Consider you are investing in the market portfolio and risk free bond. The expected return of the market portfolio is 14% and its standard deviation is 18% while the risk free rate is 4%.

a. If you invest 40% in the market portfolio and the rest in the risk free bond, what will be the expected return and standard deviation?

b. If your portfolio has the expected return of 12%, what is the portfolio weight of the market portfolio? What is the standard deviation of your portfolio return?

c. If you want a portfolio with expected return of 20%, what percentage of your investment should be invested in the market portfolio? What percentage of your investment should you invest in the risk free bond?