You have been managing a $5 million portfolio that has a beta of 1.70 and a required rate of return of 10%. The current risk-free rate is 4.25%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.90, what will be the required return on your $5.5 million portfolio? Round your answer to two decimal places.
First we need to solve for the market risk premium from the $5 million portfolio. We solve for Rm in the following formula: 10% = 4.25% + (Rm - 4.25%) x 1.70. Solving for Rm we get a market risk premium of 7.63%. Now we need to solve for the required return on the $500,000. We solve for expected return in the following formula: expected return = 4.25% + (7.63% - 4.25%) x 1.90 = 10.68%. Now we solve for the expected return of the portfolio. The expected return is the weighted average return of the two stocks. That is, $500,000/$5,500,000 x 10.68% + $5,000,000/$5,500,000 x 10% = 10.06%. The expected return of the portfolio is 10.06%.