$.$ A company has a $$20$ million portfolio with a beta of $1\mathrm{.}2.$ It would like to use futures con$-$ tracts on a well$-$diversified stock index to hedge its risk.The index futures price is currently $1080,$ and each contract is for delivery of $$250$ times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfo$-$ lio to $0\mathrm{.}6?$