Question

You have been managing a $5 million portfolio that has a beta of 1.15 and a required rate of return of 8.025%. 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 0.95, 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

Rf = Risk free rate = 4%

Beta = 1.15

Required return = 8.025%

Market Risk Premium = (Requied return - Risk free rate) / Beta

= (8.025% - 4%) / 1.15

= 4.025% / 1.15

= 3.5%

WA = Weight of Portfolio = $5,000,000 / $5,500,000 = 0.9090909

WB = Weight of new stock = $500,000 / $5,500,000 = 0.0909090

BA = Beta of Portfolio = 1.15

BB = Beta of new stock = 0.95

New Beta with stock = [WA * BA] + {WB * BB]

= [0.9090909 * 1.15] + [0.0909090 * 0.95]

= 1.04545454 + 0.08636355

= 1.13181809

Required return on $5.5 million portfolio = Rf + (New beta * Market Risk premium)

= 4% + (1.13181809 * 3.5%)

= 4% + 3.96136332%

= 7.96136332%

Therefore, Required return on $5.5 million portfolio is 7.96%