In a recent article titled "How to Win From a Rising Dollar in 2012," Fool analyst Dan Caplinger offered investors a variety of ways to profit from an increase in the strength of the U.S. dollar. Some of his best advice was to consider buying shares in the inverse-leveraged ETF ProShares UltraShort Euro (NYSE: EUO), a fund that increases in value when the price of the euro falls relative to the U.S. dollar.

Although I agree with Dan, I also think there's another side to this story -- and on this side, the U.S. dollar is falling in value. As I write, in fact, Treasury Secretary Timothy Geithner is in Beijing trying to ensure that this happens, as we've long suspected China of artificially depreciating the value of the yuan to fuel its export-led economic growth.

So is the dollar rising or falling? The answer is, it depends on which currency you're comparing it to. As you can see in the table below, illustrating the cost of a U.S. dollar in six different foreign currencies, the dollar is rising against some and falling against others. And while the reasons for these differences are beyond the scope of this article, I believe it's safe to say that these trends are likely to continue.

Currency

Exchange Rate as of January 2008

Exchange Rate as of December 2011

Rising/(Falling) U.S. Dollar

Mexican peso 10.91 13.77 26%
British pound 0.51 0.64 25%
Euro 0.68 0.76 12%
Singapore dollar 1.43 1.29 (11%)
Chinese yuan 7.24 6.35 (12%)
Japanese yen 107.82 77.80 (26%)

Source: Federal Reserve Bank of St. Louis. Currencies measured in units per U.S. dollar.

As an investor, you can exploit these trends in one of two ways. On the one hand, you can use the U.S. dollar's current strength against the euro to pick up European stocks inexpensively, like the National Bank of Greece (NYSE: NBG) or DryShips (Nasdaq: DRYS), a Greek shipping company -- though both are highly speculative in nature. Take one look at National Bank of Greece and you'll see just how bad a beat-down it's taken from its home country's political and fiscal woes. DryShips, meanwhile, has suffered through an industry-wide slump over the past several years. Both of them are trading for a fraction of their previous values.

Or you can bet on a continued appreciation of the Chinese yuan by investing in companies like Baidu (Nasdaq: BIDU) or Renren (NYSE: RENN), China's versions of Google and Facebook, respectively. And the added benefit with these companies is that they also expose your portfolio to China's exploding social and demographic trends. Indeed, despite the fact that China has four times as many people as the United States, Baidu's market cap is only 22% of Google's, and Renren's a ridiculous 1.4% of Facebook's increasingly likely $100 billion valuation.

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