1. (b) A firm plans to invest in GM stock and in Gold. The firm identifies 4 states of the economy with their probabilities, and the returns of GM stock and Gold. i. What is the expected returns? [2 point] ii. What is the standard deviation of the returns? [2 point The two are now combined in a portfolio. Analyze the joint distribution of the return of the portfolio of the investments given that the ratio of investment of stock to gold is 3:2. Plot a graph of the mean return versus the standard deviation for the combination of the different ratios. [6 points) Economic outcome Probabillty Depression Gold Return GM Return Plot your graph in this spacel -0.20 0.05 0.05 Investments GM Gold 0.10 0.30 0.20 Recession Fraction of total 0.50 0.30 -0.12 Normal Boom 0.15 0.50 0.09 Distribution of portfolio returns Economic outcome Per dollar GM Gold Depression Recession Normal Means Variances Stdevs Boom Covariance Summary measures of portfollo returns Total Correlation Mean return Variance of return Stdev of return Data table for mean and stdev of portfolio return as a function of GM investment StDev Mean GM investment