# Berger-Parker Index

## Definition

**Berger-Parker Index** for the purpose of measuring credit portfolio or market Concentration Risk, diversity or inequality metrics the Berger-Parker Index is a measure of the contribution of the largest entity of exposure to the total portfolio exposure - essentially the fraction.

It is the special case k=1 of the Concentration Ratio. It is the fraction of the population formed by the most abundant category.

## Formula

The concentration ratio is simply the percentage of portfolio exposure by the n largest exposures. Assuming the exposure data are given and ordered , calculation is easy.

where w_{i} is simply the share of the i-th exposure in the total portfolio exposure.

## Variations

None

## Issues and Challenges

Although the data requirements for the Berger-Parker calculation seem to be moderate at first sight, they often turn out to be difficult to meet in practice. They require the aggregation of all exposures to the same borrower for the whole business entity, be it a bank or a banking group. A heterogeneous IT environment can already present a serious technical obstacle to this aggregation. Furthermore, large borrowers, which are actually the most relevant entities for measuring name concentration, can themselves be complex structures that are not always easy to identify as belonging to the same borrower entity.

## Implementation

Open Source implementations of the Berger-Parker are available in

- the R package IC2
- the Python library Concentration Library

## See Also

None

## References

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