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.)

Explanation / Answer

Total investment is $110,000

E(R) of Stock X = Rf + (Rm - Rf)

30% = 4% + 2(Rm-4%)

Rm = 17%

E(R) of Stock Y = Rf + (Rm - Rf)

20% = 4%+ 1.2(Rm-4%)

Rm = 17.33%

Portfolio return:

Stock x = (30*0.74) = 22.20%

Stock Y = (20*0.26) = 5.20%

Investment in stock x ($110,000 *29%*22.2%) = $7080/-

Investment in stock Y ($110,000 *71% * 5.20%) = $4060/-

Return on portfolio ($110,000 *10%) = $11,000

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