Hannah Kay Index

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).

Details

More precisely, if we have n exposures $E_{i}$ summing up to a total exposure of

$E_{T}=\sum _{i=1}^{n}E_{i}$

where each exposure fraction is defined as

$w_{i}={\frac {E_{i}}{E_{T}}}$

Then the Hannah-Kay index is defined as

$HK_{a}={\begin{cases}\left(\sum _{i=1}^{n}w_{i}^{a}\right)^{1/(a-1)}&{\mbox{for}}\ 0\leq a\neq 1\\e^{\left(\sum _{i=1}^{n}w_{i}\log w_{i}\right)}&{\mbox{for}}\ a=1,\end{cases}}$

Usage

None

Variations

None

Issues and Challenges

None

Implementation

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

• the Python library Concentration Library

See Also

None

References

{{#set:Has Formula = True | Has SourceCode = True | Has Object = False | Has Lambda = False | Field Type= Documentation}}

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