"Buying into them has to be a long-term play," says Jack Ablin, chief investment officer at BMO Private Bank. "You have to take some leaps of faith."

The steady rise of their stock markets has apparently helped investors put aside their worries. They've dropped money into frontier market funds week after week, raising the total to $3 billion so far this year, according to EPFR Global, a company which tracks the flow of investment funds. That's triple the amount deposited in them last year and just shy of the full-year record of $3.07 billion in 2010.

Cash has streamed in so quickly that Franklin Templeton's $1.3 billion frontier fund has decided to start turning away new investors. Its top holdings include a Romanian oil and gas producer, OMV Petrom, and a batch of companies from Qatar and other countries on the Persian Gulf.

Last month, Wells Fargo's private banking group, which manages $170 billion in clients' money, took its first step into the frontier, pulling a portion of its money out of emerging-markets like Brazil, China and India and putting it into countries like Pakistan and Vietnam.

A key reason for the move was that the frontier markets are largely insulated from problems plaguing bigger countries, said Sean Lynch, the global investment strategist for Wells Fargo Private Bank.

When stock and bond markets in the U.S. and Europe were rattled by talk that the Federal Reserve would withdraw some of its support for the U.S. economy, many countries' currencies sank against the dollar. But Lynch noticed that frontier countries' currencies held up.

Why? As a group, these less-developed countries aren't as tied to the world's developed economies. Their industries are growing by selling to customers at home or nearby. Kenya's East African Breweries Ltd., for example, has most of its customers in neighboring African countries.

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