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[r]-0.5A()^2. What is the optimal portfolio for an investor with A=4? (Hint: calculate the investors utility for different portfolio combinations. Begin with 100% in risk free, 0% in S&P and go up to -50% in risk free and 150% in S&P with 10% increments. Excel would be helpful here.)