Question

A mutual fund manager has a $20 million portfolio with a beta of 1.5. The risk-free rate is 4.5%, 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?

Answer 1

CAPM return of current portfolio = risk free rate + beta *(market risk premium)

=>4.5% + 1.5*(5.5%)

=>12.75%.

for a required return of 13% beta shall be calculated, let it be x.

13% = 4.5% + x *(5.5%)

=>8.5% = x*5.5%

=>1.54545=x.

if the required return should be equal to 13%, the overall beta = 1.54545.

overall beta = (weight of old investments* beta of old investments) + (weight of new investments * beta of new investments)

here,

overall beta = 1.54545.

weight of old investments = ($20 million / ($20 million + 5 million)=>0.80.

beta of old investments = 1.50.

weight of new investment = ($5 million / $25 million) =>0.20.

beta of new investments = to be found out, let it be y.

=>1.54545 = (0.80*1.50) + (0.20*y)

=>1.54545-1.20=>0.20*y

=>0.3454545 = 0.20*y

=>y=1.72725.

so, beta of new stocks shall be = 1.72725.