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Does a bid and ask price exist for indices like the S&P500?
You can trade an index by using a Contract For Difference, or CFD. Various brokers offer this method and the spreads are quite low. They tend to widen outside of market hours, and not all brokers offer the same spreads. I would look for a broker that offers the lowest spread on the index you are interested in. You should also do your due diligence and check they are regulated by the relevant authority  pertaining to their territory, eg FSA for uk