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 20.0% and a beta of 2.50. 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? Select the correct answer.

a. rp = 12.80%, bp = 1.33

b. rp = 12.83%, bp = 1.37

c. rp = 12.86%, bp = 1.41

d. rp = 12.77%, bp = 1.29

e. rp = 12.74%, bp = 1.25

Answer 1

The expected return is computed as follows:

= Return of existing portfolio x weight of existing portfolio + Return of new stock x weight of new stock

= 0.12 x $ 9,000 / ($ 9,000 + 100 x $ 10) + 0.20 x [ (100 x $ 10) / ($ 9,000 + 100 x $ 10)

= 0.12 x $ 9,000 / $ 10,000 + 0.20 x $ 1,000 / $ 10,000

= 0.12 x 0.90 + 0.20 x 0.10

= 12.80%

Beta is computed as follows:

= Beta of existing portfolio x weight of existing portfolio + Beta of new stock x weight of new stock

= 1.20 x $ 9,000 / $ 10,000 + 2.50 x $ 1,000 / $ 10,000

= 1.20 x 0.90 + 2.50 x 0.10

= 1.33

Hence the correct answer is option a.