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 the risk-free asset and that fund.

The expected return and standard deviation of each fund is given in the following table:

Zero-coupon Government securities maturing in one year are currently priced at $95.238 per $100 par value. Your utility function is given by U = E[r] − 2σ2.

a) Assuming you can 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.

b) Now suppose that you cannot short sell either fund or the risk-free asset. What is your optimal portfolio in this case? 
 

Fund E[r] Fund A 15% 20% Fund B 9% 7.5%