You are thinking about investing your money in the stock market. You have the following two stocks in mind: stock A and stock B. You know that either the economy can go in recession or it will boom. Being an optimistic investor, you believe the likelihood of observing an economic boom is two times as high as observing an economic depression. You also know the following about your two stocks:

State of the Economy	Probability	RA	RB
Boom	30%	12%	10%
Normal	40%	9%	10%
Recession	30%	4%	10%

1. Calculate the expected return for stock A and stock B
2. Calculate the total risk (variance and standard deviation) for stock A and for stock B
3. Calculate the expected return on a portfolio consisting of 40% invested in stock A and the remainder in stock B.
4. Calculate the covariance between stock A and stock B.
5. Calculate the correlation coefficient between stock A and stock B.
6. Calculate the variance of the portfolio consisting of 60% invested in stock A and the remainder in stock B.
7. Calculate the optimal % of investment (weight) in stock A and stock B, if we want to make zero risk portfolio.