i would use options instead of futures for better hedge. since you want to hedge changing stock prices, i suppose you already have a long position in stocks. to hedge, i’d buy deep in the money put option that expires in 3 months time. if the stock price falls, i would cash in the put, if stock price rises but still below exercise price, i could still cash in the put, and if stock price rises well above exercise price, i would leave the put unexercised.

if you however insist on using futures, you could sell S&P 500 futures with a certain ratio (no of stocks bought/no of futures sold) that you can derive from GARCH(1,1) hedge (a modeling of futures and spot prices, conditional hedge ratio=covariance of futures and spot hedge / futures hedge, use MATLAB). if you’re not familiar with GARCH (1,1) hedge you could do a naive hedge (selling 1 futures for every stock bought) but of course it’s not a good hedge.