You have $108,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

You have $108,000 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 12 percent and that has only 72 percent of the risk of the overall market. If X has an expected return of 29 percent and a beta of 1.9, Y has an expected return of 18 percent and a beta of 1.4, and the risk-free rate is 6 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

Let Weight of Stock X be Wx

Weight of Stock Y be Wy

than Weight of Risk free asset = (1-Wx-Wy)

Required Beta = 72% of Market

Required Beta = 72%*1

Required Beta = 0.72

Beta of portfolio = Weight of Stock X *Beta of X + Weight of Stock Y *Beta of Y + Weight of Risk free asset *Beta of Risk free asset

0.72 = Wx*1.9 + Wy *1.4 + (1-Wx-Wy)*0

0.72 = 1.9Wx + 1.4 Wy

Wx = (0.72-1.4Wy)/1.9

expected return of portfolio = Weight of Stock X *expected return of X + Weight of Stock Y *expected return of Y + Weight of Risk free asset *expected return of Risk free asset

12 = Wx*29 + Wy *18 + (1-Wx-Wy)*6

12 = (0.72-1.4Wy)/1.9 * 29 + 18Wy + (1-(0.72-1.4Wy)/1.9 -Wy) * 6

12 = (20.88 - 40.6Wy)/1.9 + 18 Wy + (11.40 - 4.32 + 8.4 Wy - 11.40 Wy)/1.9

12 = (20.88 - 40.6Wy + 34.20 Wy + 7.08 - 3Wy)/1.9

22.80 = 27.96 - 9.40 Wy

Wy = (27.96-22.80)/9.40

Wy = 0.5489362

Amount Invested in Stock Y = 108000* 0.5489362

Amount Invested in Stock Y = $ 59,285

Answer

Amount Invested in Stock Y = $ 59,285

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