In: Finance
A stock has a beta of 0.9 and an expected return of 11 percent. A risk-free asset currently earns 3.5 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.) b. If a portfolio of the two assets has a beta of 0.29, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) c. If a portfolio of the two assets has an expected return of 11.75 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 1.38, what are the portfolio weights?
a)Expected return on a portfolio =[ER stock *weight of stock ]+[ER risk free asset *weight of risk free asset]
=[11*.50 ]+ [3.5*.5]
=5.5+ 1.75
= 7.25%
b)Beta of risk free asset is 0 as there is no risk involved.
Let the weight of stock be "X" so weight of risk free asset 1-X
Beta of portfolio = [Beta of stock *weight of stock ]+[Beta of risk free asset *weight of risk free asset]
.29 = [.90*X] +[0*(1-X)]
.29 = .90X +0
X = .29/.90
= 32.22%
Weight of stock = 32.22%
weight of risk free asset = 1-.3222 = .6778 or 67.78%
c)Let the weight of stock be "X" so weight of risk free asset 1-X
Expected return on a portfolio =[ER stock *weight of stock ]+[ER risk free asset *weight of risk free asset]
11.75 = [11*X] +[3.5 (1-X)]
11.75 = 11X +3.5 -3.5X
11.75 -3.5 = 7.5X
X = 8.25/7.5
= 1.1
weight of stock = 1.1 or 110%
weight of risk free asset = 1-1.1 = -.10 or -10%
Beta of portfolio = [Beta of stock *weight of stock ]+[Beta of risk free asset *weight of risk free asset]
=[.9* 110%]+ [0*-10%]
= .99 + 0
= .99
d)
Beta of risk free asset is 0 as there is no risk involved.
Let the weight of stock be "X" so weight of risk free asset 1-X
Beta of portfolio = [Beta of stock *weight of stock ]+[Beta of risk free asset *weight of risk free asset]
1.38 = [.9* X]+ [0*(1-X)]
1.38 = .9X +0
X =1.38 /.9
= 1.5333 or 153.33%
weight of stock = 153.33%
weight of risk free asset = 1-1.5333 = -.5333 or -53.33%