A stock has a beta of 1.25 and an expected return of 15 percent. A risk-free ass

Question

A stock has a beta of 1.25 and an expected return of 15 percent. A risk-free asset currently earns 3.2 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16))

If a portfolio of the two assets has a beta of 0.75, what are the portfolio weights? (Round your answer to 4 decimal places. (e.g., 32.1616))

If a portfolio of the two assets has an expected return of 9 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

If a portfolio of the two assets has a beta of 2.50, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)

A stock has a beta of 1.25 and an expected return of 15 percent. A risk-free asset currently earns 3.2 percent.

Explanation / Answer

A stock has a beta of 1.25 and an expected return of 15 percent. A risk-free asset currently earns 3.2 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16))

Expected return of Portfolio= Weight of stock *expected return of stock + Weight of risk-free asset *expected return of risk-free asset

Expected return of Portfolio = 50%*15 + 50%*3.2

Expected return of Portfolio = 9.10%

If a portfolio of the two assets has a beta of 0.75, what are the portfolio weights? (Round your answer to 4 decimal places. (e.g., 32.1616))

Beta of Portfolio= Weight of stock *Beta of stock + Weight of risk-free asset *Beta of risk-free asset

0.75 = Weight of stock*1.25 + (1- Weight of stock)*0

Weight of stock = 0.75/1.25

Weight of stock = 0.60

Weight of risk-free asset = 1- Weight of stock

Weight of risk-free asset = 1-0.60

Weight of risk-free asset = 0.40

If a portfolio of the two assets has an expected return of 9 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

Expected return of Portfolio= Weight of stock *expected return of stock + Weight of risk-free asset *expected return of risk-free asset

9 =Weight of stock *15 + (1-Weight of stock )*3.2

9 = 15Weight of stock + 3.2 - 3.2Weight of stock

Weight of stock =( 9-3.2)/11.80

Weight of stock = 5.80/11.80

Weight of risk-free asset = 1-5.80/11.80

Weight of risk-free asset = 6/11.80

Beta of Portfolio= Weight of stock *Beta of stock + Weight of risk-free asset *Beta of risk-free asset

Beta of Portfolio= 5.80/11.80*1.25 + 6/11.80*0

Beta of Portfolio= 0.614

If a portfolio of the two assets has a beta of 2.50, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)

Beta of Portfolio= Weight of stock *Beta of stock + Weight of risk-free asset *Beta of risk-free asset

2.50 = Weight of stock*1.25 + (1- Weight of stock)*0

Weight of stock = 2.50/1.25

Weight of stock = 2.00

Weight of risk-free asset = 1- Weight of stock

Weight of risk-free asset = 1-2.00

Weight of risk-free asset = -1

What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16))

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