When it comes to the festering European debt crisis, investors are feeling like Bill Murray's character in Groundhog Day. Same story, different day. "[Insert European country here] reported today that its economy is worsening." It can be downright depressing. But opportunistic investors know that sometimes seizing a contrarian position, in conjunction with doing some homework, can reward over the long haul.

Glimmer of hope or further horror?
The precarious financial situation in Europe saw initial, but short-lived, signs of optimism last weekend as European officials offered as much as $100 billion to prop up weak Spanish banks. And the global economy now waits with bated breath for the outcome of Greece's Sunday elections. The election is viewed as a proxy for a larger, looming question: Will the eurozone soon start unraveling like a dropped ball of twine? This uncertainty has slammed shares of companies with European exposure, but the downward spiral may have dragged down some otherwise strong companies.

May the Greek gods of investing shine on you
Trading near 500, the Athens Stock Exchange index is off 90% from five years ago. Spanish and Greek 10-year bonds yield roughly 7% and 28%, respectively. Stocks such as National Bank of Greece (NYSE: NBG) and Coca-Cola Hellenic Bottling (NYSE: CCH) could reward brave investors, but they aren't for the faint of heart. Both Greek stocks have been bludgeoned and continue their wildly volatile swings; both currently trade near 52-week lows.

Last month, National Bank of Greece, the country's largest lender by assets, announced first-quarter losses resulting from "bad loans while attempting to ease investor concerns about its cash position in the face of recent deposit withdrawals." The stock price is down nearly 98% from five years ago.

Coca-Cola Hellenic Bottling produces, sells, and distributes Coca-Cola products to 570 million people in 28 countries, primarily in Central and Eastern Europe. Coca-Cola owns 23% of its shares. Coca-Cola Hellenic Bottling generates strong free cash flow and sells products that people drink in good economic times and bad. The stock is off 47% from five years ago, lost 8% this year, and trades at 12 times forward earnings.

If Greece fizzles out of the eurozone, these two beaten-down, low-P/E stocks could get even cheaper.

Clear vodka, opaque accounting
At first glance, Polish vodka maker and alcoholic-beverage importer Central European Distribution (Nasdaq: CEDC) appears to be a diamond in the rough as a bullish position on Europe's eventual economic recovery. The company enjoyed incredible year-over-year quarterly earnings growth of 5,475% and is expected to grow sales 60% per year over the next five years. Before you run for the buy button, though, that growth comes as the result of massive goodwill being written down in the previous year's quarter, which brings us to one glaring problem here.

Goodwill and intangibles account for more than half of Central European Distribution's assets, and the company has a ton of debt on the balance sheet. Last week, the company announced that it will restate its 2010 financials after it incorrectly estimated trade rebates. A class action lawsuit was quickly filed, claiming that executives misled shareholders by overstating sales figures to the tune of $30 million to $40 million.

Tragedy to treasure?
If you'd like to wade into the global investing waters but cannonballing isn't quite your style, look to solid companies with global exposure based on this side of the pond, such as McDonald's (NYSE: MCD), or companies with broad geographic diversification, such as U.K.-based Diageo (NYSE: DEO).

McDonald's global same-store sales grew 3.3% in May. While this growth was attributed mostly to the U.S. and Europe, the company recognizes that "prolonged global economic volatility, austerity measures in Europe, and increased expenses will likely pressure second-quarter results."

Beverage company Diageo is expected to aggressively ramp up Scotch whiskey production over the next several years to keep pace with emerging-market demand. While European net sales were down, Diageo enjoyed 5% organic global net sales growth in 2011. And Diageo appears a great buy now -- it's trading at 16 times forward earnings, compared with 25 for the industry.

While investors wait out the global economic recovery, shareholders of these companies benefit from stable dividends. McDonald's has both paid and increased its dividend consecutively since the Gerald Ford administration and currently pays a 3.2% yield. Diageo pays a 2.1% yield, has offered one since 1988, and has increased it for each of the past 13 years.

No one can predict when, but the global economy will recover. And investors who are nervous about putting all their eggs in one basket should consider exchange-traded funds to profit from recovering global markets. If you'd like to unearth this diversified cornucopia of stellar ideas, grab a copy of our exclusive free report, "3 ETFs Set to Soar During the Recovery."