Gini Index

From Open Risk Manual

Definition

For the purpose of measuring name, sector or geographic concentration, the Gini Index (also Gini coefficient) is an index defined in terms of the Lorentz curve of the exposures. More precisely, if we have n exposures E_i summing up to a total exposure of


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

and the fractional exposures w_i are defined as


w_{i} = \frac{E_i}{E_T}

Then the Gini index is defined as the area under the Lorenz curve which is geometrically reduced to


G =  1 + \frac{1}{n}   \sum^{n}_{i=1} (1 - 2 i) w_{i}

NB: Sometimes the formula appears also with the opposite sign!

Implementations

Open Source implementations of the Gini index are available in


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