You have $130,000 to invest in a portfolio containing Stock X and Stock Y. Your

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. 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

Explanation / Answer

Investment in Stock Y = - $ 46,800

Beta of the portfolio = 1.39

working

Amount to be invested = $ 130,000

Stock X

Expected return = 12.8% or 0.128

Beta = 1.30

Stock Y

Expected return = 7.8% or 0.078

Beta = 1.05

Required return on portfolio = 14.60% or 0.146

Let A be the proportion to be invested in Stock X and (1-A) be the proportion to be invested in Stock Y.

Required return on portfolio = weight of stock x * return on X + weight of stock Y * return on Y

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

0.146 = A * 0.128 + 0.078 – A * 0.078

0.146 – 0.078 = A * (0.128-0.078)

A * 0.05 = 0.068

A = 0.068/0.05 = 1.36

Amount to be invested in Stock X = $ 130,000 * 1.36 = $ 176,800

Amount to be invested in stock Y   = (1-A) * $ 130,000 = (1-1.36) * $ 130,000 = -0.36 * $ 130,000

                                                               = - $ 46,800

Beta of the portfolio = weight of stock X * Beta of Stock X + Weight of stock Y * Beta of Stock Y

Beta of the Portfolio = 1.36 * 1.30 + (- 0.36) * 1.05 = 1.768 – 0.378 = 1.39

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