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 E_i summing up to a total exposure of


E_T = \sum^{n}_{i=1} E_{i}

where each exposure fraction is defined [1] 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}

Implementations

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

References

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

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