Question

A stock has annual returns of 5 percent, 21 percent, -12 percent, 7 percent, and -6 percent for the past five years. The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.

Answer 1

Answer:

Arithmetic = 3%

Geometric = 2.37%

Explanation:

The arithmetic average of 'n' returns is given by:

$A = \frac{\sum r_i}{n}$

For five returns of 5% ,21%, -12%, 7%, and -6%:

$A=\frac{0.05+0.21-0.12+0.07-0.06}{5}\\ A=0.03=3\%$

The geometric average of 'n' returns is given by:

$G=\sqrt[n]{(1+r_1)*(1+r_2)*...*(1+r_n)}-1$

For five returns of 5% ,21%, -12%, 7%, and -6%:

$G=\sqrt[5]{(1+0.05)*(1+0.21)*(1-0.12)*(1+0.07)*(1-0.06)}-1\\G=0.0237=2.37\%$