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 Company
1 $17
2 $12
3 $13
4 $21
5 $26
a. The annual rate of return at the end of year 2 is ___%
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?
Which type of average rate of return best describes the average annual rate of return earned over the period (the arithmetic orgeometric)? Why?
a.
Annual Rate of Return in Year 2 = (13 - 12)/12 = 8.33%
b.
Return in Year 1 = (12 - 17)/17 = -29.41%
Return in Year 2 = 8.33%
Return in Year 3 = (21 - 13)/13 = 61.54%
Return in Year 4 = (26 - 21)/21 = 23.81%
Average Return = (-0.2941 + 0.0833 + 0.6154 + 0.2381)
Average Return = 16.07%
c.
Geometric Return = [(0.7059)(1.0833)(1.6154)(1.2381)]^{1/4} - 1
Geometric Return = 11.21%
d.
Geometric return describes the return in a better way over the period as it takes into account the effect of compounding of return.
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