How efficiency shapes market impact

TL;DR

This paper develops a theoretical model explaining how large trading orders impact market prices, predicting a square-root relationship between order size and impact, and aligning with empirical observations.

Contribution

It introduces a stylized model of algorithmic trading that links volume distribution to impact shape and provides testable predictions for temporary and permanent market impact.

Findings

Market impact is concave and roughly proportional to the square root of order size.

At equilibrium, trading volume distribution reflects information and influences impact shape.

Permanent impact relaxes to about two thirds of the peak impact.

Abstract

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e., the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two thirds of peak impact.