Question

A mutual fund manager has a $20 million portfolio with a beta of 1.7. The risk-free rate is 3.5%, and the market risk premium is 7%. 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 14%. What should be the average beta of the new stocks added to the portfolio? Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to one decimal place.

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Answer 1

As per CAPM

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

Expected return% = 3.5 + 1.7 * (7)

Expected return% = 15.4

Total New portfolio value = Value of Existing portfolio + Value of additional inv

=20+5

=25

Weight of Existing portfolio = Value of Existing portfolio/Total New portfolio Value

= 20/25

=0.8

Weight of additional inv = Value of additional inv/Total New portfolio Value

= 5/25

=0.2

expected return of New portfolio = Weight of Existing portfolio*expected return of Existing portfolio+Weight of additional inv*expected return of additional inv

14 = 15.4*0.8+expected return of additional inv*0.2

expected return of additional inv = 8.4

As per CAPM

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

8.4 = 3.5 + Beta * (7)

Beta = 0.7