Principal Regression Analysis and the index leverage effect

TL;DR

This paper introduces Principal Regression Analysis (PRA) to study the index leverage effect, revealing how market trends influence correlation structures and identifying short and long-term effects on sectorial and market-wide correlations.

Contribution

The paper develops PRA, a novel matrix regression method, and provides analytical and numerical benchmarks to analyze the leverage effect on correlations and market modes.

Findings

Downward trends increase average correlation and uniformity of market mode.

Upward trends also increase correlation but diversify the market mode.

Identifies short-term (monthly) and long-term (yearly) effects on correlation structures.

Abstract

We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which we provide some analytical (using Random Matrix Theory) and numerical benchmarks. We find that downward index trends increase the average correlation between stocks (as measured by the most negative eigenvalue of the conditional correlation matrix), and makes the market mode more uniform. Upward trends, on the other hand, also increase the average correlation between stocks but rotates the corresponding market mode {\it away} from uniformity. There are two time scales associated to these effects, a short one on the order of a month (20 trading days), and a longer time scale on the order of a year. We also find indications of a leverage effect for sectorial correlations as well, which reveals itself in the second and third mode of the PRA.