ou have $110,000 to invest in a portfolio containing Stock X, Stock Y, and a ris

Question

ou 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

Let the proportion of investment in Stock X be x
And the proportion of investment in stock Y be y
Hence proportion of investment in risk free asset is (1-x-y)

Expected return of portfolio = 30x + 20y + 4*(1-x-y) = 10
30x + 20y + 4 - 4x - 4y = 10
26x + 16y = 6

Risk of the portfolio = 2x + 1.2y + 0*(1+x-y) = 0.74
2x + 1.2y = 0.74
x = 0.37 - 0.6y

Substituting this value of x in first equation

26*(0.37-0.6y) + 16y = 6
9.62- 15.6y + 16y = 6
0.04y = -3.62
y = -3.62/0.04 = -9.05

x = 0.37-(0.6*-9.05) = 5.80

Amount invested in stock x = $110,000*0.58 = $63,800

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