Final answer:
The required rate of return on the new portfolio is approximately 8.57%.
Step-by-step explanation:
To find the required rate of return on the new portfolio, we first need to calculate the market risk premium. The market risk premium is the difference between the expected return on the market and the risk-free rate. In this case, the risk-free rate is 4.20% and the required return on the mutual fund is 9.50%. Therefore, the market risk premium is 9.50% - 4.20% = 5.30%.
To find the new portfolio beta, we need to calculate the weighted average of the old and new investments. The old investment has a beta of 1.05 and a value of $10.00 million, while the new investment has an average beta of 0.65 and a value of $8.50 million. The total value of the portfolio is $10.00 million + $8.50 million = $18.50 million. Therefore, the weighted average beta is calculated as [(1.05 * $10.00 million) + (0.65 * $8.50 million)] / $18.50 million = 0.9135.
Finally, we can calculate the required rate of return on the new portfolio using the formula:
Required Rate of Return = Risk-Free Rate + (Portfolio Beta * Market Risk Premium)
Substituting in the values, we get:
Required Rate of Return = 4.20% + (0.9135 * 5.30%) ≈ 8.57%