We know that U.S. equity futures and S&P 500 index prices track each other very closely, so clearly arbitrage occurs.
But as futures trade way more value than stocks each day (Chart 1), that means not every futures trade leads to stock arbitrage, which raises an interesting question: How much does futures arbitrage add to stock volumes?
Today, using low latency data, we identify large amounts of the value in the S&P 500 index trading in one microsecond and estimate how much futures arbitrage is adding to stock trading per day.
Chart 1: Futures trade more notional than all stocks combined
Futures are cheaper to trade than stocks
We estimate that crossing spreads on futures is much cheaper than crossing spreads on the full portfolio of S&P 500 stocks. As we see below, spreads on S&P 500 futures are around 1 basis point (bps), while spreads on the portfolio of stocks are more than 4 bps. That makes buying and selling futures notably cheaper than buying the stocks themselves (before accounting for roll and settlement costs).
Interestingly, spreads on the S&P 500 exchange-traded funds (ETFs) are also cheaper than stocks, so some arbitrage might affect the ETF market before it affects the stock market.
Chart 2: Spreads across different S&P 500 index exposures
Both spreads need to be crossed in an arbitrage
What makes spreads even more important is the fact that, before arbitrage occurs, the bids and offers of each asset class need to overlap. In short, an arbitrageur needs to cross both spreads.
We show how arbitrage works, in theory, in the diagram below: The futures offer needs to be cheaper than the bid on all the stocks in the S&P 500 portfolio for an arbitrageur to collect profits (and that’s before settlement and fixed trading costs).
Given how small the spread on the futures is (compared to the stock basket), it’s likely the futures could tick up and down inside the stock spread without triggering stock arbitrage.
Chart 3: Spreads across exposures for different S&P 500 index product types
However, as we recently noted, an arbitrageur might not need to wait for the WHOLE basket to be mis-priced to execute an optimized arbitrage. For example, a decent risk-reward may exist when trading as few as 100 stocks against the futures price. We estimate a basket of the 100 largest stocks in the S&P 500 have a lower 3.7 bps spread.
Either way, stocks are unlikely to arbitrage every time futures tick, which helps explain why futures trade even more than stocks.
Using low latency data to spot futures trades
Another way to look for futures arb trades is to extend some of the recent work we have been doing on the U.S. market latency.
In our latest study, we looked at how an ISO order for each stock sweeps across the different stock markets in just milliseconds (us).
We also know that futures can trade in Chicago — more than 700 miles (around 3.9k us or 4 microseconds (ms) by microwave) away from where stocks trade in New Jersey. Looking at the map below, all three of the New Jersey trading centers are essentially the same distance from Chicago, so, in theory, if an arbitrageur trades stocks against futures, we should see instances when many (if not all) of the S&P 500 stocks trade in the same millisecond — regardless of whether the trade starts in Chicago or New Jersey.
So today, we look for instances when many of the S&P 500 constituents trade in the same millisecond.
Chart 4: Speed of light distance between futures and stock exchanges
We also picked a date when the market was reasonably volatile (Jan. 19, 2024, to be exact), thinking that would be more likely to make prices dislocate enough for arbitrage to occur. Then, we looked at all the S&P 500 stocks each millisecond and counted how many of them saw trade activity.
We plot the results below, summed by cumulative S&P 500 index weight that trades (blue bars). We also track the price for the S&P 500 ETF (VOO) to show volatile periods. The time axis shows only the events with over 20% of the index (by weights) trading in the same millisecond.
Chart 5: Adding up how much of the S&P 500 index trades in the same millisecond over one (somewhat volatile) day
Some things we see are:
- Instances where 70% or more of the S&P 500 by index weight is traded within the same millisecond are relatively rare (dark blue bars). Although, when they do occur, it seems that the VOO price also gaps up or down, which is consistent with price changes that may lead to more arbitrage opportunities.
- Clusters of around 30% of the index weights trading in the same millisecond happen much more frequently.
- Stronger arbitrage seems to be clustered by time. On this date, activity seems to be higher from 10 a.m. – 11:30 a.m., and again around 12:30 p.m. and between 2:30 p.m. – 3 p.m. Activity into the close is also concentrated but a notably different color, indicating a mid-sized arb portfolio.
Futures arbitrage is less important than you might think
Overall, it seems that futures arbitrage happens consistently during the day, but mostly in optimized baskets. If we look at the value of all the stock trades in the bars in Chart 5, assuming these trades are related to arbitrage, we see notional of around $8.4 billion traded. That’s around 3% of all trading on a typical day.
This all helps us understand why stocks trade less than futures. It is about half as much as our previous estimates of the impact on the underlying stock markets.
Additionally, this means that there is even more liquidity in the stock market that would resemble more stock or sector specific trades, ensuring that index trading doesn’t overwhelm price discovery and efficient capital allocation.
Nicole Torskiy, Economic Research Senior Specialist, contributed to this article.
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