Revisiting Trade-sign Long-memory and Square-root Law price impact
Why large trades leave predictable price fingerprints in financial markets
When traders execute large orders, markets exhibit two well-known patterns: past trade directions predict future ones (long-memory), and price impact grows with the square root of order size rather than linearly. This paper derives both patterns from a single mathematical framework based on how buy and sell orders pile up in the market, showing that the long-memory effect is really about timing of trades, while the square-root law reflects the market's actual survival and stability.
Large institutional investors rely on these patterns to predict how much a trade will move the market and to design execution strategies that minimize costs. Clarifying exactly why these patterns emerge—and distinguishing between patterns that depend on how often trades happen versus how many shares move—helps traders and risk managers build more accurate models of real market behavior and avoid costly surprises when market conditions shift.