Portfolio Risk and Return: Part I: practice question
With respect to the arithmetic mean and the geometric mean of a series of an investment's historical returns, which statement is most accurate?
- The geometric mean gives the compound annual growth actually realized, and it never exceeds the arithmetic mean
- The arithmetic mean gives the compound annual growth actually realized, and it never falls below the geometric mean
- The two means are equal whenever every return in the series is positive, and differ only when a negative return appears
Show answer and explanation
Correct answer: A
Explanation: A is correct. The geometric mean links the beginning and ending values of an investment through compounding, so it states the annual growth rate actually delivered, and whenever the periodic returns differ the geometric mean falls below the arithmetic mean of the same series. B is incorrect because it swaps the roles of the two measures: the arithmetic mean is the larger one when returns vary, so presenting it as the growth actually realized overstates what a buy-and-hold investor earned. C is incorrect because equality requires every period's return to be identical, not merely positive; +20% and +5%, for instance, already produce a geometric mean of about 12.25% against an arithmetic mean of 12.5%.
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