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The following table presents the performance of stock and bond funds under various scenarios. |Scenario Probability Rate of return of Rate of return of bond fund (%) stock fund (%) Severe recession 0.10 -36 -8 Mild recession 0.15 -10 12 Normal growth 0.50 15 6 Boom 0.25 34 4 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) C. 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 deviation return 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 e. Draw the investment opportunity set. (3 marks) f. Calculate the weight in stock fund, expected return and standard deviation of the minimum-variance portfolio. (6 marks) g. Given the T-bill rate is 2.50%. Calculate the weight in stock fund, expected return and standard deviation of the optimal risky portfolio. (6 marks) h. Calculate the Sharpe ratio for the optimal risky portfolio. (2 marks) i. Draw the capital allocation line (CAL) on the diagram in part (e). Show the position of the optimal risky portfolio on the CAL. (3 marks) j. Suppose an investor is to use the optimal risky portfolio and T-bill to form a portfolio and requires an expected return of 8%, what would be the investment proportions of his portfolio? (4 marks)

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