12. There are 3 possible states of the world: a boom, normal times, and a recession. The following is the return for two assets A and B in each state of the world: State of the World Probability Asset A return Asset B return Boom 1.3 20% 35% Normal .4 10% 20% Bust .3 5% -3% a. Calculate the expected returns of assets A and B. (6 points) b. Suppose you want to invest $1000 in some combination of A and B, and you want your expected return to be 15%. How much should you invest in asset A? (4 points) c. What is the standard deviation of your portfolio? (6 points)