Chaos theory reveals markets fuse into one system during crises

Financial crises do more than send share prices tumbling and volatility soaring: they cause the world’s major stock markets to become far more tightly interconnected, according to a study published in the Journal of Risk and Financial Management. Dr Domenico Vicinanza of Anglia Ruskin University in Cambridge, England, analysed the behaviour of four leading equity indices on both sides of the Atlantic — the Dow Jones Industrial Average, the S&P 500, the FTSE 100 and the DAX — during the Global Financial Crisis and the early months of the Covid-19 pandemic, and found that the connections between markets strengthened sharply under stress.

The study’s methodological novelty lies in its use of convergent cross-mapping, a statistical technique derived from chaos theory. Unlike conventional approaches that focus on correlation, in which a movement in market A is treated as directly causing a movement in market B, convergent cross-mapping asks whether the dynamics of one market contain recoverable information about another. This is an indicator of deeper nonlinear connections between markets. The approach examines nonlinear dynamical coupling, in which markets become linked through feedback loops, investor sentiment and policy announcements, revealing the extent to which the behaviour of one market leaves a detectable footprint in another. In practical terms, when coupling is strong, the behaviour of one market becomes increasingly informative about the behaviour of the others.

The research found that market interconnectedness increased sharply during both crises studied, with markets responding more strongly to the same global pressures. The most striking results emerged during the early months of the Covid-19 pandemic. Every market relationship tested between the Dow Jones, S&P 500, FTSE 100 and DAX suggested that the crisis produced a broad strengthening of links across the system rather than reflecting temporary movements alone. The study’s average coupling measure increased by 16% from the pre-crisis period to the crisis period.

The strengthening of these connections happened quickly. The strongest links between US and European markets appeared within a window of three trading days, and many emerged simultaneously. The pattern of persistence, however, differed between the two crises. Covid-19 produced a sharp but relatively short spike in connectivity during the crisis phase, whereas during the Global Financial Crisis the strong links between markets lasted longer, with coupling continuing and then peaking in the post-crisis phase.

The connections were not flowing in a single direction, although the US markets exerted a slightly stronger influence on European markets during the pandemic. Vicinanza explained the intuition behind the method with an analogy: if two markets are genuinely connected, the movement of one may leave a detectable trace in the other, a bit like seeing footprints in the sand. You may not see the person walking, but the footprint tells you something has passed through. In this case, the footprint is a pattern in the data showing that one market carries information about another.

The findings carry implications for how financial risk is understood and managed. Vicinanza noted that financial risk is not determined only by how much one market falls or how volatile it becomes; it also depends on the closeness of connections between markets when stress spreads through the system. If markets become more dynamically coupled during crises, then diversification, hedging and risk monitoring may need to take account of this changing structure. During the Covid-19 crisis in particular, the major US and European markets behaved less like separate markets and more like parts of a single, tightly connected global system, which may explain why traditional strategies offered limited protection during the sharp market sell-off of early 2020.

When markets become tightly linked, shocks can spread more rapidly and investors have fewer opportunities to reduce risk through diversification. Rather than being driven by local factors, markets in times of crisis become influenced by common global forces, and the behaviour of one market becomes more informative about the behaviour of others. Vicinanza said the study shows that methods derived from chaos theory can provide new insights into the behaviour of financial markets, complementing established tools such as correlation analysis and volatility measures by revealing how markets interact as complex, evolving systems.

The research, titled Nonlinear Market Coupling During COVID-19 and the Global Financial Crisis: A Convergent Cross-Mapping Analysis of US and European Equity Indices, highlights that the connections between markets can be just as important as the behaviour of individual markets. As with any retrospective analysis of two historical episodes, the findings describe the dynamics of those specific crises rather than guaranteeing how future crises will unfold, but they suggest that risk models assuming stable relationships between markets may understate the danger when stress causes those relationships to tighten.

Subject of Research: Nonlinear coupling between US and European stock markets during the Global Financial Crisis and the Covid-19 pandemic, measured with convergent cross-mapping

Article Title: Chaos makes sense of market movements in a crisis

Article References: Chaos makes sense of market movements in a crisis. Original publication (Bibliographic details unavailable.)

Image Credits: AI Generated

DOI: Not provided

Keywords: financial markets, chaos theory, convergent cross-mapping, market coupling, Covid-19 pandemic, Global Financial Crisis, Dow Jones, S&P 500, FTSE 100, DAX, risk management, Anglia Ruskin University