Kolm Index

From Open Risk Manual

Definition

For the purpose of measuring name, sector or geographic concentration, the Kolm Index' is defined as follows: 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)

Implementations

Open Source implementations of the Kolm index are available in


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