Stock Fund w Bond w 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Porfolio return Prtfolio SD 0.9 5.14 5.401 0.8 5.68 5.864 0.7 6.22 7.119 0.6 6.76 8.835 0.5 7.3 10.794 0.4 7.84 12.886 0.3 8.38 15.055 0.2 8.92 17.273 0.1 9.46 19.522 10 21.794 Portfolio Return Ws*Wb* Portfoilio return Portfolio Sd = WA^2*SDA^2+WB^2*SDB^2+2-WA-WBCovariance The following table presents the performance of stock and bond funds under various scenarios. Scenario Probability Rate of return of stock fund (%) -35 Rate of return of bond fund (%) Severe recession 0.1 -6 Mild recession 0.2 -10 13 Normal growth 0.5 15 6 Boom 0.2 40 -2 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) Stock Fund w Bond w 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Porfolio return Prtfolio SD 0.9 5.14 5.401 0.8 5.68 5.864 0.7 6.22 7.119 0.6 6.76 8.835 0.5 7.3 10.794 0.4 7.84 12.886 0.3 8.38 15.055 0.2 8.92 17.273 0.1 9.46 19.522 10 21.794 Portfolio Return Ws*Wb* Portfoilio return Portfolio Sd = WA^2*SDA^2+WB^2*SDB^2+2-WA-WBCovariance The following table presents the performance of stock and bond funds under various scenarios. Scenario Probability Rate of return of stock fund (%) -35 Rate of return of bond fund (%) Severe recession 0.1 -6 Mild recession 0.2 -10 13 Normal growth 0.5 15 6 Boom 0.2 40 -2 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)