Suppose that a fund that tracks the S&P has expected return E[Rm] = 8% and standard deviation M = 18%, and suppose that the T-bill rate is Rf = 2%.

1. (a) What is the expected return and standard deviation of a portfolio that:

   1. Is entirely invested in the risk-free asset?

   2. Has 50% of its value in the risk-free asset and 50% in the S&P?

   3. Has 125% of its value in the S&P, financed by borrowing 25% of its value at the risk-free rate?

2. (b) Now consider an investor that has preferences over portfolio returns characterized by:

   U(RP) = E[RP]2Var(RP) Which of the three portfolios from part (a) will be preferred by the investor with

   the above utility function?

3. (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 this portfolio?

4. (d) What is the Sharpe ratio of this portfolio and how does it compare to the Sharpe ratio of a 100% S&P investment?