Question

You have been managing a $5 million portfolio that has a beta of 1.55 and a required rate of return of 10%. The current risk-free rate is 7.25%. 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

Beta for New Portfolio = 1.55 * ($5,000,000 / $5,500,000) +0.85 * ($500,000 / $5,500,000)
Beta for New Portfolio = 1.4091 + 0.0773
Beta for New Portfolio = 1.4864

Required Rate of Return = Risk Free Rate + Beta*(Expected Rate of Return – Risk Free Rate)
10 = 7.25 + 1.55 (Expected Rate of Return – 7.25)
10-7.25 = 1.55 (Expected Rate of Return -7.25)
2.75 = 1.55 (Expected Rate o Return -7.25)
2.75 / 1.55 = Expected Rate of Return – 7.25
1.7742 = Expected Rate of Return – 7.25
1.7742 + 7.25 = Expected Rate of Return
9.0242 = Expected Rate of Return

Required Rate of Return of New Portfolio= Risk Free Rate + Beta of New Portfolio*(Expected Rate of Return – Risk Free Rate)
Required Rate of Return of New Portfolio = 7.25 + 1.4864 (9.0242 – 7.25)
Required Rate of Return of New Portfolio= 7.25 + 2.6372
Required Rate of Return = 9.8872%