A stock has a beta of .9 and an expected return of 19 percent. A risk-free asset

Question

A stock has a beta of .9 and an expected return of 19 percent. A risk-free asset currently earns 5.0 percent.

a.  
What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Expected return   %

b.  
If a portfolio of the two assets has a beta of .44, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

    Portfolio Weight
xS   %   
xrf   %   

c.  
If a portfolio of the two assets has an expected return of 10.50 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Beta  

d.  
If a portfolio of the two assets has a beta of 1.21, what are the portfolio weights? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

    Porfolio Weight
xS   %   
xrf   %   

Explanation / Answer

a. Potfolio return = Weightage of risky asset * Return of risky asset + Weightage of risk free asset * Return of risk free asset

= 0.5 * 19% + 0.5 * 5%

= 12.00%

Expected return 12.00%

b. Portfolio beta = Weightage of risky asset * Beta of risky asset + Weightage of risk free asset * Beta of risk free asset

=> 0.44 = Weightage of risky asset * 0.9 + Weightage of risk free asset * 0

=> Weightage of risky asset = 0.4889 or 48.89%

Therefore Weightage of risk free asset = 1 - 0.4889

= 0.5111 or 51.11%

Portfolio Weight
xS 48,89%
xrf 51.11%

c. Expected portfolio return = Weightage of risky asset * Return of risky asset + Weightage of risk free asset * Return of risk free asset

=> Expected portfolio return = Weightage of risky asset * Return of risky asset + (1 - Weightage of risky asset) * Return of risk free asset

=> 10.5% = Weightage of risky asset * 19% + (1 - Weightage of risky asset) * 5%

=> Weightage of risky asset = 0.3929 or 39.29%

Therefore, Weightage of risk free asset = 1 - 0.3929

= 0.6071 or 60.71%

Now, Portfolio beta = Weightage of risky asset * Beta of risky asset + Weightage of risk free asset * Beta of risk free asset

= 0.3929 * 0.9 + 0.6071 * 0

= 0.3536

Beta 0.3536

d.

Portfolio beta = Weightage of risky asset * Beta of risky asset + Weightage of risk free asset * Beta of risk free asset

=> 1.21 = Weightage of risky asset * 0.9 + Weightage of risk free asset * 0

=> Weightage of risky asset = 1.3444 or 134.44%

Therefore Weightage of risk free asset = 1 - 1.3444

= -0.3444 or -34.44% (-ve sign signifies short position)

Portfolio Weight
xS 134.44%
xrf   -34.44%

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