Question

You have been managing a $5 million portfolio that has a beta of 1.35 and a required rate of return of 7.725%. The current risk-free rate is 3%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.55, what will be the required return on your $5.5 million portfolio?

Answer 1

As per CAPM

required return = risk free rate + beta*market risk premium

from the above given information

7.725% = 3% + 1.35*market risk premium

market risk premium = 3.5%

required return on the new stock:

given beta = 1.55

return = 3 + 1.55*3.5%

= 8.425%

Portfolio return = weighted average return

weights:

existing = 5,000,000 / 5,500,000 = 0.909

New = 500,000 / 5,500,000 = 0.091

required return on $5.5 million portfolio:

=(0.909*7.725%) + (0.091*8.425%)

= 7.79%(rounded to two decimals)