Consider a market portfolio with 9% expected return and 20% return standard deviation.

(a) If the Sharpe ratio of the market portfolio is 0.4, what is the risk-free rate?

(b) Consider the following three portfolios on the tangency line:

Portfolio 1 has 5% expected return.

Portfolio 2 has 8% expected return.

Portfolio 3 has 15% expected return.

Find the return standard deviation of each of these three portfolios.

(c) Now consider an investor that has preferences over portfolio returns characterized by:

U(RP) =P2(p)²

That is, the utility of the portfolio return is its expected return minus twice its variance. Which of the three portfolios from part (b) will be preferred by the investor with the above utility function?

(d) Are there portfolios that would be even better from the perspective of the investor in part (c)? Why or why not?