You have been managing a 5 million portfolio that has a beta

You have been managing a $5 million portfolio that has a beta of 1.25 and a required rate of return of 12%. The current risk-free rate is 5.25%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.00, what will be the required return on your $5.5 million portfolio? (At least two decimal places are needed for your calculation) A) 13.24% B) 12.24% C) 11.38% D) 12.78% 11.88%

Solution

First we would have to calculate the market return.

Return as per CAPM: Return = Rf + (Rm - Rf)*Beta

12 = 5.25 + (Rm - 5.25)*1.25

Rm = (12 - 5.25)/1.25 + 5.25 = 10.65%

Since the amount of the portfolio is changed, we would have to calculate the new beta. Beta of the portfolio is the weighted average of the beta of the assets in the portfolio. Thus,

New Beta of the portfolio = [(5000000*1.25)+(500000*1)] / 5500000 = 1.23

New required return on $5.5 million (using CAPM) = 5.25 + (10.65 - 5.25)*1.23 = 11.88% Option E.