CFA Level 1: Computing Kurtosis

D

I is true. II is false because the fourth power of a negative number is not a negative number: -2 * -2 * -2 * -2 = +16. III is true.

Kurtosis is a statistical measure that quantifies the shape of a distribution. It provides information about the tail behavior and the presence of outliers in the data compared to a normal distribution. In the given question, we need to determine which statements about kurtosis are true.

I. "It raises the deviation from the mean to the fourth power." This statement is true. Kurtosis involves calculating the fourth power of the deviations from the mean. By raising the deviations to the fourth power, kurtosis amplifies the effect of extreme values in the data and provides a measure of the tails' heaviness.

II. "The formula preserves the direction of the deviation." This statement is true. The formula used to compute kurtosis preserves the direction of the deviation from the mean. Positive deviations (values above the mean) and negative deviations (values below the mean) are both considered in the calculation.

III. "Kurtosis measures how clustered the values in a distribution are to the mean." This statement is not true. Kurtosis does not directly measure how clustered the values in a distribution are around the mean. Instead, it focuses on the shape of the distribution's tails. A higher kurtosis value indicates heavier tails compared to a normal distribution, while a lower kurtosis value suggests lighter tails.

Based on the analysis above, the correct answer is: D. I and III