Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A

Question

Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? d. If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain. Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? d. If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.

Explanation / Answer

Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent.
a. What is the expected return on a portfolio that is equally invested in the two assets?

Expected return on a portfolio = Weight of Stock A * Expected return of Stock A +  Weight of risk-free asset * Expected return of risk-free asset

Expected return on a portfolio = 50%*10.4 + 50%*3.8

Expected return on a portfolio = 7.10%

b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights?

Portfolio Beta = Weight of Stock A * Beta of Stock A +  Weight of risk-free asset * Beta of risk-free asset

0.70 = Weight of Stock A * 1.15 +  Weight of risk-free asset *0

Weight of Stock A = 0.70/1.15

Weight of Stock A = 0.6087

Weight of Stock A = 60.87%

Weight of risk-free asset = (1-Weight of Stock A )

Weight of risk-free asset = 1 - 0.6087

Weight of risk-free asset = 0.3913

Weight of risk-free asset = 39.13%

c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta?

Expected return on a portfolio = Weight of Stock A * Expected return of Stock A +  Weight of risk-free asset * Expected return of risk-free asset

9 = Weight of Stock A* 10.4 + (1-Weight of Stock A)*3.8

9 = 10.4Weight of Stock A + 3.8 - 3.8Weight of Stock A

6.6Weight of Stock A = 9 - 3.8

Weight of Stock A = 5.2/6.6

Weight of Stock A = 0.7879

Weight of Stock A = 78.79%

Weight of risk-free asset = 21.21%

Portfolio Beta = Weight of Stock A * Beta of Stock A +  Weight of risk-free asset * Beta of risk-free asset

Portfolio Beta = 78.79%*1.15 + 21.21%*0

Portfolio Beta = 0.91

d. If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.

Portfolio Beta = Weight of Stock A * Beta of Stock A +  Weight of risk-free asset * Beta of risk-free asset

2.3 = Weight of Stock A * 1.15 +  Weight of risk-free asset *0

Weight of Stock A =2.3/1.15

Weight of Stock A = 2

Weight of Stock A = 200%

Weight of risk-free asset = (1-Weight of Stock A )

Weight of risk-free asset = 1 - 2

Weight of risk-free asset = - 1

Weight of risk-free asset = -100%

In this case the weight of risk free asset is negative that denotes instead of investing in risk free asset , investor has borrowed in risk fee asset and now his money and borrowed fund through risk free asset is invested in Stock , As per weight its intreprete that investor highly risk seeking or investor are expecting that market would highly positive volatile

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