Suppose that you are considering investing in two stocks A and B. After analyzing the two stocks you think that there are three possible states for the economy over the next year. The economic states and the probabilities, as well as the rates of return on the two securities in each state are as follows:

(a) Find the weight vector W_m = (, (1- )) of the minimum-variance portfolio.

(b) Can you develop a risk-free portfolio with Stock A and Stock B? If yes, what is the expected rate of return of the risk-free portfolio? If no, explain why.

Probability Return of Stock A Return of Stock B 20% 20% 2% 40% 10% 4% 40% -5% 6%