PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of

Question

PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of 0.95. The risk-free rate is 6.75%, and the market risk premium is 5.5%. 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 13%, 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.

Explanation / Answer

average beta of new stocks = 1.88.

first let us know the return earned by existing portfolio:

=>risk free rate + beta *(premium)

=>6.75% + 0.95*(5.5%)

=>11.975%.

since, the new investment is $5 million, total portfolio will be $20m + $5 m =>$25 million.

for the required return to be 13%

=> weighted return on $5 million + weighted return on $20 million = 13%

weight of $ 5 million = $5 million/ $25 million =>0.20

weight of $20 million = $20 million / 25 million =>0.80.

let x be the return on new investment

weighted return:

0.20*(x) + 0.80*(11.975%) =>13%

=>0.20x + 9.58 = 13%

=>0.20x = 3.42%

=>x = 17.10%.

the required return on new investment = 17.10%

to find the beta:

risk free rate + beta (risk premium) =17.10%

=>6.75% + beta(5.5%)=>17.10%

=>5.5 *beta = 17.10-6.75

=>beta =10.35/5.5

=>beta = 1.88 ..........(rounded to two decimals).

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