From a statistical point of view, the prevalence of non-Gaussian distributions in nancial returns and their volatilities shows that the Central Limit Theorem (CLT) often does not apply in nancial markets. In this paper we take the position that the independence assumption of the CLT is violated by herding tendencies among market participants, and investigate whether a generic probabilistic herding model can reproduce non-Gaussian statistics in systems with a large number of agents. It is well-known that the presence of a herding mechanism in the model is not sucient for non-Gaussian properties, which crucially depend on the details of the communication network among agents. The main contribution of this paper is to show that certain hierarchical networks, which portray the institutional structure of fund investment, warrant non-Gaussian properties for any system size and even lead to an increase in system-wide volatility. Viewed from this perspective, the mere existence of nancial institutions with socially interacting managers contributes considerably to nancial volatility.