Do fundamentals shape the price response? A critical assessment of linear impact models

TL;DR

This paper compares two models of price impact, revealing they predict similar high-frequency dynamics but differ in impact strength, and identifies a crossover from sub-linear to linear price responses across timescales.

Contribution

It demonstrates the universality of high-frequency price dynamics across different impact models and clarifies the transition from sub-linear to linear price responses over time.

Findings

High-frequency models predict identical price dynamics due to universality.

Disagreement on impact strength relates to market excess-volatility.

A crossover from sub-linear to linear price response is identified.

Abstract

We compare the predictions of the stationary Kyle model, a microfounded multi-step linear price impact model in which market prices forecast fundamentals through information encoded in the order flow, with those of the propagator model, a purely data-driven model in which trades mechanically impact prices with a time-decaying kernel. We find that, remarkably, both models predict the exact same price dynamics at high frequency, due to the emergence of universality at small time scales. On the other hand, we find those models to disagree on the overall strength of the impact function by a quantity that we are able to relate to the amount of excess-volatility in the market. We reveal a crossover between a high-frequency regime in which the market reacts sub-linearly to the signed order flow, to a low-frequency regime in which prices respond linearly to order flow imbalances. Overall, we reconcile results from the literature on market microstructure (sub-linearity in the price response to traded volumes) with those relating to macroeconomically relevant timescales (in which a linear relation is typically assumed).