CAPM AND PORTFOLIO RETURN You have been managing a 5 million

CAPM AND PORTFOLIO RETURN You have been managing a $5 million portfolio that has a beta of 1.05 and a required rate of return of 14%. The current risk-free rate is 4.00%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.45, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

Solution

$5 million portfolio:

Beta = 1.05
Required Return = 14%
Risk-free Rate = 4.00%

Required Return = Risk-free Rate + Beta * Market Risk Premium
14% = 4.00% + 1.05 * Market Risk Premium
10.00% = 1.05 * Market Risk Premium
Market Risk Premium = 9.5238%

$5.5 million portfolio:

Weight of New Stock = $0.5 million / $5.5 million = 1/11
Weight of Old Portfolio = $5.0 million / $5.5 million = 10/11

New Portfolio Beta = Weight of Old Portfolio * Beta of Old Portfolio + Weight of New Stock * Beta of New Stock
New Portfolio Beta = (10/11) * 1.05 + (1/11) * 1.45
New Portfolio Beta = 1.086

New Portfolio Required Return = Risk-free Rate + New Portfolio Beta * Market Risk Premium
New Portfolio Required Return = 4.00% + 1.086 * 9.5238%
New Portfolio Required Return = 14.34%