You are required to show your work. Providing answers alone will not get you full credit. The following table presents the performance of stock and bond funds under various scenarios. Scenario Severe recession Mild recession Normal growth Boom Probability Rate of return of stock fund (%) 0.05 -40 0.20 -15 0.50 12 0.25 30 Rate of return of bond fund (%) -9 11 5 -2 a. Calculate the expected returns of the stock and bond funds. (4 marks) b. Calculate the standard deviations of the stock and bond funds. (4 marks) c. Calculate the correlation coefficient of the stock and bond funds. (2 marks) d. Suppose an investor forms a portfolio with stocks and bonds. Find the investment opportunity set in differing proportions. (10 marks) Weights in Portfolio expected Portfolio standard stock fund return deviation 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0