(Calculating the geometric and arithmetic average rate of return) The common sto
ID: 2820961 • Letter: #
Question
(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:
Time
Brangus cattle Comapny
1
$14
2
10
3
12
4
22
5
29
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 Brangus Cattle Company's stock over this period?
c.What is the geometric average rate of return earned by investing in Brangus Cattle Company's stock over this period?
d.Which type of average rate of return best describes the average annual rate of return earned over the period (the arithmetic or geometric)? Why?
a.The annual rate of return at the end of year 2 is %.
(Round to two decimal places.)The annual rate of return at the end of year 3 is %.
(Round to two decimal places.)The annual rate of return at the end of year 4 is %.
(Round to two decimal places.)The annual rate of return at the end of year 5 is %.
(Round to two decimal places.)
b.The arithmetic average rate of return earned by investing in Brangus Cattle Company's stock over this period is %.
(Round to two decimal places.)
c.The geometric average rate of return earned by investing in Brangus Cattle Company's stock over this period is %.
(Round to two decimal places.)
Time
Brangus cattle Comapny
1
$14
2
10
3
12
4
22
5
29
Explanation / Answer
a)
The annual rate of return at the end of year 2 = ( 10 - 14) / 14 = -0.2857 or -28.57%
The annual rate of return at the end of year 3 = ( 12 - 10) / 10 = 0.20 or 20%
The annual rate of return at the end of year 4 = ( 22 - 12) / 12 = 0.8333 or 83.33%
The annual rate of return at the end of year 5 = ( 29 - 22) / 22 = 0.3182 or 31.82%
b)
Arithmetic average = ( -0.2857 + 0.20 + 0.8333 + 0.3182 ) / 4
Arithmetic average = 0.2665 or 26.65%
c)
Geometic average = [ ( 1 + (-0.2857) * ( 1 + 0.2) * ( 1 + 0.8333) * ( 1 + 0.3182 )]1/4 - 1
Geometic average = [ 0.7143 * 1.2 * 1.8333 * 1.3182 ]1/4 - 1
Geometic average = 0.1997 or 19.97%
d)
Geometric average best describe the returns. Geometric average takes into account acompunding effect that occurs from period to period. it is also the number that represents the reality. When we are dealing with volatile numbers as in the case of stock markets, geometric average represents far more accuarte picture of performance by taking into account the effect of compounding.
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