Will Apple (Nasdaq: AAPL) soon join the Dow Jones Industrial Average? A rising chorus of pundits suggests so. A few other firms may also be added, since the analysts who chose the index‘s components rarely make just one move. But to make way for any new members, some existing Dow members may soon get their walking papers.

The economy changes over the years, and this is often reflected in this index. Since its founding in 1896, companies like the U.S. Leather Co., the Distilling & Cattle Feeding Co.  and the American Cotton Oil Co. were once Dow components, but don’t even exist as standalone companies any more. In their place are vaunted names like Microsoft (Nasdaq: MSFT), McDonald’s (NYSE: MCD), and Coca-Cola (NYSE: KO) among others.

So why should you care which firms might be leaving the index? Because leaving the Dow means funds that are required to hold Dow components will need to dump their shares. This means that if you own any of these possible rejects, then you should be prepared for the stock to take a hit.

The Dow analysts use various criteria to determine what should be included (such as company size, importance to the American economy, etc.). But if the Dow analysts judged companies strictly by market size, then some obvious candidates would be likely ejected.

These seven Dow components have the smallest market value…

Although the U.S. industrial base has eroded in the past few decades, Boeing (NYSE: BA), Caterpillar (NYSE: CAT) and 3M (NYE: MMM) are clear success stories — especially in terms of exports. Yet it’s the three smallest firms in this table that should feel vulnerable.

Alcoa (NYSE: AA), for example, is a fine company. I still think this stock is quite undervalued in the context of mid- to peak-cycle earnings, but even if shares doubled from here, then its market value would still be below $20 billion.

Travelers (NYSE: TRV) is a trickier choice. This stock was only added three years ago, and the Dow analysts rarely drop a company that was only recently invited to join the index. Travelers was added to provide more exposure to financial services at a time when big banks like Citigroup (NYSE: C) were looking like a bad representative of the financial services sector. Travelers’ market value is just one-third that of Citigroup.

The third-smallest company in the Dow? That would be Hewlett-Packard (NYSE: HPQ). Quite suddenly, being the world’s largest makers of PCs is no longer something to boast about. In just a few short years, smartphones and tablet computers have completely upended this industry. The fact that CEO Meg Whitman is overseeing the layoffs of thousands of employees makes you wonder what kind of future this company has. Besides, Intel (Nasdaq: INTC), IBM (NYSE: IBM) and Cisco Systems (Nasdaq: CSCO) give the index ample exposure to high-tech, even before the inclusion of Apple or others.

Lastly, Kraft (NYSE: KFT) may soon get the boost as the packaged foods maker aims to slice itself in two on Oct. 1, and each resulting half may be too small for the Dow.

Risks to Consider: Betting on Dow exclusion is no sure thing. Analysts have long-expressed concerns that Alcoa should no longer be in the Dow, but there it stays. So predicting its exit from the Dow has been a losing bet thus far.

Action to Take –> Alcoa and Hewlett-Packard are already so inexpensive that it’s hard to see much more downside. Travelers, on the other hand, is trading near its 52-week high, and looks more vulnerable. For that matter, Du Pont (NYSE: DD) and United Technologies (NYSE: UTX) shouldn’t rest easy, either. These companies are no longer the industry dominators they once were — a key consideration for the Dow Jones analysts. And as noted earlier, Kraft may get the heave-ho when its splits itself in two on October 1.

As noted earlier, exclusion from the Dow adds short-term selling pressure from index funds. So you may want to cut your exposure to these possible Dow rejects.

[Editor’s note: Which stocks are likely to be added to the Dow? And should you consider buying them before they make it on the index? Click here to find out …]