Question

A mutual fund manager has a $40 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the market risk premium is 6.00%. The manager expects to receive an additional $29.50 million which she plans to invest in additional stocks. After investing the additional funds, she wants the fund's required and expected return to be 13.00%. What must the average beta of the new stocks be to achieve the target required rate of return? Do not round your intermediate calculations.

Answer 1

Solution :-

You were nearly there with the final attempt using CAPM but the last term (6 - 4.25) is incorrect.

You are already given the market risk premium as 6%, this is telling you that the return of the market over the risk free rate is 6%, ie the term (Rm - RFR ) = 6%

So you have effectively subtracted the risk free rate twice, that seems to be why you can't get the correct answer.

Using CAPM, A portfolio return of 13% requires a total portfolio beta of:

13 = 4.25 + B(6)

B(6) = 13 - 4.25

B(6) = 8.75

B= 1.458

The Beta of the total portfolio must be 1.458 to give a return of 13%.

To determine the average beta of just the new stocks (as requested):

0.5755 ( 1 ) + 0.4244 ( B ) = 1.458

0.4244 ( B ) = 0.88246

B = 2.079

If there is any doubt please ask in comments

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