Question

A stock has had returns of −19.7 percent, 29.7 percent, 32.4 percent, −10.8 percent, 35.5 percent, and 27.7 percent over the last six years.

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

Arithmetic average return	%
Geometric average return	%

Answer 1

Arithmetic average return is the simple average of all period returns

Arithmetic average return R

$R = (R_{1}+R_{2}+R_{3}+ ... R_{n})/n$

Arithmetic average return R = (−0.197 + 0.297+ 0.324 −0.108+ 0.355 + 0.277)/6

R = 0.948/6 = 0.158 or 15.8%

Arithmetic average return R = 15.8%

Geometric average return R

$R = ((1+R_{1})*(1+R_{2})*...(1+R_{n}))^{1/n}-1$

$\small R = ((1-0.197)*(1+0.297)*(1+0.324)*(1-0.108)*(1+0.355)*(1+0.277))^{1/6}-1$

R=1.134157-1

R = 0.134157

Geometric average return​ R=13.42%