Cross-ownership as a structural explanation for rising correlations in crisis times

TL;DR

This paper models how cross-ownership among firms influences equity correlations during crises, revealing that such interlinkages can amplify correlations independently of asset levels.

Contribution

It provides a mathematical framework linking firm interconnections, asset correlations, and equity sensitivities, highlighting the role of cross-ownership in correlation dynamics during crises.

Findings

Equity correlation exceeds asset correlation in the two-firms case.

Equity correlations increase as asset values decline.

The correlation relationship is independent of overall equity levels.

Abstract

In this paper, we examine the interlinkages among firms through a financial network where cross-holdings on both equity and debt are allowed. We relate mathematically the correlation among equities with the unconditional correlation of the assets, the values of their business assets and the sensitivity of the network, particularly the $\Delta$-Greek. We noticed also this relation is independent of the Equities level. Besides, for the two-firms case, we analytically demonstrate that the equities correlation is always higher than the correlation of the assets; showing this issue by numerical illustrations. Finally, we study the relation between equity correlations and asset prices, where the model arrives to an increase in the former due to a fall in the assets.