Question

A mutual fund manager has a $20 million portfolio with a beta of 0.75. The risk-free rate is 4.25%, 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 16%. 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

SML Equation:

E(R_{i}) = R_{f} + b_{i} (R_{m}
- R_{f})

R_{f} = 4.25% , (R_{m} - R_{f}) = 4.5%
and E(R_{i}) = 16% after investing 5 million more.

Therefore, required b_{i} of the overall portfolio
is

16% = 4.25% + b_{i}(4.5%)

b_{i} = 2.6111

This the required beta of overall portfolio.

After investing 5 million more,

Total fund invested = 25 million

Percentage invested in new stocks (w) = 20%

b_{i} = (w)(Beta of new stocks) + (1 - w)(Beta of old
stocks)

2.6111 = (.20)(B) + (.80)(0.75)

Beta of new stocks = 10.0555

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