**WITH EXCELL STEPS**

Question #2: Optimal Risky Portfolio [22 Points] 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: Probability Large Stock Equity Fund Bond Fund Expected Rate of Return Next Year's Possibilities Severe Recession Mild Recession Normal Growth Strong Growth 0.15 0.05 0.60 0.20 Expected Rate of Return 0.37 0.11 0.14 0.30 0.10 0.07 0.02 (a) Given the probabilities for the four possible economic conditions and their associated rates of return, calculate the expected return for each fund. [4 Points] (b) Given the probabilities for the four 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. [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 80% in the stock equity fund and 20% in the bond fund Show your work [6 Points]