  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.
