Suppose a particular investment earns an arithmetic return of 10% in year 1,20% in year 2 and 30% in year 3.The geometric average return for the year period will be __________.
A)greater than the arithmetic average return
B)equal to the arithmetic average return
C)less than the arithmetic average return
D)equal to the market return
E)cannot tell from the information given

Question

Quizplus · Accepted Answer

The geometric average return takes into account the compounding effect of returns over the period of investment. Using the formula, geometric average return = [(1+R1)(1+R2)(1+R3)]^(1/n) - 1, where R1, R2, and R3 are the returns earned in each year, and n is the number of years, we get:
Geometric average return = [(1+0.1)(1+0.2)(1+0.3)]^(1/3) - 1 = 0.197 or 19.7%.
This is less than the arithmetic average of 20%, indicating that the returns were unevenly distributed over the investment period.

Suppose a Particular Investment Earns an Arithmetic Return of 10