Abstract
Although metaphorical and conceptual connections between the human brain and the financial markets have often been drawn, rigorous physical or mathematical underpinnings of this analogy remain largely unexplored. Here, we apply a statistical and graph theoretic approach to the study of two datasets – the time series of 90 stocks from the New York stock exchange over a 3-year period, and the fMRI-derived time series acquired from 90 brain regions over the course of a 10-min-long functional MRI scan of resting brain function in healthy volunteers. Despite the many obvious substantive differences between these two datasets, graphical analysis demonstrated striking commonalities in terms of global network topological properties. Both the human brain and the market networks were non-random, small-world, modular, hierarchical systems with fat-tailed degree distributions indicating the presence of highly connected hubs. These properties could not be trivially explained by the univariate time series statistics of stock price returns. This degree of topological isomorphism suggests that brains and markets can be regarded broadly as members of the same family of networks. The two systems, however, were not topologically identical. The financial market was more efficient and more modular – more highly optimized for information processing – than the brain networks; but also less robust to systemic disintegration as a result of hub deletion. We conclude that the conceptual connections between brains and markets are not merely metaphorical; rather these two information processing systems can be rigorously compared in the same mathematical language and turn out often to share important topological properties in common to some degree. There will be interesting scientific arbitrage opportunities in further work at the graph-theoretically mediated interface between systems neuroscience and the statistical physics of financial markets.
Highlights
Over the last two decades, graphical modeling of networks has been used successfully to describe a plethora of complex systems – from metabolic pathways (Jeong et al, 2000) to the world wide web (Barabási and Albert, 1999)
MINIMUM SPANNING TREES Asset trees, introduced in 1999 (Mantegna, 1999), are the first example of financial networks found in the literature
One of the key observations resulting from these studies is that stocks generally tend to group on different branches of the market tree according to industrial sector, e.g., all healthcare or technology companies will tend to be located on the same branch of the minimum spanning tree (MST)
Summary
Over the last two decades, graphical modeling of networks has been used successfully to describe a plethora of complex systems – from metabolic pathways (Jeong et al, 2000) to the world wide web (Barabási and Albert, 1999). A shared conceptual and mathematical framework has emerged for describing these diverse networks, each considered as a set of nodes and edges, in a quantitative lingua franca, often focusing on their topological properties This approach has led to the discovery that many complex systems, including human brain networks, demonstrate a number of important organizational features in common. The so-called “small-world” property of high clustering and high efficiency (or short path length) has proved to be almost ubiquitous in real-life complex systems (Watts and Strogatz, 1998) Despite these deeply interdisciplinary insights, graph theory has often been used as a tool independently by different disciplines, with relatively few efforts to translate new discoveries or methodological advances between traditionally disparate fields that share an interest in topological analysis of complex networks. Our focus on these two systems in particular is motivated by several parallels immediately apparent between the two systems, that are perhaps made most obvious by the anthropomorphic language commonly used in the financial press, describing markets in terms of their “moods,” “beliefs,” and “decisions.”
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