Source: Wikimedia Commons.

When most people think about the Dow Jones Industrial Average, they rightly assume it reflects the biggest corporations in the United States.

But there are three notable exceptions: Apple, Berkshire Hathaway (BRK.A 0.58%) (BRK.B 0.38%), and Google. These companies are the first, third, and fourth largest America businesses by market capitalization, producing some of the best-known goods and services in the world.

Given their size and prominence, one would be excused for wondering why they're not part of such a prominent blue-chip stock index. And the answer is that they can't be -- or, at least, not under the current construction of the Dow.

"The mechanics of the first stock average were dictated by the necessity of computing it with paper and pencil," the official description explains. "Add up the prices and divide by the number of stocks."

In other words, the weighting on the index is a simple average of the components' stock prices; the higher the price, the heavier the weight.

Currently, for instance, IBM (IBM 0.13%) trades for $186.60 per share, making it the most expensive stock on the Dow. And correspondingly, it carries the heaviest weighting, accounting for 9.43% of the Dow's daily price movements.

Alcoa (AA), on the other hand, trades for only $8.06 per share, making it the least expensive component and thus the least weighted, accounting for a measly 0.41% of the daily movement. This goes a long way toward explaining why the index committee recently decided to replace it with Nike on the index.

By this point, it's probably obvious why Berkshire, which trades for $170,489 a share, could never be a member of the Dow. But if not, take a look at the following figure.

As you can see, if Berkshire was added to the Dow, the movement of the index would be virtually synonymous with the Omaha-based company's stock, as its shares would dictate 98.86% of the daily volatility of the Dow.

This is the reason Rob Arnett, a pioneer of alternative forms of index investing, told my colleague Morgan Housel last year, "If you had Berkshire Hathaway in the Dow, it would be the Berkshire Hathaway Index."

The point here is that, while the Dow remains the most widely cited stock index in the world, its overly simplistic construction prevents it from truly representing the biggest and most prestigious companies in the United States.