CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
A return distribution has a mean of 8% and a standard deviation of 5%. Using Chebyshev's inequality, the minimum percentage of observations lying within the interval from -2% to 18% is closest to:
At least 75% of observations lie in the interval. The range from -2% to 18% is the mean plus or minus 10%, which is two standard deviations. Chebyshev's inequality gives 1 minus 1/k squared, or 1 minus 1/4, equal to 75%, for any distribution.
- A68%
- B75%Correct
- C89%
Explanation
The interval 8% ± 10% is 2 standard deviations (10/5). Chebyshev gives at least 1 - 1/k² = 1 - 1/4 = 75%. The 68% figure is the normal-distribution value for one standard deviation, and 89% corresponds to k = 3.
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