A mutual fund manager has a $20 million portfolio with a beta of 1.3. The risk-free rate is 3.5%, and the market risk premium is 9%. 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? Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to one decimal place.
Assuming that CAPM holds; we have following formula
Required rate of Return of new portfolio = risk free rate + βp*market risk premium
Where,
Required rate of Return of new portfolio = 17%
Risk-free rate = 3.5%
The market risk premium = 9%
And beta of portfolio βp =?
Therefore
17% = 3.5% + βp * 9%
Or βp = (17% - 3.5%)/9% = 1.5
Now we know that beta of total portfolio (fund) is weighted average beta of two portfolios of $50 million and $5 million
And assume that the average beta of the new stocks added to the portfolio is β2
Therefore,
Beta of portfolio βp = Weight of portfolio 1 *β1+ weight of portfolio 2* β2
Where,
Beta of portfolio βp = 1.5
Weight of portfolio 1 = $50 million/ ($50 million + $5 million)
Beta of portfolio 1, β1= 1.3
Weight of portfolio 2 = $5 million/ ($50 million + $5 million)
Beta of portfolio 2, β2 =?
Therefore,
1.5 = ($50 million/$55 million) * 1.3 + ($5 million/$55 million) * β2
Or β2= (1.5 – 1.18)/ (0.0909) = 3.5
Therefore the average beta of the new stocks added to the portfolio is 3.5
A mutual fund manager has a $20 million portfolio with a beta of 1.3. The risk-free...
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