The Federal Reserve’s plan to wind down its trillion-dollar stimulus program is only half of the biggest story in the global economy this year. The other is how markets will react as that spigot starts to dry up.

A new report by the World Bank suggests that the withdrawal won’t be as painful as many investors have feared. The Fed pushed long-term interest rates to record lows over the past year as it pumped money into the U.S. economy. Now, the World Bank is projecting a slow and steady rise in global interest rates to 3.6 percent by mid-2016.

The long timeline would allow investors to rebalance their holdings in an orderly fashion, moving money out of the developing world, where they had sought higher returns, and back into more stable assets in high-income countries. The report estimates capital inflows would fall from 4.6 percent of emerging market GDP to 4 percent.

Of course, that’s a best-case scenario. But there are good reasons to believe it will come true. Stock markets across the globe rallied when the Fed announced in December that it would begin tapering its stimulus this year. That’s because investors interpreted the move as a sign of confidence in the nation’s economic recovery, and a healthy America is good news for the rest of the world.

Still, recent history teaches us that things don’t always go so smoothly. Last summer, when the Fed initially broached the idea of tapering, investors freaked. Yields on the 10-year Treasury note spiked from a low of 1.6 percent in May to 2.7 percent by August. According to the World Bank, investors withdrew $64 billion from developing-country mutual funds over the summer, while currencies and stock markets in several emerging markets dropped as much as 15 percent.

What if the taper is not so tame? If rates spike by a full percentage point, the World Bank predicts that capital inflows to the developing world will drop an average of 30 percent this year. If interest rates skyrocket 2 percentage points – the financial equivalent of all heck breaking loose – flows could fall an average of 45 percent.

Those are some pretty scary scenarios. But the key to achieving the World Bank’s baseline forecast rests primarily on the simple assumption that the U.S. economy is indeed getting stronger. If you believe that, then the taper should be nothing to fear.