Question

ABC, a mutual fund manager, has a $40 million portfolio with a beta of 1.50. The risk-free rate is 4.00%, and the market risk premium is 5.00%. ABC 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?

Answer 1

Using CAPM, required rate can be calculated as Rf+Beta*(Rm-Rf); where Rf is risk free rate, Rm is market return and Rm-Rf is market risk premium.

For the current portfolio, expected return= 4%+(1.5*5%)= 11.5%

with an additional funds of $60 million with an existing portfolio of $40 million, the weights of old and new stocks in the portfolio will be 0.4 and 0.6 respectively.

Expected Return of a 2 stock portfolio is a weighted average of individual returns. It is calculated as (w1*r1)+(w2*r2)

So, Expected Return= 13% = (0.4*11.5%)+(0.6*R)

R= 8.4%/0.6= 14%.

Using CAPM again, Expected Return= 14%= 4%+Beta*5%

Beta= 10%/5%= 2.

So, Average Beta of new stocks should be 2.