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7. 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 $8.50 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) 8.57% B) 9.00% C) 7.80% D) 8.14% E) 7.97%

User Mwspencer
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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%

User PostureOfLearning
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Answer:

The correct answer is option (A).

Step-by-step explanation:

According to the scenario, the computation of the given data are as follows:

First, we will calculate the Market risk premium, then

Market risk premium = (Required return - Risk free rate ) ÷ beta

= ( 9.50% - 4.20%) ÷ 1.05 = 5.048%

So, now Required rate of return for new portfolio = Risk free rate + Beta of new portfolio × Market premium risk

Where, Beta of new portfolio = (10 ÷ 18.5) × 1.05 + (8.5 ÷ 18.5) × 0.65

= 0.5676 + 0.2986

= 0.8662

By putting the value, we get

Required rate of return = 4.20% + 0.8662 × 5.048%

= 8.57%

User Parth Soni
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