Question

You have been managing a $5 million portfolio that has a beta of 1.05 and a required rate of return of 15.675%. The current risk-free rate is 7%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.00, 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

- Portfolio's Beta = 1.05

Portfolio's value = $5 million

Required Rate of Return of portfolio = 15.675%

- calculating Market risk Premium using CAPM,

where, rf = Risk free return = 7%

Rmp = Market Risk premium

Beta = 1.05

Required Rate of Return = 15.675%

15.675% = 7% + 1.05*(Rmp)

Market risk Premium = 8.262%

- Now, you receive another $500,000 having a beta of 1 which is combined with the existing portfolio

Calculating Beta of combined portfolio:-

Beta of combined $5.5 million portfolio = ($5 million/$5.5 million)(1.05) + ($0.5 million/$5.5 million)(1.00)

Beta of combined $5.5 million portfolio = 0.9545 + 0.0909

Beta of combined $5.5 million portfolio = 1.0454

- Now, Calculating the Required return of combined $5.5 million portfolio:-

where, rf = Risk free return = 7%

Rmp = Market Risk premium = 8.262%

Beta of combined Portfolio = 1.0454

Required Rate of Return = 7% + 1.0454*(8.262%)

Required Rate of Return = 15.64%

So, the required return on your $5.5 million portfolio is 15.64%

If you need any clarification, you can ask in comments.    

If you like my answer, then please up-vote as it will be motivating