Emergence of correlations between securities at short time scales

TL;DR

This paper studies how the correlation structure of U.S. stocks changes with different time scales, revealing the emergence of dominant eigenvalues at longer time horizons and suggesting time-scale dependence of market mechanisms.

Contribution

It introduces a spectral analysis of correlation matrices across multiple time scales and proposes a lead-lag factor model to explain the observed dependence.

Findings

Dominant eigenvalues emerge at longer time scales.

Correlation structures depend on the time scale of returns.

A simple model captures the observed spectral dependence.

Abstract

The correlation matrix is the key element in optimal portfolio allocation and risk management. In particular, the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode, sectors and style factors. We investigate how these eigenvalues depend on the time scale of securities returns in the U.S. market. For this purpose, one-minute returns of the largest 533 U.S. stocks are aggregated at different time scales and used to estimate the correlation matrix and its spectral properties. We propose a simple lead-lag factor model to capture and reproduce the observed time-scale dependence of eigenvalues. We reveal the emergence of several dominant eigenvalues as the time scale increases. This important finding evidences that the underlying economic and financial mechanisms determining the correlation structure of securities depend as well on time scales.