Question

You have been managing a $5 million portfolio that has a beta of 1.95 and a required rate of return of 10.395%. The current risk-free rate is 6%. 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? 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)

10.395=6+1.95*(market rate-6)

(10.395-6)=1.95*(market rate-6)

market rate=(10.395-6)/1.95+6

=8.25384615%(Approx)

Hence required rate for $500,000=6+0.85*(8.25384615-6)

=7.91576923%

Required rate of portfolio=Respective return*Respective weight

=(5,000,000/5,500,000*10.395)+(500,000/5,500,000*7.91576923)

=10.17%(Approx).