You hold the market portfolio and believe that the risk premium for holding the market portfolio is 5% per year. The risk-free rate is 5%. You are given the opportunity to invest a small amount in one of two new stock issues: Allied Inc. or Apex Corp. Allied's stock has an annual standard deviation of 30%, a beta of 0.5, and an expected return of 8.0%. Apex's stock has an annual standard deviation of 30%, a beta of 1.0, and an expected return of 9.0%. If you could add at most one stock to your portfolio and main focus is to increase the alpha for the total portfolio, which stock would you add?

Please show a detailed solution, thanks.