A stock has a beta of 1.4 and an expected return of 16 percent. A risk-free asse
ID: 2714261 • Letter: A
Question
A stock has a beta of 1.4 and an expected return of 16 percent. A risk-free asset currently earns 4.0 percent.
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.)
If a portfolio of the two assets has a beta of .14, 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.)
Xs = ?
Xrf = ?
If a portfolio of the two assets has an expected return of 13.00 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
If a portfolio of the two assets has a beta of 1.45, 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.)
Xs = ?
Xrf= ?
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.)
b.If a portfolio of the two assets has a beta of .14, 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.)
Xs = ?
Xrf = ?
c.If a portfolio of the two assets has an expected return of 13.00 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
d.If a portfolio of the two assets has a beta of 1.45, 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.)
Xs = ?
Xrf= ?
Explanation / Answer
a)
Expected return on a portfolio = Weight of Stock *Expected Return of Stock + Weight of RF * Risk free rate of return
Expected return on a portfolio = 0.5*16 + 0.5*4
Expected return on a portfolio = 10%
b)
Beta of Portfolio = Weight of Stock *Beta of Stock + Weight of RF * Beta of Risk free Asset
0.14 = Weight of Stock *1.4 + Weight of RF * 0
Weight of Stock = 0.14/1.4
Weight of Stock = 10%
Weight of RF = 1-10%
Weight of RF = 90%
Answer
Xs = 10%
Xrf = 90%
c)
Expected return on a portfolio = Weight of Stock *Expected Return of Stock + Weight of RF * Risk free rate of return
13 = Weight of Stock * 16 + (1-Weight of Stock)*4
13 = 16Weight of Stock + 4 - 4 Weight of Stock
Weight of Stock = (13-4)/12
Weight of Stock = 75%
Weight of RF = 1-75%
Weight of RF = 25%
Beta of Portfolio = Weight of Stock *Beta of Stock + Weight of RF * Beta of Risk free Asset
Beta of Portfolio = 75%*1.4 + 25%*0
Beta of Portfolio = 1.05
d)
Beta of Portfolio = Weight of Stock *Beta of Stock + Weight of RF * Beta of Risk free Asset
1.45 = Weight of Stock *1.4 + Weight of RF * 0
Weight of Stock = 1.45/1.4
Weight of Stock = 103.57%
Weight of RF = 1-103.57%
Weight of RF = -3.57%
Answer
Xs = 103.57%
Xrf = -3.57%
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