In this post, I will show you that stock indexes have biases that matter for your investments.

One of the most given advice to new stock market’s investors, and it is also true for seasoned investors, is to invest in an index, like the S&P 500 or the Dow Jones, by using exchange-traded funds. It is not only cheap, but it also reduces the risks of investing because you benefit from the inherent diversification of the index.

However, do you know that all indexes are not equals? Some indexes have biases you are not aware of! I am not talking about a bias toward a particular industry, like the Nasdaq, which is more oriented toward technology stocks. No, I am talking about something way more subtle than that. There are multiple ways to create an index, and professional investors are aware of how an index is built since it affects their investments. Let me unveil for you a hidden aspect of indexes.

You can also watch my video “Stock Indexes Explained – Hidden biases – Price, Market Cap, Fundamental, and Equal Weighting” on my YouTube’s channel. Check it out!

The essence of an index

Did you ask yourself how the index you are investing in is built? Probably not. You may be surprised by it, but there are multiple ways to create an index, and the two major indexes in the U.S., the Dow Jones Industrial Average and the S&P 500 are very dissimilar! Not only in the number of stocks each index has, but each index’s essence is different. Let imagine the Dow Jones with precisely the same constituent stocks as the S&P 500. Even that way, the Dow Jones would have a different performance! Why? Because the Dow Jones is a price-weighted index, whereas the S&P is a market-capitalization-weighted index. And there are even other methods, equal weighting, and fundamental weighting!

Price-weighted indexes

Let’s start with the price weighting. It is one of the earliest methods due to its simplicity. Charles Dow used it when he created the Dow Jones Industrial Average on May 26, 1896. With price weighting, the most important thing is the price. The percentage of each stock in the index is determined by the ratio of the stock price divided by the sum of all stocks’ prices.

\( \text{Weight}_i=\frac{\text{Stock Price}_i}{\sum \text{Stock Price}} \)

Imagine we are building a price-weighted index with ten stocks, and the sum of all stock prices is $1,000.

\( \sum{\text{Stock Price}}=\$1,000 \)

We have the stock of a huge company, the company “A,” which has earnings in billions. However, “A” emitted a lot of shares. Stock “A” is diluted and has a low price, and it trades at $10. Then this stock will constitute 1% of the index.

\( \text{Weight}_A=\frac{\$10}{\$1,000}=1\% \)

The business “B,” which is smaller, its earnings are expressed in millions, has, on the other hand, emitted a small number of shares, so its stock trades at $750. In our price-weighted index, the stock “B” will weigh 75%!

\( \text{Weight}_B=\frac{\$750}{\$1,000}=75\% \)

The stock market performance is misrepresented

Now you see the big issue of price-weighted indexes, like the Dow Jones Industrial Average, they do not necessarily represent the economic activity, nor the stock market performance, because they ignore the companies’ sizes and the weights are somewhat arbitrary. A higher-priced stock will have a more substantial impact on the index value than a lower-priced stock.

\( \text{Stock Price}_{A, old}=\$10\enspace\rightarrow\enspace\text{Stock Price}_{A, new}=\$11\quad(+10\%) \)
\( \text{Stock Price}_{B, old}=\$750\enspace\rightarrow\enspace\text{Stock Price}_{B, new}=\$749\quad(-0.13\%) \)

If stock “A” soars by 10% to $11, but at the same time stock “B,” loses a mere $1, a 0.13% decline, our index does not move at all!

\( \sum{\text{Stock Price}_{old}}=\$1,000\enspace\rightarrow\enspace\sum{\text{Stock Price}_{new}}=\$1,000\)

Naive approaches are sensitive to stock splits and consolidations

Another unique characteristic of price weighting is that in its purest form, a price-weighted index will jump when companies do stock splits and stock consolidations (also known as reverse stock splits). With our example, imagine the company “B” decides that $750 for its stock is too high, as it has an impact on the liquidity of its stock. It chooses to do a stock split, for each share an investor owns, he now has three shares.

\( \text{Outstanding Shares}_{B, new}=\text{Outstanding Shares}_{B, old}\times3 \)

The board of the company “B” increased the total number of outstanding shares threefold, while at the same time dividing the stock price by three to $250.

\( \text{Stock Price}_{B, new}=\frac{\$750}{3}=\$250 \)

The value of the company did not change. If our index was at 1,000, its level will instantaneously go down to 500.

\( \sum{\text{Stock Price}_{old}}=\$1,000\enspace\rightarrow\enspace\sum{\text{Stock Price}_{new}}=\$500\)

Though in the real economy nothing happened! Now, the stock “B” weighs only 50%. All other stocks will have their weights increase, for example, the stock “A” will jump from 1% of our index to 2%.

\( \text{Weight}_{A, new}=\frac{\$10}{\$500}=2\%\qquad\text{Weight}_{B, new}=\frac{\$250}{\$500}=50\% \)

The Dow divisor

If you start to be frightened by price-weighted indexes, I will clarify one thing: the Dow Jones Industrial Average is not the purest form of a price-weighted index. Stock splits and consolidations do not move the index, because weights are attributed relative to another number, the Dow divisor, which prevents jumps for corporate actions such as splits and consolidations.

\( \text{DJIA}=\frac{\sum \text{Stock Price}}{\text{Dow Divisor}} \)

A new divisor is calculated every time a stock split happens, so the index value is not impacted.

\( \text{DJIA}=\frac{\sum \text{Stock Price}_{old}}{\text{Dow Divisor}_{old}}=\frac{\sum \text{Stock Price}_{new}}{\text{Dow Divisor}_{new}} \)
\( \text{Dow Divisor}_{new}=\text{Dow Divisor}_{old}\times\frac{\sum \text{Stock Price}_{new}}{\sum \text{Stock Price}_{old}} \)

The Nikkei 225

Another well-known price-weighted index is the Nikkei 225, which is the leading Japanese index. It is composed of the top 225 Japan’s companies on the Tokyo Stock Exchange.

Main bias of price-weighted indexes

Overall, the primary bias of price-weighted indexes, like the Dow Jones Industrial Average, is toward higher-priced stocks.

Equal-weighted indexes

Equal weighting is another simple alternative. In this case, it is elementary! Each stock has the same weight.

\( \text{Weight}_i=\frac{100\%}{\text{Number of components}} \)

For a ten stock index, every stock weighs 10%. Some indexes are built that way. Also, you can easily find ETFs tracking equal-weighted versions of the Dow Jones and the S&P 500.

Main biases of equal-weighted indexes

Small-cap bias

This kind of weighting scheme is strongly biased toward small-caps stocks since their index weights are much higher than their importance in the economy. Small-caps are overrepresented, while corporate giants are underrepresented. In the long run, it should provide higher returns because small-caps usually have higher potential returns than large-caps, but it comes at the price of higher risks since small-caps stocks are generally more volatile than large caps.

Higher transaction costs

Another drawback of equal weighting is that prices don’t stay the same, and frequent adjustments are necessary. Hence equal-weighted ETFs incur higher transaction costs than market-cap weighted index funds. This higher volume of trading is causing a higher portfolio turnover, which is tax-inefficient.

Contrarian bias

Can you guess what the other colossal bias of equal-weighting is?

An equal-weighted index has a “contrarian” bias. It does the opposite of what other market participants are doing! If a stock “A” is performing well because there is an immense buying pressure, an equal-weighted ETF will, on the contrary, sell the stock “A.” The opposite is also true. If a stock “B” is out of favor, his price tumbling down, the ETF will buy it! An equal-weighted index and ETFs replicating it are doing the opposite of other market participants’ consensus! Isn’t it something every buyer of that kind of ETF should be aware of? I do think so!

Market-capitalization-weighted indexes

Let’s focus now on the major weighting scheme: the market-capitalization weighting. The idea here is to have an index that represents the importance of the companies in the economy and the stock market. A market-capitalization-weighted index will take the stock price, multiply it by the number of shares, which gives us the capitalization of the company and divide it by the sum of the capitalization of all companies in the index. Hence a small-cap will get a small weight and a large-cap a high weight.

\( \text{Weight}_i=\frac{\text{Stock Price}_i\times\text{Outstanding Shares}_i}{\sum _{k=1}^n{\text{Stock Price}_k\times\text{Outstanding Shares}_k}} \)
\( \text{Weight}_i=\frac{\text{Market Capitalization}_i}{\sum \text{Market Capitalization}} \)

However, usually, market-capitalization indexes go one step further. All the shares of a company are not available to the general investing public. So to take it into account, those indexes focus on the number of shares the investing public can freely exchange, which is called the free-float. Index providers replace the total number of shares of the previous calculation by the free-float, which now gives us the “market float,” the total capitalization available to the investing public. They are “free-float-adjusted market-capitalization-weighted indexes.”

\( \text{Weight}_i=\frac{\text{Stock Price}_i\times\text{Free Float}_i}{\sum _{k=1}^n{\text{Stock Price}_k\times\text{Free Float}_k}}=\frac{\text{Market Float}_i}{\sum \text{Market Float}} \)

To name some major indexes built that way, we have the S&P 500 in the U.S. or the Dow Jones EuroStoxx 50 in Europe.

Global indexes may go even further by considering the number of shares available to foreign investors to compute the weights of each constituent stock.

Main bias of market-capitalization indexes

It is the perfect weighting scheme, isn’t it? You get the best representation of the stock market, don’t you?

Momentum bias

It is more complicated than it looks. You get a fair representation of the target market, but you also have a strong “momentum” bias. When a stock price rises, all else equals, the weight of that stock increases in the index, and if it falls, the weight decreases. You buy more of a soaring stock, and you sell poor performers. You follow the momentum of each stock. It is the exact contrary of the equal-weighting scheme.

Fundamentally-weighted indexes

To correct that momentum bias, some index providers create fundamentally-weighted indexes. Instead of using the price as one of the main drivers of the constituents’ weights, these indexes use fundamental factors to assess the company’s size, like the company’s book value, cash flows, earnings, total sales, total cash dividends, or other relevant factors.

\( \text{Weight}_i=\frac{\text{Fundamental Value}_i}{\sum _{k=1}^n{\text{Fundamental Value}_k}} \)

Main bias of fundamentally-weighted indexes

It effectively removes the momentum bias, to introduce a “value” tilt. Check out my video on Warren Buffett’s 2020 vision; I briefly explain the difference between growth and value investing styles; the link is in the description. In a word, fundamentally-weighted indexes favor companies that are low-priced relative to their earnings. It also means that those indexes have a “contrarian” bias since they will weigh more heavily a stock that has declined more in price than its fundamental value, hence increased its relative value. And if a stock price soared, and the fundamental value did not move up by the same magnitude, the relative value of this particular stock declined, its weight will be adjusted downward.

Conclusion

To come back to the advice to invest in an index by using exchange-traded funds. It is a good one, but now you know that all indexes are not the same, and you now understand how to choose an index that fits your investment preferences.

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Question of the day:
Do you invest in an index? Which one? And why?