A Theory for Market Impact: How Order Flow Affects Stock Price

TL;DR

This paper develops a quantitative theory explaining how order flow influences stock prices, capturing the concave impact of order size and reproducing key universal properties of stock returns.

Contribution

It introduces a model linking order flow to market impact, incorporating autocorrelation and asymmetry, and matches empirical data from the London Stock Exchange.

Findings

Market impact scales logarithmically with order size.

The model reproduces uncorrelated, power-law distributed returns.

Returns exhibit autocorrelation and clustered volatility.

Abstract

It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the market impact of hidden orders (orders that reflect the true intention of buying and selling) that matches the empirically measured result and that reproduces some of the non-trivial and universal properties of stock returns (returns are percent changes in stock price). The theory is based on a simple premise, that the stock market can be modeled in a mechanical way - as a device that translates order flow into an uncorrelated price stream. Given that order flow is highly autocorrelated, this premise requires that market impact (1) depends on past order flow and (2) is asymmetric for buying and selling. I derive the specific form for the dependence in (1) by assuming that current liquidity responds to information about all currently active hidden orders (liquidity is a measure of the price response to a transaction of a given size). This produces an equation that suggests market impact should scale logarithmically with total order size. Using data from the London Stock Exchange I empirically measure market impact and show that the result matches the theory. Also using empirical data, I qualitatively specify the asymmetry of (2). Putting all results together, I form a model for market impact that reproduces three universal properties of stock returns - that returns are uncorrelated, that returns are distributed with a power law tail, and that the magnitude of returns is highly autocorrelated (also known as clustered volatility).