Question 4 (12 points) Stocks A and B have the following returns in each of the states given below. Boom Normal Economy Recession 12% -5% 1% 15% Stock A return Stock B return 10% -5% The probability of the boom is 0.5, the probability of the normal economy is 0.3 and the probability of the recession is 0.2. (a) Calculate the variance of the returns of A and the variance of the returns of B (b) What is the covariance between the returns of A and B? (c) What is the standard deviation of a portfolio of A and B with equal amounts invested in both?