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 (%) 0.1 -35 0.2 - 10 0.5 15 0.2 40 Rate of return of bond fund (%) -6 13 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) Weights in stock fund Portfolio expected return Portfolio standard deviation 0.0 0.2 0.4 0.6 0.8 1.0 e. Draw the investment opportunity set in part (d). (2 marks) f. Calculate the weight in stock fund, expected return and standard deviation of the minimum-variance portfolio. (6 marks) 1 g. Given the T-bill rate is 2%. 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 (2 marks) j. 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) 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 (%) 0.1 -35 0.2 - 10 0.5 15 0.2 40 Rate of return of bond fund (%) -6 13 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) Weights in stock fund Portfolio expected return Portfolio standard deviation 0.0 0.2 0.4 0.6 0.8 1.0 e. Draw the investment opportunity set in part (d). (2 marks) f. Calculate the weight in stock fund, expected return and standard deviation of the minimum-variance portfolio. (6 marks) 1 g. Given the T-bill rate is 2%. 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 (2 marks) j. 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)
