Your company has a portfolio of stocks that is currently worth $$150$ million. The beta of the portfolio is $1\mathrm{.}3.$ The company would like to use CME futures on the S&P $500$ to immune the portfolio from systematic risk. The index is currently $1,200,$ and each contract is on $$250$ times the index. What position $($long$/$short and the number of contracts$)$ should the company take in the futures market? How would the strategy change, if instead, the company decided to increase its exposure to systematic risk and change the beta to $1\mathrm{.}9?$

$(10$ points$)$