Suppose that a mutual 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 100% invested in the risk-free asset?
(b) What is the expected return and standard deviation of a portfolio that is 50% invested in the risk-free asset and 50% in the mutual fund?
(c) What is the expected return and standard deviation of a portfolio that is 125% invested in the mutual fund, financed by borrowing 25% at the risk-free rate?
(d) What are the portfolio weights that produce a standard deviation equal to twice the standard deviation of the mutual fund? What is the expected return on that portfolio?