Assume that you manage a $10.00 million mutual fund that has a beta of 1.05 and a 9.50% required return. The risk-free rate is 4.20%. You now receive another $5.00 million, which you invest in stocks with an average beta of 0.65. What is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new portfolio beta.)

The required rate of return of Portfolio is 8.83%

Explanation:

First we need to find the risk Premium of Existing Portfolio using the CAPM model.

Required rate of return = RF + (Rm - RF) x Beta

9.50% = 4.20% + (Rm - RF) x 1.05

9.50% - 4.20% = (Rm - RF) x 1.05

5.30% = (Rm - RF) x 1.05

(Rm - RF) = 5.30%/1.05

(Rm - Rf) = 5.05%

Second we need to find the New Portfolio Beta Using the Following step

Portfolio Beta = (Existing Portfolio / Total Investment) x Beta + (New stock / Total Investment) x Beta

Portfolio Beta = (10M / 15M) x 1.05 + (5M/15M) x 0.65 = 0.9167

Third Step we will use the CAPM model again to get Required Rate of Return of New Portfolio.

Required rate of return = RF + (Rm - RF) x Beta

Required rate of return = 4.20% + 5.05% x 0.9167

Required Rate of Return = 8.83%