A Statistical Physics View of the S&P 500: Pairwise Interactions and Time-Varying Dynamics

2026-05-24

AI Summary

This study investigates the structural interactions among S&P 500 constituent stocks and their time-varying evolutionary dynamics. By integrating a static pairwise maximum entropy Ising model with a dynamic Ising framework incorporating time-varying external fields, self-memory, and directed lagged couplings, this work presents the first unified approach combining static and dynamic modeling in financial markets. The analysis reveals that intra-sector coupling strength is approximately 2.8 times stronger than inter-sector coupling. During three major market disruptions, the external field exhibits a gradual transition rather than abrupt shifts. Although the dynamic network displays greater asymmetry and weaker self-memory, it effectively reproduces the overall market evolution, thereby elucidating the underlying organizational structure of financial markets and their response mechanisms to external shocks.

Abstract

We analyze a fixed panel of S\&P 500 stocks from 1996 to 2026 using complementary static and kinetic Ising models applied to daily binary open-to-close movements. The static pairwise model provides a long-run maximum-entropy summary of low-order dependence and reveals a sectorally organized interaction network with modest small-world structure and within-sector couplings about 2.8 times stronger than between-sector couplings, with especially coherent real estate and energy sectors. The kinetic model incorporates smooth time-varying external fields, self-memory, and directed lagged couplings to describe next-day dynamics. It reveals slow field-regime shifts around three major market-wide perturbations -- the dot-com bust, the global financial crisis, and the COVID-19 episode. Self-memory is generally weak, and the directed coupling structure is much less sector-concentrated and more asymmetric than the static network, while still reproducing the broad evolution of aggregate market movement. Taken together, the two complementary models characterize both persistent market organization and short-horizon cross-stock dynamics, providing a compact statistical physics view of interaction structure and time-varying behavior in the S\&P 500.

Problem

• S&P 500
• pairwise interactions
• time-varying dynamics
• market perturbations
• statistical physics

Innovation

• Ising model
• pairwise interactions
• time-varying dynamics
• maximum-entropy
• directed couplings