CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
According to Chebyshev's inequality, the minimum proportion of observations of any distribution that lies within 2.5 standard deviations of the mean is closest to:
At least 84% of observations lie within 2.5 standard deviations of the mean. Chebyshev's inequality gives 1 - 1/k², so with k = 2.5 the result is 1 - 0.16 = 0.84. It holds for any distribution, not only the normal one.
- A84%Correct
- B75%
- C96%
Explanation
Chebyshev: proportion within k standard deviations is at least 1 - 1/k². With k = 2.5, 1 - 1/6.25 = 1 - 0.16 = 0.84, or 84%. 75% corresponds to k = 2, and 96% corresponds to k = 5.
Did you get it right without looking?
One question tells you little. A timed set on Statistical Characteristics of Asset Returns shows your real accuracy, how long you take and where you lose marks.
More Statistical Characteristics of Asset Returns questions
- An analyst wants a single measure of the typical annual growth of an investment whose value compounds over several years with varying return…
- The sample standard deviation of Asset M's returns is 12% and that of Asset N's returns is 5%. The correlation between the two is -0.40. If …
- A risk analyst compares a histogram of daily returns with a Q-Q plot against the normal distribution. The plotted points curve upward above …
- The covariance between the returns of Asset A and Asset B is 0.0048. The standard deviation of Asset A is 8% and that of Asset B is 10%. The…
- The covariance between the returns of Asset X and Asset Y is 0.0060. The standard deviation of X returns is 0.20 and the standard deviation …
- A data set of monthly returns for a small-cap fund contains a few extremely large positive outliers. Compared with the arithmetic mean, the …