Price Adjustment When Updating Requires Execution: Evidence from Automated Market Makers

In the world of modern finance, prices are rarely static; they are constantly shifting to reflect new information, much like a thermometer rising and falling with the weather. In traditional markets, prices can adjust instantly, even if no one is actively buying or selling at that exact second. However, in a specific type of digital marketplace known as an automated market maker, the rules are different. Here, a price only changes when a trade actually happens. If no one swaps one asset for another, the price stays exactly where it was, regardless of how much the outside world might have moved. This creates a unique puzzle for researchers: when they look at the average price movement over time, they are seeing a mix of two very different things. They are seeing the frequency of trades and the size of the price jumps that happen during those trades, all blended together. It is difficult to tell if a market is becoming more efficient because prices are correcting faster, or simply because the market is visiting different conditions where trades happen more often.

A researcher named Wen-Ting Wang tackled this puzzle by studying two specific digital currency pools on the Ethereum and Base blockchains. These pools act as automated market makers, where a fee is charged on every trade, and the price of the assets inside is determined strictly by the ratio of what is held in the pool. Wang focused on two pools that were nearly identical in their design, both charging a fee of five basis points on trades between Ethereum and a stablecoin called USDC. The study covered a period of 57 days in the summer of 2026, analyzing over 2.5 million blocks of data. The goal was to break down the total price correction into three distinct parts: how often the market visited a state where the price was off, how often a trade actually occurred in those states, and how much the price corrected itself when a trade did happen. Because these pools only change price when a trade executes, the math becomes exact; if no trade occurs, the price correction is zero. This allowed the researcher to separate the "how often" from the "how much" without needing to guess at hidden variables.

The study began by looking at the raw numbers, which told a seemingly straightforward story. When comparing two different time windows within the study period, the average price correction appeared to rise slightly in the later window. In the first window, the average correction was about 0.484 basis points for the Ethereum pool and 0.107 for the Base pool. In the second window, these numbers climbed to 0.580 and 0.143, respectively. At first glance, this might suggest that the market was becoming more responsive or that prices were snapping back to their true value more aggressively. However, the researcher suspected that this simple average was hiding a more complex reality. To test this, they used a method similar to comparing two groups of people by giving them the same weight, regardless of how many people were in each group. They asked: if the market had visited the same mix of price conditions in both windows, would the correction still have gone up?

The answer was a clear reversal. When the researcher adjusted the data to account for the fact that the market had visited different conditions in the two windows, the story flipped. The later window actually showed a weaker price response than the earlier one. The reason the raw average had gone up was that the market had shifted its behavior, visiting a different set of conditions more frequently. Specifically, the market began visiting extreme price discrepancies much more often. In the later window, a large portion of the data came from a rare, open-ended category of very large price gaps, which occurred far more frequently than before. This shift in the "state composition" of the market pushed the raw average up, even though the actual price correction happening inside each specific condition had gotten smaller.

To understand this, imagine a doctor measuring the average recovery time of patients. If the doctor compares two weeks, and in the second week, the hospital admits many more patients with very severe injuries who naturally take longer to heal, the average recovery time for the week will go up. This does not mean the doctors are worse at treating patients; it simply means the mix of patients has changed. In this study, the "doctors" are the automated market makers, and the "patients" are the price discrepancies. The market started seeing more of the extreme cases, which skewed the overall average, masking the fact that the treatment itself—the price correction per trade—had actually become less effective in the conditions that were most common.

The researcher also examined how often trades happened versus how much the price moved when they did. They found that the frequency of trades and the size of the price correction moved in opposite directions. In the later window, the market visited conditions where trades were more likely to happen, but when those trades did occur, the price correction was smaller than before. These two forces cancelled each other out almost perfectly. The increase in how often the market visited certain states was offset by a decrease in how strongly the price corrected itself in those states. This delicate balance meant that the headline number, the raw average correction, barely moved, while the underlying mechanics of the market shifted substantially.

This finding challenges the way market quality is often measured. A simple statistic that says "prices are correcting more" can be misleading if it does not account for the conditions under which those corrections happen. The study showed that a market can appear to be improving simply because it is visiting different states, even if its actual ability to correct prices is weakening. The researcher confirmed this by testing a simple rule that predicted price behavior based on the size of the price gap. This rule, which seemed to work in the first part of the study, failed to hold up in the second part, further proving that the relationship between price gaps and corrections is not stable. The results were specific to the two pools studied and the time period observed, but the method used to separate these effects offers a new way to look at digital markets.

The study also looked at what happens when the most extreme data points are removed. When the researcher excluded the rare, open-ended category of huge price gaps, the pattern of opposing forces remained visible, though it was less pronounced. This confirmed that the effect was not just a statistical trick caused by a few outliers, but a real feature of how these markets operate. The shift in the mix of market conditions was the primary driver of the change in the average, not a change in the fundamental rules of the market. The research concludes that when price updates depend entirely on execution, looking at the average alone is insufficient. One must look at the composition of the market, the frequency of trades, and the size of the correction separately to understand what is truly happening.

In the end, the paper reveals that the digital market is a dynamic system where the story told by the average can be the opposite of the story told by the details. The market did not become more efficient; it simply changed its shape. The researcher's work provides a clear, non-mathematical way to see through the noise of aggregate statistics and understand the real mechanics of price adjustment in automated systems. It serves as a reminder that in complex financial environments, the whole is often a sum of parts that are moving in different directions, and only by separating those parts can we see the true picture.