Problem 3: Scenarios-scenarios-scenarios [25 points] You work as an analyst for a financial firm.You make the following predictions for the future returns of stocks A, B & C, depending on the state of the economy:

Economy Stock A Stock B Stock C Probability

Very Good 60% 50% 30% 30%

Good 50% 40% 25% 20%

Neutral 40% 30% 20% 20%

Bad 30% 20% 15% 20%

Very Bad 20% 10% 10% 10%

1. Explicitly estimate the expected return and the variance of stock A (show all your work).

2. Great!! Now, estimate the expected return and the variance of stocks B and C.

3. Estimate the expected return and the variance of stock A, if the states are equally probable to occur.