The geometric return on a stock over the past 10 years was 8.42 percent. The arithmetic return over the same period was 9.02 percent. What is the best estimate of the average return on this stock over the next 5 years?
A) 8.75 percent
B) 9.05 percent
C) 9.08 percent
D) 9.13 percent
E) 9.47 percent

Question

Quizplus · Accepted Answer

Since the geometric return is lower than the arithmetic return, it suggests that the returns are volatile and there may have been periods of negative returns. Therefore, the geometric return is a better estimate of the average return over a long time period. Hence, we can assume that the geometric return will continue in the future. To estimate the return for the next 5 years, we can use the formula, 
10-year geometric return = (1 + r1) * (1 + r2) * ... * (1 + r10)^(1/10) - 1, where r is the annual return. Solving for the annual return for the next 5 years, we get, 
(1 + r11) * (1 + r12) * ... * (1 + r15)^(1/5) - 1 = (1 + 0.0842)^(10/5) - 1 = 0.0875 or 8.75%
Therefore, the best estimate of the average return on this stock over the next 5 years is 8.75%, which is closest to choice (A).

The Geometric Return on a Stock Over the Past 10