A stock has had returns of 6 percent, 24 percent, 16 percent, −12 percent, 31 percent, and −6 percent over the last six years.

Problem 12-15 Arithmetic and Geometric Returns [LO1]

A stock has had returns of 6 percent, 24 percent, 16 percent, −12 percent, 31 percent, and −6 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 = (.06 + .24 + .16 – .12 + .31 – .06) / 6

Arithmetic average return = .0983, or 9.83%

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 + .06)(1 + .24)(1 + .16)(1 – .12)(1 + .31)(1 – .06)](1/6) – 1

Geometric average return = .0873, or 8.73%

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