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Answer: The fund's standard deviation is less than 5%
## Explanation **Analysis of return sequence: +7.0%, +15.0%, +20.0%, +5.0%, +18.0%** **Let's evaluate each statement:** **A: The arithmetic mean return is 13%** - **TRUE** - Calculation: (7 + 15 + 20 + 5 + 18)/5 = 65/5 = 13% **B: The geometric mean return is approximately 12.8%** - **TRUE** - Calculation: [(1.07 × 1.15 × 1.20 × 1.05 × 1.18)^(1/5) - 1] ≈ 12.8% **C: The fund achieved positive returns in all five years** - **TRUE** - All returns are positive: +7.0%, +15.0%, +20.0%, +5.0%, +18.0% **D: The fund's standard deviation is less than 5%** - **FALSE** - To calculate standard deviation: - Mean = 13% - Deviations: (7-13)=-6%, (15-13)=2%, (20-13)=7%, (5-13)=-8%, (18-13)=5% - Squared deviations: 36, 4, 49, 64, 25 - Variance = (36+4+49+64+25)/5 = 178/5 = 35.6 - Standard deviation = √35.6 ≈ 5.97% - **The standard deviation is approximately 5.97%, which is GREATER than 5%** **Therefore, statement D is the false statement.**
Author: LeetQuiz Editorial Team
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Quadholding Mutual is a mutual fund in the United States who reports the following sequence of per annum returns over the last five years: +7.0%, +15.0%, +20.0%, +5.0%, +18.0%. Each of the following statements about this mutual fund is true EXCEPT which is false?
A
The arithmetic mean return is 13%
B
The geometric mean return is approximately 12.8%
C
The fund achieved positive returns in all five years
D
The fund's standard deviation is less than 5%
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