Question

 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 or​geometric)? ​ Why?

Answer 1

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.