Guest columnist Barry Eichengreen is George C. Pardee and Helen N. Pardee Professor of Economics and Political Science at the University of California, Berkeley.

Investing in currencies is notoriously tricky. If anyone needed a reminder, just consider the recent behavior of the dollar. The pundits, pointing to the Fed's zero interest rates and to the prospect of budget deficits as far as the eye can see, have been predicting a weaker dollar. Yet just within the last few weeks the greenback rallied by 3% against the euro. Anyone taking the conventional bet would have been caught out.

This movement is a reminder of what is special about exchange rates. An exchange rate is the relative price of two currencies. For someone betting that the dollar will fall against the euro, it is not enough to observe that the U.S. has economic problems. Rather, those economic problems have to be even more serious than Europe's.

A European example
Earlier this month, the markets suddenly woke up to the fact that Greece, a fringe member of the euro zone, was in dire economic and financial straits. Then the rating agencies and investors were disappointed by the Greek prime minister's limp promises to get the country's fiscal house in order. They began to ask whether other euro-area countries might have to come to Athens' rescue, implying credit creation, inflation, and worse -- not just for their Greek neighbor but for themselves.

No sooner had the markets digested this information than they learned that the Austrian government was being forced to take over one of the country's big banks, which had branched aggressively into Eastern Europe and now found itself saddled with a portfolio brimming with bad loans.

These were reminders that not just the United States has economic problems. And it is not simply the existence of problems but their severity relative to those of other countries that matters for the dollar exchange rate.

An Asian example
But if there is no guarantee that the dollar will fall against the euro, surely it will have to fall against the currencies of countries like China, you say. Belief in the underlying strength of China's economy has led to a recent surge in stock prices for companies like CNOOC (NYSE:CEO), (NASDAQ:BIDU), (NASDAQ:NTES), Fuqi International (NASDAQ:FUQI), and Aluminum Corp. of China (NYSE:ACH). The country's growth rate vastly exceeds that of the United States. It does not have financial difficulties like ours. Surely the renminbi will strengthen at the first sign that the Chinese authorities are prepared to let it.

But the worry here (I'm in Beijing as I write this column) is that China, too, may have problems. Housing prices here in Beijing are allegedly up 40% since April. The authorities are worried. Three weeks ago, at the annual Central Economic Work Conference, they agreed to impose a 5.5% sales tax on residential property held less than five years to discourage speculation. Meanwhile, they have also been arm-twisting the banks to tighten mortgage lending standards.

It is not clear that their measures will work. People are not "flipping" houses. Rather, many individuals are buying and holding them vacant for extended periods because of the dearth of other investment opportunities. For these investors (a more appropriate label than "speculators") a short-term transactions tax will be no deterrent. Housing prices will continue to rise. The bubble will inflate to even more dangerous levels.

The authorities, frustrated, will tighten access to financing still further. And at that point the bubble could burst. If prices fall very sharply, all this "shadow inventory" could come back on the market. Construction activity could slow dramatically. If so, the Chinese economy, where construction has played a big role recently, could slow by more than the authorities are banking on.

What ultimately happens in China is anyone's guess. But for the dollar to benefit, it is not necessary for China to suffer a major crisis. It is only necessary for its economy to slow by more than people currently expect. At that point, any possibility that Chinese officialdom would allow the renminbi to rise against the dollar would be out the window.

Our own example
Of course, the U.S. economy could still surprise on the downside. The Fed could bungle its exit from zero interest rates. It could raise rates too fast and put a damper on demand. An abrupt end to its extraordinary asset-purchase programs could create renewed problems in financial markets. Or the failure of Congress to confront the medium-term fiscal situation and put our public finances on a stable footing could undermine investor confidence. Any of these developments would be bad for the dollar.

But when taking bets on currencies, it is not only our problems that matter. Look at the bright side: It is not only our policymakers who could get it wrong.

After you share your thoughts in the comments section below, be sure to check out another guest columnist: Tyler Cowen explains the real reason gold is above $1,000.

Guest columnist Barry Eichengreen does not own shares of any companies mentioned. and are Motley Fool Rule Breakers selections. CNOOC is a Motley Fool Global Gains recommendation. The Motley Fool has a disclosure policy.