6. (5%) Suppose that a portfolio is worth $50 million and the S&P 500 is at 1000. Each option contract is for $100 times the index. Suppose that the portfolio has a beta of 1.5, the risk-free interest rate is 5% per annum, and the dividend yield on both the portfolio and the index is 3% per annum. What options (and how many contracts) should be purchased to provide protection against the value of the portfolio falling $45 million in one year's time?