A stock has the following returns over 3 years: -5%, +15%, -4%. The annual geometric rate of return over the three years is ________.
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A. B. C. D. E. F. G. H.B
The annual geometric rate of return equals [(1-5%)(1+15%)(1-4%)]^(1/3) - 1 = (0.95 * 1.15 * .96)^0.33 - 1 = 0.016 = 1.60%
To calculate the annual geometric rate of return over the three-year period, we need to use the formula:
(1 + R1) × (1 + R2) × (1 + R3) = (1 + G)^3
Where R1, R2, and R3 are the individual annual returns, and G is the geometric rate of return.
Let's calculate it step by step:
R1 = -5% = -0.05 R2 = 15% = 0.15 R3 = -4% = -0.04
(1 - 0.05) × (1 + 0.15) × (1 - 0.04) = (1 + G)^3
0.95 × 1.15 × 0.96 = (1 + G)^3
1.0368 = (1 + G)^3
Take the cube root of both sides of the equation:
(1 + G) = ∛(1.0368)
(1 + G) ≈ 1.0128
G ≈ 1.0128 - 1
G ≈ 0.0128
G ≈ 0.0128 × 100%
G ≈ 1.28%
Therefore, the annual geometric rate of return over the three-year period is approximately 1.28%.
Among the given answer choices, the closest option is B. 1.60%, but since the calculated result is lower than that, none of the provided answer choices matches the calculated rate exactly.