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.) a. 8.83% b. 9.05% c. 9.27% d. 9.74% e. 9.51%

The required rate of return on new portfolio is 8.83%. So, option a is the correct answer.

Explanation:

To use the CAPM approach to calculate the new required rate of return, we first need to determine the beta for the new portfolio.

Portfolio beta is the weighted average of the individual stock betas that form up the portfolio. The weightage is assigned based on the investment in the stocks as a proportion of the total investment.

Total investment in new portfolio = 10 + 5 = 15 million

New portfolio beta = 10/15 * 1.05 + 5/15 * 0.65  

New portfolio beta = 0.9167

We need to calculate the market risk premium, using the old required rate of return, to use in CAPM.

r = rRF + Beta * rpM

0.095 = 0.042 + 1.05 * rpM

0.095 -0.042 = 1.05rpM

(0.053) / 1.05 = rpM

rpM = 0.05047 or 5.047% rounded off to 5.05%

The new required rate of return using CAPM,

r = 0.042 + 0.9167 * 0.0505

r = 0.08829 or 8.829% rounded off to 8.83%