Which method correctly calculates the geometric mean of investment returns if the investor's return series is: 18.3%, 0.7%, −7.6%, 11.9%, and 2.5%?

Which method correctly calculates the geometric mean of investment returns if the investor's return series is: 18.3%, 0.7%, −7.6%, 11.9%, and 2.5%?

• A. 4.77%
• B. 8.01%
• C. 4.20%
• D. 8.20%

Answer: (A)

To determine the geometric mean of the investment returns, you first need to convert the percentage returns into a decimal format by adding 1 to each return and then multiplying these values together. After this multiplication, the result is then raised to the power of one divided by the number of returns, and finally, you subtract 1 and convert back to percentage form. 1. Convert the percentage returns to decimal form: - 1 + 0.183 = 1.183 - 1 + 0.007 = 1.007 - 1 - 0.076 = 0.924 - 1 + 0.119 = 1.119 - 1 + 0.025 = 1.025 2. Multiply these values together: \(1.183 \times 1.007 \times 0.924 \times 1.119 \times 1.025 = 1.18750816\) 3. Calculate the geometric mean: Take the fifth root (because there are five returns) of the product: \((1.18750816)^{1/5} \approx 1.07724894\) 4.

To determine the geometric mean of the investment returns, you first need to convert the percentage returns into a decimal format by adding 1 to each return and then multiplying these values together. After this multiplication, the result is then raised to the power of one divided by the number of returns, and finally, you subtract 1 and convert back to percentage form.

1. Convert the percentage returns to decimal form:

• 1 + 0.183 = 1.183

• 1 + 0.007 = 1.007

• 1 - 0.076 = 0.924

• 1 + 0.119 = 1.119

• 1 + 0.025 = 1.025

2. Multiply these values together:

(1.183 \times 1.007 \times 0.924 \times 1.119 \times 1.025 = 1.18750816)

3. Calculate the geometric mean:

Take the fifth root (because there are five returns) of the product:

((1.18750816)^{1/5} \approx 1.07724894)