You have $124,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

You have $124,000 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 13 percent and that has only 74 percent of the risk of the overall market. If X has an expected return of 22 percent and a beta of 1.7, Y has an expected return of 20 percent and a beta of 1.6, and the risk-free rate is 7 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

Assume Investment in X is a% Investment in Y is b% So Investment in Risk free asset =(1-a-b)% As per condition beta of portfolio =0.74 And return of portfolio =13% Expected return Beta Stock X 22%                   1.70 Stock Y 20%                   1.60 Risk Free asset 7%                        -   So , a*1.7+b*1.6=0.740 a=(0.740-1.6*b)/1.7 And a*0.22+b*0.20+ (1-a-b)*0.07=0.13 0.22a+0.20b+0.07-0.07a-0.07b=0.13 0.15a+0.13b=0.06 replacing a with (0.740-1.6*b)/1.7 0.15*(0.740-1.6b)/1.7 +0.13b=0.06 0.0653-0.1412b+0.13b=0.06 0.0112b=0.0053 b=47.37% So Investment in Y=47.37% of 124000=           58,738.80 So Investment in Y =$58,738.80

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.