Question

PORTFOLIO BETA

A mutual fund manager has a $20 million portfolio with a beta of 1.50. The risk-free rate is 6.50%, 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 17%. What should be the average beta of the new stocks added to the portfolio? Do not round intermediate calculations. Round your answer to two decimal places. Enter a negative answer with a minus sign.

Answer 1

Expected return for existing portfolio

As per CAPM

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

Expected return% = 6.5 + 1.5 * (4.5)

Expected return% = 13.25

Total New Portfolio value = Value of Existing portfolio + Value of New stocks

=20+5

=25

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

= 20/25

=0.8

Weight of New stocks = Value of New stocks/Total New Portfolio Value

= 5/25

=0.2

Expected return of New Portfolio = Weight of Existing portfolio*Expected return of Existing portfolio+Weight of New stocks*Expected return of New stocks

17 = 13.25*0.8+Expected return of New stocks*0.2

Expected return of New stocks = 32

As per CAPM

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

32 = 6.5 + Beta * (4.5)

Beta = 5.67