How can we represent hierarchical information present in large type inventories for entity typing? We study the ability 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 investigate two different techniques for creating a large hierarchical entity type inventory: from an expert-generated ontology and by automatically mining type co-occurrences. We find that the hyperbolic model yields improvements over its Euclidean counterpart in some, but not all cases. Our analysis suggests that the adequacy of this geometry depends on the granularity of the type inventory and the way hierarchical relations are inferred.