FRM Part I · FRM Exam Part I · The Building Blocks of Risk Management
A bank has 1,000 identical, independent loans, each of 1 million USD with a one-year default probability of 2% and zero recovery. The bank wants to estimate the standard deviation of the portfolio's number of defaults. What is it, rounded to two decimals?
The standard deviation is about 4.43 defaults. Defaults follow a binomial distribution, so variance is n×p×(1−p) = 1,000×0.02×0.98 = 19.6, and its square root is 4.43. The value 19.60 is the variance, not the standard deviation.
- A0.44
- B4.43Correct
- C19.60
- D20.00
Explanation
Number of defaults is binomial with n=1,000 and p=0.02. Variance = 1,000 × 0.02 × 0.98 = 19.6, so standard deviation = sqrt(19.6) = 4.43. The 19.60 option is the variance, and 20 is the expected number of defaults.
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