"They really seem impervious to what's happening on the main stage," says Ablin.

The main attraction for investors is the rapid economic growth. In theory, it should pull many people in those countries out of poverty, and as they begin to spend their higher pay on refrigerators and mobile phones, local businesses should flourish.

"A lot of them have growing populations and expanding workforces, and they don't just rely on exports of food or oil," Lynch says. "Look at Vietnam. They traditionally exported coffee, seafood and rice. Now they're making high-end machinery."

Not so long ago, these same traits lured investors to emerging markets. But after more than a decade of strong economic growth, the upstarts have slowed. Brazil, Russia and India are now closely tied to swings in global markets as well as to each other.

When China's economy slows, for instance, it drags down financial markets in Brazil, which counts China as the top customer for its exported goods.

But if a frontier market like Ghana ran into trouble, Vietnam and Kuwait wouldn't even notice.

As U.S. markets recently turned turbulent over concerns about the Fed, Ablin watched one frontier fund, the iShares MSCI Frontier 100, climb higher day after day. He recently bought a bunch of shares in the fund for his children and his BMO investment team is mulling a shift into frontier funds, too.

Still, a frontier market like Pakistan can leave some investors skittish. Osama bin Laden hid in Pakistan before he was killed in a U.S. raid in 2011. The country is often at loggerheads with neighboring India. And Pakistan has been the target of U.S. drone strikes against suspected Islamic militants near the border with Afghanistan.

Wells Fargo's Lynch and many others in the investment world argue that the good news out of Pakistan is going unnoticed. An election last month brought Nawaz Sharif to leadership as prime minister. Sharif is considered pro-business and has pledged to take on unemployment, inflation and corruption. In early July, his government lined up a $5 billion loan from the International Monetary Fund.

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