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.)

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.)

Explanation / Answer

Lest assume amount invested in stock X and amount invested in stock Y is Y, so amount invested in risk free asset would be 1- X- Y.

Portfolio return = sum of weights x return

0.10 = 0.30X + 0.20 Y + 0.04 x (1-X-Y)

0.06 = 0.26 X +0.16 Y   -----------------------(1)

Portfolio beta = sum of weights x beta

                0.74 x 1 = 2 X + 1.20 Y + 0 (1-X-Y)

                0.74 = 2X +1.20Y--------------------(2)

Solving equation (1) and equation (2), we get:

0.12 = 0.52 X + 0.32 Y

0.1924 = 0.52 X + 0.312Y

Subtracting equation 2 from equation 1 we get:

0.0724 = -0.008Y

Y= -9.05

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