Question

You have been managing a $5 million portfolio that has a beta of .7 and a required rate of return of 15%. 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 .85, what will be the required return on your $5.5 million portfolio?

Answer 1

Required Rate = Risk Free Rate + beta *( Market return - Risk Free Rate)
15% = 3% + 0.7*(Market Return - 3%)
Market return = 12%/0.7 + 3% = 20.14%

Portfolio Beta = (Portfolio of 5 million * Beta 0.7 + Portfolio of 0.5 million* Beta 0.85)/5.5 million
= (5,000,000*0.7 + 500,000*0.85)/5,500,000 = 0.7136

Required rate of 5.5 million = Risk Free Rate + Portfolio Beta *(Market Return - Risk Free Rate)
= 3% + 0.7136*(20.14%-3%) = 15.23%

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