Please help me solve the following: (Calculating the geometric and arithmetic av
ID: 2727882 • Letter: P
Question
Please help me solve the following:
(Calculating the geometric and arithmetic average rate of return) The common stock of the Brangus Cattle Company had the following end-of-year stock prices over the last five years and paid no cash dividends. Calculate the annual rate for each year from the above information. What is the arithmetic average rate of return earned by investing in the company's stock over this period? What is the geometric average rate of return earned by investing in the company's stock over this period? Which type of average rate of return best describes the average annual rate of return earned over the period (the arithmetic or geometric)? Why?Explanation / Answer
a.
Annual rate of return = Change in stock price/Stock price for previous period
Time
Beginning stock price
Ending price
Change in stock price
Rate of return
A
B
C
(C/D)
2
15
10
-5
-50.00%
3
10
12
2
16.67%
4
12
23
11
47.83%
5
23
25
2
8.00%
b.
Arithmetic average rate of return = (-50%+16.67%+47.83%+8%)/4 = 22.49%/5 = 4.50%
c.
Geometric average rate of return = (0.50*1.1667*1.4783*1.08)1/4 – 1 = 0.9824 – 1 = -0.0176 = -1.76%
Time
Beginning stock price
Ending price
Change in stock price
Rate of return
A
B
C
(C/D)
2
15
10
-5
-50.00%
3
10
12
2
16.67%
4
12
23
11
47.83%
5
23
25
2
8.00%