Question

A stock had returns of 16 percent, 12 percent, 19 percent, 17 percent, 18 percent, and -1 percent over the last six years.

What is the arithmetic return for the stock?
What is the geometric return for the stock?

Answer 1

What is the arithmetic return for the stock?

• arithmetic returns basically refer to the mean (or average) of the returns = (16% + 12% + 19% + 17% + 18% - 1%) / 6 = 81% / 6 = 13.5%

What is the geometric return for the stock?

• geometric returns involves multiplying the returns and then squaring them = ⁶√(1.16 x 1.12 x 1.19 x 1.17 x 1.18 x 0.99) - 1 = 1.1328 - 1 = 0.1328 = 13.28%

Normally, geometric returns are lower than arithmetic returns, and they represent compounding rates.