Question

You have $110,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 15 percent. Stock X has an expected return of 13.2 percent and a beta of 1.16, and Stock Y has an expected return of 10.2 percent and a beta of .88.

  

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 a.

Total Investment = $110,000

Let Weight of Stock X be x and Weight of Stock Y be (1 - x)

Expected Return of Portfolio = Weight of Stock X * Expected Return of Stock X + Weight of Stock Y * Expected Return of Stock Y
0.1500 = x * 0.1320 + (1 - x) * 0.1020
0.1500 = x * 0.1320 + 0.1020 - x * 0.1020
0.0480 = x * 0.0300
x = 1.60

Weight of Stock X = 1.60

Weight of Stock Y = 1 - x
Weight of Stock Y = 1 - 1.60
Weight of Stock Y = -0.60

Investment in Stock Y = (-0.60) * $110,000
Investment in Stock Y = -$66,000

Answer b.

Portfolio Beta = Weight of Stock X * Beta of Stock X + Weight of Stock Y * Beta of Stock Y
Portfolio Beta = 1.60 * 1.16 + (-0.60) * 0.88
Portfolio Beta = 1.328