FRM Part II · FRM Exam Part II · Backtesting VaR
A 99% one-day VaR model is tested over 250 days. If the model is correct, the exception count is approximately binomial with p = 1%. The expected number of exceptions and the standard deviation of the count are closest to:
The expected exceptions are 250 times 1%, or 2.5. The binomial variance is 250 × 0.01 × 0.99 = 2.475, giving a standard deviation of about 1.57, roughly 1.58. This spread governs how likely a correct model is to be wrongly rejected.
- A2.5 and 1.58Correct
- B2.5 and 2.50
- C1.0 and 1.00
- D2.5 and 0.99
Explanation
Mean = 250 × 0.01 = 2.5. Variance = 250 × 0.01 × 0.99 = 2.475, so SD = 1.573, about 1.58. Using 2.5 as SD confuses variance with standard deviation.
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