Question

A stock had returns of 12 percent, 16 percent, 10 percent, 19 percent, 15 percent, and -6 percent over the last six years. What is the geometric average return on the stock for this period?

Answer 1

10.68%

Step-by-step explanation:

Data provided in the question:

Returns on stock : 12%, 16%, 10%, 19%, 15%, -6%

Now,

Geometric average return on the stock is calculated as:

Geometric average return =
`({(1 + r_1)*(1 + r_2).......*(1 + r_n)})^(1)/(n)- 1`

Thus,

For the given returns on stock

Geometric average return

=
`[ (1 + 0.12)*(1 + 0.16)*(1 + 0.10)*(1 + 0.19)*(1 + 0.15)*(1 + (- 0.06)) ]^{(1)/(6)}-1`

=
`[ 1.12*1.16*1.10*1.19*1.15*0.94 ]^{(1)/(6)}-1`

=
`[1.8384056768]^{(1)/(6)}-1`

= 1.1068 - 1

= 0.1068

or

= 0.1068 × 100%

= 10.68%