11. Suppose that a fund that tracks the S&P has mean E(Rm)-16% and standard deviation m-10%, and suppose that the T-bill rate Rf 8%. Answer the following questions: (a) What is the expected return and standard deviation of a portfolio that is completely invested in the risk-free asset? (b) what is the expected return and standard deviation of a portfolio that has 50% of its wealth in the risk-free asset and 50% in the S&P? (c) What is the expected return and standard deviation of a portfolio that has 125% of its wealth in the S&P, financed by borrowing 25% of its wealth at the risk-free rate? (d) What are the weights for investing in the risk-free asset and the S&P that produce a standard deviation for the entire portfolio that is twice the standard deviation of the S&P? What is the expected return on that portfolio? (e) Assume an investor' preference is characterized by the utility function U E[ri-0.5A(o)12. What is the optimal portfolio for an investor with A-4? (Hint: calculate the investor's utility for different portfolio combinations. Begin with 100%innsk ree.0 oun S&P and go up to-509 in riskfree and 150%inS&P with 10% increments. Excel would be helpful here.)