exceptions and the risk committee argues it should be treated as a model failure. Which assessment is most consistent with the traffic light framework's logic?
Five exceptions places the bank in the yellow zone. A correct model would produce five or more exceptions roughly 10% of the time, so the evidence is suggestive but inconclusive, which is why the framework applies a graduated add-on rather than rejecting the model.
- AFive exceptions is yellow zone; it signals possible problems but the probability of a correct model producing 5 or more exceptions is not negligible, so the result is not conclusiveCorrect
- BFive exceptions is red zone because it exceeds the expected 2.5 by a factor of two
- CFive exceptions is green because the expected count is 2.5 and the allowed band is within two exceptions of it
- DFive exceptions proves the model is accurate because Type I error is eliminated by the zone design
Explanation
Five exceptions is the first yellow-zone count. Under a correct model the probability of 5 or more is roughly 10%, so the evidence is suggestive but not conclusive, which is why the framework uses graduated multipliers rather than outright rejection. Red requires 10 or more.
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