Question

Ted, 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 7.00%. Ted expects to receive an additional $60 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?

*Show the formula you used and formula inputs.

Answer 1

mutual fund manager has a $40 million portfolio with a beta of 1.00.

The risk-free rate is 4.25%,

The market risk premium is 7.00%.

The manager expects to receive an additional $60 million which she plans to invest in additional stocks. expected return to be 13.00%.

Bi = 1
rf = 4.25%
rm = 7%

Using CAPM You are already given the market risk premium as 7%, this is telling you that the return of the market over the risk free rate is 7%, ie the term (Rm-RFR) =7%,

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

13=4.25+B(7)
B(7) = 13 - 4.25
B(7) = 8.75
B= 1.25

The Beta of the total portfolio must be 1.25 to give a return of 13%.

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

.4(1)+0.7(B)=1.25

0.7B=0.85

B=1.2142