Shannon Index

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.

Details

More precisely, if we have n exposures $E_{i}$ summing up to a total exposure of

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

where each exposure fraction is defined as

$w_{i}={\frac {E_{i}}{E_{T}}}$

then the Shannon index is defined as

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

Usage

None

Variations

None

Issues and Challenges

None

Implementation

Open Source implementations of the Shannon index are available in

• the Python library Concentration Library

See Also

• Generalized Entropy Index
• Theil Index

References

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