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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 12

Explanation / 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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