Question

You have been managing a $5 million portfolio that has a beta of 0.85 and a required rate of return of 4.975%. The current risk-free rate is 2%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.55, what will be the required return on your $5.5 million portfolios? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

We will use CAPM to solve the problem. First, we need to find the Market Risk Premium(MRP) by using the $5 million portfolio. MRP will remain same for the $5.5 million portfolio as well.

According to CAPM:
Required return = Risk free Rate + MRP*Beta
0.04975 = 0.02 + MRP*0.85
MRP = (0.04975 - 0.02) / 0.85
MRP = 0.035 or 3.5%

Beta of the new portfolio will be the weighted average beta of old portfolio and new investment.
Beta of the new portfolio = [(5*0.85) + (0.5*0.55)] / 5.5 = 0.822727

Required Return on new portfolio of $5.5 million = Risk free rate + MRP*New Beta
   = 0.02 + 0.035*0.822727
   = 0.0488 or 4.88%