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 1.25. The risk-free rate is 4.75%, and the market risk premium is 7.0%. 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? Do not round intermediate calculations. Round your answer to two decimal places. Enter a negative answer with a minus sign.

Explanation / Answer

Solution:-

Given

Risk free rate (Rf)= 4.75%,

Market risk premium(RPm)= (Rm - Rf)= 7%

Required rate of return (RR) = 17%

We know as pre CAPM model

RR = Rf + Betaportfolio*(Rm-Rf)

17 =4.75+Betaportfolio*7

Beta portfolio = (17-4.75)/7

Beta portfolio =1.75

We know that beta of portfolio can be calculated as follows:-

Betaportfolio = Beta existing stoxks*Wexistingstocks + BetaNew stocks*WNewstocks

Where,

Beta existing stoxks= 1.25

Wexistingstocks=20/25 = 0.80

WNewstocks=5/25=0.20

Substituting the values we get :-

1.75 =1.25*0.80+ BetaNew stocks*0.20

BetaNew stocks = (1.75-1)/0.20

Beta New stocks= 3.75

Hence the average beta of the new stocks added to the portfolio = 3.75

Please feel free to ask if you have any query in the comment section.

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