## What is the Herfindahl-Hirschman index?

The Herfindahl index is a variation of the market concentration marketing metric. Instead of a simple sum of the market shares of the larger brands in the marketplace, the Herfindahl index applies a multiple (squared) effect to the difference in the market shares for all/most brands.

#### The Herfindahl-Hirschman index formula

The Herfindahl index is calculated by:

*The sum of the squares of each brand’s market shares*

**Notes on the Herfindahl-Hirschman index**

- Usually only the top 50 brands are included in the calculation of the index
- The maximum index score = 1 (which occurs in the case of a monopoly)
- The minimum index score = 1/number of brands (which occurs if all brands have an equal market share)

#### First Example of the Herfindahl-Hirschman index

Letâ€™s use an example marketplace with five brands – their market shares are as follows:

- Brand A = 40% (0.40)
- Brand B = 30% (0.30)
- Brand C = 20% (0.20)
- Brand D = 7% (0.07)
- Brand E = 3% (0.03)

The Herfindahl index is the calculated by squaring each of the market shares as follows: 0.40 X 0.40 + 0.30 X 0.30 + 0.20 X 0.20 + 0.07 X 0.07 + 0.03 X 0.03 = 0.160 + 0.090 + 0.040 + 0.0049 + 0.0009 = 0.2958 = 0.30 (rounded)

Given that there are five brands in the market, the minimum Herfindahl index would be 1/5 = 0.20 – see below for how to use this index.

#### Second Example of the Herfindahl-Hirschman index

In this second example, let’s use five brands again, but this time have a more concentrated market, as follows:

- Brand A = 60% (0.60)
- Brand B = 30% (0.30)
- Brand C = 8% (0.08)
- Brand D = 1% (0.01)
- Brand E = 1% (0.01)

For this second example, the Herfindahl index is calculated as follows: 0.60 X 0.60 + 0.30 X 0.30 + 0.08 X 0.08 + 0.01 X 0.01 + 0.01 X 0.01 = 0.360 + 0.090 + 0.0064 + 0.0001 + 0.0001 = 0.4566= 0.46 (rounded)

And given that there are still five brands in the market, the minimum Herfindahl index in this example would also be 1/5 = 0.20 – see below for how to use this index.

#### Using the Herfindahl-Hirschman index scores

The H-index for market concentration is **best used as a comparative measure.** In the two examples above, the first market had an index score of 0.30 (max = 1, min = 0.20) and the second market had an index score of 0.46 (max = 1, min = 0.20). **Therefore, the second market is far more concentrated that the first market.**

The H-index **removes the subjective decision** of how many brands to include in the calculation, which is a limitation of the more basic approach to measuring market concentration.

As you can see from the two examples above; a firm with **a large market share will add significantly to the overall index**. However, relatively minor market shares will have very little impact. Therefore, **several large players are required to generate a higher index score**.

This index can be **compared to the minimum score** that could be generated it all brands were equal in market share. For example, a market with just ten brands, with each brand having a 10% market share – when multiplied by itself (squared) each market share becomes 10% X 10% = 0.01 and all 10 brands would add up to an index of just 0.10.

It is a relatively **simple calculation to perform by a spreadsheet** and once it is set up a can be tracked over time and several industries can be compared on this index.

**Related topics**

What is market concentration?

The free Excel template for calculating market concentration.