Question

Problem 8-16
CAPM and portfolio return

You have been managing a $5 million portfolio that has a beta of 1.15 and a required rate of return of 11%. The current risk-free rate is 4.75%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.30, 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

$5 million Portfolio:

Required Return = 11%
Beta = 1.15
Risk-free Rate = 4.75%

Required Return = Risk-free Rate + Beta * Market Risk Premium
11% = 4.75% + 1.15 * Market Risk Premium
6.25% = 1.15 * Market Risk Premium
Market Risk Premium = 5.435%

Another investment of $500,000:

Beta = 1.30
Market Risk Premium = 5.435%
Risk-free Rate = 4.75%

Required Return = Risk-free Rate + Beta * Market Risk Premium
Required Return = 4.75% + 1.30 * 5.435%
Required Return = 11.816%

Portfolio of $5.50 million:

Required Return = 11% * ($5.0 million / $5.5 million) + 11.816% * ($0.5 million / $5.5 million)
Required Return = 11.07%