Energy investors may have a new concern.
Even as crude oil has plunged to a six-year low, oil stocks have maintained their appeal to some investors by dint of their rich dividend yields. BP's ADR, for one, now yields more than 6 percent. And ConocoPhillips and Chevron both yield more than 4 percent—much higher than before plunging oil sank their shares.
But whether those dividend payouts will last forever is another matter. In fact, BP, ConocoPhillips, Chevron and Hess are all expected to pay out more in dividends than analysts project them to earn (on a per-share basis).
"Chevron and Exxon have been very clear that the dividend is their top priority, so I think that is going to stand put. ... But I think Europe is a very different story," said , head of equity sales trading with Cowen & Co.
The trader points to the recent dividend reduction by Italian oil company Eni, saying it could foretell further cuts by European oil companies. (The British oil and gas company Ensco has already slashed its dividend, as has the Swiss rig company Transocean.)
Stacey Gilbert, head of derivatives strategy at Susquehanna, says the options market broadly agrees with Seaburg's take—American oil dividends are safe, while fat European dividends like BP's could be subject to downside. In fact, she says that BP options are pricing in a small dividend cut in 2016, something on the order of 10 to 20 percent.
When reached for comment, BP spokesman Scott Dean told CNBC: "Our commitment to the dividend is the first priority within our financial framework. With the interventions we are making, we believe we have sufficient flexibility to support our dividend in 2015 in the current price environment, while staying within our gearing band. Over time, our intention is to grow distributions in line with the improving circumstances of the firm and to maintain a progressive dividend policy."
BP's staunch support of its dividend echoes Wall Street's view that for now, the odds of a big dividend cut appear small.
There's a "very low probability" of a cut by any of the big U.S. oil companies, said Fadel Gheit, an oil company analyst with Oppenheimer. "The dividend is the only way they compensate their shareholders, since they have no growth."
"We're a commodity business. ... We're going to be one of these steady-hold, safe, you-can-sleep-well-at-night, you-can-count-on-the-dividend stocks. And so we're kind of a Steady Eddy, is the way I see it." Tillerson said.
"For large-cap energy companies, dividends are sacrosanct. It's nearly unthinkable for dividends to get cut, even in a depressed oil environment," commented Pavel Molchanov, oil industry analyst with Raymond James.
"Among smaller companies, dividends get cut more often, though it's still not common," he said.
But for big oil companies especially, management will do "whatever it takes" to avoid reducing those holy dividends.