The Physics of Price Discovery: Deconvolving Information, Volatility, and the Critical Breakdown of Signal during Retail Herding

TL;DR

This paper addresses how the pure informational signal of price discovery, isolated by Market Cap Normalization $S_{MC}$, is transmitted and how it can break down under retail herding. It combines two physics-inspired approaches: (i) $S_{MC}$-based, $L$-lag impulse-response deconvolution via Tikhonov regularization to recover the kernels of investor flows, and (ii) Multivariate Hawkes processes to quantify regime-dependent self-excitation and criticality. The authors find a dual-channel market where Foreign and Institutional flows exert positive, permanent impact, while Individual flows provide negative, transient liquidity effects, with a near-critical branching ratio $n \approx 0.998$ that triggers a regime flip: during high retail herding, institutional price impact reverses from positive to negative, eroding price discovery. The results imply price discovery is a state variable, highly sensitive to the level of retail contagion, with practical implications for trading, risk management, and market regulation.

Abstract

Building on the finding that Market Cap Normalization ($\SMC$) isolates the ``pure'' directional signal of informed trading \citep{kang2025}, this paper investigates the physics of how that signal is transmitted -- and how it breaks down. We employ \textbf{Tikhonov-regularized deconvolution} to recover the impulse response kernels of investor flows, revealing a dual-channel market structure: Foreign and Institutional investors act as ``architects'' of price discovery (positive permanent impact), while Individual investors act as liquidity providers (negative total impact). However, using \textbf{Multivariate Hawkes Processes}, we demonstrate that this structure is fragile. We find that individual investor order flow exhibits near-critical self-excitation (Branching Ratio $\approx$ 0.998). During periods of high retail herding, the market undergoes a \textbf{phase transition} into a ``critical state.'' In this regime, the signal-to-noise ratio collapses, causing the price impact of sophisticated investors to reverse from positive to negative. These findings suggest that retail contagion acts as a physical barrier that temporarily disables efficient price discovery.

Figures (3)

• Figure 1: Global Market Impulse Response by Investor Type. This figure illustrates the "Global Market Kernel" derived via pooled Tikhonov-regularized deconvolution (100 subsampled stocks, 5 iterations). The y-axis represents the cumulative price impact (log returns) of a unit shock in Market Cap-normalized order flow ($S_{\text{MC}}$) over a 60-day lag window. Foreign (panel A) and Institutional (panel B) investors exhibit positive, persistent impact (+0.0056 and +0.0024 respectively), confirming their role as informed traders contributing to fundamental price discovery. Individual investors (panel C) exhibit negative cumulative impact (-0.0045), indicating that retail buying pressure typically precedes price reversion. These distinct kernel shapes validate the physical segmentation of the market: sophisticated agents drive value, while retail agents provide liquidity (noise), with their buying peaks marking local maxima before reversion.
• Figure 2: KL Divergence Ratios: The Effect of Volatility Adjustment. This chart compares the informational content of Market Cap Normalization ($S_{\text{MC}}$) versus Volume Normalization ($S_{\text{TV}}$) by displaying the ratio of their KL Divergences (KL$_{S_{\text{MC}}}$/KL$_{S_{\text{TV}}}$). A ratio $>$ 1 indicates $S_{\text{MC}}$ provides better separation between "Buy" and "Sell" return distributions. Left bars (Raw Returns):$S_{\text{TV}}$ appears superior for Institutional investors (Ratio 0.35$\times$), suggesting volume-normalized flows better capture raw variance. Right bars (Volatility-Standardized): After standardizing returns by 20-day rolling volatility ($R_{\text{adj}} = R/\sigma_{20d}$), the Institutional ratio jumps to 4.85$\times$ (a 14-fold improvement). This confirms that $S_{\text{TV}}$ primarily predicts volatility regimes, whereas $S_{\text{MC}}$ isolates the true directional information of the trade. Once the "noise" of volatility is removed, $S_{\text{MC}}$ is the superior carrier of fundamental signal.
• Figure 3: The Breakdown of Signal During Retail Herding. This figure demonstrates the "Regime Flip" in price efficiency conditional on retail market structure. Panel A (Hawkes Intensity): Classifies market days into "Normal" (90%) and "High Herding" (10%) regimes based on the self-excitation intensity of individual investors (Branching Ratio = 0.998). Panel B (Conditional Kernels): Shows the cumulative price impact of Institutional flows in both regimes. In "Normal" conditions (blue line), impact is positive and persistent (+0.0047). In "High Herding" conditions (red line), impact collapses and becomes deeply negative (--0.0447). This provides evidence of a phase transition in market efficiency. When retail herding reaches critical levels, the "noise" overwhelms the "signal," causing even sophisticated institutional flows to lose their predictive power and resulting in market inefficiency.