Asset	Expected Return	Standard Deviation
P	8.25%	13.6%

a. Consider again the investor with A=7. Solve for the portfolio allocation between risky asset P and T-bills with a higher risk-free rate of 3.7%, everything else unchanged. What are the expected return and risk of this allocation? Demonstrate numerically and graphically that utility is higher with the higher risk-free rate.

b. When the risk-free rate is 2.7%, for what level of risk aversion will an investor choose a complete portfolio of only risky asset P?

c. Solve for the optimal complete portfolio allocation between risky asset P and T-bills when A=2.2 and the T-bill rate is 2.7%. Consider now a higher risk-free rate of 3.7%, everything else unchanged. Demonstrate numerically and graphically that utility is lower with the higher risk-free rate.

d. Explain why utility declines in the latter case (A=2.2), and increases in the former case (A=7) when there is an increase in the risk free rate.

e. Consider again the investor with A=2.2, and a risk-free rate = 2.7%. Now, when the investor wants to buy the risky asset on margin, he cant borrow at the risk-free rate. The borrowing rate is 3.5%. What is the investors optimal allocation to the risky asset, P? Graph your result. At what borrowing rate will this investor no longer buy on margin (i.e., y* = 1)?