Investing — ETF — Portfolio optimization

The Herfindahl-Hirschman Index: How Diversified Are Your ETFs?

Learn how to use the Herfindahl-Hirschman Index on your passive portfolio and prepare to be surprised.

7 min readFeb 6, 2021


Photo by Annie Spratt on Unsplash

Last year was no exception, far from it. In 2020, investors in the world poured billions of cash into ETFs, passive funds that track indexes with a diversified approach, or is it? Let’s see how you could use the Herfindahl-Hirschman Index to measure the diversification of ETFs and other investment funds.

How Much Diversified Are You When Buying ETFs?

Diversification is a protection against ignorance.

— Warren Buffett

When investing, diversification is of key importance. This is one of the most precious rules, and healthiest concepts you should remember when investing in the stock market.

Mostly, a portfolio’s performance will depend on a few stocks. When we apply the Pareto principle to investing, we find that 80% of the profits come from only 20% of a portfolio. Unfortunately, no one is a fortune-teller. It’s impossible to know in advance which stock will progress, or when it will.

Don’t try to shoot for the stars. Instead, diversify to ensure that you don't put all your eggs in one basket. If one stock or another suffer from headwinds, a well-diversified portfolio should easily mitigate its negative impact. Eventually, your portfolio will be fine. Here is why portfolio allocation optimization is a core concept that everyone should apply!

ETFs as a Diversification Tool: The Devil Is in the Details

A commonly held idea is that when it comes to diversify your exposition to the stock market, nothing beats Exchange Traded Fund (ETF). ETFs supposedly allow to build a global, diversified and low-cost portfolio by tracking complete stock market indexes; a perfect way to start investing on the stock market. Let’s focus on them.

Photo by NASA on Unsplash

For example, the MSCI World is one of the largest indexes, with more than 1,500 large and mid-cap companies in about 20 developed market countries. And what about S&P 500? It tracks the 500 large U.S. companies accounting for nearly 80% of US stock market capitalization?

If you think it's a perfect way to diversify your investments, then you're in for a surprise! Indeed, index composition and weightings are more important than the number of constituents. Here is the rub!

The Hidden Face of S&P 500

The S&P 500, unlike the Dow Jones Industrial Average, is a capitalization-weighted index. The higher the market capitalization, the greater the constituent weight in the index.

The ten largest stocks in the S&P 500 weighted more than 26% of the index at the end of 2020, a level not seen since the tech bubble in 2000. Source: Morningstar

However, as shown above, the top 10 S&P 500 stocks weighted nearly 26% of the index at the end of 2020. It’s even slightly more now (~ 28%). We're dealing with the most concentrated U.S. market of recent decades.

Weights of the 10 largest S&P 500 stocks (February 4, 2021). Clearly, the S&P 500 is now extremely concentrated. GAFAM stocks have a disproportionate weight in the index. Obviously, it goes against basics of diversification.

Can we still consider that the S&P 500 and related ETFs are diversified? By buying an S&P 500 ETF, you’re therefore making a big bet on a handful of stocks. You accept the general idea that these 5 stocks are more important than the 495 others.

In other words, you expose yourself to GAFAM stocks when you buy S&P 500 ETFs. Furthermore, as these stocks are highly valued, you increase your downside risk. I’m ready to bet it isn’t the diversification you dreamed while buying such an ETF, right?

Luckily, It’s Never Too Late to Catch Up

The good news is that it’s possible to avoid this concentration issue, especially for S&P 500.

A good option is to buy “Equal Weight” indexes, wherein each stock has the same weight. For S&P 500, each stock will therefore weight ~ 0.2% (i.e., 100% divided by 500). Apple will have the same weight as other well-known names (like JP Morgan Chase, Intel or Walt Disney) or more confidential ones (like L3Harris Technologies or Newell Brands). See S&P 500 Equal Weight index for more details.

In 2018, S&P 500 published a study about Equal Weight strategy. Among other, they stressed that over the long term, equal weighting does seem to generate excess return. One explanation postulates that every industry’s top companies face unique challenges, from time to time. More specifically, if a company achieves a dominant position in its sector, additional frictions may arise due to increased regulatory risk or anti-competitive action. By their size, large weights could therefore have an adverse effect on the performance of the index.

Performance comparison of the “classic” S&P 500 (red curve) and the S&P 500 Equal Weighted (blue curve). Since 2004, the equally weighted index has beaten its capitalization-weighted counterpart.

Another strategy is the “Reverse Cap Weighting”. As its name suggests, this approach reverse S&P 500’s order based on market cap (weight = 1/market cap). This strategy overweight underrepresented companies. Conversely, the largest companies in the S&P 500 index will be underweighted: each GAFAM stock will barely weight 0.01%! Check out the Reverse Cap Weighted U.S. Large Cap ETF (RVRS) for more details.

To sum up, investing in ETFs involves to think beyond the comparison of fees, daily volumes or management team composition. Diversification was and still is one of the main advantages of ETFs, but it’s difficult to quantify it properly. Is that so ?

The Herfindahl-Hirschman Index: A Simple Measure of ETF Concentration

From Antitrust to Index Funds, There Is Only One Step

Originally developed for industrial competition assessment and antitrust investigation, the Herfindahl-Hirschman Index (HHI) measures how much concentrated is an underlying. Applied to stock markets, the HHI allows measuring funds’ diversification.

It will be useful to highlight the negative impact of large stocks weights in funds. The higher the HHI, the higher the concentration. Conversely, the lower the HHI, the better the diversification.

Photo by Joshua Hoehne on Unsplash

The time has come to do some mathematics! But rejoice because, it won’t be long. To calculate the HHI, add up squares of the constituent's weights:

Where Si is the weight of company i and n is the number of lines making up the ETF. That’s simple!

Weights used in calculation can be either in decimal value (e.g., 0.05) or in % (e.g., 5%). By multiplying a decimal-based HHI by 10,000, you will find its percent-based HHI counterpart. Here, we will use the percentage format.

Let’s calculate some ETF’s HHI examples:

  • The HHI of a single-component ETF (i.e., a constituent set at 100%) will be 10,000 (100²);
  • The HHI of an ETF with a hundred of equally weighted constituents (i.e., a hundred constituents set at 1%) will be 100;
  • The HHI of an ETF with four components respectively weighting 40%, 30%, 15% and 15% will be 2950 (40² + 30² + 15² + 15²);
  • The HHI of an ETF with ten equally weighted lines (i.e., ten components set at 10% each) will be 1000 (10² + 10² + 10² + 10² + 10² + 10² + 10² + 10² + 10² + 10²);
  • The HHI of an ETF with ten lines, with the first two weighting 25% each and the other weighting 6.25% each, will be 1563 (25² + 25² + 6.25² + 6.25² + 6.25² + 6.25² + 6.25² + 6.25² + 6.25² + 6.25²).

The first example is a very concentrated ETF, with a high HHI. The second one, thanks to equal weight strategy, has a lower HHI. Also, you can see that highly weighted components impact the fifth HHI example, even if it has the same number of components than its equally weighted counterpart in the fourth example.

The Herfindahl-Hirschman Index for the S&P 500

Let’s go back to the S&P 500, using December 2020 data:

  • For the S&P 500, the HHI was 138;
  • For the S&P 500 Equal Weight, the HHI was 20.

Both indexes have the same number of components. However, due to GAFAM’s overweight, the former had an HHI 7 times higher than the equal weight version, at the end of 2020.


The Herfindahl-Hirschman Index (HHI), originally created to measure industry’s concentration, has the great advantage of being easily usable on funds, whether they're passive (e.g., ETFs) or active (e.g., mutual funds).

Photo by Markus Winkler on Unsplash

Now, you know that some strategies exist to avoid ETF’s concentration (such as equal weighting or reverse weighting). By using the HHI, you will be able to evaluate an ETF diversification. Most of the time, you will have to calculate HHIs yourself. Sometimes the funds’ issuers will provide HHIs in fact sheets or products characteristics.

Now it’s your turn to find ETFs with low HHIs to increase diversification!

Raphaël is the founder of, a financial website for French-speaking private investors. This article was originally issued on Investiforum. Read the original article (in French).

This article is for educational and entertainment purposes only and shouldn't be considered as financial or legal advice. Not all information will be accurate but all the data is sourced. Consult a professional before making any significant financial decisions. This article shouldn't be seen as an incentive to buy or sell any of the securities mentioned therein. The author has no position in any of the ETF mentioned.




Blogger at (investing for french investors). I talk about investing, financials & money with a long term mindset.