CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
An analyst bootstraps the mean of a sample of returns using 5 resamples and obtains means of 2.0%, 3.0%, 4.0%, 5.0% and 6.0%. Using these resampled means, the bootstrap estimate of the standard error of the sample mean (using n-1 in the divisor) is closest to:
The bootstrap standard error is about 1.58%. The resampled means average 4.0%, the squared deviations sum to 10, dividing by 4 gives 2.5, and the square root is 1.58%. Dividing by 5 instead would wrongly give 1.41%.
- A1.41%
- B1.58%Correct
- C2.00%
Explanation
The mean of the resampled means is 4.0%. Squared deviations are 4, 1, 0, 1, 4, summing to 10. Dividing by 4 gives 2.5, and the square root is 1.58%. The 1.41% figure divides by n (5) instead of n-1, and 2.00% is the variance 10/5.
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