  We report evidence of a deep interplay between cross-correlations
hierarchical properties and multifractality of New York Stock Exchange daily
stock returns. The degree of multifractality displayed by different stocks is
found to be positively correlated to their depth in the hierarchy of
cross-correlations. We propose a dynamical model that reproduces this
observation along with an array of other empirical properties. The structure of
this model is such that the hierarchical structure of heterogeneous risks plays
a crucial role in the time evolution of the correlation matrix, providing an
interpretation to the mechanism behind the interplay between cross-correlation
and multifractality in financial markets, where the degree of multifractality
of stocks is associated to their hierarchical positioning in the
cross-correlation structure. Empirical observations reported in this paper
present a new perspective towards the merging of univariate multi scaling and
multivariate cross-correlation properties of financial time series.
