Building an Executable S&P 500 Index Arbitrage from Order Books

Summary

This discussion examines how to compare a cash basket of S&P 500 constituents with an E-mini futures contract when assessing index arbitrage. It asks whether to aggregate constituent bid and ask quotes separately and discount those totals, or use mid prices throughout. The practical issue is that summing displayed prices can produce implausible basket values when constituent quotes are not selected or combined consistently.

It also asks how to choose stock order-book prices when displayed quantities differ. A quote at the best price may represent only a trivial quantity far from the market’s meaningful liquidity, so using it without a size criterion can distort the apparent arbitrage. The document provides no worked solution, execution rule, or empirical test. A usable comparison would need consistent basket weights and discounting, synchronized data, and quotes sized to the intended trade; those details are not established here. Its main value is identifying quote selection and depth as central issues in measuring an executable cash-and-carry relationship.

Key ideas

• Index arbitrage compares the priced constituent basket with the related E-mini futures contract.
• Bid and ask sides should be evaluated with consistent basket and discounting conventions.
• Mid prices can describe a reference value but do not establish executable arbitrage.
• A one-unit quote far from the main liquidity may distort a basket valuation.
• The discussion raises order-book depth and quote sizing without settling on a specific rule.

Tags

# Calculating index arbitrage


# Calculating index arbitrage












I have a days-worth of level 2 market data. I am calculating S&P500 index arbitrage. I have a few questions about the calculation:

1) Should I be summing all the bids and asks from the stocks separately and then do the discounting on the sum of the bids, discounting on the sum of the asks and then compare with the E-Mini future bid and ask- all separately? Or in contrast should I be using mid values throughout?

If I calculate the prices separately and (see question below) I ask for the best bid/ask of at least quantity 1 I end up getting stupid values like S&P500 total of all stock bids is 1687 but the ask sum is like 1200.

2) Related to the above, do you only choose the best "bid" (or "ask") dependent on the quantity available in the orderbook and if so, what quantity level do you choose to select the best bid/ask?

If there is an order with quantity 1 (which is many price levels away from the main liquidity) it can cause problems if I just ask for the "best" price level.

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