Complete Question:
Marsh Inc. had the following end-of-year stock prices over the last five years and paid no cash dividends:
Time Marsh
1 $99
2 141
3 121
4 88
5 99
a. Calculate the annual rate of return for each year from the above information.
b. What is the arithmetic average rate of return earned by investing in Marsh's stock over this period?
c. What is the geometric average rate of return earned by investing in Marsh's stock over this period?
d. Considering the beginning and ending stock prices for the five-year period are the same, which type of average rate of return (the arithmetic or geometric) better describes the average annual rate of return earned over theperiod?
Answer:
Marsh Inc.
a. annual rate of return for each year
Year
2 42. 4%
3 -14.2%
4 -27.3
5 12.5
b. The arithmetic average rate of return earned by investing in Marsh's stock over this period is:
= 3.35%
c. The geometric average rate of return earned by investing in Marsh's stock over this period is:
= -0.7502%
d. Considering the beginning and ending stock prices for the five-year period are the same, the geometric type of average rate of return better describes the average annual rate of return earned over the period.
Explanation:
a) Data and Calculations:
Time Marsh ARR
1 $99
2 141 42. 4% ($42/$99 * 100)
3 121 -14.2% (-$20/$141 * 100)
4 88 -27.3 (-$33/$121 * 100)
5 99 12.5 ($11/$88 * 100)
Sum of ARR = 13.4%
Arithmetic mean = 3.35% (13.4%/4)
Geometric mean = {(1 + 0.424 * 1 - 0.142 * 1 - 0.273 * 1 + 0.125)∧1/4} - 1
= {(1.424 * 0.858 * 0.727 * 1.125)∧1/4} - 1
= {(0.99927)∧1/4} - 1
= 0.2498 - 1
= -0.7502
< 0
