Question

What are the arithmetic and geometric average returns for a stock with annual returns of 11 percent, 9 percent, -5 percent, and 15 percent? List the arithmetic answer first.

9.94 percent; 7.22 percent
9.94 percent; 7.50 percent
7.22 percent; 7.50 percent
7.50 percent; 7.22 percent
7.50 percent; 9.94 percent

Answer 1

The arithmetic average return for the stock with given annual returns is 7.50%, and the geometric average return is approximately 7.22%.

Step-by-step explanation:

The arithmetic average return is calculated by simply adding up all the individual yearly returns and dividing by the number of years. In this case, (11% + 9% - 5% + 15%) / 4 = 7.50%. The geometric average return, on the other hand, is calculated by multiplying the yearly returns (expressed as decimals), taking the fourth root (since there are four years), and then subtracting 1 and converting to a percentage. So we have ((1 + 0.11) × (1 + 0.09) × (1 - 0.05) × (1 + 0.15))^(1/4) - 1, which gives us approximately 7.22%.