Question

A stock has had returns of 11 percent, 18 percent, 20 percent, −13 percent, 25 percent, and −9 percent over the last six years. What are the arithmetic and geometric average returns for the stock?

Answer 1

Answer: a) 8.67%, b) 7.64%.

Step-by-step explanation:

Since we have given that

Stock has returns is given by

11 percent, 18 percent, 20 percent, −13 percent, 25 percent, and −9 percent

Number of years = 6

Arithmetic average returns for the stock is given by

$\dfrac{11+18+20-13+25-9}{6}\\\\=8.67\%$

Geometric average returns for the stock is given by

$[(1+0.11)\times (1+0.18)\times (1+0.20)\times (1-0.13)\times (1+0.25)\times (1-0.09)]^{\frac{1}{6}}-1\\\\=[1.11\times 1.18\times 1.20\times 0.87\times 1.25\times 0.91]^{\frac{1}{6}}-1\\\\=7.64\%$

Hence, a) 8.67%, b) 7.64%.