The power of owning dividend-paying stocks is often underappreciated. Consider, for example, that a study by Hartford Funds and Ned Davis Research found that between 1973 and 2023, companies that grew or initiated dividend payments delivered annualized returns of 10.2%, while dividend non-payers delivered only 4.3% (and an equal-weight S&P 500 fund averaged 7.7%).

Healthy and growing dividend payers will tend to have stock prices that rise over time, while paying dividends that are also increased over time. Given that stock profile, you might think it's smart to snap up the fattest dividend yields you can find -- perhaps focusing on the biggest dividend yields in the S&P 500.

Here's a look at why you might want to think twice before taking this approach.

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Fat dividend yields: Good or bad?

It's important to understand what a dividend yield is. It's a ratio, typically expressed as a percentage, where a stock's total annual dividend amount is divided by its current stock price. So imagine the hypothetical Buzzy's Broccoli Beer (ticker: BRRRP), recently trading at $50 per share and paying out $0.50 per quarter -- which is $2 annually. Divide that $2 by $50 and you'll arrive at 0.04, or a dividend yield of 4%.

Companies usually pay dividends quarterly, and their dividend amounts generally stay the same for one or more years. Company share prices, though, change frequently. So the dividend yield changes frequently, too, by at least a little. Remember that the ratio is the dividend divided by the stock price. So if the stock price rises sharply, the yield will fall -- and vice versa.

Thus, an especially fat dividend yield may be the result of a stock having plunged, and not simply reflecting a super-generous business. Therefore, it's always smart to look at a fat yield extra closely, to see if the company is facing any trouble.

Below are three companies that were the highest-yielding stocks in the S&P 500 recently. Let's take a closer look at each.

1. Walgreens Boots Alliance

Walgreens Boots Alliance (WBA -0.62%) was recently sporting a massive dividend yield of 12.1%. That certainly looks enticing. Invest, say, $10,000 in Walgreens and collect $1,210 over the year! But hold on -- a closer look at the company will reveal that it's been struggling recently. The stock was down almost 65% year to date as of this writing, and down 21% just in the past month.

What's going on? Well, the company has been unprofitable in recent years, and is closing some 1,200 stores in an effort to get back on track. Part of the problem is that Walgreens has been facing increasing competition from the likes of Amazon.com, GoodRX, Costco Wholesale, and even Walmart.

It's always good to check out a dividend payer's "payout ratio" -- the portion of earnings it's paying out in dividends. Walgreens' was recently 290%, suggesting that it's paying out far more than it really can or should, and suggesting that a dividend cutback may be in the offing. So this isn't an appealing dividend stock to me.

If you're interested in it, perhaps just keep an eye on the company's developments for a while, looking for signs of a successful turnaround.

2. Altria

Altria (MO -0.42%) is also facing some challenges, as fewer Americans are smoking these days. The U.S. smoking rate hit an 80-year low earlier this year, per Gallup. Altria saw the writing on the wall and has been investing in cigarette alternatives, such as vaping products. Still, cigarettes remain its main offering for now.

Altria's stock has been growing, though not at a breakneck speed, and its dividend -- recently yielding 7.3% -- does look attractive. The recent payout ratio of 67% suggests it's sustainable (at least in the short term), with room for growth, and Altria has been increasing its payout for more than 50 years in a row.

So consider investing in Altria, but don't buy it and forget about it. You'll need to follow its progress to make sure its performance, which hasn't been stellar lately, doesn't falter more. Some expect the company to fare better in the future, if less traditional tobacco products gain traction.

3. Pfizer

Then there's Pfizer (PFE 0.23%), recently yielding 6.7%. It, too, has been facing some headwinds, such as a drop in demand for its COVID-19 vaccines and related treatments. But like other pharmaceutical companies, it has plenty of other irons in the fire, in the form of drugs in development in its rich pipeline. Its expansion into cancer treatments is especially promising.

Some worry that Pfizer has taken on too much debt buying other companies (and their drugs), and others worry that the incoming administration in Washington D.C. may shrink interest in vaccines. But there's more to medicine than vaccines. Among other promising drugs Pfizer has in development is one tackling weight loss. Current weight loss medications are selling briskly, and multiple products can become big sellers in that niche.

So go ahead and check out these or other fat-dividend stocks. Just be wary whenever a payout is especially steep. And remember that smaller yields can be just fine -- especially if they're being increased at a rapid pace.