Indexes can be categorized in several different ways, including:
reach, or coverage
geographical
There are broad market indexes like the S&P 500, which cover all the important sectors and contain all the key large-capitalization stocks within a geographical region. In this case it’s the US. There are similar indexes for all the other major–and most minor–stock markets of the world.
There are also indexes that cover larger geographical regions, like North America, the Americas, Europe, the EU, Greater China, Asia, the Pacific…
There are also indexes like EAFE (Europe, Australasia and the Far East), which covers the world ex the US and Canada. It’s purpose is to provide a benchmark for foreign stock portfolios held by US or Canadian investors. There are similar indexes for the World ex Japan, World ex UK…
sectoral
There are also indexes that focus on specific sectors or industries, sometimes divided into local and foreign, depending on the portfolio being measured.
size
There are also indexes that focus only on mid-cap or small-cap stocks, like the S&P 400 (mid-cap) or S&P 600 (small-cap). With these, the definition of what counts as mid-cap and what’s small-cap may vary from index provider to provider.
investing style
Personally, I find these more problematic, but there are also indexes that claim to contain only value stocks and others that contain only growth stocks. The sectoral composition of such indexes can deviate wildly from each other, as well as from a larger, style-neutral index.
how the index is calculated
Virtually all today’s stock market indexes are capitalization-weighted. That is, the effect of the price change of any given stock in the index is based on the total market value of all that company’s outstanding shares. Stocks where this value is large have more influence on the index movement than whose where the value is small.
Example:
Let’s say the index contains three stocks, whose value totals 100.
Stock A has a market value of 70
Stock B has a market value of 20
Stock C has a market value of 10
On a given day, A rises by 1%, B by 2%, C by 3%.
The change in the index is calculated as follows:
(.7 x .01) + (.2 x .02) + (.1 x .03) = .007 +.004 + .003 = .014
The index rises by 1.4% that day. The greatest influence on the index performance is stock A because it’s much larger than the other two.
A variation on capitalization weighting is free float weighting. It may be that in a given country, the government or a powerful family owns a large chunk of one or more large-cap stocks. The part that’s so held is never traded. It’s said not to be part of the pubic “float.” Where this is the case, indexes often weight the stock using only the float, not the full market capitalization.
variations
equal weighting
The Value Line index is an example. In an equal weighted index, all constituent stocks count the same. In the example above, an equal-weighted index would be up by 2%.
Versus a capitalization-weighted index, an equal weighted one gives much greater emphasis to smaller stocks.
the Dow and Nikkei Dow
These indexes are wacky. They use the per share stock price as a weighting factor. In other words, a $100 stock counts for 10x what a $10 stock does, no matter what the total size of either company is. To my mind, this is sort of like saying a nickel is worth more than a dime because the coin is larger.
“fundamental” weighting
At one time in the recent past, some investment managers claimed they were offering an index product in which stocks were selected as index constituents either because they had a strong record of high and increasing dividend payments, or because they combined strong earnings growth with modest stock market valuations.
To my mind, this is a marketing ploy. These are active management offerings, not index funds/ETFs. The active manager has decided to rely exclusively on mechanical rules that embody his investment judgment. Many value managers do much the same thing.
As far as I can see, the investment managers I’ve heard making index claims for their products have stopped doing so–with or without the prompting of regulators I don’t know.