Revisiting simple concentration indexes
Our white paper Revisiting simple concentration indexes reviews the definitions of widely used concentration metrics such as the concentration ratio, the HHI index and the Gini and clarify their meaning and relationships.
This new analytic framework helps clarify the apparent arbitrariness of simple concentration indexes and brings to the fore the underlying unifying concept behind these metrics, thereby enabling their more informed use in portfolio and risk management applications.
We also propose that the sensitivity of concentration indexes to growing concentration should be a defining criterion for adopting an index and explore the sensitivity of common indexes to changing portfolio concentrations. We show that this sensitivity can vary significantly between indexes for parametric families of portfolio distributions and hence selecting and using a simple concentration index should take this aspect carefully into consideration.
White paper structure
The white paper has three sections:
- A concept section discussing the issues and the proposal in non-technical terms,
- a technical paper offering precise definitions and numerical studies and
- an open source implementation section Available here