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The following table presents the performance of stock and bond funds under various scenarios. Scenario Probability Rate of return of stock fund (%) 0.1 -28 Rate of return of bond fund (%) -4 15 0.2 Severe recession Mild recession Normal growth Boom -6 20 0.5 4 0.2 35 7 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 stock and bond funds. Find the investment opportunity set in differing proportions. (8 marks) Weights in stock fund Portfolio expected return Portfolio standard deviation 0.0 0.2 0.4 0.6 0.8 1.0 e. Calculate the weight in stock fund, expected return and standard deviation of the minimum-variance portfolio. (6 marks) f. Given the T-bill rate is 3%. Calculate the weight in stock fund, expected return and standard deviation of the optimal risky portfolio. (6 marks) g. Calculate the Sharpe ratio for the optimal risky portfolio. (2 marks) h. Draw the investment opportunity set in part (d) and the capital allocation line (CAL) on the same diagram. Show the position of the optimal risky portfolio on the CAL. (4 marks) i. Suppose an investor decides to invest in the optimal risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 7%. a. What is the proportion y? (2 marks) b. What is the standard deviation of the investor's portfolio? (2 marks)

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