Question

A stock had annual returns of 5.1 percent, 12.2 percent, −3.8 percent, and 9.4 percent for the past four years. The arithmetic average of these returns is ________ percent while the geometric average return for the period is ________ percent.

Answer 1

Answer: 5.725%; 5.55%

Explanation:

The arithmetic average or mean is the sum of a collection of numbers that is divided by the count of the numbers in the collection.

Arithmetic average = Total return ÷ total time period

=(5.1+12.2-3.8+9.4) ÷ 4

= 22.9 ÷ 4

= 5.725%

Geometric average will be:

=[(1+rate1)(1+rate2)(1+rate3)(1+rate4)]^(1/4) - 1

=[(1+0.051)(1+0.122)(1-0.038)(1+0.094)]^(1/4)-1

=5.55%