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%**

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