Stocks that pay out double-digit-percentage dividend yields tend to be more trouble than they are worth. Ultra-high-dividend yields, after all, are often the result of a company's rapidly falling share price in response to a fundamental problem (new competition, political risks, an evaporating market, etc.).

This unfavorable dynamic, though, hasn't kept some ultra-high-yield stocks from generating a popular following on various social medial platforms. The Brazilian state-controlled oil and gas producer Petroleo Brasileiro (PBR 2.51%) (PBR.A 2.06%) (aka "Petrobras") and the Israel-based cargo company Zim Integrated Shipping Services (ZIM 16.07%) are two prime examples.

A roll of U.S. currency next to a sticky note that reads dividends.

Image source: Getty Images.

These two income stocks have amassed a sizable audience on social media as a result of their sky-high payouts. On a trailing-12-month basis, Petrobras' annualized dividend yield presently stands at an eye-catching 45.7%, and Zim's effective yield (after accounting for the 25% withholding tax for Israel-based companies) has clocked in at close to 94% over the prior 12 months.

Which of these ultra-high-yield dividend stocks is the better buy? Let's dig deeper to find out. 

The case for Petrobras

Petrobras is riding a handful of tailwinds right now. The company's ongoing deleveraging effort has drastically improved its capital structure, the rising price of oil has ramped up free cash flows, it has enacted a highly disciplined capital allocation strategy, and it has control over Brazil's low-cost supply presalt reservoirs.

What's more, Wall Street analysts believe the Brazilian energy giant's stock is undervalued by as much as 16.2% at current levels. Petrobras, in fact, is the only major oil and gas producer that is trading under analysts' fair value estimate right now. 

What's the catch? There is a high degree of uncertainty surrounding the company's future following the election of President Luiz Inácio Lula da Silva last year. As a state-controlled entity, Petrobras is subject to changes in its capital allocation strategy and operations. This key risk factor is a major reason Petrobras' shares lost ground in a market that has been exceedingly generous to top-tier oil and gas companies over the past 12 months. 

PBR Chart

PBR data by YCharts

The case for Zim Integrated Shipping Services

After a dreadful 2022, Zim's shares have raced higher by a noteworthy 26.7% during the first two months of 2023. The backstory is that Zim's stock enjoyed a radical revaluation during the pandemic due to soaring global freight rates. In 2022, however, the Israeli cargo company's shares cratered (down 70%) over falling freight rates and a growing fear of a global recession.

Zim's stock has suddenly returned to its high-flying ways in early 2023 mostly in response to a positive note from J.P. Morgan analyst Samuel Bland. Per the analyst note, Bland thinks the markets have unfairly punished Zim's stock for falling carrier rates. The company's balance sheet, after all, ought to be strong enough to withstand a mild economic recession in 2023.  

Moreover, Zim's shares are only trading at 0.43 times trailing-12-month earnings. So, while the global shipping industry is likely to go through a down cycle over 2023 to 2024, this bearish sentiment may be overdone at this point.

The verdict?

In this head-to-head comparison, Zim is arguably the more attractive ultra-high-yield stock. Zim's shares appear to be trading in deep bargain territory. Petrobras, by contrast, has too many unknowns in the mix at this point. The company's stock may turn out to be an incredible bargain if this political risk fails to materialize. But the possibility of a marked shift in its capital allocation strategy looms large with this dividend stock.