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# The scale-free topology of market investments

## Author

Listed:
• Diego Garlaschelli
• Stefano Battiston
• Maurizio Castri
• Vito D. P. Servedio
• Guido Caldarelli

## Abstract

We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree ($k_{in}$) and the sum of incoming link weights ($v$) of an investor correspond to the number of assets held (\emph{portfolio diversification}) and to the invested wealth (\emph{portfolio volume}) respectively. An empirical analysis of three different real markets reveals that the distributions of both $k_{in}$ and $v$ display power-law tails with exponents $\gamma$ and $\alpha$. Moreover, we find that $k_{in}$ scales as a power-law function of $v$ with an exponent $\beta$. Remarkably, despite the values of $\alpha$, $\beta$ and $\gamma$ differ across the three markets, they are always governed by the scaling relation $\beta=(1-\alpha)/(1-\gamma)$. We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of `hidden' vertex properties.

## Suggested Citation

• Diego Garlaschelli & Stefano Battiston & Maurizio Castri & Vito D. P. Servedio & Guido Caldarelli, 2003. "The scale-free topology of market investments," Papers cond-mat/0310503, arXiv.org, revised Dec 2004.
• Handle: RePEc:arx:papers:cond-mat/0310503
as

File URL: http://arxiv.org/pdf/cond-mat/0310503

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