FRM Part I · FRM Exam Part I · Sample Moments
An analyst records five monthly returns for a fund: 2%, 4%, 6%, 8% and 10%. What is the sample standard deviation of these returns (using the unbiased estimator)?
The sample standard deviation is 3.16%. The mean is 6%, the sum of squared deviations is 40, and dividing by n-1 = 4 gives a variance of 10, whose square root is 3.16%. Dividing by n would understate dispersion and give 2.83%.
- A2.83%
- B3.16%Correct
- C2.00%
- D10.00%
Explanation
Mean = 6%. Squared deviations: 16, 4, 0, 4, 16 = 40. Unbiased sample variance = 40/(5-1) = 10, so standard deviation = sqrt(10) = 3.16%. Dividing by n gives variance 8 and 2.83%, which is the biased estimator and is wrong here.
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