Detection of Market Stress Through Adaptive Liquidity-Scaling Signals

Conventional risk models often treat liquidity events and return-scaling behaviors as separate phenomena, which limits early detection of regime shifts. This study introduces a unified risk-modeling framework that links an entropy-weighted Composite Liquidity Index (CLI) with a distribution-based measure of time-varying self-similarity to produce an adaptive, regime-sensitive risk signal.

The CLI aggregates three liquidity proxies, Amihud illiquidity, the Pastor–Stambaugh liquidity factor, and rolling log-volatility, with weights that adjust daily based on each measure's cross-sectional discriminatory power rather than fixed weighting. In parallel, a matrix of Hurst exponents is estimated by minimizing Kolmogorov–Smirnov distances between rescaled return distributions across pairs of investment horizons, yielding a non-parametric indicator of scaling stability. The framework is applied to daily data for 50 large-cap S&P 500 constituents from 2000 to 2025.

The composite liquidity signal and the median Hurst exponent decline jointly during major stress episodes, including the Dot-Com Crash, the Global Financial Crisis, the COVID-19 shock, and the recent monetary tightening cycle. Dispersion in the Hurst-exponent matrix widens during these periods, indicating that scaling behavior becomes increasingly fragmented across horizons as liquidity conditions deteriorate.

Entropy-adaptive liquidity weighting combined with fractal scaling diagnostics provides an extensible, model-agnostic building block for next-generation risk models. The framework enables detection of liquidity-driven instability and non-stationary return dynamics, with potential extensions to sector-level analysis, higher-frequency data, and alternative asset classes.