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: 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.