How can we represent hierarchical information present in large type inventories for entity typing? We study the suitability of hyperbolic embeddings to capture hierarchical relations between mentions in context and their target types in a shared vector space. We evaluate on two datasets and propose two different techniques to extract hierarchical information from the type inventory: from an expert-generated ontology and by automatically mining the dataset. The hyperbolic model shows improvements in some but not all cases over its Euclidean counterpart. Our analysis suggests that the adequacy of this geometry depends on the granularity of the type inventory and the representation of its distribution.