You have $114,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

You have $114,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 11 percent and that has only 74 percent of the risk of the overall market. If X has an expected return of 33 percent and a beta of 2.2, Y has an expected return of 16 percent and a beta of 1.1, and the risk-free rate is 5 percent, how much money will you invest in Stock Y? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.)

You have $114,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 11 percent and that has only 74 percent of the risk of the overall market. If X has an expected return of 33 percent and a beta of 2.2, Y has an expected return of 16 percent and a beta of 1.1, and the risk-free rate is 5 percent, how much money will you invest in Stock Y? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.)

Explanation / Answer

ERp => 0.11 = (0.33Wx + 0.16Wy) + ( 1-Wx-Wy)*0.05

=> 0.06 = 0.28Wx + 0.11Wy ----- (1)

Beta => 0.7 = (2.2.Wx + 1.1Wy) + (1-Wx-Wy)*0

=> 0.07 = 2.2Wx + 1.1Wy ----- (2)

Solving these two equations

Wx => -0.166667

Wy => 0.969697

Stock Y => (114000 * 0.969697) => $110545

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