(a) 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 year's time? Show that with the purchased option, the portfolio value will never fall below US$45 million in one year's 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).

(b) Consider a call option and a put option on a given stock both with a strike of $25. They cost $1.25 and $0.3 respectively. Explain how a straddle can be created from these two options. Draw the net payoff diagram for the strategy. State the trading ranges at maturity in which the strategy generates a profit.