Calculating the geometric and arithmetic average rate of refura) The common stoc
ID: 2779511 • Letter: C
Question
Calculating the geometric and arithmetic average rate of refura) The common stock of the Brangs Canle Companry had the following end of year stock prices over the last five years and paid no cash dividends $13 10 28 a. Cakculate the annsal rate of return for each year from the above information b. What is the arithmetic average rate of return earned by investing in Beangus Catle Company's stock over this period? c. What is the geometric average rate of return earned by investing in Brangus Cattle Company's stock ever this period? a. The annial rate of return at the end ofyear 2 is%Rond to two decinal places) The annual rate ofreturn at the end of year sistdRound to two decinal places) The anmual rate of return at the end of year 4 iss Round to two decinal places) The anmual rate of return at the end of year 5 is Round to two decimal places.) b. The arithmetic average rate of return earned by mvesmg ezgus Cade Company's stock over this period is Click to select your answer(s). % Round to two decinal places )Explanation / Answer
(‘a) Annual Rate of Return
Times
Ending Stock Price
Beginning Stock Price
Return ( Ending Price- Beginning Price)
Annual Rate of Return = Return/ Beginning Price (%)
1
13.00
NA
NA
NA
2
10.00
13.00
-3.00
-23.08 %
3
11.00
10.00
1.00
10.00 %
4
22.00
11.00
11.00
100.00 %
5
28.00
22.00
6.00
27.27 %
(‘b) Arithmetic Average rate of return
Arithmetic return = Sum of annual return / Number of observations
Arithmetic rate of return = (-23.08 +10+100+27.27)/4
Arithmetic rate of return over the period = 28.55 %
(‘c) Geometric rate of return
Geometric Return = [(1+R1) x (1+r2) x (1+r3) x ……….(1+rn)]1/n -1
‘r1
-23.08 %
‘r2
10.00 %
‘r3
100.00 %
‘r4
27.27 %
Geometric return = [(-0.7692) x (1.10) x ((2.00) x (1.2727) ]0.25 -1
Geometric Return = 21.14 %
(‘d)
Geometric average returns are more accurate than arithmetic rate. Because it consider the compounding effect over a period of time. So when an investment is held over a period of time, geometric return shows the compounding effect of return received over multi period of time.
Hence option (‘d) is the correct answer.
Times
Ending Stock Price
Beginning Stock Price
Return ( Ending Price- Beginning Price)
Annual Rate of Return = Return/ Beginning Price (%)
1
13.00
NA
NA
NA
2
10.00
13.00
-3.00
-23.08 %
3
11.00
10.00
1.00
10.00 %
4
22.00
11.00
11.00
100.00 %
5
28.00
22.00
6.00
27.27 %
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