Calculate the geometric return of an investment with ﬁve year returns of 15%, 10%, 5%, (5%) and (10%).

Question

Quizplus · Accepted Answer

To calculate the geometric return, we use the formula:
(1+r)^n = [(1+r1) * (1+r2) * ... * (1+rn)]
where r is the geometric return, n is the number of years, and r1, r2, ...,rn are the annual returns for each year.
Using the given returns, we can calculate:
(1+r)^5 = (1+0.15) * (1+0.1) * (1+0.05) * (1-0.05) * (1-0.1)
(1+r)^5 = 1.056375
Therefore, r = (1.056375)^(1/5) - 1
r = 0.1357 or 13.57%
Thus, choice A is the correct answer.

Calculate the Geometric Return of an Investment with ﬁVe Year