# Sector Concentration Measurement

## Contents

## Definition

**Sector Concentration Measurement** is the quantitative assessment of the degree to which a portfolio may be concentrated in a set of particular business sectors.

## Approaches

For any quantification of risks, it is convenient to have quantitative benchmarks, for example to measure the distance from a neutral reference state of no concentration or full diversification.

Some concentration/diversification indicators can be simply defined at portfolio level, providing synthetic measures of credit risk sector concentration.

### Concentration Ratio

Concentration Index is the simplest method to quantify concentration is computing the share of Exposure (EAD) held by the k largest sectors in the portfolio relative to total exposure. A weaknesses of the index is that the choice of k is arbitrary and the index does not use all the information available. Instead of using of EAD, exposures can be measured as product of EAD*LGD, thus considering the expected severity of losses which can actually differentiate the effective contribution to credit risk.

### Gini Index and the Lorenz Curve

Th Gini Index G varies between 0 (perfect equality of exposures) to 1 for perfect inequality (limit in which one sector accounts for the whole exposure and the others tend to zero). The index is sensitive to inhomogeneity of exposures but not to exposure number.

### Herfindhahl-Hirschman Index

The Herfindahl-Hirschman Index reflects both exposures heterogeneity and their number (e.g. in tends to zero with n for homogeneous pool).