How Leverage and Mean Reversion Shape Return Distributions

Summary

The document examines why the leverage effect, despite being widely observed, may have little apparent influence on the return distributions of some assets. The leverage effect describes a generally negative relationship between asset returns and changes in volatility. The proposed explanation is an interaction with mean reversion: the effect on the return distribution is strongest when leverage is large and mean reversion is weak, while strong mean reversion can mute the effect even when leverage is large. The authors also propose an indirect method for measuring this interaction.

In empirical application, S&P 500 data is reported to have a weak interaction effect, consistent with little influence of leverage on its return distribution. The interaction is also linked to firm size: smaller firms tend to show stronger interaction, while larger firms tend to show weaker interaction. The document gives no numerical estimates or details of the measurement procedure, and its findings do not establish that the same relationships hold for all assets or samples.

Key ideas

• The leverage effect is a generally negative correlation between returns and changes in volatility.
• Its influence on return distributions depends on how it interacts with mean reversion.
• The interaction is reported to be strongest when leverage is large and mean reversion is small.
• The proposed indirect measurement method is applied to empirical data.
• S&P 500 data shows a weak interaction, while smaller firms tend to show stronger interaction than larger firms.

Tags

# Does the leverage effect affect the return distribution?


# Does the leverage effect affect the return distribution?









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.