The scale-free topology of market investments

Details The scale-free topology of market investments The scale-free topology of market investments

2003-10-21

arxiv.org/abs/cond-mat/0310503v2

Physica A 350 (2-4), 491-499 (2005)

Physics

Condensed Matter

Statistical Mechanics

Final version accepted for publication on Physica A

Scientific paper

10.1016/j.physa.2004.11.040

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.

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