Difference between revisions of "Kolm Index"

Latest revision as of 16:05, 18 June 2021

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

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

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Open Source implementations of the Kolm index are available in

@@ Line 18: / Line 18: @@
 Then the Kolm index is defined as
 :<math>
-K = \mu + \frac{1}{a} \left( \log( \sum_{i=1}^n e^{- a \mu n w_i} ) - \log(n) \right)
+K = \frac{1}{a} \left( \log( \sum_{i=1}^n e^{ a [w_i - \mu]} ) - \log(n) \right)
 </math>