The S&P $500$ futures contract is on $$250$ times the price of the index and the current price of the futures index $2,973.$ Construct a hedge on a portfolio that is identical to the S&P $500$ which is currently worth $$150,000,000.$ The hedge position is for an individual who owns the portfolio.

In addition, calculate what position would be needed to change the portfolio$$s $($beta$)$ to $0\mathrm{.}5.$