Question 4 (20 marks) You are the investment analyst of a securities firm and your supervisor has made the scenario analysis on the performances of a stock fund and a bond fund in the coming year: Scenario Stock fund's return Bond fund's return Probability 0.35 Good 17% 11% Normal 0.50 12% 6% Poor 0.15 -5% -1% (a) Calculate the expected returns and standard deviations of both funds. (4 marks) After you present the expected returns and standard deviations of both funds to your supervisor, he would like to know the minimum variance portfolio if the correlation coefficient between their rates of returns is -0.10. (b) Calculate the weightings invested in each of the two funds, expected returns and the standard deviation of the minimum variance portfolio. (6 marks) (c) Your supervisor would like to build an optimal risky portfolio based on the 2 funds mentioned before; given the risk-free rate is 2.0%. (i) Calculate the weightings invested in each of the two funds, the expected returns and the standard deviation of the optimal risky portfolio. (8 marks) (ii) Calculate the Sharpe ratio of the optimal risky portfolio. (2 marks)