FRM Part II · FRM Exam Part II · Backtesting VaR
A bank's 99% one-day VaR model is backtested over 250 trading days and produces 1 exception. The head of risk argues that this proves the model is excellent. Which response is most appropriate from a backtesting perspective?
The expected number of exceptions is 2.5 (250 x 1%). One exception is below that, and persistently too few exceptions suggest VaR is overly conservative, which is also a model flaw. Backtesting seeks accuracy in both directions, so fewer exceptions is not automatically better.
- AAgree, because fewer exceptions than expected always indicates a more accurate model
- BDisagree, because only more exceptions than expected can indicate a problem
- CDisagree, because the expected number is about 2.5 and a persistently low count may indicate overly conservative VaR, which is also a misspecificationCorrect
- DAgree, because backtesting only tests for underestimation of risk
Explanation
Expected exceptions are 250 x 1% = 2.5. One exception is below this, and in a two-sided test a persistently low count suggests VaR is too high, implying inefficient capital use. Backtesting aims at accuracy, not just avoiding underestimation. One observation alone is not conclusive, but the claim that fewer is always better is wrong.
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