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.)

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.)

Explanation / Answer

Desired portfolio:

Expected return =11%.

Let x be the amount invested in Stock X and (1-x)be the amount invested in Stock Y.

0.11 =0.25 *x +0.16(1-x)

0.11 =0.25x+0.16 - 0.16x

0.09x = 0.11 -0.16

x=-0.05/0.09

x=- 55%

Therefore the amount to be invested in Stock y =100+55%

=155% of the amount invested in stock X

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