Consider two utility maximizing investors (A and B) with negative exponential utility functions.

Suppose that there is a risk-free asset and that returns on risky assets are normally distributed. Hence, the preferences of these Investors can be described by

E U = e p 1 s 2p , t

where ep denoted expected return on the Investors portfolio, sp denotes the standard deviation of returns, and t is Investors risk tolerance.

The optimal portfolio for Investor A has the expected return 10% and standard deviation of returns 10%. The optimal portfolio for the Investor B has the expected return 12% and standard deviation of returns 15%.

1. (a) Find the equation for the efficient frontier. Graph the efficient frontier in (ep, sp) space where ep is the expected return on the portfolio and sp the standard deviation of the return on the portfolio. Mark in the graph the optimal portfolio choices for the two investors.