Question

You have $100,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 12.7 percent. Stock X has an expected return of 11.4 percent and a beta of 1.25, and Stock Y has an expected return of 8.68 percent and a beta of .85. How much money will you invest in Stock Y? What is the beta of your portfolio? (2 pts)

Answer 1

Answer: See explanation

Step-by-step explanation:

a. How much money will you invest in Stock Y?

Let the weight of Stock X = x

Let the weight of Stock Y = (1 - x)

Expected return of stock X = 11.4%

Beta of stock X = 1.25

Expected return of stock Y = 8.68%

Beta of stock X = 0.85

The Portfolio Return will then be calculated as:

= (Weight of Stock X × Return of Stock X) + (Weight of Stock Y × Return of Stock Y)

0.127 = [x × 0.114 + (1 - x) × 0.0868]

0.127 = [x × 0.114 + 0.0868 - x × 0.0868]

0.127 = x × 0.0272 + 0.0868

0.127 - 0.0868 = x × 0.0272

0.0402 = 0.0272x

x = 0.402/0.0272

x = 1.4779

Weight of Stock X = 1.4779

Therefore, Weight of Stock Y will be:

= 1 - 1.4779

= -0.4779

The amount that's invested in Stock Y will be:

= $100,000 × (-0.4779)

= -$47,790

b. What is the beta of your portfolio?

Portfolio Beta will be calculated as:

= 1.4779 × 1.25 + (-0.4779) × 0.85

= 1.44