Question

CAPM and portfolio return

You have been managing a $5 million portfolio that has a beta of 1.50 and a required rate of return of 16%. The current risk-free rate is 6.50%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.75, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

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

Hence for $5million:

16=6.5+1.5*(MArket rate-6.5)

(16-6.5)=1.5*(MArket rate-6.5)

MArket rate=(16-6.5)/1.5+6.5

=12.833%(Approx)

Hence for $500,000;

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

=6.5+1.75*(12.833-6.5)

=17.583%(Approx)

Hence required return on portfolio=Respective return*Respective investment weights

=(5,000,000/5,500,000*16)+(500,000/5,500,000*17.583)

=16.14%(Approx).