Entropic Signatures of Market Response under Concentrated Policy Communication¶

Authors: Drzazga-Szczȩśniak, Gupta, Kaczmarek, Gnyp, Jarosik, Waligóra, Kielak, Gupta, Gurzyńska, Gil, Szczepanik, Kielak, Szczȩśniak (13 authors) Institutions: Częstochowa University of Technology; Jan Długosz University; Purdue; NC State; Gdańsk; Le Mans; Analitico (Katowice) Year: 2026 (March 2026) arXiv: 2603.12040 Categories: q-fin.ST

Scope note¶

This paper sits at the macro / equity-index level, not LOB microstructure. It was included in the signal-design batch because its abstract mentioned "entropic signatures" — but on full reading the signals operate on daily / 5-minute equity-index returns globally, not on order-book features. It is still useful as an information-theoretic complement to dispersion-based volatility measures, and introduces two entropy signals (Shannon and cumulative) that could in principle be adapted to LOB features.

Plain-language abstract¶

Uses the first 100 days of the second Trump presidency (Jan 20 – Apr 30 2025) as a "concentrated policy communication" natural experiment. Analyses major equity indices across the Americas, Europe, Asia, and Oceania using both standard deviation (dispersion) and Shannon entropy (information complexity). Documents a decoupling between the two measures — entropy is not a proxy for amplitude, it reflects the diversity of populated outcomes. Introduces a sliding-window cumulative entropy to localise extreme episodes. Finds short-term globally-coupled but regionally-modulated market impacts with clear links to specific policy announcements.

Key contributions¶

Shannon entropy as a market disturbance measure — defines entropy on binned return distributions with Velleman's rule for bin count. Complementary to standard deviation: entropy compresses under "structured volatility" (large but repetitive moves driven by a small set of narratives) even when std is high.

$$H = -\sum_{i=1}^{m} p_i \log p_i$$

where $p_i$ is the empirical frequency of returns falling in bin $i$.

Cumulative entropy with sliding window — constructs an expanding-window Shannon entropy trajectory that produces "ramp-like" signatures around extreme events without needing to pre-specify event windows or a parametric shock model.
Structured-volatility hypothesis: when a small number of salient narratives channel market reactions into similar configurations, entropy compresses while volatility stays high. Provides a quantitative test by reading $H$ and $\sigma$ jointly on the same windows.
Cross-regional empirics across 15 indices (US, Brazil, Canada, Eurozone, UK, Germany, Poland, Japan, China, Hong Kong, India, Australia, New Zealand) at daily and 5-minute granularity.

Method summary¶

Data¶

15 equity indices across Americas / Europe / Asia / Oceania.
Daily: full 100-day windows before and after 2025-01-20 (Trump inauguration).
5-minute: used only for cumulative-entropy calculations, for information density.
Multiple data vendors: Stooq, Investing.com, EOD Historical Data, Dukascopy, Bluecapital.
Standardised into a MariaDB relational database for analysis.

Signals¶

Shannon entropy on binned return distributions — computed per window with Velleman-rule bin count.

Cumulative entropy — a spectrum of entropies over increasing subsets $T_0 \subset T_1 \subset \ldots \subset T_m$ where each $T_k$ extends $T_{k-1}$ by a fixed $\Delta t$. Produces a trajectory $H_0, H_1, \ldots$ whose shape encodes when informational complexity builds fastest and how persistent the elevated state is.

Jointly reading $H$ vs $\sigma$¶

State	$\sigma$	$H$	Interpretation
Calm	low	high	Efficient random walk
Structured volatile	high	low	Large moves but narratively constrained (policy shock regime)
Unstructured volatile	high	high	Large moves with diverse drivers (idiosyncratic / multi-shock)

The paper's key finding is that the policy-concentrated period shows structured volatility — high $\sigma$, low $H$ — which standard volatility-only analysis would mislabel as generic turbulence.

Main results¶

Decoupling between standard deviation and Shannon entropy is substantial across most indices in the post-inauguration window — entropy adds genuine information beyond volatility.
Cumulative entropy ramps align precisely with major announcement days (tariffs, geopolitical interventions, industrial-policy declarations).
Global coupling: extreme entropy signatures appear near-simultaneously across regions, consistent with event-driven global market response.
Regional modulation: magnitude and persistence of entropy elevations vary by region; indices with tighter US trade linkage (Canada's TSX, Germany's DAX, Japan's Nikkei) show sharper responses.

Limitations¶

Macro / index-level, not LOB-level: entropy is computed on daily/5-min index returns, not on order-book features. The framework could be adapted to LOB signals but this paper doesn't do that.
One natural experiment: 100-day Trump-2 window + 100-day pre-window reference. No cross-validation on other policy-concentration periods.
Binning sensitivity: entropy values depend on bin count via Velleman's rule; robustness to alternative binning not extensively tested.
Descriptive, not predictive: the paper shows entropy correlates with extreme events but does not build a forward-looking signal.
Thirteen authors, eight institutions — unusually broad authorship; may reflect a methods paper with shared credit rather than a tight empirical focus.

Connections¶

Conceptually adjacent to microstructure signal-design but operating at a different scale. The idea that information complexity is orthogonal to price amplitude is directly applicable to LOB signals — e.g., binning OFI realisations and computing Shannon entropy would give a complement to OFI magnitude.
Contrasts with the OFI / LOB tradition: microstructure papers in this wiki (price-impact-order-book-events, gould-bonart-queue-imbalance, mlofi-xu-gould-howison) focus on directional signals; this paper focuses on distributional signals (how many distinct outcomes are populated, not which direction they go).
Future research vector: the cumulative-entropy construction could be a natural extreme-event detector for LOB data — potentially useful for volatility-regime-aware execution algorithms (cf. mpc-trade-execution).
Mostly useful as: a reference for entropy as a market signal, an example of information-theoretic analysis applied to financial time series, and a reminder that dispersion-only volatility measures miss structural information about the distribution shape.