Exchange Entropy in Financial Information Processing An Operational Metric for Information Processing Fidelity in Asset Markets

Abstract We introduce Exchange Entropy (H_ex) as an operational metric for the fidelity with which financial markets process and incorporate fundamental information into asset prices. Unlike Shannon entropy, which measures the uncertainty of a signal source, Exchange Entropy measures the degree to which the semantic content of fundamental information is preserved—rather than displaced by narrative amplification—during the collective processing of market participants. We provide a formal definition grounded in mutual information theory, derive a tractable empirical estimator based on covariance decomposition of price changes, and demonstrate the metric's properties through analytical results and calibrated simulations. We show that H_ex declines monotonically as information silo intensity increases, and that it exhibits a phase-transition-like discontinuity at a critical silo threshold. Empirical estimation strategies using earnings announcement data, social media text analysis, and network topology measures are discussed in detail. The metric offers potential applications in bubble early-warning systems, cross-market efficiency comparison, and regulatory assessment of information environment quality. Keywords: exchange entropy; information processing fidelity; mutual information; covariance decomposition; information silos; bubble detection; market microstructure; text analysis 1. Introduction A central challenge in empirical finance is measuring the quality of information processing in asset markets. The Efficient Market Hypothesis (EMH) posits that prices fully reflect available information, but provides no metric for the degree to which this ideal is approached or departed from. Behavioral finance documents systematic deviations but lacks a unified quantitative framework for characterizing the information processing failure. We propose Exchange Entropy (H_ex) to fill this gap. The intuition is straightforward: when a market processes information well, price changes should covary strongly with fundamental signals and weakly with narrative signals that are orthogonal to fundamentals. When information processing is degraded—due to silo formation, algorithmic amplification of narratives, or cognitive homogenization—the covariance structure reverses: price changes are driven primarily by narrative amplification within investor clusters, and the fundamental signal is attenuated or lost. The term "exchange entropy" is chosen deliberately. In thermodynamics, entropy measures the dispersal of energy across microstates. In information theory (Shannon, 1948), entropy measures the uncertainty of a source. Exchange Entropy, as we define it, measures something different: the degree to which information retains its semantic identity—its "value relevance"—as it is exchanged, processed, and transformed by the collective cognitive system of market participants. High H_ex means the market is a high-fidelity information processor; low H_ex means the market is distorting the information it receives. This paper makes four contributions. First, we provide a formal definition of H_ex grounded in mutual information theory. Second, we derive a tractable empirical estimator. Third, we establish analytical properties of H_ex, including its relationship to silo intensity and its phase-transition behavior. Fourth, we discuss estimation strategies and potential applications.