I won't waste your time by rehashing the pithy sayings from investment greats who encourage you to be a contrarian investor. (Believe me, they're out there.) But even if you're sick of hearing those sayings, you'd be well-advised to heed them.

When everyone in the market "knows" that something will happen, then investors move prices, ensuring that the sure thing ends up priced into the given stock or set of stocks.

However, when something that everybody "knows" doesn't happen, contrarian investors can score big. Here are a few of the things that investors "know" today that could be setting up great investment opportunities.

Assumption: Europe will be mired in economic malaise for a long time to come.

The devil's advocate:
After a lot of dithering, the other eurozone countries have taken drastic action. They seem to be ready to fight tooth and nail to defend the euro. Plus, the euro's fall against other currencies could actually be a boon for European exporters, whose customers will suddenly find themselves paying with less of their home currency.

There seems to be a pretty strong consensus that Europe is in bad trouble. We could see some European stocks do well if things are bad, but not catastrophic.

Investment ideas:
The telecom services industry still has some excitement up its sleeve in emerging markets like Latin America, where Telefonica collected 37% of its 2009 revenue. Telefonica's stock has dropped 37% from its 52-week high, and it's currently sporting a 7% yield.

What do Hellmann's mayonnaise, Lipton tea, Dove soap, Vaseline, and Axe body spray have in common? They're all Unilever (NYSE: UL) brands. The company sells its wares all over the world, and Western Europe only accounted for 30% of its 2009 revenue. The stock is off its yearly high by 18%, and it's throwing off a 4.2% yield -- more generous than U.S. counterpart Procter & Gamble.

Assumption: U.S. banks will continue to limp along.

The devil's advocate:
The U.S. government stepped in to save most of the country's major banks; the Federal Reserve is still helping them along with ultracheap money; and financial reform likely won't be too onerous. While it's probably silly to expect a return to precrash profit levels, banks like JPMorgan Chase, Bank of America (NYSE: BAC), and Wells Fargo (NYSE: WFC) are now a lot larger, thanks to major acquisitions during the crisis.

Bank of America, for example, now includes both Countrywide and Merrill Lynch, yet it posted net income over the past 12 months that was 75% below its stand-alone profit in 2006. If the profits of the new Bank of Amerrillwide start to approach some normal level again, investors will come flocking.

Investment ideas:
JPMorgan and Wells Fargo might make the top of many people's lists, because they've been better-managed than the other major banks. Unfortunately, that also means that they're priced like they're better banks.

If the "bad banking" assumption does turn out to be wrong, the real opportunity will lie in Bank of America and Citigroup (NYSE: C). Both stocks are currently trading at book value multiples far below what they fetched before the crisis, which promises plenty of upside if the consensus proves incorrect.

Assumption: The U.S. is headed for a double-dip recession.

The devil's advocate:
Just recently, I highlighted an article by Yale economist Robert Shiller, who suggested that the fear of a double-dip recession could, in fact, spur a double-dip recession.

The potential for a self-fulfilling prophecy aside, a lot of the economic data has been encouraging. Sure, employment has been sluggish, but there's definitely been forward progress. In fact, experts expect that nonfarm payrolls will grow by 500,000 in the month of May. Particularly battered areas of the economy like banking and housing are still having problems, but even they are starting to report positive numbers.

Investment ideas:
Combine this recent wave of fear with rising corporate profits, and suddenly there's a parade of stocks once again trading at single-digit earnings multiples. Best of all, we don't have to speculate on truly troubled companies to take advantage of the possibility that double-dip mania is off the mark.

With respective forward earnings multiples of 7.1, 9.3, and 7.6, Chevron (NYSE: CVX), Hewlett-Packard (NYSE: HPQ), and Freeport-McMoRan (NYSE: FCX) appear to have dipped into "cheap" territory. Certainly, all three would be hurt by a second recession; demand for natural resources like oil and copper is driven by economic growth, while tech spending depends heavily on business confidence. But if these fears prove overblown, investors buying any of the three today might snag a bargain price.

Are these assumptions ready to be proven wrong, or will contrarians end up stepping in front of a freight train? Head down to the comments section and share your thoughts.

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