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A stock has a beta of 0.9 and an expected return of 11 percent. A risk-free...

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?

Solutions

Expert Solution

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%

jeff jeffy answered 6 months ago
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