The S&P $500$ is composed of some of the $500$ largest listed listed firms. The ETF $($Exchange Traded Fund$)$ with Ticker symbol: SPY tracks the S&P $500.$

A money manager has a portfolio composed of $120$ of the largest listed firms. The manager's portfolio is valued at $$5$ million. The manager is concerned the market may fall and decides the closest portfolio for cross$-$hedging for which futures are available is the SPY$.$

The current portfolio value of the DIA futures is $$439\mathrm{.}05.$

The beta of the manager's portfolio is $1\mathrm{.}04,$ while the beta of the SPY futures is $0\mathrm{.}995.$

How many short futures contract should the manager enter into for hedging the entire portfolio against market moves?