The following table presents the performance of stock and bond funds under various scenarios. Scenario Rate of return of bond fund (%) -6 Severe recession Mild recession Normal growth Boom 13 Probability Rate of return of stock fund (%) 0.1 -35 0.2 -10 0.5 15 0.2 40 6 -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. (8 marks)