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

This is a math problem. Let x = $amt of Stock X and y = $amt of Stock Y.

Return on stock x = rf + beta *(rm-rf)

= 5% + 2.1*(25%-5%)

= 47%

Return on stock 4 = rf + beta *(rm-rf)

= 5% + 1.4*(16%-5%)

= 20.4%

x + y = 102,000
1.47x + 1.204y = 1.11 * 102000 = 113220

Substituting y = 102000 - x in the second equation,
1.47x + 1.204 (102000 - x) = 113220
1.47x + 122808 - 1.204x = 113220
.266x = 9588
x = 36045
Therefore y = 65955

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