## 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.

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.

Download the free Excel spreadsheet: market-concentration-template

#### 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

Let’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.

#### Reading the Herfindahl-Hirschman index scores

In the above example, we used a comparative approach. But as a general guide, the HHI index is assessed using the following scale:

- HHI = Less than 0.150 = a competitive (low concentration) market
- HHI = 0.150 to 0.250 = a medium/moderate concentrated market
- HHI = More than 0.250 = a highly concentrated market

*Note: sometimes this index is presented as being multiplied by 10,000. *

This table provides a comparison of two markets, both with the same number of competitors.

Market A has a dominant market leader. In each case, the other competitors hold 5% market share each and the market leader holds the balance of market share. For example, for five competitors, the market leader has 80%, and the other for firms hold 5% each, totaling 20%.

In Market B, there is the same number of competitors shown (comparing one to 10 competitors), except in this market all players have an equal market share. For example, for five competitors, each player has 20% share of the market, totaling 100% between them.

As can be seen, Market A is always a highly concentrated market, because it always contains a substantial and dominant competitor versus smaller players who only have a maximum of 5% of the market each.

Whereas for Market B, once we reach four competitors who are all equal, the measure drops to moderately concentrated, and when we reach seven equal competitors, it is considered a relatively low level of concentration.

**Related topics**

What is market concentration?

The free Excel template for calculating market concentration.