FRM Part I · FRM Exam Part I · Sample Moments
Returns on a portfolio are assumed i.i.d. with a population standard deviation of 6% per year. An analyst estimates the mean using 36 annual observations. What is the standard error of the sample mean?
The standard error is 1.00%. For i.i.d. data, the standard deviation of the sample mean equals the population standard deviation divided by the square root of the sample size: 6% divided by the square root of 36, which is 6, gives 1%.
- A0.17%
- B1.00%Correct
- C6.00%
- D1.50%
Explanation
Standard error = sigma / sqrt(n) = 6% / sqrt(36) = 6% / 6 = 1.00%. Using 6%/36 gives 0.17%, which wrongly divides by n rather than the square root of n.
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