It is July $16.$ A company has a portfolio of stocks worth $$100$ million. The beta of the portfolio is $1\mathrm{.}5.$ The company would like to use the December futures contract on a stock index to change the beta of the portfolio to $0\mathrm{.}9$ during the period July $16$ to November $16.$ The index futures price is currently $2,000$ and each contract is on $$250$ times the index.

What position should the company take?

Suppose that the company changes its mind and decides to increase the beta of the portfolio from $1\mathrm{.}5$ to $1\mathrm{.}9.$ What position in futures contracts should it take?