Comparing an S&P 500 Futures Contract with Its Stock Basket

Summary

The document outlines the basic comparison used to investigate whether an S&P 500 futures contract is mispriced relative to the underlying shares. The proposed reference is the value of the index, represented in practice by a representative basket of constituent stocks. A potential arbitrage arises when the stock basket and futures contract diverge by more than the cost of carrying the stocks: the trader buys the cheaper side and sells the more expensive side, with carry added or subtracted in the comparison.

The response is only a brief conceptual outline. It does not provide a worked numerical example, explain how to construct or trade the representative basket, or detail financing, dividends, transaction costs, execution constraints, and other factors that affect whether an apparent spread is exploitable. Consequently, it gives the core no-arbitrage intuition but not a complete test for a live trading opportunity.

Key ideas

• Compare the futures contract with the value of the underlying index or a representative stock basket.
• A potential arbitrage depends on the price difference after accounting for the stocks’ cost of carry.
• The basic trade buys the cheaper side and sells the more expensive side.
• A practical assessment needs additional details that the short answer does not provide.

Tags

# Calculating arbitrage- S&P 500 stocks vs S&P 500 Index future?


# Calculating arbitrage- S&P 500 stocks vs S&P 500 Index future?












How exactly would I go about investigating whether the S&P 500 stocks were currently over-valued compared with the price of the S&P 500 Index futures contract? Is it just a case of taking each S&P 500 stock price, ratio-ing it down using its S&P 500 constituent weighting and then summing them all up and comparing the number with the Index futures price?

Any small examples would be most welcome

## Answer by user2183336 (score 0)

https://quant.stackexchange.com/a/8936

http://en.wikipedia.org/wiki/Futures_contract#Arbitrage_arguments

S(t) is the value of the index. Arb opportunity opens when you can buy (sell) the stocks (typically done with a representative basket of stocks) against the future for less (more), of course adding (subtracting) the cost of carry of the stocks.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.