The scale-free topology of market investments
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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 $γ$ and $α$. Moreover, we find that $k_{in}$ scales as a power-law function of $v$ with an exponent $β$. Remarkably, despite the values of $α$, $β$ and $γ$ differ across the three markets, they are always governed by the scaling relation $β=(1-α)/(1-γ)$. 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.
Final version accepted for publication on Physica A
Final version accepted for publication on Physica A