The return pattern on your favorite stock has been 5%, 8%, -12%, 15%, 21% over the last five years. What is your average return and total change in wealth per year over the period?
A) 4.5%, 6.5%
B) 15%, 21%
C) 7.4%, 6.8%
D) 9.2%, 8.6%

Question

Quizplus · Accepted Answer

The average return is calculated by summing the individual yearly returns and dividing by the number of years. Thus, $ \frac{5 + 8 - 12 + 15 + 21}{5} = \frac{37}{5} = 7.4\%$. The total change in wealth per year, or the geometric mean, is calculated by multiplying the returns (converted to growth factors) and taking the nth root, where n is the number of years. The growth factors for each year are 1.05, 1.08, 0.88, 1.15, and 1.21. Multiplying these together gives 1.4096. Taking the fifth root gives 1.068, or a 6.8% total change in wealth per year.

The Return Pattern on Your Favorite Stock Has Been 5