  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.
