Question

You have $130,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.6 percent. Stock X has an expected return of 12.8 percent and a beta of 1.30, and Stock Y has an expected return of 7.8 percent and a beta of 1.05. a. How much money will you invest in Stock Y? (Do not round intermediate calculations. A negative answer should be indicated by a minus sign.) b. What is the beta of your portfolio? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

Answer 1

Let X be the amount invested in stock A

Let 1-X be the amount invested in stock B

Expected rate = (Required rate of X* X) + (Required ratebof Y * (1-X))

0.146 = (0.128 * X) + (0.078 * (1-X))

0.146 = 0.128X + 0.078 - 0.078X

0.146 - 0.078 = 0.128X - 0.078X

X = 0.068/0.05

X = 1.36

Amount to be invested in Stick X = $130,000 * 1.36

= $176,000

Amount to be invested in Stock Y = (1-X) * Available amount

= (1-1.36) * $130,000

= $46,800

Therefore, the amount to be invested in Stick Y = -$46,800

Calculation of the portfolio beta

bp = w1b1 + w2b2 + ........ + wnbn

bp = (1.36*1.3) + ((-0.36) * 1.05)

bp = 1.768 - 0.378

bp = 1.29

Therefore, the portfolio beta is 1.39