Question

A mutual fund manager has a $20 million portfolio with a beta of 1.40. The risk-free rate is 5.75%, and the market risk premium is 5.5%. 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 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 two decimal places.

Answer #1

Beta of new portfolio:

As per CAPM |

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

14 = 5.75 + Beta * (5.5) |

Beta = 1.5 |

Total new Portfolio value = Value of Current portfolio + Value of Additional investment |

=20+5 |

=25 |

Weight of Current portfolio = Value of Current portfolio/Total new Portfolio Value |

= 20/25 |

=0.8 |

Weight of Additional investment = Value of Additional investment/Total new Portfolio Value |

= 5/25 |

=0.2 |

Beta of new Portfolio = Weight of Current portfolio*Beta of Current portfolio+Weight of Additional investment*Beta of Additional investment |

1.5 = 1.4*0.8+Beta of Additional investment*0.2 |

Beta of Additional investment = 1.9 |

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