Suppose your optimal risky portfolio has an expected return E(rp) = 6.5% and standard deviation as 6%. You can also invest in a risk-free asset with rf = 3.5%. Your risk aversion A = 1/15.

(a) Calculate the Sharpe ratio.

(b) What is the expected return for your complete portfolio, if the standard deviation is 3%?

(c) What is the optimal allocation that maximizes your utility? Write down the portion (in a number between 0 and 1, or greater than 1 if you are buying on margin) in the risky portfolio.

(d) Which transaction are you doing in your optimal allocation? Write down A or B. A: Normal cash account that invests part of your balance in Treasury bill. B: Buy on margin and pays back your loan in the future.

(e) Suppose when you are buying on margin, your broker charges you a 4% interest rate, instead of the risk-free rate. What is your expected return for your complete portfolio, using the optimal allocation weight in (c), in this case?