Problem 2 - Stochastic Dominance [12 marks] You are considering three mutually exclusive investments (X, Y and Z) to invest all your wealth. The table below illustrates the returns of each investment in different states: 2 3 13 13 13 State Prob Rx Ry Rz 1 -2.00% 6.00% -3.00% 2.00% 1.00% 2.00% 1 6.00% -3.00% 5.00% 3 For each of the following questions show your work and clearly indicate how you arrived to your conclusion. a) Based on FOSD rank the three investments in order of preference. If you cannot rank an investment based on this criterion, clearly indicate that this is the case and explain why it cannot be ranked. Which investment would you choose based only on FOSD? [3 marks] b) Based on SOSD rank the three investments in order of preference. If you cannot rank an investment based on this criterion, clearly indicate that this is the case and explain why it cannot be ranked. Which investment would you choose based only on SOSD? [3 marks] c) Based on both FOSD and SOSD can you fully rank these investments in order of preference? If this is the case, show their ranking. [3 marks] d) Are your results from part (c) consistent with the mean-variance criterion? Why is this the case? [3 marks]