B1. [3+3=6 marks] You have $100k to invest. Among risky assets, there are two funds that you can choose from. However, you are allowed to choose only one of the two funds. After you select a fund, you are allowed to divide your $100k in any way you would like across risk- free bonds and that fund. The expected return and standard deviation of each fund is given in the following table: E[r] O Fund X 10% 12.0% Fund Y 15% 20.3% Zero-coupon Commonwealth Government securities maturing in one year are currently priced at $97.561 per $100 par value. Your utility function is given by U = E[r]-20 a) Assuming you can costlessly short sell both the risk-free asset and whatever fund you choose, what is your optimal portfolio? That is, which fund do you select, how much of your $100k do you invest in that fund, and how much money do you invest in the risk-free asset? Show your calculations. [3 Marks] b) Now suppose that you cannot short sell either fund or the risk-free asset. What is your optimal portfolio in this case? [3 Marks]