FRM Part I · FRM Exam Part I · Sample Moments
A sample of 100 i.i.d. monthly returns has a sample standard deviation of 4%. Holding the standard deviation fixed, how many observations are needed in total to halve the standard error of the sample mean?
400 observations are needed. The standard error falls with the square root of n, so halving it requires quadrupling the sample from 100 to 400. Doubling to 200 would only reduce it by about 29%, giving a standard error near 0.283%.
- A200
- B400Correct
- C300
- D141
Explanation
Standard error = s/sqrt(n) = 4/10 = 0.4%. To halve to 0.2%, sqrt(n) = 20, so n = 400. Doubling n to 200 only reduces the standard error by a factor of about 1.414, which is the common mistake.
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