A stock has had returns of 13 percent, 20 percent, 22 percent, −11 percent, 27 percent, and −5 percent over the last six years.

A stock has had returns of 13 percent, 20 percent, 22 percent, −11 percent, 27 percent, and −5 percent over the last six years.

What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Arithmetic return	%
Geometric return	%

 

Explanation:

The arithmetic average return is the sum of the known returns divided by the number of returns, so:

Arithmetic average return = (.13 + .20 + .22 – .11 + .27 – .05) / 6

Arithmetic average return = .1100, or 11.00%

Using the equation for the geometric return, we find:

Geometric average return = [(1 + R1) × (1 + R2) × … × (1 + RT)]1/T – 1

Geometric average return = [(1 + .13)(1 + .20)(1 + .22)(1 – .11)(1 + .27)(1 – .05)](1/6) – 1

Geometric average return = .1005, or 10.05%

Remember, the geometric average return will always be less than the arithmetic average return if the returns have any variation.