Question

A mutual fund manager has a $20 million portfolio with a beta of 1.55. The risk-free rate is 3.00%, and the market risk premium is 4.5%.  The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks.  After investing the additional funds, she wants the fund's required return to be 18%.  What should be the average beta of the new stocks added to the portfolio? Round your answer to two decimal places.

Answer 1

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 3 + 1.55 * (4.5)

Expected return% = 9.98

Total Portfolio value = Value of Add inv + Value of Old port

=5+20

=25

Weight of Add inv = Value of Add inv/Total Portfolio Value

= 5/25

=0.2

Weight of Old port = Value of Old port/Total Portfolio Value

= 20/25

=0.8

return of Portfolio = Weight of Add inv*return of Add inv+Weight of Old port*return of Old port

18 = return of Add inv*0.2+9.98*0.8

return of Add inv = 50.08

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

50.08 = 3 + Beta * (4.5)

Beta = 10.46