You have $112,000 to invest in a portfolio containing Stock X, Stock Y, and a ri
ID: 2727217 • Letter: Y
Question
You have $112,000 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 76 percent of the risk of the overall market. If X has an expected return of 31 percent and a beta of 2.1, Y has an expected return of 18 percent and a beta of 1.3, 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.)
You have $112,000 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 76 percent of the risk of the overall market. If X has an expected return of 31 percent and a beta of 2.1, Y has an expected return of 18 percent and a beta of 1.3, 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
Statement showing computation Particulars Amount Expected Return Beta Stock X 24% 1.60 Stock Y 18% 1.60 Risk Free Asset 6% - 126,000.00 12% 0.76 Let investment in Stock X and Stock Y is a Invt in Rf would be 1-x .76 = 1.60 *a + 0*(1-a) .76/1.60 = a a = 47.5% Rf = 1-a = 52.5% Now Futher lets assume that Stock X has weight of m Stock Y = 47.5%-m 24%*m + 18%(47.5%-m) + 6%*52.5% = 12% .24m + 8.55% - .18m + 3.15% = 12% .06m = 12%- 11.70% m = .30%/.06m Stock X,m= 5% Stock Y =47.5%-5% = 42.5% Amount in Y = 126,000*.425 Amount in Y = $53,550
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