All of that has helped drive up Pakistan's stock market 11 percent this month. For the year, it's up 28 percent. By contrast, China's Shanghai Stock Exchange composite index has lost 10 percent this year, and Brazil's Bovespa has dropped 22 percent.

Still, a surging economy can often prove to be a dud of an investment, says Christian Deseglise, managing director at HSBC Global Asset Management.

Take China. Over the past five years, its economy has expanded by more than 10 percent on average. And over those same five years, China's stock market has lost 2 percent. Poorly-managed companies can still struggle to turn profits even as an improving economy sends them more customers.

"Some of these countries will have economies that do well but markets that do poorly, and vice versa," Deseglise says.

That's the main reason investors say they avoid staking too much on a single frontier country. It's too easy to imagine something going wrong. So, investors often buy a little of all of them, spreading their bets over Africa, Europe and Asia.

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