CFA Level I · CFA Level I Exam · Returns of Financial Assets and Instruments
A portfolio returns +50% in Year 1 and −50% in Year 2. Which statement about its performance over the two years is most accurate?
The geometric mean is about −13.4% per year. Compounding 1.5 and 0.5 gives 0.75, a 25% total loss, and the square root of 0.75 is 0.866. The arithmetic mean of 0% misleadingly suggests no loss.
- AThe geometric mean return is about −13.4% per yearCorrect
- BThe arithmetic mean return is −25% per year
- CThe ending value equals the starting value
Explanation
Growth factors: 1.5 × 0.5 = 0.75, so ending value is 75% of the start, a 25% total loss. The geometric mean is sqrt(0.75) − 1 = 0.8660 − 1 = −13.4%. The arithmetic mean is 0%, not −25%, and the ending value is lower than the start.
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