You have $140,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

You have $140,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 18 percent and that has only 90 percent of the risk of the overall market. If X has an expected return of 44 percent and a beta of 1.4, Y has an expected return of 22 percent and a beta of 1.5, and the risk-free rate is 6.8 percent, how much money will you invest in Stock Y? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Explanation / Answer

Let x be the weight of stock x and y be the weight of stock y, Now,

0.44 x Wx + 0.22 x Wy + (1-Wx-Wy)x0.068 = 0.18

0.372Wx + 0.152Wy = 0.112   ....Equation 1

1.40 x Wx + 1.50 x Wy + (1-Wx-Wy)x0 = 0.70

1.40Wx + 1.50Wy = 0.70   ....Equation 2

Dividing both sides of equation 2 by 1.50 and multiplying the result with 0.152 gives us

0.142Wx + 0.152Wy = 0.071   ....Equation 3

Now by subtracting Equation 3 from Equation 1 we get

Wx = 0.178

Now Putting this value in any of the equation we get

Wy = 0.301

Thus Wx = 0.178, Wy = 0.301 and weight of risk free security = 1-0-178-0.301 = 0.521

Therefore,

Amount to be invested in stock Y = $140000 x 0.301

= $42140

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

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