If the first full week of 2016 was a bad one for stock markets, this second week might be shaping up to be even worse. Dashing hopes of an early bullish run, the FTSE 100 slumped by 329 points (5.3%) last week to 5,912, and as I write it’s down another 13 points to 5,899.

It’s mainly down to fallout from China as the world begins to realise just how much trouble the country could be in. And that impact, along with no let-up in oversupply from Opec, has hit the price of oil hard yet again. Monday saw Brent crude falling near to a 12-year low, at just $36.67, continuing the renewed slide that started at the turn of the year.

And that just has to hurt the prospects for super-high dividends from our big two oil producers. On a share price of 1,376p, which is down a whopping 35% in the past 12 months, Royal Dutch Shell (LSE: RDSB) is on for a dividend yield of 7.7% for the year just ended in December 2015, based on current expectations. That’s forecast to remain unchanged in 2016.

Dividend pledge

The City’s confidence is based on the company’s pledge to maintain its dividend at 188 cents per share, but can that promise really hold up? Well, expected 2015 earnings wouldn’t cover the dividend, and cover would barely squeak into positive territory based on 2016 forecasts of an 8% recovery in EPS to around 128p. But that forecast is old, doesn’t encompass the latest slide in oil prices, and would need a significant increase in the price of a barrel to get close to being sustainable.

Things don’t look much better at BP (LSE: BP), whose shares are down a relatively modest 17% in a year to 333p. After an 83% fall in EPS for 2014, there’s a 56% recovery on the cards for 2015 followed by another 6% for 2016. But again, that clearly doesn’t encompass the latest oil falls, and I’d expect the reality to be less rosy than that.

Current indications suggest a dividend yield of 7.3% from BP for 2015, dropping slightly to 7.2% in 2016. BP has made no specific dividend promise, but has made it clear that its strategy is to maintain steady payments. And when the price started to fall, CEO Bob Dudley voiced an early opinion that we could be in for low oil for two or three years, though that was at a time of significantly higher prices than today.

BP’s dividend cover position is weaker than Shell’s, with earnings expected to meet just 85% of its 2015 payment, rising a little to 90% in 2016. But again, that doesn’t take into account the most recent falls, and the reality could well be tougher.

Too big a gamble?

The big question for income investors is whether taking the plunge would provide an effective sustained annual income in excess of 7%, or whether it’s a so-called value trap, where a dividend cut is forced on the two companies.

If they really do want to tough it out, both could certainly find the resources to keep up those annual payments for a few years yet. If I had to choose one, my money would be on Shell right now.

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Alan Oscroft has no position in any shares mentioned. The Motley Fool UK has recommended Royal Dutch Shell. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.