FRM Part I · FRM Exam Part I · Sample Moments
A risk analyst has five daily returns (in %): 1, 3, 5, 7, 9. She treats them as a sample from a larger return distribution. What is the unbiased sample variance (in %²)?
The unbiased sample variance is 10.0 (%²). The mean is 5, the sum of squared deviations is 40, and dividing by n-1 = 4 gives 10. Dividing by 5 would give 8.0, which understates variance when estimating from a sample.
- A8.0
- B10.0Correct
- C6.4
- D12.5
Explanation
Mean = 25/5 = 5. Squared deviations: 16+4+0+4+16 = 40. Dividing by n-1 = 4 gives 10.0. Dividing by n gives 8.0, which is the population-style (biased) estimator and is wrong for a sample.
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