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CFA Level I · CFA Level I Exam · Types of Financial Returns

An analyst compares the arithmetic mean and the geometric mean of a series of annual returns that vary from year to year. Which statement is most accurate?

The geometric mean return is never larger than the arithmetic mean return. They are equal only when every period's return is identical. The more the returns vary, the wider the gap between the two means, so the geometric mean is lower whenever returns differ.

  1. AThe geometric mean is never larger than the arithmetic mean.Correct
  2. BThe geometric mean is always larger than the arithmetic mean.
  3. CThe two means are equal only when all returns are positive.

Explanation

By the AM-GM inequality, the geometric mean of growth factors is at most the arithmetic mean, with equality only when all returns are identical. The geometric mean is never larger. Equality does not depend on returns being positive, so the last option is wrong.

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