A stock has a beta of 1.33 and an expected return of 13.1 percent. A risk-free a

Question

A stock has a beta of 1.33 and an expected return of 13.1 percent. A risk-free asset currently earns 4.45 percent.

a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return             %

b. If a portfolio of the two assets has a beta of .93, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

c. If a portfolio of the two assets has an expected return of 12.3 percent, what is its beta? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Beta            

d. If a portfolio of the two assets has a beta of 2.53, what are the portfolio weights? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

Explanation / Answer

A.Expected Return = 0.5*13.1%+0.5*4.45%

=8.775%

B. If a portfolio of the two assets has a beta of .93,what are the portfolio weights?

Beta of Portfolio = 0.93

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

0.93 = Weight of Stock A*1.33+ (1-Weight of Stock A)*0

Weight of Stock A = 0.93/1.33

Weight of Stock A = 69.92%

Weight of risk free asset =1-69.92%= 30.08%

C. If a portfolio of the two assets has an expected return of 12.3 percent, what is its beta?

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

12.3= Weight of Stock A*13.1+ (1-Weight of Stock A)*4.45

12.3=13.1 Weight of Stock A + 4.45 - 4.45*Weightf Stock A

12.3-4.45= 8.65 Weight of Stock A

7.85= 8.65 Weig of Stock A

Weight of Stock A = 7.85/8.65

Weightof risk free asset = 1-7.85/8.65= 0.8/8.65

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

Beta of Portfolio = 7.85/8.65*1.33+ 0.8/8.65*0

Beta of Portfolio = 1.21

D) Beta of portfolio= Weight of Stock A*Beta of Stock A + Weight of risk free asset*Beta of risk free asset

2.53= Weight of Stock A*1.33 + (1-Weight of Stock A)*0

Weight of Stock A = 2.53/1.33

Weight of Stock A = 1.90

Weight of risk free asset = 1-1.90= -0.90

The Portfolio represent that the amount is being borrowed at risk free rate & invested in stock.

Thanks

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