FRM Part I · FRM Exam Part I · Sample Moments
A risk manager estimates the mean of daily returns using n i.i.d. observations with standard deviation 1.5%. She wants the standard error of the sample mean to be no more than 0.15%. What is the minimum sample size required?
The minimum sample size is 100. The standard error is 1.5% divided by the square root of n, and setting this at 0.15% gives a square root of n equal to 10, so n must be at least 100. Failing to square the ratio gives 10.
- A10
- B25
- C100Correct
- D10,000
Explanation
Need 1.5/sqrt(n) <= 0.15, so sqrt(n) >= 10 and n >= 100. Choosing 10 forgets to square the ratio. Choosing 10,000 squares the wrong ratio (using 100 instead of 10).
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