Question

Calculating the geometric and arithmetic average rate of​ return) Marsh Inc. had the following​ end-of-year stock prices over the last five years and paid no cash​ dividends: Time Marsh 1 ​$ 2 3 4 5 ​(Click on the icon in order to copy its contents into a spreadsheet.​) 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 the​ period?

Answer 1

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 the​period?

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

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