Question

A stock had returns of 19 percent, 18 percent, 15 percent, 17 percent, 16 percent, and 14 percent over the last six years.

1. What is the arithmetic return for the stock?
2. What is the geometric return for the stock?

Answer 1

The arithmetic return for the stock is 16.5% and the geometric return is 16.16%.

Step-by-step explanation:

The arithmetic return for the stock is found by summing up all the annual returns and dividing by the number of years. In this case, the arithmetic return is:

((19 + 18 + 15 + 17 + 16 + 14) / 6) = 16.5%

The geometric return for the stock is found by multiplying all the annual returns and taking the nth root, where n is the number of years. In this case, the geometric return is:

((1 + 0.19) * (1 + 0.18) * (1 + 0.15) * (1 + 0.17) * (1 + 0.16) * (1 + 0.14))^(1/6) - 1 = 0.161618 - 1 = 0.161618 = 16.16%