Political uncertainty in countries like Mexico and Brazil, tighter monetary policy from the U.S. Federal Reserve and, most recently, a sharp drop in the Turkish lira are just come of these challenges.
Turkey's currency fell to a record low earlier in August after President Donald Trump approved a doubling of U.S. steel and aluminum tariffs on Turkish imports unless detained American pastor Andrew Brunson is released.
Exchange-traded funds that track Turkish, Brazilian and Chinese stocks are down 14.9 percent, 9.3 percent and 2.7 percent, respectively, since Aug. 9.
Between that day and Aug. 16, emerging market funds have registered outflows of $1.3 billion, according to data from the Institute of International Finance.
"Much of this comes from forces beyond our control," Leverenz said. That is why "we have a north star when it comes to investing and that is our approach."
Leverenz's approach has made the fund one of the best performers of the "Diversified Emerging Markets" category. The fund has outperformed 91 percent of its peers over the past 10 years, gaining 5.5 percent in that time period, Morningstar data show. This year, the fund is down 4.4 percent but still ranks in the eighth percentile in its category.
The manager, who has been running the Oppenheimer Developing Markets fund since 2007, said "there are some good companies out there" in emerging markets even in the midst of the broad sell-off. He and his team like companies in the health-care, luxury goods and internet sectors.
"What we do is focus on companies that have extraordinary growth, great competitive advantage and have opportunities to build businesses we have never seen before," he added.
Leverenz said an example of such a company is Amazon, as it started out as an online bookseller and eventually turned into one of the biggest online retailers. But companies like these can be found outside of tech as well, he said.
The fund holds shares in Fomento Economico Mexicano, better known as Femsa, a Monterrey, Mexico-based multinational that owns about half of Coca-Cola Femsa, one of the largest Coke bottlers in the world. It is also the parent company Oxxo, the largest convenience store chain in Mexico. Leverenz described Oxxo as the "CVS or Walgreens of Mexico."
But the company was originally best known as the parent company of Cerveceria Cuauhtemoc Moctezuma, the maker of beers such as Dos Equis, Tecate and Sol. In 2010, Femsa sold Cuauhtemoc to Heineken in exchange for a 20 percent stake in the beer giant.
"What happened was the core of the business went from being beer to Coke bottling," said Leverenz. "I don't know if you spend a lot of time in Latin America, but soda consumption there is much higher than it is in the U.S."
Leverenz's fund first invested in Femsa shares on Feb. 28, 2011, according to Morningstar. Since then, the stock has surged nearly 170 percent.