The geometric return on a stock over the past 10 years was 7.9 percent. The arithmetic return over the same period was 8.8 percent. What is the best estimate of the average return on this stock over the next 5 years?
A)8.40%
B)9.05%
C)9.08%
D)9.13%
E)9.47%

Question

Quizplus · Accepted Answer

Since the geometric return is lower than the arithmetic return, this implies that there is some volatility or variability in returns over the 10-year period. Therefore, it is better to use the geometric mean as a measure of the average return over a longer period of time. Using the formula for compound growth, we can solve for the expected average return over the next 5 years:

(1 + r)^10 = 1.079
1 + r = (1.079)^(1/10) = 1.075
r = 1.075 - 1 = 0.075

Now we can use the arithmetic mean formula to solve for the expected average return over the next 5 years:

(8.8% + 7.5%) / 2 = 8.15%

However, this answer is more likely to overestimate the true average return due to the volatility of the past 10 years. Therefore, it is better to use the geometric return as a more accurate estimate of future returns. The answer that is closest to the geometric return of 7.9% is choice A, which is 8.40%.

The Geometric Return on a Stock Over the Past 10