FRM Part I · FRM Exam Part I · Sample Moments
Returns are i.i.d. with unknown mean and a standard deviation of 8%. A risk manager wants the standard error of the sample mean to be no more than 1%. Assuming the sample mean is used as the BLUE estimator, what is the minimum number of observations required?
The minimum sample size is 64. The standard error of the sample mean is sigma divided by the square root of n, so 8% over the square root of n must be at most 1%, which requires the square root of n to be at least 8.
- A64Correct
- B8
- C16
- D32
Explanation
Standard error = sigma/sqrt(n) = 8/sqrt(n) <= 1, so sqrt(n) >= 8 and n >= 64. Choosing 8 mistakes sqrt(n) for n. Choosing 16 or 32 comes from arbitrary halving or misapplied scaling.
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