Question

Assume that you hold a well-diversified portfolio that has an expected return 12%and a beta of 1.20. You are in the process of buying 100 shares of Alpha Corp at $10 a share and adding it to your portfolio. Alpha has an expected return of 15.0% and a beta of 2.00. The total value of your current portfolio is $9000. What is the expected return and beta on the portfolio be after the purchase of the Alpha stock?

Answer 1

Total value of portfolio

= Value of current portfolio + (No. of shares x price per share) of stock Alpha

= $ 9,000 + 100 x $ 10 = $ 9,000 + $ 1,000 = $ 10,000

Port folio weight for each stock = Stock’s value/Total portfolio value

Port folio weight for existing stock W_exc= $9,000/ $ 10,000 = 0.9

Port folio weight for stock Alpha, W_A = $1,000/ $ 10,000 = 0.1

Beta of portfolio, ß_P = W_exc x (ß_exc) + (1 – W_A) x (ß_A)

                                    = 0.9 x 1.2 + 0.1 x 2

                                    = 1.08 + 0.2 = 1.28

Expected return of portfolio, E(R_P) = E(R_exc) x W_exc + R_A x (1 – W_A)

                                                             = 0.12 x 0.9 + 0.15 x 0.1

                                                             = 0.108 + 0.015 = 0.123 or 12.3 %