The Institute of International Finance, which lobbies for big banks, estimates that $825 billion will flow into developing countries this year, 42 percent more than in 2009. Investments in debt of emerging economies alone is expected to triple, to $272 billion.

While developing countries often benefit from foreign investments, huge inflows of capital complicate their macroeconomic management. They push up the value of their currency, boosting imports and slowing exports, and they promote fast credit expansion — which can cause inflation, inflate asset bubbles and usually leave a pile of bad loans. This money turns tail at the first sign of trouble, tipping countries into crisis.

Those are the dynamics behind Mexico’s 1994 “tequila crisis,” the 1997 Asian crisis, the 1998 Russian catastrophe, the 1999 Brazilian debacle and the 2002 Argentine collapse. The housing bubble that burst here in 2008 was painfully similar, with irrational investments and then a sudden flight.

A collapse in emerging market bonds would further damage the weak balance sheets of American banks. Still, it is not time to panic. Developing countries are in relatively good economic shape, while interest rates in the wealthy countries are likely to stay low for years. Yet the financial system remains fragile. And a shock — say a default in Ireland or Greece — could prompt a fast U-turn away from emerging markets.

There is little policy makers in the rich world can do to stop these flows. Governments in the developing world must prepare now for when the money masters change their minds.

That means they cannot let their budgets get out of hand. And they have to keep a very close eye on their own banks. This might also be a good time to consider capital controls to slow inflows. Chile managed them successfully in the 1990s. Even the International Monetary Fund — long a foe of anything that got in the way of money — acknowledged this year that controls should be part of the toolkit.