CFA Level I · CFA Level I Exam · Returns of Financial Assets and Instruments
An analyst compares the arithmetic mean return and the geometric mean return for a series of annual returns that are not all equal. Which statement is most likely correct?
The geometric mean is lower than the arithmetic mean whenever the returns vary. The two are equal only if all returns are identical, and the gap grows with volatility, because compounding penalizes dispersion in the return series.
- AThe geometric mean is lower than the arithmetic meanCorrect
- BThe two means are equal
- CThe geometric mean is higher than the arithmetic mean
Explanation
For returns that vary, the geometric mean is always lower than the arithmetic mean, and the gap widens as dispersion increases. The two are equal only when every return is identical. Hence the geometric mean is lower.
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