Question

16) You have been managing a $5 million portfolio that has a beta of 1.45 and a required rate of return of 10%. The current risk-free rate is 4.25%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.70, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

______%

Answer 1

Using CAPM model market rate of return can be computed as:

E(r) = Rf + ß x (Rm – Rf)

Rm = {E(r) – Rf}/ ß – Rf

Rm = [(10 % - 4.25 %)/1.45] + 4.25 %

     = [(0.1 – 0.0425)/1.45] + 0.0425

      = [(0.0575)/1.45] + 0.0425

      = 0.039655172 + 0.0425

      = 0.082155 or 8.22 %

New beta for portfolio $ 5.5 m is the sum of weighted average of beta for both old and new portion.

ß _P = 1.45 x ($ 5,000,000/5,500,000) + 0.7 x ($ 500,000/5,500,000)

     = 1.45 x 0.909090909 + 0.7 x 0.090909091

     = 1.318181818 + 0.063636364

     = 1.381818182 or 1.38

Required return on portfolio, Rp is:

Rp = Rf + ß_p x (Rm – Rf)

     = 0.0425 + 1.381818182 x (0.082155 – 0.0425)

     = 0.0425 + 1.381818182 x 0.0396552

    = 0.0425 + 0.054796238

    = 0.097296238 or 9.73 %

Required return on $ 5.5 million portfolio is 9.73 %