Usually when fair value is refered to it is regarding the fair value of the futures contract and the futures versus fair value is really just the futures versus the fair value of the futures.

Taking a step back , the “spot” or instantaneus value of the index, in this case the s&p500 is just the spot value of its individual constituents added together. During times of peak liquidity ( when the US Markets are open) this is usually refered to as the last taded price of the individual constituent which sums to the index spot but things can be viewed in a slightly different light by looking at the best bid and best ask of the index ( usually with a comparitive amount of notional to the value of a futures contract which we’ll get into a second. The mid point of these 2 could be used as the fair value of the index …

Now to futures on the SP500. THere are 2 different sizes of contract one is 50x the index close at the futures date (the emini) and the other is 250x the index at the futures date. Both are traded on the CME electronically ( I believe 6 out of 7 days a week 24/7 ) and I also believe next to currencies and US Treasuries are the most highly transacted intrument in the world.
Now index futrures usually have a September / December / March / July expiration and I believe it is the same as most other futures and options contract which is technically the satrday following the 3rd friday of the month ( athough Friday is the last trading day).

Most of the open interest is in the “front” month or closest to expiry and only a few trading days before the expiry does the open interest “roll” to the next expiration.

Now to get to the theoretical arbitrage free fair value price of the future ….. The fair value price of the future would be the price assuming the value of the index didn’t change at all between now and the expiration date but also discounting for the timevalue of money or basically taking the amount of time untill the expiration of the front month and reducuing the spot of the index to what you would have to put in now to end up getting the value of the index being paid intrest in accordance with the risk free rate corresponding to the amount of time and the currencey of the index. In this case the us treasuey yield cureve is usually used ….

Now if the actual futures market is trading at one price the fair value of the futures would be the last index price discounted the time value between now and the futures expiration.

I could go on into index arb buty yhay really has to do with taking advantage of either the difference between the index spot bid and the fair value of the futures spot ask or the index spot ask and the fair value of futures spot bid. If either of these exceeded the transaction cost and a certain degree of risk taking place due to very short term market volatility … You could make money in a guarenteed fashion.

Let me be very clear that no individual investor could accomplish this task. Not only does this require huge amounts of capital but, almost zero transaction costs due to either being such a high volume prime-brokergae customer or an actual exchange member AND extremely low latency … the amount of time from getting the quotes to acting on them and having them execute is extremely low ( accomplished through low latencey co location )

Anyway thats my shpeel on index futrures any questions let me know. I have traded professionally bilions of dollars worth of them using high frequency strategies in my time …

Vince and Ed English had there own little conversation.

So Paul Lepage Your second to last sentence was uncalled for. The rest was good. Thank you for your last sentence.

Bloomberg posts these everyday all day.