"I'd advise only those investors with much higher risk tolerances to invest in emerging market debt as they become much more volatile," David Sekera, corporate bond strategist with Morningstar, said on a webcast.

Brazil, Bane Or Benefit?

Brazil, Latin America's largest economy, has dragged down many funds this year, including T. Rowe Price's Latin America Fund, which has declined about 11 percent.

The Dreyfus Brazil equity fund and the Fidelity Latin America fund are also both down about 11 percent.

Investors are still not swayed, however, to trim their exposure in Brazil.

"Even after the 13-14-15 percent declines, I am sticking with my big bets. I am thinking long-term," said Jose Costa Buck, who oversees the T. Rowe fund, adding that he plans to hold many of his stocks for "at least three years."

BlackRock's Landers shares the same sentiment and sees opportunity in the selling pressure. He said in an email to Reuters: "For a long-term investor, this offers an opportunity to buy some cheap stocks," citing Vale, down about 6 percent so far in 2014; Itau, down about 0.4 percent; and Ambev, down about 9.5 percent.

Brazil is also grappling with other concerns, from outdated infrastructure to a stubbornly high inflation rate, and a reputation for state intervention that has spooked many investors.

Landers cautioned that significant improvements in the Brazilian economy probably will not happen until after the October presidential election.

Scott Mather, head of global portfolio management at Pimco, also signaled he sees the declines as an opportunity. He tweeted on Wednesday: "Indiscriminate selling in EM bonds & panic buying of developed world is subsiding. Time for value investors to consider stepping in."