3. You are a financial manager at a hedge fund, responsible for managing $20,000,000 over three months. Suppose that there are four different assets you can invest in: A, B, C, D. Your task is to allocate the $20,000,000 across the four assets, and your plan is to liquidate the portfolio in three months. The analysts at the fund believe that two events will affect the returns of the assets significantly: the Reserve Bank's announcement of the cash rate next quarter (increase or decrease); and the outcome of the federal election in Australia (Labour win or Liberal win). Thus, there are four possible scenarios for the state of the world in three months' time, each with different returns for each asset: Scenario 1 Scenario 2 Scenario 3 Scenario 4 4% -1% 0.5% -1% B -1% 2% 0% 0.5% -1% 2% -1% 2% D 0.5% 1.5% 0.5% -1% Hint: for the below questions, you may want to define A = {A, B, C, D} to be the set of assets, m to be the number of scenarios (for our problem, m = : 4), rij to be the return of asset j in scenario i, and W to be the money that is allocated (for our problem, W $20,000,000). (a) (5 points) Suppose you want to find the best return that you can guarantee, no matter which scenario occurs. Formulate a model to find this amount. (b) (5 points) Suppose that the analysts believe that each scenario is equally likely. Formulate a model to compute the optimal expected return. (c) (5 points) Suppose that you want to make the difference between the returns in each scenario as small as possible. Formulate a model to solve for this portfolio. (d) (3 points) Which objective do you think you should use and why? Note: there is no right or wrong answer here, but you should think of reasons for your answer, which should be about 4-8 sentences long. Think of possible pros and cons of each objective. (e) (7 points) Please submit this part via the Jupyter notebook. This question asks you to write Python functions which, when given data on the asset returns, constructs the models using Gurobi then solves them