Question

You have $150,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.1 percent. Stock X has an expected return of 12.93 percent and a beta of 1.42 and Stock Y has an expected return of 8.51 percent and a beta of .74. How much money will you invest in Stock Y? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) What is the beta of your portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer a.

Total Investment = $150,000

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

Expected return of Portfolio = Expected return of Stock X * Weight of Stock X + Expected return of Stock Y * Weight of Stock Y
0.1410 = 0.1293 * x + 0.0851 * (1 - x)
0.1410 = 0.1293 * x + 0.0851 - 0.0851 * x
0.0559 = 0.0442 * x
x = 1.264706

Weight of Stock X = 1.264706 or 126.4706%

Weight of Stock Y = 1 - Weight of Stock X
Weight of Stock Y = 1 - 1.264706
Weight of Stock Y = -0.264706 or -26.4706%

Amount Invested in Stock Y = $150,000 * -26.4706%
Amount Invested in Stock Y = -$39,705.90

Answer b.

Portfolio Beta = Weight of Stock X * Beta of Stock X + Weight of Stock Y * Beta of Stock Y
Portfolio Beta = 1.264706 * 1.42 + (-0.264706) * 0.74
Portfolio Beta = 1.60