Suppose that a fund that tracks the S&P has mean E(R_M) = 16% and standard deviation sigma_m = 10%, and suppose that the T-bill rate R_f = 8%. Answer the following questions about efficient portfolios:
a) 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?
b) 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?
c) 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?
d) Assume investors' preferences are characterized by the utility function U = E[r] - 0.5 A sigma^2. What would be the optimal allocation, i.e. the investment weights on S&P and T-bill, for an investor with a risk-aversion coefficient of A=4? What is the expected return and standard deviation of this optimal portfolio?