You want to use S&P 500 index options to hedge your portfolio. Portfolio has a beta of -1.0. It is currently worth $500,000 and index stands at 1000. The risk-free rate is 0% per annum. There is no dividend yield on both the portfolio and the index. 1) What option contracts would you consider? 2) How many option contracts should be purchased? 3) What strike price should we consider for insurance against the portfolio value falling below $450,000 in three months? 4) What happens if index level turns out to be 1200 after three months