Question

You have $106,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 16 percent. Stock X has an expected return of 13 percent and a beta of 1.14, and Stock Y has an expected return of 9.0 percent and a beta of .84.

How much money will you invest in stock Y? (Do not round intermediate calculations. A negative amount should be indicated by a minus sign.)
Investment in Stock Y $
What is the beta of your portfolio? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.)
Beta of the portfolio

Answer 1

Answer: ER(P) = ERX(WX) + ERY(WY)

16 = 13(1-WY) + 9(WY)

16 = 13 - 13WY + 9WY

16 = 13 - 4WY

4WY = 13-16

4WY = -3

WY = -3/4

WY = -0.75

WX = 1 - WY

WX = 1 - (-0.75)

WX = 1 + 0.75

WX = 1.75

The amount to be invested in stock Y = -0.75 x $106,000

= -$79,500

The Beta of the portfolio could be calculated using the formula:

BP = BX(WX) + BY(WY)

BP = 1.14(1.75) + 0.84(-0.75)

BP = 1.995 - 0.63

BP = 1.365

Explanation: The expected return of the portfolio is equal to expected return of stock X multiplied by the weight of stock X plus the expected return of stock Y multiplied by weight of security Y. The weight of security Y is -0.75. The weight of security X is equal to 1 - weight of security Y. Thus, the weight of security X is 1.75 since the weight of security Y is negative. The amount to be invested in security Y is -0.75 x $106,000, which is equal to -$79,500

The Beta of the portfolio equals Beta of stock X multiplied by weight of stock X plus the Beta of stock Y multiplied by weight of stock Y. The weights of the two stocks have been obtained earlier. Therefore, the Beta of the portfolio is 1.365.