FRM Part I · FRM Exam Part I · Hypothesis Testing
A risk analyst computes the mean of 64 independent daily returns on a portfolio and obtains a sample mean of 0.30% with a sample standard deviation of 1.60%. What is the standard error of the sample mean?
The standard error of the mean is the sample standard deviation divided by the square root of the sample size: 1.60% divided by 8 equals 0.20%. The 1.60% figure describes dispersion of individual returns, not the uncertainty of the average.
- A0.025%
- B0.200%Correct
- C0.250%
- D1.600%
Explanation
Standard error = s / sqrt(n) = 1.60% / sqrt(64) = 1.60% / 8 = 0.20%. Choosing 0.025% comes from dividing by n (64) after a further scaling error, and 0.25% divides 1.60 by 6.4 (wrong root). 1.60% is the standard deviation of returns, not of the mean.
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