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A mutual fund manager has a $20 million portfolio with a beta of 1.7. The risk-free...

A mutual fund manager has a $20 million portfolio with a beta of 1.7. The risk-free rate is 4.5%, 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 15%. What should be the average beta of the new stocks added to the portfolio?

a) Find the weights of the new and old portions of the total new portfolio

b) Find beta of the new additional part of the portfolio

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Answer #1

Beta of new portfolio:

As per CAPM
expected return = risk-free rate + beta * (Market risk premium)
15 = 4.5 + Beta * (7)
Beta = 1.5

New portfolio size = old portfolio size + additional investment=20+5 = 25 mln

beta of new portfolio = old portfolio size/new portfolio size*beta old portfolio+additional investment/new portfolio size*beta of additional part

1.5 = 20/25*1.7+5/25*beta of additional part

beta of additional part = 0.7

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