Question

A mutual fund manager has a $40 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the market risk premium is 6.00%. The manager expects to receive an additional $60 million which she plans to invest in additional stocks. After investing the additional funds, she wants the combined fund’s required return to be 13.00%. What must the average beta of the new stocks be to achieve the required rate of return of 13%?

Answer 1

As per CAPM,

where, rf = Risk free return = 4.25%

Rmp = Market Risk Premium = 6%

Required rate of Return of new Portfolio = 13%

Calculating Beta of new portfolio:-

13% = 4.5% + Beta(6%)

Beta new portfolio= 1.4167

- Beta of old portfolio is 1.0 with $40 million investment

Additional funds of $60 million is added to the Portfolio

Total Investment in new portfolio = $40M + $60M = $100M

Calculating the average Beta of the new stocks added:-

Beta of new portfolio = (Weight of old portfolio)(Beta of old portfolio) + (weight of new stocks)(Beta of new stocks)

1.4167 = ($40M/$100M)(1.00) + ($60M/$100M)(Beta of new stocks)

1.4167 = 0.4 + 0.6*Beta of new stocks

Beta of new stocks = 1.6944

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