Please show all your work for full credits.

1. Suppose you are managing a stock portfolio worth $100 million, which tracks closely with the S&P 500. You fear that a decline is coming and wants to completely hedge the value of the portfolio over the next year. Assume the current index of the S&P 500 futures is 800, and the value of a futures contract= $250 the index. a. How many futures contracts will you buy or sell? b. Suppose next year, the S&P 500 index declines by 10% from 800 to 720. How much is the gain or loss on the portfolio? How much is the gain or loss on futures position? What is the net position?