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A stock has a beta of 1.13 an as expected return of 12.1 percent. A risk-free asset currently earns 5 percent. a. what is the expected return on a portfolio that is equally invested in the two assets? b.If a portfolio of the two assets has a beta of .50, what are the portfolio weights? c.If a portfolio of the two assets has an expected return of 10 percent, what is it's beta? d. If a portfolio of the two assets has a beta of 2.26 what are the portfolio weights? How do you interpret the weights for the two assets in this case? explain

Respuesta :

13.023% is the expected return on a portfolio,  0.4425 and 0.5575 are the portfolio weights, 0.7042 is it's beta and 2, -1 are the portfolio weights.

Using CAPM:

(A) B = 1.13

     Rmarket = 12.1%

     Rf = 5%

     E(R) Rf + B*(Rmarket -Rf) =

     =0.05 1.13(0.121-0.05)

     = 13.023%

     So, if we invest equally, Raverage = 0.5*R1 + 0.5*R2 = 9.0115%

(B) Bnet = B1*W1 + B2*W2

     0.50 = 1.13*w1 + 0*W2

     portfolio weight, W₁ = 0.4425

     W2 = 1 - W₁

            = 0.5575

(C) Rnet = R1*W1 + R2*w2

    10 = 13.023*w1 + 5*(1-W1)

     W₁ = 0.6232; w₂ = 0.3768

     Bnet = B1 W1 + B2*w2

     beta = 1.13*0.6232+0*0.3768

     beta = 0.7042

(D) Bnet = B1*W1 + B2*W2

     2.26 = 1.13*w1 + 0*W2

     portfolio weight, W₁ = 2

     W2 = 1-W₁

            = -1

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