1. Suppose the current value of the S&P 500 index is 1000, the future value of the dividends over the next six months will be $20 and the T-bill rate is 5% (continuously compounded rate). Suppose the Northwestern endowment has $100,000,000 invested in the S&P 500. a. What will be the futures price for an S&P 500 futures contract which settles in 6 months? b. Suppose the portfolio manager for the endowment thinks that T-bills will outperform the S&P over the next six months. If the contract size for the S&P 500 contract is 250 times the value of the index, what futures position should she take? What rate of return will the manager earn over this period? Draw the manager's position before and after she puts on the hedge