Question

# A mutual fund manager has a \$20 million portfolio with a beta of 1.35. The risk-free...

A mutual fund manager has a \$20 million portfolio with a beta of 1.35. The risk-free rate is 5.75%, and the market risk premium is 6.5%. 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 12%. 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.

Value of existing portfolio = \$20 million

Beta = 1.35

after added \$5 million required return = 12%
Beta of new portfolio = (12% - 5.75%) / 6.50%

= 6.25% / 6.50%

= 0.96

Beta of new portfolio is 0.96.

Weight of existing portfolio in new portfolio = \$20 / 25

= 80%

Weight of new value added = 20%.

So, beta of additional fund is calculated below:

0.96 = (80% × 1.35) + (20% × Beta)

0.96 = 1.08 + (20% × Beta)

(20% × Beta) = -0.118

Beta = -0.59

Beta of new portfolio is -0.59.

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