The Dow Jones Industrial Average is a collection of stocks that have been selected as a group to represent the broader economy. There aren't nearly as many stocks in it (30) as there are in the S&P 500 (500, of course), but the two generally track each other pretty well all the same.

But is buying the highest-yielding dividend stocks in the Dow, or the S&P for that matter, a good investing approach? It depends on the stocks, and here's a look at the three highest-yielding Dow stocks today to see what that means.

1. A big telecom

Verizon (VZ 0.43%) has a 6.9% dividend yield, putting it at the top of the Dow's high-yield list. It is one of the largest telecommunications companies in the United States, with a dominant position in the cellphone space.

It has increased its dividend annually for 19 consecutive years. The yield, meanwhile, is toward the high end of the company's historical range, suggesting that the stock is on the sale rack today.

With a huge customer base, Verizon has a large recurring revenue stream that it has used to reward investors. But the cellphone industry is highly competitive, and the company's landline operations are in a slow and steady decline. Business is tough, and likely will remain so.

On top of that, maintaining high-quality service is costly. Verizon has a material amount of leverage, with a debt-to-equity ratio of roughly 1.6 times, which is higher than that of its closest peer, AT&T, which sits at around 1.4 times. That said, the payout ratio has averaged around 50% or so of late, which is reasonable. 

In other words, this is not a slam dunk; there are trade-offs. Yes, you'll be getting a high yield, but dividend growth is likely to be slow (it has averaged around 2% a year over the past decade). And given the company's spending needs, the yield will likely be the biggest contributor to your return. If you are looking to maximize your income, it might fit, but growth investors will probably want to look elsewhere.

2. Changing with the times

Walgreens Boots Alliance (WBA -1.26%) also has a historically high dividend yield, at around 6%. The company is a giant among drugstores, which are a necessity. It has increased its dividend annually for 48 consecutive years. The big story here is change.

Right now, drugstores are shifting to a new business model that integrates health services with the historical role of drug distribution. So Walgreens has been buying medical clinics and pairing them up with its stores. This is a relatively new business model, so there's really no way to tell if it will be a long-term success, even though main competitor CVS (CVS 0.21%) is going down the same path.

The risk is that Walgreens' acquisitions have left its leverage at a historically elevated level, with a debt-to-equity ratio of around 0.6 times. And yet Walgreens' leverage is lower than that of CVS, which has a debt-to-equity ratio of 0.8 times. 

While dividend growth of late has been rather miserly, over the past decade it has averaged a respectable 6% or so a year. If you like to buy historically well-run companies when they are unloved on Wall Street, which is a value approach, Walgreens might interest you. And if its transition works out well, it could even turn into a more growth-oriented stock.

3. A lot of risk

The last name on the list today is industrial giant 3M (MMM -1.60%), with a yield of around 5.9%. It has a broadly diversified business and a long history of innovation, and it has increased its dividend annually for 65 years, making it a highly elite Dividend King

The reason that 3M's dividend is historically high today is that it is facing a great deal of uncertainty. But the uncertainty is of a different sort than with Verizon and Walgreens, where business activities are at issue.

3M is facing major lawsuits around product liability and regulatory and environmental issues. These are very hard to quantify. But they have already been very costly, and are likely to remain costly for years to come. And if the company loses in court, it could face massive settlement charges.

It is a special-situations stock right now that only the most aggressive investors should be looking at, since it is nearly impossible to handicap court outcomes.

Maybe, maybe not

Buying the three highest-yielding Dow Jones stocks really requires more thought than simply yes or no. You need to dig in a little bit to the stories behind them.

Verizon is probably a decent fit for those looking to maximize their current income stream. Walgreens is in transition, but if it works out well, it could return to its historical growth and income path. And 3M is facing material outside risks that should probably put off all but the most aggressive investors.