All investors only allowed to invest in assets X, Y and Z. Given the correlation between the returns on asset X and Z is 0.5, return on asset Y is not correlated with the returns on the other two assets, the expected rate of return and standard deviation are as follow: Assets Expected rate of return (%) Standard Deviation (%) X 3 5 Y 4 8 Z 5 10 (i) Write down the simultaneous equations that can be minimized to find the minimum variance portfolio by using Lagrangian function. (ii) By taking the simultaneous equations from part (i), calculate the minimum variance portfolio that gives an expected return of the portfolio of 4.5%. (iii) Calculate the standard deviation of the portfolio. All investors only allowed to invest in assets X, Y and Z. Given the correlation between the returns on asset X and Z is 0.5, return on asset Y is not correlated with the returns on the other two assets, the expected rate of return and standard deviation are as follow: Assets Expected rate of return (%) Standard Deviation (%) X 3 5 Y 4 8 Z 5 10 (i) Write down the simultaneous equations that can be minimized to find the minimum variance portfolio by using Lagrangian function. (ii) By taking the simultaneous equations from part (i), calculate the minimum variance portfolio that gives an expected return of the portfolio of 4.5%. (iii) Calculate the standard deviation of the portfolio