Intermediate Financial Management, 12th edition. Problem 2-13: HIstorical Realiz
ID: 2612660 • Letter: I
Question
Intermediate Financial Management, 12th edition. Problem 2-13: HIstorical Realized Rates of Return:
You are considering an investment in eithe rindividual stocks or aportfolio of stocks. THe two stocks you are researching, Stock A and stock B, have the following historical returns:
-5%
b. Suppose you held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period?
c. Calculate the standard deviation of returns for each stock and for the portfolio.
Year A B 2011 -20%-5%
2012 42 15 2013 20 -13 2014 -8 50 2015` 25 12Explanation / Answer
b.
Assets
Portfolio
Year
Return A
Return B
Realied rate
A
B
(A+B)/2
2011
-20.00%
-5.00%
-12.50%
2012
42.00%
15.00%
28.50%
2013
20.00%
-13.00%
3.50%
2014
-8.00%
50.00%
21.00%
2015
25.00%
12.00%
18.50%
Total
59.00%
59.00%
59.00%
Average Return = Total /5
11.80%
11.80%
11.80%
c.
Calculation of Standard Deviation :
For Stock A
Year
Return A
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
2011
-20.00%
11.80%
-31.80%
10.112%
2012
42.00%
11.80%
30.20%
9.120%
2013
20.00%
11.80%
8.20%
0.672%
2014
-8.00%
11.80%
-19.80%
3.920%
2015
25.00%
11.80%
13.20%
1.742%
Sum of C^2
25.568%
N-1 = 5-1
4
Standard Deviation = (Sum of C^2 /N-1)^(1/2)
= (25.568% /4)^(1/2)
25.28%
For Stock B
Year
Return A
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
2011
-5.00%
11.80%
-16.80%
2.822%
2012
15.00%
11.80%
3.20%
0.102%
2013
-13.00%
11.80%
-24.80%
6.150%
2014
50.00%
11.80%
38.20%
14.592%
2015
12.00%
11.80%
0.20%
0.000%
Sum of C^2
23.668%
N-1 = 5-1
4
Standard Deviation = (Sum of C^2 /N-1)^(1/2)
= (23.668% /4)^(1/2)
24.32%
b.
Assets
Portfolio
Year
Return A
Return B
Realied rate
A
B
(A+B)/2
2011
-20.00%
-5.00%
-12.50%
2012
42.00%
15.00%
28.50%
2013
20.00%
-13.00%
3.50%
2014
-8.00%
50.00%
21.00%
2015
25.00%
12.00%
18.50%
Total
59.00%
59.00%
59.00%
Average Return = Total /5
11.80%
11.80%
11.80%
c.
Calculation of Standard Deviation :
For Stock A
Year
Return A
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
2011
-20.00%
11.80%
-31.80%
10.112%
2012
42.00%
11.80%
30.20%
9.120%
2013
20.00%
11.80%
8.20%
0.672%
2014
-8.00%
11.80%
-19.80%
3.920%
2015
25.00%
11.80%
13.20%
1.742%
Sum of C^2
25.568%
N-1 = 5-1
4
Standard Deviation = (Sum of C^2 /N-1)^(1/2)
= (25.568% /4)^(1/2)
25.28%
For Stock B
Year
Return A
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
2011
-5.00%
11.80%
-16.80%
2.822%
2012
15.00%
11.80%
3.20%
0.102%
2013
-13.00%
11.80%
-24.80%
6.150%
2014
50.00%
11.80%
38.20%
14.592%
2015
12.00%
11.80%
0.20%
0.000%
Sum of C^2
23.668%
N-1 = 5-1
4
Standard Deviation = (Sum of C^2 /N-1)^(1/2)
= (23.668% /4)^(1/2)
24.32%
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