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Suppose that on October 15, 1997, we have a long position in the S&P500, worth $50 million. We are becoming increasingly concerned with the market

Suppose that on October 15, 1997, we have a long position in the S&P500, worth $50 million. We are becoming increasingly concerned with the market prospects, and want to set up a zero-beta portfolio by using futures contract on the S&P500. We consider the December futures. Relevant information:

S&P500 futures contract size: 500 units of the index.S&P500 index value on October 15 is 965.72.

S&P500 futures price on October 15 is 973.50.

(a) How many S&P500 futures contracts should we sell?

(b) Suppose that the spot and futures price over the next two weeks are the following

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