The Malin Investment Trust Company plans to liquidate part of its stock portfolio in June. It would like to hedge the portfolio sale. The portfolio the company plans to sell is well diversified, has a beta of $1\mathrm{.}5,$ and is currently worth $$100$ million. The S&P $500$ spot index is currently at $3,000,$ and a June S&P $500$ futures contract is currently at $3,000$ with a $$250$ multiplier.

a$.$ Using the price sensitivity model, determine how many S&P $500$ futures contracts the Malin Investment Trust Company would need in order to totally hedge the sale of this $$100$ million portfolio in June.

b$.$ Show in a table the values of the portfolio, futures cash flows, and the hedged portfolio values on the June expiration date for possible spot index values of $2,500$ and $3,500.$ Assume no quantity, quality, or timing risks.