Problem: Optimal Portfolio Weight
Suppose the lending rate is 0.04 (4%) while the borrowing rate is 0.07 (7%). You are constructing a portfolio consisting of one risky and one risk free asset. Expected return and standard deviation of the risky asset is 0.10 (10%) and 0.20 (20%) respectively. Your client's utility function is defined as where E, S, and are expected return, standard deviation, and risk aversion parameter. What is the range of risk aversion for which the client will neither borrow nor lend, that is, for which your client invest 100% in risky asset only?