Question

you have been managing a $5 million portfolio that has a beta of 1.15 and a required rate of return of 11.475%. The current risk-free rate is 4%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.85, what will be the required return on your $5.5 million portfolio?

Answer 1

required return=risk-free rate +Beta*(market rate- risk-free rate)

Currently:

11.475=4+1.15*(Market rate-4)

(11.475-4)=1.15*(Market rate-4)

Market rate=(11.475-4)/1.15+4

=10.5%

Hence required return for $500,000=4+0.85*(10.5-4)

=9.525%

Required rate of portfolio=Respective return*Respective investment weight

=(5,000,000/5,500,000*11.475)+(500,000/5,500,000*9.525)

=11.30%(Approx).