Question

You have been managing a $5 million portfolio that has a beta of 1.05 and a required rate of return of 9.775%. The current risk-free rate is 4%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.75, what will be the required return on your $5.5 million portfolio

Answer 1

Answer:

9.62%

Explanation:

Re = Rf + (B x Rp)

Re = cost of equity = 9.775%

Rf = risk free rate = 4%

B = beta = 1.05

Rp = risk premium = ?

Rp = (Re - Rf) B = (9.775% - 4%)/1.05 = 5.5%

Re portfolio = Rf + {Rp x [(B₁ x $5/$5.5) + (B₂ x $0.5/$5.5)]}

Re portfolio = 4% + {5.5% x [(1.05 x $5/$5.5) + (0.75 x $0.5/$5.5)]}

Re portfolio = 4% + {5.5% x [0.9545 + 0.0682]}

Re portfolio = 4% + 5.6249% = 9.62%