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President Donald Trump may want a weaker dollar, but this desire is in stark contrast with his other goal: making America great again. Or rather, maintaining America's greatness, at least on the foreign exchange market.

President Richard Nixon's treasury secretary John Connally famously told a G-10 meeting in Rome in 1971: "The dollar is our currency, but it's your problem." Indeed, after World War II this has been the U.S.'s "exorbitant privilege," as Barry Eichengreen noted in his book Exorbitant Privilege: The Rise and Fall of the Dollar and the Future of the International Monetary System.

Trump's administration has accused major countries, especially China and Germany, of manipulating their currencies to weaken them against the dollar and thus gain a competitive advantage compared with U.S. exporters.

But China, if anything, is trying to manipulate its currency to be stronger, not weaker, and the president's criticism could come back and hurt the U.S. economy. And Germany does not even have its own currency, because it shares the euro with 18 other states. 

The prosperity of the U.S. under the current system depends on the dollar remaining relatively strong, and perhaps this is why Federal Reserve Chairwoman Janet Yellen has turned so hawkish. The U.S. can borrow unlimited amounts of money at interest rates that it practically sets for itself, thanks to the fact that the dollar is the world reserve currency. No other country has this privilege.

The U.S. dollar made up 63.28% of allocated world reserves in the third quarter of last year, the most recent period for which the IMF has published data. The dollar was followed by the euro, which made up 20.29% of world reserves, and the British pound and Japanese yen, with around 4.5% each.

Of course, this gives the U.S. a huge competitive advantage. It has been something that other major economies have tried to challenge in the past, but with weak results. China—the currency of which, the renminbi or yuan, was introduced among those making up the IMF's Special Drawing Rights basket in 2015—has been relatively outspoken on the issue.

In March 2009, Chinese central bank governor Zhou Xiaochuan gave a speech in which he called for a reform of the global reserve currency system, clearly hinting at unease with the U.S. dominance. He said:

"Theoretically, an international reserve currency should first be anchored to a stable benchmark and issued according to a clear set of rules, therefore to ensure orderly supply; second, its supply should be flexible enough to allow timely adjustment according to the changing demand; third, such adjustments should be disconnected from economic conditions and sovereign interests of any single country."

The dollar has weakened during the global financial crisis as the Fed tried to counteract the credit crunch by printing money and keeping interest rates at historic lows. It gradually has come back, but market participants no longer are used to seeing a strong dollar.

In February's fund manager survey by Bank of America Merrill Lynch (BAC) - Get Report, the percentage of asset managers who believe the dollar is overvalued is the highest since September 2006 and the "long U.S. dollar" trade is seen as the most crowded by far.

For the dollar to remain the global reserve currency and allow cheap borrowing to finance all that spending on infrastructure, President Trump will need to accept that the U.S. must run a trade deficit with the rest of the world. The U.S. simultaneously cannot borrow from the world and run a trade surplus. It looks like the strong dollar trade could become even more crowded for a while.