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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A portfolio manager models the number of days in a 250-day year on which a desk's loss exceeds its 99% one-day VaR as a binomial variable, assuming the VaR model is correct and exceptions are independent. What are the expected number and the standard deviation of exceptions?

The mean is 2.5 exceptions and the standard deviation is about 1.57. The mean is 250 x 0.01, and the variance is 250 x 0.01 x 0.99 = 2.475, whose square root is roughly 1.57.

  1. AMean 2.5; standard deviation 1.57Correct
  2. BMean 2.5; standard deviation 2.48
  3. CMean 25; standard deviation 4.97
  4. DMean 2.5; standard deviation 6.25

Explanation

n = 250, p = 0.01. Mean = np = 2.5. Variance = np(1-p) = 250 x 0.01 x 0.99 = 2.475; standard deviation = 1.573. The 2.48 option reports the variance rather than the standard deviation.

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