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CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns

An analyst compares the dispersion of two funds' annual returns. Fund X has a mean return of 8% and a standard deviation of 12%. Fund Y has a mean return of 15% and a standard deviation of 15%. Based on the coefficient of variation, which statement is most accurate?

Fund Y has less relative dispersion. The coefficient of variation divides standard deviation by the mean: Fund X gives 12/8 = 1.50 and Fund Y gives 15/15 = 1.00, so Fund Y has less risk per unit of mean return even though its standard deviation is higher.

  1. AFund Y has less dispersion per unit of mean return than Fund X.Correct
  2. BFund X and Fund Y have the same relative dispersion.
  3. CFund X has less dispersion per unit of mean return than Fund Y.

Explanation

CV = standard deviation / mean. Fund X: 12/8 = 1.50. Fund Y: 15/15 = 1.00. Fund Y has lower relative dispersion. Looking only at standard deviation would wrongly suggest Fund X is less dispersed.

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