Question

Mary Guilott recently graduated from Nichols State University and is anxious to begin investing her meager savings as a way of applying what she has learned in business school.​ Specifically, she is evaluating an investment in a portfolio comprised of two​ firms' common stock. She has collected the following information about the common stock of Firm A and Firm​ B:

Expected Return Standard Deviation

Firm A Common Stock .16 .17

Firm B Common Stock .17 .24

Correlation Coefficient .50

a. If Mary invests half her money in each of the two common​ stocks, what is the​ portfolio's expected rate of return and standard deviation in portfolio​ return?

b. Answer part a where the correlation between the two common stock investments is equal to zero.

c. Answer part a where the correlation between the two common stock investments is equal to +1.

d. Answer part a where the correlation between the two common stock investments is equal to −1.

e. Using your responses to questions a—d​, describe the relationship between the correlation and the risk and return of the portfolio.

Answer 1

1.
=0.5*0.16+0.5*0.17=16.5000%

2.
=sqrt((0.5*0.17)^2+(0.5*0.24)^2+2*0.5*0.17*0.5*0.24*0.50)=17.8396%

1.
=0.5*0.16+0.5*0.17=16.5000%

2.
=sqrt((0.5*0.17)^2+(0.5*0.24)^2+2*0.5*0.17*0.5*0.24*0)=14.7054%

1.
=0.5*0.16+0.5*0.17=16.5000%

2.
=sqrt((0.5*0.17)^2+(0.5*0.24)^2+2*0.5*0.17*0.5*0.24*1)=20.5000%

1.
=0.5*0.16+0.5*0.17=16.5000%

2.
=sqrt((0.5*0.17)^2+(0.5*0.24)^2+2*0.5*0.17*0.5*0.24*(-1))=3.5000%

As correlation decreases, expected return does not change but risk reduces or decrease