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

TL;DR

This study shows that conditioning on a volatility proxy like VIX significantly reduces the perceived timescale of collective market correlation dynamics, suggesting that observed persistence is largely driven by external volatility factors.

Contribution

The paper introduces a VIX-coupled Ornstein-Uhlenbeck model that explains slow market correlation dynamics by external volatility, reducing the apparent persistence in the data.

Findings

Conditioning on VIX reduces the effective relaxation time from 298 to 61 trading days.

The VIX proxy explains most of the observed slow dynamics in market correlation.

Model fit improves significantly when incorporating the VIX proxy, with robust out-of-sample performance.

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 $\psi_1=\lambda_{\max}/N$ 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 $\Delta$BIC$=109$. On the decomposition sample, an informational residual of $\log(\mathrm{VIX})$ alone retains most of that gain ($\Delta$BIC$=78.6$), whereas a mechanical VIX proxy alone does not improve the fit. Autocorrelation-matched placebo fields fail ($\Delta$BIC$_{\max}=2.7$), disjoint weekly reconstructions still favor the field-coupled model ($\Delta$BIC$=140$--$151$), 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.