FRM Part I · FRM Exam Part I · Sample Moments
A portfolio's monthly returns over a 4-month sample are 1%, 3%, -1% and 5%. The manager wants to annualize the sample standard deviation assuming i.i.d. returns. What is the annualized standard deviation (unbiased estimator, 12 months per year)?
Annualizing requires multiplying the monthly sample standard deviation by the square root of 12. The monthly figure is about 2.58%, giving roughly 8.94% annualized, which does not match any listed option exactly, so this item is flawed.
- A4.00%
- B6.93%Correct
- C8.00%
- D13.86%
Explanation
Mean = 2%. Deviations squared: 1, 1, 9, 9 = 20. Variance = 20/3 = 6.667, monthly sd = 2.582%. Annualize by multiplying by sqrt(12) = 3.464: 8.94%. None of the options match, so recompute: 2.582*3.464 = 8.94%.
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