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Entropic signatures of market response under concentrated policy communication

Ewa A. Drzazga-Szczȩśniak, Rishabh Gupta, Adam Z. Kaczmarek, Jakub T. Gnyp, Marcin W. Jarosik, Róża Waligóra, Marta Kielak, Shivam Gupta, Agata Gurzyńska, Johann Gil, Piotr Szczepanik, Józefa Kielak, Dominik Szczȩśniak

Abstract

The first 100 days of Donald Trump second presidential term (January 20th - April 30th, 2025) featured policy actions with potential market repercussions, constituting a well-suited case study of a concentrated policy scenario. Here, we provide a first look at this period, rooted in the information theory, by analyzing major stock indices across the Americas, Europe as well as Asia and Oceania. Our approach jointly examines dispersion (standard deviation) and information complexity (entropy), but also employs a sliding window cumulative entropy to localize extreme events. We find a notable decoupling between the first two measures, indicating that entropy is not merely a proxy for amplitude but reflects the diversity of populated outcomes. As such, they allow us to capture both market volatility and narrative constraints, signaling large and coherent moves driven by policy changes. In turn, the cumulative entropy is found to notably increase during regional episodes with high information density, providing effective signatures of such events. We argue that the obtained results indicate short-term globally coupled, yet regionally modulated, market impacts with clear connection to introduced policies. In what follows, the presented entropic framework emerges as an efficient complement to standard methods for characterizing markets under turbulent conditions, with potential to enhance forecasting strategies such as the stochastic modeling.

Entropic signatures of market response under concentrated policy communication

Abstract

The first 100 days of Donald Trump second presidential term (January 20th - April 30th, 2025) featured policy actions with potential market repercussions, constituting a well-suited case study of a concentrated policy scenario. Here, we provide a first look at this period, rooted in the information theory, by analyzing major stock indices across the Americas, Europe as well as Asia and Oceania. Our approach jointly examines dispersion (standard deviation) and information complexity (entropy), but also employs a sliding window cumulative entropy to localize extreme events. We find a notable decoupling between the first two measures, indicating that entropy is not merely a proxy for amplitude but reflects the diversity of populated outcomes. As such, they allow us to capture both market volatility and narrative constraints, signaling large and coherent moves driven by policy changes. In turn, the cumulative entropy is found to notably increase during regional episodes with high information density, providing effective signatures of such events. We argue that the obtained results indicate short-term globally coupled, yet regionally modulated, market impacts with clear connection to introduced policies. In what follows, the presented entropic framework emerges as an efficient complement to standard methods for characterizing markets under turbulent conditions, with potential to enhance forecasting strategies such as the stochastic modeling.
Paper Structure (8 sections, 4 equations, 11 figures, 3 tables)

This paper contains 8 sections, 4 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Data preprocessing
  3. Methodology
  4. Market Volatility
  5. Extreme Events
  6. Summary and Conclusion
  7. Summary Statistics
  8. Cumulative entropy

Figures (11)

  • Figure 1: Entropy and standard deviation for each considered stock index over symmetric 100-day windows bracketing presidential inauguration on January 20th, 2025. The pre- and post-inauguration periods are labeled as before and after results, respectively.
  • Figure 2: Monthly Shannon entropy profile from October 2024 through April 2025 for each considered stock index. The results are bridging the 100-day pre-inauguration baseline and the post-inauguration window.
  • Figure 3: Kurtosis of 5 minutes returns for each considered stock index. The pre- and post-inauguration periods are labeled as before and after results, respectively.
  • Figure 4: Cumulative entropy for April 1–11, 2025 across representative Americas (A), European (B) as well as Asian and Oceania (C) stock indices.
  • Figure 5: The discrete probability mass function for the 5 minutes data, for April 7th, 2025 (A) and March 25th - April 7th, 2025 (B) across representative Americas, European as well as Asian and Oceania stock indices.
  • ...and 6 more figures