The scale-free topology of market investments

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 (nu) of an investor correspond to the number of assets held (portfolio diversification) and to the invested wealth (portfolio volume), respectively. An empirical analysis of three different real markets reveals that the distributions of both k(in), and nu display power-law tails with exponents gamma and alpha. Moreover, we find that k(in), scales as a power-law function of nu 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. (c) 2004 Elsevier B.V. All rights reserved.