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

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

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

$K = \mu + \frac{1}{a} \left( \log( \sum_{i=1}^n e^{- a \mu n w_i} ) - \log(n) \right)$

Usage

None

Variations

None

Issues and Challenges

None

Implementations

Open Source implementations of the Kolm index are available in

• the R package Ineq
• the Python library Concentration Library

See Also

None