Scenario Probability Rate of return of stock fund (%) 0.1 -28 Rate of return of bond fund (%) -4 0.2 -6 15 Severe recession Mild recession Normal growth Boom 0.5 20 4 0.2 35 7 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) Scenario Probability Rate of return of stock fund (%) 0.1 -28 Rate of return of bond fund (%) -4 0.2 -6 15 Severe recession Mild recession Normal growth Boom 0.5 20 4 0.2 35 7 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)