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

Question

You have $114,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 16 percent and that has only 84 percent of the risk of the overall market. If X has an expected return of 31 percent and a beta of 1.2, Y has an expected return of 18 percent and a beta of 1.1, and the risk-free rate is 4 percent, how much money will you invest in Stock Y? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

You have $114,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 16 percent and that has only 84 percent of the risk of the overall market. If X has an expected return of 31 percent and a beta of 1.2, Y has an expected return of 18 percent and a beta of 1.1, and the risk-free rate is 4 percent, how much money will you invest in Stock Y? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Explanation / Answer

Expected return Beta Stock x 31.00% 1.2 Stock y 18.00% 1.1 Risk Free Rate (Rf) 4.00% 0 We have to find out the weights E(Rp) = .16 = wX(.31) + wY(.18) + (1 – wX – wY)(.04) Portfolio Beta = .84 = wX(1.2) + wY(1.1) + (1 – wX – wY)(0) We have two equations and two unknowns. Solving these equations, we find that: E(Rp) = .16 = .31Wx + .18Wy + .04 - .04wX -.04wY E(Rp) = .12 = .27Wx + .14Wy Beta= .84 = 1.2Wx +1.1Wy Weight X 11.16% Weight Y 64.19% Weight Rf 24.65% Investment in stock Y = $114,000 x 64.19% $73,172.04

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