The premise makes enough superficial sense -- if you buy stocks with the highest dividend yields, you'll collect the highest-possible dividend income. In fact, the theory may even be reality for a while.

As the old adage reminds us, though, there's always more to the story. Your job as an investor is to identify and weigh any hidden cost or risk that's yet to be realized.

With that as the backdrop, before diving into the Nasdaq Composite's highest-paying dividend stocks simply because they're dishing out the biggest dividend right now, here's a closer look at each of them. You may well end up changing your mind before pulling the trigger.

The Nasdaq's highest-yielding stocks each require a footnote

Cutting straight to the chase, the Nasdaq's highest-yielding names right now (excluding small caps and exchange-traded funds) are Icahn Enterprises (IEP -1.87%), AGNC Investment (AGNC -0.53%), and Torm PLC (TRMD -0.21%). Their forward-looking dividend yields currently stand at 16%, 15%, and 21%, respectively. Those are enormous numbers, particularly in comparison to the S&P 500's trailing dividend yield of 1.3%.

They're also numbers investors can't afford to count on.

Oh, that's not to suggest you'll never see this sort of yield on any capital you commit to any of these three names. You probably will, in fact, at least for a short while. These sorts of payouts aren't likely to persist, though, and even if they do, your capital is put at an uncomfortable amount of risk in the meantime.

Take the aforementioned Icahn Enterprises as an example. The conglomerate steered by activist investor Carl Icahn has enjoyed a few moments of bullish brilliance since going public all the way back in 1987. But its lack of diversification has proven more problematic than not. It's remained heavily invested in energy and automotive-related stocks, for instance, sticking with these holdings for too long at the wrong time. Not only are Icahn Enterprises shares back to where they were trading in 2004, but this stock's dividend has been cut to a quarter of its early 2023 level as Icahn scrambles to play defense. It's just too little, and too late.

It's a tale of what can happen when a speculative approach to picking stocks suddenly -- and without warning -- stops working. AGNC Investment serves up the same lesson, albeit for completely different reasons.

AGNC Investment is a real estate investment trust, or REIT, for short. That just means it holds real estate investments and passes along the bulk of its profits to shareholders. REITs can own a wide array of assets ranging from apartment complexes to office buildings to hotels. Even by REIT standards, AGNC Investment is an oddball. It buys, holds, and sometimes sells bundles of mortgage loans made by government agencies like Fannie Mae and Freddie Mac.

As you can imagine, rapid changes in interest rates and real estate price volatility have wreaked havoc on this REIT's business model. Although AGNC's monthly dividend payment of $0.12 per share hasn't budged since being lowered in early 2020, the REIT hasn't always cleared enough money to fully fund these payments. Concerns over the organization's sustainability are a big part of the reason the stock's sell-off that began in late 2013 is still underway.

Finally, know that while Torm's expected dividends for the coming year translate into a huge forward-looking yield, there's absolutely no historical consistency to its payouts.

This isn't exactly the company's fault. Torm operates a fleet of about 90 oil tankers, but demand for crude and other petroleum-based products is inherently inconsistent. So is pricing for these transportation services. In this vein, Torm has also never suggested its dividend payments would remain stable. It simply shares a piece of its quarterly net profits, whatever those profits may be.

That's not necessarily disqualifying. It's just not something most investors can digest, hence this stock's 40% pullback from its June peak when crude prices began a slide that's still going.

Nothing out of the ordinary here

This isn't to suggest every investor should unquestioningly avoid all three of these stocks. There may be a unique case for stepping into at least one of these names if you can stomach the risk or see something bullish others don't.

For the vast majority of investors, though, each of these Nasdaq-listed names brings more risk to the table than they're worth. This risk is a combination of weakening dividend payments in addition to a permanent loss of capital.

Then there's the bigger-picture moral of the story. That is, in almost all cases if something seems too good to be true, there's a catch. Sound stock-picking -- regardless of your ultimate goal -- requires the sort of discernment needed to spot these drawbacks before taking the plunge.