Question

A stock has had returns of 12 percent, 19 percent, 21 percent, 21 percent, -12 percent,...

A stock has had returns of 12 percent, 19 percent, 21 percent, 21 percent, -12 percent, 26 percent, and -5 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.)

a.) Arithmetic return?

b) Geometric return?

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Homework Answers

Answer #1

Arithmetic average rate of return is calculated by using the below formula:

Arithmetic average rate of return= Sum of individual return/ Total number of returns

= 12% + 19% + 21% + 21% -12% + 26% - 5% / 6

= 82% / 6

= 13.67%.

Geometric average return is calculated using the below formula:

GAR = ((1 + 0.12)*(1 + 0.19)*(1 + 0.21)*(1 + 0.21)*(1 - 0.12)*(1 + 0.26)*(1 - 0.05)^1/6 - 1

= (1.12*1.19*1.21*1.21*88*1.26*0.95)^1/6 - 1

= 2.0555^0.1667

= 1.1276 - 1

= 0.1276*100

= 12.76%.

In case of any query, kindly comment on the solution.

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