How is a stock index calculated?

Usually I don't help out with homework assignments, but I'll make an exception in this case because it's such an interesting question! Turns out I've written about stock index calculations before, though last time it was more about how to use a shell script to automatically grab individual stock values. Curious about that article, which includes some good history of stock indices that I'm not going to repeat here? Check out How to create a custom stock market index.

A bit of history about Charles Dow will help explain how the DJIA came to be created. Wall Street Journal editor Dow launched his original stock average in 1884 based on 11 stocks, mostly railroad stocks. May of 1896 he introduced another index called the industrial average, comprised of: American Cotton Oil, American Sugar, American Tobacco, Chicago Gas, Distilling & Cattle Feeding, Laclede Gas, National Lead, North American Company, General Electric, Tennessee Coal & Iron, Tennessee Coal & Iron, U.S. Leather and U.S. Rubber.

Today the Dow Jones Industrial Average (DJIA) is based on thirty stocks: Alcoa, American Express, American International Group (AIG), AT&T, Bank of America, Boeing, Caterpillar, Chevron, Citigroup, Coca-Cola, DuPont, Exxon, General Electric, General Motors, Hewlett-Packard, Home Depot, Intel, IBM, Johnson & Johnson, Morgan Chase, McDonalds, Merck, Microsoft, Pfizer, Procter & Gamble, United Technologies, Verizon, Wal-Mart and Walt Disney.

That's a Who's Who of big industrial companies, but you'll notice how little new tech is on the list. That's one of the criticisms of the stock index, actually, but that's not really relevant to this particular discussion, so we'll leave it aside.

To show how the Dow Jones Industrial Average (DJIA) is calculated, I'm going to take a snapshot of the stock values and the calculated DJIA. After closing hours on Friday, April 11, 2008, the DJIA is calculated as 12325.42.

Sum all the stock values at this same moment and here's your rather impressive addition problem:

I'll save you the challenge of figuring this out. The sum value of all these stock values is 1545.32.

So how do you get from 1,545 to 12,325? By using the official industrial averages divisor (it's at the bottom of that page). As of this very moment, the divisor is 0.122834016.

Now we can calculate things, though the result might surprise you:

So why is there a difference? Because of what's called after-hours trading. The stock values we used for this math were the closing values of those stocks, but after the stock exchange was closed, the stocks continue to be traded. The result: the market went down 256.56. Now, let's try this math again:

Truth be told, at this point I don't really understand why this isn't an exact calculation, but it's pretty darn close so it'll certainly illustrate what you're trying to calculate. The key is that the general calculation for the DJIA is:

And now... you know. :-)