Kolm Index

Definition

The Kolm Index' is a concentration index useful for the purpose of measuring name, sector or geographic concentration

Details

If we have n exposures $E_{i}$ summing up to a total exposure of

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

average exposure

$\mu ={\frac {E_{T}}{n}}$

and the fractional exposures $w_{i}$ are defined as

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

Then the Kolm index is defined as

$K={\frac {1}{a}}\left(\log(\sum _{i=1}^{n}e^{a[w_{i}-\mu ]})-\log(n)\right)$

Usage

None

Variations

None

Issues and Challenges

None

Implementation

Open Source implementations of the Kolm index are available in

• the R package Ineq
• the Python library Concentration Library

See Also

None

References

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