CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
A portfolio has monthly returns of 2%, 4%, 6%, 8% and 10%, which the analyst treats as a sample. The sample standard deviation of the returns is closest to:
The sample standard deviation is about 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 give 2.83%, which is the population measure.
- A2.83%
- B3.16%Correct
- C4.47%
Explanation
Mean = 6%. Squared deviations: 16, 4, 0, 4, 16 = 40. Sample variance = 40/(5-1) = 10, so the standard deviation = 3.16%. Dividing by n gives variance 8 and 2.83%, the population figure, which is wrong for a sample.
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