Nana, if you want a document that explain perfectly how to compute Fair Value and some example go on the cme education section and download the following document: «Index Arbitrage and Stock Price Volatility» inside this document many interesting example about the Fair Value on the S&P 500. Cf education section: http://www.cme.com/edu/rcsrs/stratpaper649.html and the paper is http://www.cme.com/files/indexarb.pdf
Will the programs buy a basket of stocks when there´s and arbitrage opportunity or do they buy the etf? Seems hard to buy hundreds of stocks in such short time..
even if you have arbitrage, it is not automatic that you could use it because you have the NYSE rule 80A that limit arbitrage, just check in my link above for the CME education, more explanation about that.