CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
Annual returns on a fund are normally distributed with a mean of 8% and a standard deviation of 10%. Using the approximate rule that about 95% of observations fall within two standard deviations of the mean, the range containing about 95% of annual returns is most likely:
About 95% of annual returns should fall between -12% and 28%. This is the mean of 8% plus or minus two standard deviations of 10% each, or 20 percentage points. A one-standard-deviation band would cover only about 68%.
- A-2% to 18%
- B-12% to 28%Correct
- C-22% to 38%
Explanation
Mean ± 2 × 10% = 8% ± 20%, giving -12% to 28%. The range -2% to 18% uses only one standard deviation, which covers about 68%.
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