Copula Central Asymmetry of Equity Portfolios

TL;DR

This paper introduces a non-parametric test for detecting asymmetry in the dependence structure of asset returns, revealing that such asymmetry varies over time and across portfolio types, especially during market downturns.

Contribution

It develops a novel, robust test for copula central asymmetry using the Cramér-von Mises distance, applicable to large asset series and time series data.

Findings

Asymmetry varies over time and is less in recent years.

Size-based portfolios show more asymmetry than book-to-market or momentum portfolios.

Industry portfolios exhibit asymmetry during market downturns.

Abstract

Financial crises are usually associated with increased cross-sectional dependence between asset returns, causing asymmetry between the lower and upper tail of return distribution. The detection of asymmetric dependence is now understood to be essential for market supervision, risk management, and portfolio allocation. I propose a non-parametric test procedure for the hypothesis of copula central symmetry based on the Cram\'er-von Mises distance of the empirical copula and its survival counterpart, deriving the asymptotic properties of the test under standard assumptions for stationary time series. I use the powerful tie-break bootstrap that, as the included simulation study implies, allows me to detect asymmetries with up to 25 series and the number of observations corresponding to one year of daily returns. Applying the procedure to US portfolio returns separately for each year shows that the amount of copula central asymmetry is time-varying and less present in the recent past. Asymmetry is more critical in portfolios based on size and less in portfolios based on book-to-market and momentum. In portfolios based on industry classification, asymmetry is present during market downturns, coherently with the financial contagion narrative.