Suppose that a fund that tracks the S&P has mean E(Rm) = 16% and standard deviation σm = 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(σ)^2. What is the optimal portfolio for an investor with A=4? (Hint: calculate the investor's 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.)