In a one-period model where the returns of all the risky assets are normally distributed, any greedy and risk-averse investor will place herself on the upward-sloping part of the mean-variance frontier. But where? Consider an agent that maximizes expected utility of end-of-period wealth with a negative exponential utility function u(W) = −e−aW for some constant

a. Suppose that M risky assets (with normally distributed returns) and one risk-free asset are traded. What is the optimal portfolio of the agent? Where is the optimal portfolio located on the mean-variance frontier?