Shannon Index

From Open Risk Manual

Definition

For the purpose of measuring name or sector concentration, the Shannon Index (also entropy index) is defined as the sum product of relative portfolio shares of the exposures, times the natural logarithm 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}

where each exposure fraction is defined as


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

then the Shannon index is defined as


S = - \sum^{n}_{i=1} w_{i} \ln{w_{i}}

Implementations

Open Source implementations of the Shannon index are available in


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