You are trying to decide whether to buy Vanguard's Large Stock Equity Fund and/or its Treasury Bond Fund (both are risky assets). You believe that next year involves several possible scenarios to which you have assigned probabilities. You have also estimated the expected returns for each of the two funds for each scenario. Your spreadsheet looks like the following: Next Year's Probability Large Stock Equity Fund Expected Rate of Return Bond Fund Expected Rate of Return Possibilities Recession 0.34 -0.27 -0.10 Normal Growth 0.48 0.18 0.06 Strong Growth 0.18 0.34 0.04 (a) Given the probabilities for the three possible economic conditions and their associated rates of return, calculate the expected return for each fund. [4 Points] (b) Given the probabilities for the three possible economic conditions and their associated rates of return, calculate the standard deviation for each fund. [6 Points] (c) Using your answers from Parts (a) and (b) calculate the covariance between the two funds, and the correlation coefficient. Round your answer to four (4) decimal places. [6 Points] (d) Using the formulas for the expected return and risk of a portfolio, calculate the expected return and standard deviation of a portfolio that is weighted 42% in the Vanguard's Large Stock Equity Fund and 58% in the Treasury Bond Fund. Show your work. Round your answer to four (4) decimal places. [6 Points]