Annual Geometric Rate of Return Calculator

Calculate the Annual Geometric Rate of Return for a Stock

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A stock has the following returns over 3 years: +2%, +15%, +25%. The annual geometric rate of return over the three years is ________.

A. 7.42%

B. 19.36%

C. 11.31%

D. 9.34%

E. 12.21%

F. 10.15%

G. 14.64%

H. 13.61%

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A. B. C. D. E. F. G. H.

The annual geometric rate of return equals [(1+2%)(1+15%)(1+25%)]^(1/3) - 1 = (1.02 * 1.15 * 1.25)^0.33 - 1 = 0.1361 = 13.61%

To calculate the annual geometric rate of return over multiple periods, you need to use the formula:

Geometric Rate of Return = [(1 + R1) * (1 + R2) * ... * (1 + Rn)]^(1/n) - 1

where R1, R2, ..., Rn are the individual period returns, and n is the number of periods.

In this case, the stock has returns of +2%, +15%, and +25% over three years.

Using the formula, we can calculate the annual geometric rate of return as follows:

[(1 + 0.02) * (1 + 0.15) * (1 + 0.25)]^(1/3) - 1

= (1.02 * 1.15 * 1.25)^(1/3) - 1

= (1.44875)^(1/3) - 1

≈ 1.1449 - 1

≈ 0.1449

To express the result as a percentage, we multiply by 100:

0.1449 * 100 ≈ 14.49%

Therefore, the annual geometric rate of return over the three years is approximately 14.49%.

Among the given answer choices, the closest option is:

G. 14.64%

Please note that the answer choices provided are rounded, so there may be slight variations due to rounding errors.

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