Conditioning on a Volatility Proxy Compresses the Apparent Timescale of Collective Market Correlation

Abstract

We address the attribution problem for apparent slow collective dynamics: is the observed persistence intrinsic, or inherited from a persistent driver? For the leading eigenvalue fraction ψ_1=λ_/N of S\&P 500 60-day rolling correlation matrices (237 stocks, 2004--2023), a VIX-coupled Ornstein--Uhlenbeck model reduces the effective relaxation time from 298 to 61 trading days and improves the fit over bare mean reversion by ΔBIC=109. On the decomposition sample, an informational residual of (VIX) alone retains most of that gain (ΔBIC=78.6), whereas a mechanical VIX proxy alone does not improve the fit. Autocorrelation-matched placebo fields fail (ΔBIC_=2.7), disjoint weekly reconstructions still favor the field-coupled model (ΔBIC=140--151), and six anchored chronological holdouts preserve the out-of-sample advantage. Quiet-regime and field-stripped residual autocorrelation controls show the same collapse of persistence. Stronger hidden-variable extensions remain only partially supported. Within the tested stochastic class, conditioning on the observed VIX proxy absorbs most of the apparent slow dynamics.

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