FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A bank's trading desk has a daily 99% VaR. Assume each trading day is independent and the probability of a VaR exception is 1% on any day. Over 250 trading days, what are the expected number of exceptions and the standard deviation of the number of exceptions, respectively?
The expected number is 2.5 exceptions with a standard deviation of about 1.57. For a binomial with n=250 and p=0.01, the mean is np = 2.5 and the variance is np(1-p) = 2.475, whose square root is approximately 1.57.
- A2.5 and 1.57Correct
- B2.5 and 2.48
- C1.0 and 1.57
- D2.5 and 6.19
Explanation
Exceptions are Binomial(250, 0.01). Mean = 250 × 0.01 = 2.5. Variance = 250 × 0.01 × 0.99 = 2.475, so standard deviation = 1.573. The 2.48 option reports the variance rather than the standard deviation.
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