# Hannah Kay Index

From Open Risk Manual

## Definition

For the purpose of measuring concentration (e.g., name, sector or geographic concentration), the **Hannah-Kay Index** is defined as the sum product of relative portfolio shares of the exposures raised to a desired exponent (power). More precisely, if we have n exposures summing up to a total exposure of

where each exposure fraction is defined ^{[1]} as

Then the Hannah-Kay index is defined as

## Implementations

Open Source implementations of the Hannah-Kay index are available in

- the Python library Concentration Library

## References

- ↑ O.Bajo R. Salas, "Inequality Foundations of Concentration Measures