Financial prices look random. Their increments are approximately uncorrelated, their paths approximately Brownian. This is what makes markets hard to predict and what underpins most of quantitative finance.
But order flow — the sequence of buy and sell market orders — is not random at all. Institutional investors split large orders into many small ones, executed over hours or days. The resulting flow is strongly persistent: a buy is likely to be followed by another buy, a sell by another sell. The autocorrelation decays slowly, as a power law. This is the Lillo-Mike-Farmer effect, documented extensively and uncontested.
These two facts appear contradictory. If order flow is predictable and orders move prices, then prices should be predictable. But prices are diffusive. Kanazawa et al. (arXiv:2502.17906) show that the resolution lies in the second empirical anomaly of market microstructure: the square-root law of price impact. A metaorder of size Q moves the price not proportionally to Q but proportionally to √Q. Each additional correlated order in a persistent sequence has diminishing impact.
The two paradoxes cancel. Persistent order flow would make prices predictable — if impact were linear. But impact is concave. The hundredth correlated buy in a sequence moves the price a tenth as much as the first. The persistence of the flow is exactly absorbed by the concavity of the impact. What remains, after the cancellation, is diffusion. Brownian motion is not the absence of structure. It is the signature of two structures — persistent flow and concave impact — operating at precisely the scale needed to annihilate each other's predictability.
The structural point is that randomness here is not primitive but emergent. The price looks random not because nothing is happening but because two highly ordered processes — one in the flow, one in the impact — destructively interfere. Remove either regularity and the other becomes visible. Linearize the impact, and the persistent flow makes prices predictable. Remove the persistence, and the concave impact becomes irrelevant. The market's apparent efficiency is not a property of any single mechanism. It is the residue of two mechanisms, each individually anomalous, whose anomalies are tuned to erase each other.