Bundle: Financial Management: Theory & Practice, 16th + MindTap, 1 term Printed Access Card
Bundle: Financial Management: Theory & Practice, 16th + MindTap, 1 term Printed Access Card
16th Edition
ISBN: 9780357252673
Author: Brigham, Eugene F., EHRHARDT, Michael C.
Publisher: Cengage Learning
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Chapter 25, Problem 7SP

a.

Summary Introduction

Determine: Expected return and standard deviation of the portfolio invested.

a.

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that expected return of A is 0.07, expected return of B is 0.10, expected return of C is 0.20, standard deviation of A is 0.3311, standard deviation of B is 0.5385, standard deviation of C is 0.8944, correlation coefficient between A and B is 0.35, portfolio invested in A is 30% and in B is 70%.

Formula to calculate expected return is as follows:

Expected return=Return of A×Portfolio invested in A+Return of B×Portfolio invested in B

Substituting Equation with 0.10 for the return of A and 30% for the portfolio invested in A, 0.16 for the return of B and 70% for the portfolio invested in B to calculate expected return.

Expected return=0.10×30%+0.16×70%=0.03+0.112=0.142 or 14.2%

Hence, the expected return from portfolio investment of 30% in stock A and 70% in stock B is 14.2%.

Formula to calculate standard deviation of the portfolio invested is as follows:

σ=(wa2σa2+wb2σb2+2wa×wb×rab×σa×σb)

Substituting Equation with 0.30 for Wa, 0.20 for σa, 0.70 for Wb, 0.40 for σb to calculate standard deviation of the portfolio invested.

σ=(0.302×0.202+0.702×0.402+2×0.30×0.70×0.35×0.20×0.40)=(0.13+0.65+0.01176)=0.79176=0.8898 or 88.98%

Hence, standard deviation of the portfolio invested is 88.98%.

b.

Summary Introduction

Determine: Expected return and standard deviation of the portfolio invested.

b.

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that expected return of A is 0.10, expected return of B is 0.16, standard deviation of A is 0.20, standard deviation of B is 0.40, correlation coefficient between A and B is 0.35, portfolio invested in A is 30% and in B is 70%.

Formula to calculate expected return is as follows:

Expected return=Return of A×Portfolio invested in A+Return of B×Portfolio invested in B

Substituting Equation with 0.10 for the return of A and 30% for the portfolio invested in A, 0.16 for the return of B and 70% for the portfolio invested in B to calculate expected return.

Expected return=0.10×30%+0.16×70%=0.03+0.112=0.142 or 14.2%

Hence, the expected return from portfolio investment of 30% in stock A and 70% in stock B is 14.2%.

Formula to calculate standard deviation of the portfolio invested is as follows:

σ=(wa2σa2+wb2σb2+2wa×wb×rab×σa×σb)

Substituting Equation with 0.30 for Wa, 0.20 for σa, 0.70 for Wb, 0.40 for σb to calculate standard deviation of the portfolio invested.

σ=(0.302×0.202+0.702×0.402+2×0.30×0.70×0.35×0.20×0.40)=(0.13+0.65+0.01176)=0.79176=0.8898 or 88.98%

Hence, standard deviation of the portfolio invested is 88.98%.

c.

Summary Introduction

Determine: Expected return and standard deviation of the portfolio invested.

c.

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that expected return of A is 0.10, expected return of B is 0.16, standard deviation of A is 0.20, standard deviation of B is 0.40, correlation coefficient between A and B is 0.35, portfolio invested in A is 30% and in B is 70%.

Formula to calculate expected return is as follows:

Expected return=Return of A×Portfolio invested in A+Return of B×Portfolio invested in B

Substituting Equation with 0.10 for the return of A and 30% for the portfolio invested in A, 0.16 for the return of B and 70% for the portfolio invested in B to calculate expected return.

Expected return=0.10×30%+0.16×70%=0.03+0.112=0.142 or 14.2%

Hence, the expected return from portfolio investment of 30% in stock A and 70% in stock B is 14.2%.

Formula to calculate standard deviation of the portfolio invested is as follows:

σ=(wa2σa2+wb2σb2+2wa×wb×rab×σa×σb)

Substituting Equation with 0.30 for Wa, 0.20 for σa, 0.70 for Wb, 0.40 for σb to calculate standard deviation of the portfolio invested.

σ=(0.302×0.202+0.702×0.402+2×0.30×0.70×0.35×0.20×0.40)=(0.13+0.65+0.01176)=0.79176=0.8898 or 88.98%

Hence, standard deviation of the portfolio invested is 88.98%.

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