Fair value is a technical measure of the correct relationship between futures and a stock index.
The actual relationship between futures and an index is called the spread or the premium. Fair value remains constant throughout the day, but the spread is constantly changing because the futures contracts and the stocks that make up an index trade independently of each other. Through the trading day, the spread generally stays pretty near to fair value. But futures continue to trade on the Chicago Mercantile Exchange for another 15 minutes after stocks finish trading, and then they trade throughout the night and into the morning in the electronic Globex session. Trading programs are essentially going to rapidly put the spread and fair value back into whack.