No matter how volatile the stock market might appear at times, there are a few constants that investors should keep in mind.

For starters, whatever the depth of a correction is, or the length of time it takes to arrive at the trough, the market has always put each and every one of its drops in the rearview mirror by eventually marching to new highs. In other words, the companies that make up the major stock market indexes generally rise in value over time, which is why long-term investors with diversified portfolios are often rewarded handsomely for their patience.

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Another oft-overlooked fact about the stock market is that, over the long haul, dividend-paying stocks handily outperform their counterparts that don't pay dividends. Companies that pay out a dividend are almost always profitable and typically have time-tested business models. What's more, investors have the opportunity to reinvest their payouts into more shares of dividend-paying stock, which has the effect of compounding their returns over time. This is the tactic most professional money managers employ to really deliver market-topping returns for their clients.

But there's an under-the-radar dark side to dividend stocks. Namely, the higher the yield, more often the riskier the investment. Since yield is simply a function of share price, a rapidly declining share price indicative of a struggling business model could pump up a company's yield and offer false hope to prospective investors of substantial income and returns.

In short, high-yield (4%-plus) dividend stocks require extra research and caution if they're being used for their supposedly superior income potential.

As the stock market enters the second half of 2019 with its foot mashed against the gas pedal, I view three ultra-high-yield dividend stocks as attractive buy candidates.

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AT&T: 6.2% dividend yield

If I could hand out an award for the most stable ultra-high-yield stock on the planet, it would go to telecom and content giant AT&T (NYSE:T). Though I still consider myself relatively young and with many years of investing ahead of me, even I grabbed shares of AT&T for my personal portfolio because of its can't-miss dividend and the ability to reinvest that payout over time.

The investment thesis on AT&T breaks down into three parts, as I see it. First, there's the company wireless division, which appears set for multiyear gains from the ongoing rollout of 5G networks. Although smartphone providers are the ones that'll initially see the benefits of 5G rollouts, wireless-service providers like AT&T are the real beneficiaries of the upgrade cycle, since they reap substantial margins from data usage. As consumers' appetite for data grows with 5G, the company should see notable increases in average revenue per wireless subscriber.

Second, I view the acquisition of Time Warner as a long-term positive. AT&T is making a play to be a major content provider, and bringing the TBS, TNT, and CNN networks under its umbrella is a sizable dangling carrot for the company. These networks have the capacity to lure streaming consumers away from rivals, and give more pricing power when dealing with advertisers.

Third and finally, don't overlook what the recent decline in bond yields could mean for AT&T. As a telecom and content provider, it regularly uses debt to finance infrastructure upgrades. As bond yields fall, signaling an eventual drop in interest rates, it allows AT&T's expansion to become less costly from the perspective of interest paid.

AT&T looks as solid as it's ever been, which makes its ultra-high-yield payout practically a must-have for income seekers.

A person holding lumps of coal in their cupped hands.

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Alliance Resource Partners: 12.7% dividend yield

Coal might be a dirty word to most folks, but it doesn't have to be. It has certainly taken a back seat to natural gas and renewable energies like solar and wind in terms of electrical generation in the U.S. in recent years, but it's still the nation's second-largest producer of electricity. That's why Alliance Resource Partners (NASDAQ:ARLP) and its nearly 13% dividend yield deserve a look.

Alliance Resource Partners is nothing like its peers. Whereas most coal producers have gone bankrupt this decade under the weight of falling coal prices and high debt levels, Alliance's management team never allowed the company to get too deeply into debt. Even today, it has $547 million in net debt and a debt-to-equity ratio of 42%, which places very minimal financial constraints (if any) on the company's long-term growth strategy.

For those of you worried about the rise of solar and wind in the U.S., don't be. Alliance has dramatically stepped up its export game over the past couple of years. After exports accounted for less than 5% of total sales in 2016, they now account for close to a quarter of annual revenue. Even with international pricing pressures on coal in 2019, the longer-term outlook for demand from fast-growing emerging markets like India and China is a positive for coal and Alliance Resource Partners.

This is also a company that prides itself on securing volume and price commitments well in advance. Nearly 39 million tons of the 43.5 million to 45 million tons of coal it expects to produce in 2019 were locked in via price and volume commitments through March, with another 21.6 million tons committed domestically in 2020. Having little exposure to the volatile wholesale market is a good thing, and yet another reason its cash flow and dividend are highly predictable. 

Suffice it to say this coal producer is a diamond in the rough among dividend stocks.

A small pyramid of tobacco cigarettes that are laid atop a bed of dried tobacco shavings.

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Philip Morris International: 5.9% dividend yield

A third ultra-high-yield dividend stock that I believe investors should consider for the second half of 2019 is tobacco giant Philip Morris International (NYSE:PM). It's a stone's throw away from generating 6% a year for its shareholders, which is more than triple the U.S. inflation rate at the moment.

Generally speaking, tobacco has the same reputation as coal: avoid, avoid, avoid! But unlike many of its peers, Philip Morris International has a few tricks up its sleeve.

To begin with, the company's name says it all: "International." It sells its products in more than 180 countries worldwide, and the anti-tobacco United States isn't one of those countries. Even if the company faces more stringent regulations in certain developed markets, Philip Morris can lean on emerging market economies with burgeoning middle classes for future profits.

Furthermore, don't overlook the pricing power inherent with the tobacco industry. Nicotine is an addictive chemical that has allowed tobacco companies to offset declines in cigarette shipping volumes by consistently raising their prices. We haven't yet hit a point where consumers have been substantially driven to the sidelines by price, and that's ultimately a positive for Big Tobacco.

Maybe most intriguing is what the future might hold with its IQOS heated tobacco device. Shipments of heated tobacco rose by 20% to 11.5 billion units in the first quarter, with the number of IQOS systems in use in Europe more than doubling to over 1 million. While the rollout of alternative nicotine consumption options might take longer than expected, the company is nevertheless seeing sales growth from IQOS. Additionally, with a refinement to its advertising, my personal suspicion is that Philip Morris can capture a larger portion of mature smokers (age 45 and up) with IQOS.

As these three companies show, if you're willing to do some homework, there are ultra-high-yield dividend bargains to be had.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.