PROBLEM 2: Suppose there are three equally likely outcomes or scenarios for the economy: a recession, normal growth, and a boom. An investment in auto stock will have a rate of return of 8% in a recession, 5% in a normal period, and 18% in a boom. Also, suppose that a stock in a gold mining firm will provide a rate of return of 20% in a recession, 3\% in a normal period, and 20% in a boom. [10 points] (a) Firms that do well when the economy does well are called cyclical whilst firms that have the opposite performance in their rate of return are called countercyclical. Based on the given information above, classify the auto and gold stocks as either cyclical or countercyclical. [1 pt] (b) Which stock investment is more volatile and why? Reason out based on the concept of variation. [1 pt] (c) Confirm your answer in (b) by measuring the standard deviation of returns of the two assets. [4 pts] (d) Compute the correlation between the auto and gold stocks. [1 pt] (e) Suppose the probabilities of the recession or boom are 0.30. Would you expect the variance of returns on these two investments to be higher or lower and why? Use general economic/statistical principle(s). [1 pt] (f) Confirm your answer in (e) by calculating the standard deviation of the auto stock. [2 pts]