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 2.20%. You now receive another $14.50 million, which you invest in stocks with an average beta of 0.65. What is the required rate of return on the new portfolio

7.83%

Explanation:

To calculate the required rate of return we need to portfolio beta.

Portfolio beta is the average beta calculated on the basis of weightage of each investment. The beta of every investment is multiplied with the weightage of each investment in a portfolio. All the value is added to get the portfolio beta.

Total Portfolio after addition = $10 million + $14.5 million = $24.5 million

Portfolio Beta = ( Existing beta x Existing Weightage) + ( New Stock beta x New Stock Weightage)

Portfolio Beta = ( 1.05 x 10/24.5 ) + ( 0.65 x 14.5/24.5 )

Portfolio Beta = 0.43 + 0.38 = 0.81

We will use CAM to calculate the revised required rate of return

Capital asset pricing model measure the expected return on an asset or investment. it is used to make decision for addition of specific investment in a well diversified portfolio.

Formula for CAPM

First Calculate the market premium from existing portfolio

Required Rate of return = Risk free rate + beta ( market return - risk free rate )

Required Rate of return = Rf + β ( Rm - Rf )

9.50% = 2.2% + 1.05 ( Mp )

9.5% - 2.2% = 1.05 ( Mp )

7.3% = 1.05 ( Mp )

Mp = 7.3% / 1.05

Mp = 6.95%

Place this Market premium in revised rate of return calculation

Cost of Capital = Rf + β ( Rm - Rf )

Cost of Capital = 2.20% + 0.81 ( 6.95% )

Cost of Capital = 7.83%

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