Does the leverage effect affect the return distribution?

TL;DR

This paper investigates how the leverage effect influences return distributions, revealing that its impact depends on the interaction with mean-reversion and varies across firm sizes.

Contribution

It introduces a new perspective on the leverage effect by analyzing its interaction with mean-reversion and proposes an indirect measurement method.

Findings

Leverage effect's impact depends on mean-reversion strength.

Small firms exhibit a stronger interaction effect.

S&P 500 returns are minimally affected by leverage effect.

Abstract

The leverage effect refers to the generally negative correlation between the return of an asset and the changes in its volatility. There is broad agreement in the literature that the effect should be present for theoretical reasons, and it has been consistently found in empirical work. However, a few papers have pointed out a puzzle: the return distributions of many assets do not appear to be affected by the leverage effect. We analyze the determinants of the return distribution and find that the impact of the leverage effect comes primarily from an interaction between the leverage effect and the mean-reversion effect. When the leverage effect is large and the mean-reversion effect is small, then the interaction exerts a strong effect on the return distribution. However, if the mean-reversion effect is large, even a large leverage effect has little effect on the return distribution. To better understand the impact of the interaction effect, we propose an indirect method to measure it. We apply our methodology to empirical data and find that the S&P 500 data exhibits a weak interaction effect, and consequently its returns distribution is little impacted by the leverage effect. Furthermore, the interaction effect is closely related to the size factor: small firms tend to have a strong interaction effect and large firms tend to have a weak interaction effect.