Question

A stock has had returns of −19.4 percent, 29.4 percent, 28.8 percent, −10.5 percent, 35.2 percent, and 27.4 percent over the last six years.

Required:
What are the arithmetic and geometric returns for the stock?

Answer 1

The arithmetic return for the stock is 18.3%, and the geometric return is 44.5%.

Step-by-step explanation:

To calculate the arithmetic return, you need to find the average of the annual returns. Add up all the returns and divide by the number of years. For this stock, the arithmetic return would be:

(-19.4 + 29.4 + 28.8 - 10.5 + 35.2 + 27.4) / 6 = 18.3%

To calculate the geometric return, you need to find the product of the annual returns and take the nth root, where n is the number of years. For this stock, the geometric return would be:

(1 - 0.194)(1 + 0.294)(1 + 0.288)(1 - 0.105)(1 + 0.352)(1 + 0.274) - 1 = 0.445 or 44.5%