You have $102,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

You have $102,000 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 80 percent of the risk of the overall market. If X has an expected return of 25 percent and a beta of 2.1, Y has an expected return of 16 percent and a beta of 1.4, 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.)

Amount $___________

You have $102,000 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 80 percent of the risk of the overall market. If X has an expected return of 25 percent and a beta of 2.1, Y has an expected return of 16 percent and a beta of 1.4, 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.)

Amount $___________

Explanation / Answer

E(RP) = 0:11

Let weight of X be=wx

Let weight of Y be=wy

Let weight of risk free asset=wr

0.11= wx(0.25) + wy(0.16) + (1 -wx - wy)(0.05)

0.11=0.25wx+0.16wy+0.05-0.05wx-0.05wy

0.06=0.20wx+0.11wy

beta = 0.8 = wx(2.1) +wy(1.4) +(1 -wx -wy)(0)

0.8 = wx(2.1) +wy(1.4)

solving these two equations in two unknowns gives

wx = -0.081634

wy = 0.693877

wr = 0.387757

and the amount of stock X to sell short =0.081634($102,000)=$8,326.668

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