Question

A stock has had returns of 7 percent, 25 percent, 17 percent, −13 percent, 25 percent, and −6 percent over the last six years. What are the arithmetic and geometric average 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.) g

Answer 1

Answer: Geometric average return would be 0.10% and arithmetic average return would be 9.17%.

Step-by-step explanation:

Since we have given that

Returns are as follows:

7%, 25%, 175, -13%, 25% and -6%.

Geometric return is given by

$\sqrt[6]{(1+0.07)(1+0.25)(1+0.17)(1-0.13)(1+0.25)(1-0.06)}-1\\\\=\sqrt[6]{(1.17)(1.25)(1.17)(0.87)(1.25)(0.94)}-1\\\\=0.097\%=0.10\%$

Arithmetic average return would be

$\dfrac{7+25+17-13+25-6}{6}=9.17\%$

Hence, geometric average return would be 0.10% and arithmetic average return would be 9.17%.