Information-Processing Entropy and Heterogeneous Sentiment Reaction Windows: Evidence from S&P 500 Stocks

This study examines the heterogeneous timing of market responses to financial news and its implications for informational uncertainty in price-adjustment dynamics. Empirically, stocks do not incorporate positive and negative sentiment at the same speed; instead, they exhibit asset-specific delays that stem from differences in investor attention, cognitive processing, and microstructural constraints. These unequal reaction windows increase the entropy of the information-transmission process, as sentiment shocks diffuse across assets in a dispersed and temporally misaligned manner. To quantify this heterogeneity, we develop a framework that integrates FinBERT-based sentiment classification, Bollinger Bands signal identification, and a Genetic Algorithm (GA) to estimate stock-specific sentiment reaction windows. Using S&P 500 data from 2021 to 2024, with 2022 to 2024 reserved for out-of-sample validation, the results show that GA-derived windows capture actual price-adjustment lags more accurately and significantly improve trading performance compared with fixed-window and technical-only benchmarks. In particular, incorporating news headline sentiment into the Bollinger Bands framework increases the win rate by approximately 5% over the testing period and leads to a significant improvement in overall returns. These findings demonstrate that the assimilation of sentiment is a time-dependent and non-uniform process shaped by behavioral and structural factors, offering new evidence that informational entropy—arising from delayed and heterogeneous reactions—plays a meaningful role in market efficiency and return dynamics.