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

Answer:

10.68%

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 = $({(1 + r_1)\times(1 + r_2).......\times(1 + r_n)})^\frac{1}{n}- 1$

Thus,

For the given returns on stock

Geometric average return

=$[ (1 + 0.12)\times(1 + 0.16)\times(1 + 0.10)\times(1 + 0.19)\times(1 + 0.15)\times(1 + (- 0.06)) ]^{\frac{1}{6}}-1$

= $[ 1.12\times1.16\times1.10\times1.19\times1.15\times0.94 ]^{\frac{1}{6}}-1$

=  $[1.8384056768]^{\frac{1}{6}}-1$

= 1.1068 - 1

= 0.1068

or

= 0.1068 × 100%

= 10.68%