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You have been managing a $3 million portfolio. The portfolio has a beta of 1.10 and a required rate of return of 10%. The current risk-free rate is 5.6%. Assume that you receive another $600,000. If you invest the money in a stock that has a beta of 0.60, what will be the required return on your $3.6 million portfolio?

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Answer:

The Required rate of return on Portfolio is 9.67%

Explanation:

In order to get the answer first we need to calculate the new beta of portfolio.  The weight of portfolio and new stock is calculated using total value of investment in portfolio and multiplying by the total investment we get new beta.  

(3M / 3.6M) x 1.10 + (0.6M / 3.6M) x 0.60 = 1.01667

Through using the CAPM Model we get risk premium of Existing Portfolio:

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

10% = 5.6% + (Rm -RF) x 1.10

10% - 5.6% = (Rm - RF) x 1.10

4.4% / 1.10 = (Rm - RF)

(Rm - RF) = 4%

After getting the Risk Premium we can CAPM model equation to get New Required rate of return.

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

Required rate of return of portfolio = 5.6% + 4% x 1.01667

Required Rate of Return of Portfolio = 9.67%

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