FRM Part I · FRM Exam Part I · Sample Moments
A risk analyst records five daily returns (in percent): 2, 4, 6, 8, 10. Using the unbiased estimator, what is the sample variance of these returns (in percent squared)?
The unbiased sample variance is 10.0 percent squared. The mean is 6, the squared deviations sum to 40, and dividing by n-1 = 4 gives 10. Dividing by n would give 8, which is the biased maximum likelihood style estimate.
- A8.0
- B10.0Correct
- C6.0
- D12.5
Explanation
The mean is 6. Squared deviations are 16, 4, 0, 4, 16, which sum to 40. Dividing by n-1 = 4 gives 10.0. Dividing by n = 5 would give 8.0, which is the biased (population-style) estimate and is wrong here.
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