Suppose a US equity portfolio is currently worth US$50 million and the S&P500 index is at 1000 points. If the value of the portfolio mirrors the value of the index points, what options should be purchased to hedge against the value of the portfolio from falling below US$45 million (i.e. 10% of the current value) in one years time? Show that with the purchased option, the portfolio value will never fall below US$45 million in one years time, excluding the cost of the option. Note that each option on the S&P500 covers a value equal to $100 times the index point (i.e. contract multiplier=100).