# How to Calculate the Herfindahl Index

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How do government agencies and industry analysts evaluate a particular market for possible signs of monopolies or violations of antitrust laws? One tool designed to shed light on these concerns is the Herfindahl Index. This is a mathematical formula used by government and industry experts to assess the concentration of firms in a particular industry or market.

#### TL;DR (Too Long; Didn't Read)

To calculate the Herfindahl Index, you'll need to know the market share for each company that's competitive in the market in question. Square the market share of each company, then add together each result. The resulting sum is the Herfindahl Index.

## What Is the Herfindahl Index?

First of all, it's important to understand the definition and function of an index. In the investment and business context, an index is simply a metric or an indicator of something. Generally, it refers to a measurement of change in the context of investments and securities.

In this case, however, it refers to a metric that represents industry concentration. The purpose of the Herfindahl Index is to assess the relative or comparative size of the major companies in a particular industry or market.

You may also see the Herfindahl Index (HI) referenced by other names, such as the concentration index and the Herfindahl Hirschman Index (HHI) or sometimes the HHI score.

## What the Herfindahl Index Measures

The Herfindahl Index takes into account a number of factors that give analysts and experts a better, more comprehensive view of the health of a specific market. When that market is populated by a lot of big companies, all of them relatively the same size, the index will be at or near zero. On the other hand, if a specific industry or market is dominated by a single company, the index will be dramatically bigger.

The index is inversely proportionate to the number of companies in that market. It's also inversely proportionate to the difference in size between those companies.

This means that the closer a market is a true monopoly, the larger that firm's market share would be. For example, let's assume a specific industry only has a single viable business, Smith Inc. If Smith Inc. really is the only company active in that industry, its market share will be 100 percent. As a result, its HI would be 10,000.

Let's assume the opposite scenario. If an industry has thousands of companies, each of them roughly the same size, the HI would be close to zero. An HI score close to zero would indicate a market that's enjoying a nearly ideal state of competition. The risk of a monopoly like the HI would be nearly zero.

Of course, there's a lot of room in between these two extreme examples. The U.S. Department of Justice, in analyzing potential monopoly and antitrust cases, considers any market with a Herfindahl Index lower than 1,500 to be in a state of healthy competition.

The U.S. DOJ also analyzes corporate mergers for the change in the HI that the merger would trigger. So, for example, any merger that would result in a change in the HI of 200 points or more raises serious antitrust concerns for the DOJ analysts and investigators.

## Market Share vs. Herfindahl Index

While the concepts may sound similar, market share and the Herfindahl Index are not the same, nor do they measure the same thing.

Market share is a figure that represents a specific company’s sales as a percentage of the total sales for the industry in question. It's usually measured in a single year or another time period. Knowing a company's market share gives you an idea of how big a specific company is, relative to its competitors or other companies in the same market or type of business.

HI or HHI utilizes market share in its formula, but it doesn't measure the same thing. The HI looks at the market as a whole, while market share looks specifically at an individual company within that market.

## How to Calculate the Herfindahl Index

To calculate the Herfindahl Index, you'll need to know the market share for each company that's competitive in the market in question. Square the market share of each company, then add together each result. The resulting sum is the Herfindahl Index.

Let's look at an example with figures. Imagine the medical supplies industry has five companies with varying market shares:

1. ABC Corp. with 30-percent market share.
2. XYZ Inc., also with 30-percent market share.
3. Smith Co. with 20-percent market share.
4. Jones Inc. with 15-percent market share.
5. Underdog Corp. with 5-percent market share.

To calculate the Herfindahl Index for this industry, simply square each of the market shares, expressed in decimals, then add the results together. In other words: (0.30)^2+ (0.30)^2 + (0.20)^2 + (0.15)^2 + (0.05)^2 = 0.245. Therefore, the Herfindahl index for this industry is 0.245. Because the market share is dominated by the top three companies, with two companies responsible for 60 percent of the entire market, there is a significant degree of concentration in this market.