Question

What are the arithmetic and geometric average returns for a stock with annual returns of 6 percent, 9 percent, −3 percent, and 17 percent?

Answer 1

7.25% , 1.66%

Explanation:

The arithmetic average return is calculated by summing up the annual returns and dividing by the number of years.

Arithmetic average return = (6% + 9% - 3% + 17%) / 4 = 29% / 4 = 7.25%

The geometric average return is calculated by multiplying all the annual returns together and taking the nth root of the product, where n is the number of years.

Geometric average return = (1.06 x 1.09 x 0.97 x 1.17)^(1/4) ≈ 1.0665^(1/4) ≈ 1.0166 - 1 = 1.66%

Therefore, the arithmetic average return is 7.25% and the geometric average return is 1.66%.