Question $31(5$ points$)$

You are managing a $$52\mathrm{.}5$ million US stock fund and have decided to hedge against a potential market meltdown using S&P $500$ index futures contract that is currently quoted at $4,555.$ The multiplier of the contract is $$250.$ Your stock fund is well diversified.

a$)$ Briefly explain whether you need to buy or sell the futures contracts to hedge your portfolio against the downside risk and why.

b$)$ Calculate how many futures contracts are needed for this hedging purpose.

c$)$ Draw chart$($s$)/$diagram$($s$)$ to illustrate how your position in futures contracts protect your initial position $($portfolio$)$ against the downside risk.