Question

Your mother's well-diversified portfolio has an expected return of 12.0% and a beta of 1.20. She is in the process of buying 100 shares of Safety Corp. at $10 a share and adding it to her portfolio. Safety has an expected return of 15.0% and a beta of 2.00. The total value of your current portfolio is $9,000. What will the expected return and beta on the portfolio be after the purchase of the Safety stock?

Answer 1

Answer: (a) 12.3%

(b) 1.28

Explanation:

Current Portfolio expected return = 12.0%

Current Portfolio beta = 1.20

New investment = Shares purchased × Price per share

                           = 100 × $10

                           = $1,000

New investment expected return = 15% and Beta = 2.00

Total value of your current portfolio = $9,000

New portfolio investment cost = $9,000 + $1,000

                                                   = $10,000

$Weight\ of\ current\ portfolio = \frac{9,000}{10,000}$

                                                   = 0.90

$Weight\ of\ New\ investment = \frac{1,000}{10,000}$

                                                       = 0.10

Expected return of new portfolio = Sum of (weight × Return)

                                                      = 0.90 × 12% + 0.10 × 15%

                                                      = 12.3%

Expected beta of new portfolio = Sum of (weight × Beta)

                                                     = 0.90 × 1.20 + 0.10 × 2.0

                                                      = 1.28