You have $110,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

You have $110,000 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 10 percent and that has only 74 percent of the risk of the overall market. If X has an expected return of 30 percent and a beta of 2.0, Y has an expected return of 20 percent and a beta of 1.2, and the risk-free rate is 4 percent, how much money will you invest in Stock Y? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.) Amount $

Explanation / Answer

Wx => Weight of Stock X

Wy => Weight of Stock Y

E(RP ) => 0.10 => Wx(0.30) + Wy (0.20) + (1- Wx - Wy )(0.04)

0.10 => 0.30Wx + 0.20Wy + 0.04 - 0.04Wx - 0.04Wy

0.06 = 0.26Wx + 0.16Wy ----- Equation 1

BP => 0.74 => Wx(2.0) + Wy(1.2) + (1 - Wx - Wy)(0)

=> 0.74 = 2Wx + 1.2Wy  ----- Equation 2

solving these two equations in two unknowns gives

Wy => -9.05

Money will you invest in Stock Y => -9.05 * 110000 => $995500

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