Blindly buying high-yield stocks probably isn't the best investment approach. But buying the highest-yielding stocks that have already been preselected for inclusion into an index is at least likely to cull out some of the worst options. And yet that still doesn't mean you will be investing in companies that you'll be happy owning. So, should you buy the three highest-yielding Dow Jones Industrial Average (^DJI 1.51%) stocks? Let's look at Dow (DOW 1.66%), Verizon (VZ 2.03%), and 3M (MMM 1.98%) to find out.

3. Dow, the chemicals company

Just to make things complicated, one of the highest-yielding stocks on the Dow is Dow. Dow Inc. (just Dow from now on) is a large chemicals company, and it yields roughly 4.7%, which is fairly attractive given that the yield on the S&P 500 index is a tiny 1.3%. The one big negative for some investors will be that Dow's dividend has been static at $0.70 per share per quarter for years. But given the nature of the chemicals industry, that's actually not shocking.

To simplify a complex business, chemicals are often commodity items subject to material-price volatility. The inputs into the chemical-making process, meanwhile, are also commodities (oil and natural gas), which can lead to material changes in Dow's costs. Put the two together and you get a company that has highly variable earnings. It would be a risk for Dow to jack up its dividend payment during good years if it knows that an industry downturn is going to, eventually, come around and require a dividend cut. Thus, a dividend that is sustainable through the cycle is probably the best option. Dow is a fine company, but you need to go in understanding that the business is volatile, and the dividend isn't likely to grow over time.

2. Verizon has a capital-intensive business

Telecom giant Verizon has a much more reliable business than Dow because its cellphone customers create annuity-like revenue as they pay their bills each month. That provides the cash flow needed to support the company's big 6.5% dividend yield. Meanwhile, Verizon has increased its dividend annually for two decades. So far so good.

The problem is that Verizon's business is a mature one operating in a mature industry. Annualized-dividend growth over the past decade was less than 3%, which means it lags behind the historical growth rate of inflation.  Yes, you are getting a material amount of income today, but the buying power of the dividend is shrinking over time. Verizon is really stuck between a rock and a hard place because the telecom industry is highly capital intensive, requiring massive capital investments just to keep pace with peers. If you are looking to maximize your income stream over the short term, Verizon could be a good option. But if you are planning to be retired for a couple of decades, like most 65 year olds will be, you might want to keep looking.

1. 3M's yield isn't what it seems

The last stock up is the easiest dividend story to tell in some ways and yet the most complex in others. Starting with the complex, 3M is facing material legal and regulatory headwinds today that have already resulted in large costs. It is likely that the costs will continue into the future, putting pressure on earnings and the company's dividend-paying ability. Moreover, to help raise capital for the expenses it is incurring, 3M recently spun off its healthcare business. And following that, the company has hinted strongly that a dividend cut is on the way. So, if you are looking to buy high-yielding Dow Jones stocks, you should probably hold off on industrial giant 3M until the next dividend announcement so you can really quantify what you are buying.

This is where the story gets simple. The yield today is listed at around 6% on some quote services and 23% on others. Why? Because of the complex story, since some services include the value of the spin-off in the yield calculation. That 23% figure isn't real, and, as noted, the 6% figure might not hold up, either. If you need your dividends to pay for living expenses, 3M is best avoided right now.

A couple of maybes and a no

Given the nature of Dow's business, investors need to understand that dividend growth probably isn't going to be in the cards. That's not going to be attractive to a lot of income investors, and it suggests that deep pullbacks are the best time to buy the stock. Verizon's capital-spending needs are likely to keep dividend growth at this long-time dividend grower fairly modest. Again, not exactly a compelling investment story, though some might still find the high yield attractive. But both Dow and Verizon have better stories than 3M, which looks like it is about to cut its dividend.