Describe how you would use a six-month E-mini S&P 500 futures contract to perform each of the following tasks. Remember that one E-mini pays 50 times the S&P 500 index level. (For the purposes of this question, ignore the fact that the S&P 500 component stocks pay dividends.) The current level of the index is 1250.

a) Simulate investing $250,000 in the S&P 500 index for six months. b) Fully hedge an investment of $550,000 in a well diversified portfolio that has a beta of 1.2. c) Partially hedge an investment of $550,000 in a well-diversified portfolio that has a beta of 1.2 so that the new portfolio has a beta of 0.5.