FRM Part I · FRM Exam Part I · Sample Moments
A sample of n = 100 returns has a sample standard deviation of 4%. Assuming i.i.d. returns, by what factor must the sample size increase to cut the standard error of the sample mean to half its current level?
The sample size must increase by a factor of 4. The standard error equals s divided by the square root of n, so halving it requires doubling the square root of n, meaning n goes from 100 to 400.
- A2
- B4Correct
- C8
- D16
Explanation
Standard error = s/√n. Halving it requires √n to double, so n must quadruple, from 100 to 400. Check: 4/√100 = 0.4; 4/√400 = 0.2.
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