Show all work including setting up all mathematical equations with the proper inputs identified. Only nal qumbers without a trace of work will result in zero credit without exception. Use four decimal places. Calculate the followings and verify the diversification effect with the data in the table assuming that with the initial endowment of $10,000, you invest $6,000 in Stock A and $4,000 in Stock B. Also four states of the economy are assumed to be equally likely. State of the Economy Depression Recession Normal Boom Rate of Return on Stock A -20% 10% 30% 50% Rate of Return on Stock B 5% 20% -12% 9% Q. I: Expected rate of return for each security Q.2: Expected rate of return for the portfolio with the stock A and B Q.3: Variance for each security Q.4: Standard deviation for each security Q. 5: Weighted average of standard deviations of two securities Q.6: Covariance between securities Q. 7: Correlation coefficient between securities Q. 8: Variance of a portfolio 0.9: Standard deviation of a portfolio Q. 10: Compare the weighted average of standard deviations of two securities with the portfolio standard deviation. (a) Did you see diversification effect? (b) Why? Justify your answer in part (a)