FRM Part II · FRM Exam Part II · Backtesting VaR
A bank backtests a 99% VaR model over 250 days and rejects it if there are 5 or more exceptions. The true exception probability is 1%, and the binomial probabilities of 0, 1, 2, 3 and 4 exceptions are approximately 8.1%, 20.5%, 25.7%, 21.5% and 13.4%. The probability of a Type I error is closest to:
The Type I error probability is the chance a correct model shows five or more exceptions. Cumulative probability for zero to four exceptions is about 89.2%, so the rejection probability is 100% minus 89.2%, which equals roughly 10.8%.
- A10.8%Correct
- B89.2%
- C13.4%
- D24.2%
Explanation
P(0 to 4) = 8.1 + 20.5 + 25.7 + 21.5 + 13.4 = 89.2%. Type I error is rejecting a correct model: P(5 or more) = 100 − 89.2 = 10.8%. 89.2% is the probability of correctly accepting.
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