If you could buy any stock in the whole wide world, which one would it be?

Seems like a simple exercise -- along the lines of picking your favorite athlete, cereal or movie star, maybe. But it's actually quite complicated, considering the options available in domestic stocks as well as those listed on European, Asian and emerging markets.

It's also a challenge faced by more and more global stock fund managers as the dollar's decline pushes investors to diversify internationally. Unlike most foreign funds, which buy stocks from a single country or region outside the U.S., global funds mix domestic and international stocks. That set-up forces the fund manager to allocate not only among their favorite stocks, but in various countries as well.

Due to the integration of U.S. and non-U.S. stocks, global funds are often recommended as core holdings so investors can avoid overlap in their portfolios. And when choosing a particular global fund to be the cornerstone of one's holdings, Karen Papalois, analyst at fund tracker Morningstar, advises investors to seek out fund managers dedicated to finding the best opportunities wherever they are instead of simply trying to mix and match international and domestic funds from their own fund families.

"The key is to find a fund that is thoughtfully put together, because there are a lot of moving pieces when it comes to global funds," says Papalois.

She also recommends avoiding funds that are too rigid when it comes to splitting up assets among countries, something that cannot be said of Francis Claro and Donald Bisson, portfolio managers for the $176 million

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Evergreen Global Opportunities fund. The pair recently raised their domestic stake to 35% from 30% after the two fund managers determined "the dollar has already taken most of its beating."

Bisson handles the domestic portion of the portfolio, leaving Claro to scour the rest of the world. The pair starts with a top-down approach to global investing, choosing worthy countries based on factors such as interest rates, liquidity and currency valuations. After divvying up the world, each partner uses a bottom-up approach to picking his favorite stocks from his respective corner of the world.

Right now Claro is tilting toward European stocks, with slightly more than 20% of the fund's assets in French and German names. The fund's largest holdings include the French tech company

Bull

as well as German sneaker giant

Adidas

, which he predicts will be spurred by the recent resurgence in high-priced shoes on top of Germany's hosting of next summer's World Cup.

Claro's current affinity for European stocks could certainly be called contrarian since most of the economic news coming out of Europe -- excluding the U.K., which has been hot -- has been dismal. Nevertheless, Claro says France and Germany's economic malaise may soon be ending. And even if their economies continue to stagger, Claro is confident his picks will still shine.

"Even during the market downturn, we still found opportunities in Europe," says Claro. "We're early in

Puma

, which is another sneaker company where we did very well."

Claro is less sanguine about emerging-market economies, which he believes are at risk due to rising interest rates and the unwinding of the carry trade. The fund is only 4% to 5% in Latin American stocks.

Domestically, Claro's partner Bisson, a relative newcomer who joined the fund last October, sees steady growth for U.S. companies. But like many other market watchers, he says "oil and interest rates remain the big question mark." He looks for companies in one of three classifications: core companies with sustainable competitive advantages; stocks that were hit when the market "overreacted" to a short-term event like an acquisition or missed quarter; and stocks he calls "underestimated" when it comes to market size.

In the core category, Bisson likes online education powerhouse

Strayer Education

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and its 20%-plus top-line growth. In the "overreacted" camp, one of his top choices is

Avid Technologies

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; the HDTV provider saw its shares decline after it announced a deal to acquire

Pinnacle Systems

( PCLE). Finally, when it comes to underestimated markets, Bisson says Internet traffic manager

F5 Networks

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looks promising.

Despite the fund's strong three-year track record of 14.9% annual returns, Bisson's stock-picking will surely be scrutinized. After all, he is the new manager on the block, after replacing a predecessor who stayed less than two years. Morningstar analyst Gregg Wolper already has the spotlight on the fund, saying that recent manager turnover could harm returns going forward.

It's also worth noting that the Evergreen Global Opportunities fund only minimally hedges currency risk. Not all global funds play as loose with currency exposure, which is something Andrew Clark, strategist at Lipper, suggests checking into before buying a global fund.

"Dollar volatility can wipe out gains," says Clark. "So it's important to know whether or not you want that added exposure."

Glen Hilton, portfolio manager for the $100 million

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AIM Global Value fund, for example, generally hedges currencies, but he says there is no hard, fast rule to his approach.

Hilton currently has 30% in U.S. stocks and nearly 40% in Canadian stocks. The fund's heavy exposure to Canadian natural resource stocks, now hot commodities in their own right, has lifted returns to an impressive 3.7% so far this year.

Hilton says Canada has a better "public balance sheet" now that America is faced with massive twin deficits. He also says owning Canadian oil, coal and precious metals companies works well in a fund that he designs to be "strong on defense, since it is meant to be a core holding."

Hilton's top Canadian picks include uranium miner

Cameco

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and coal miner

Fording Canadian Coal Trust

( FDG).

On the coal front, he also likes Australian coal producer

MacArthur

. Hilton says the characteristics of Australian and Canadian economies are similar in that they are reliant on natural resources companies. Aside from MacArthur, Hilton's Australian holdings include mega-miner

BHP Billiton

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, with the pair making up close to 4% of the fund's assets.

Hilton's U.S. picks also reflect his "winning by not losing" strategy. The fund's biggest domestic holdings are

Microsoft

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and

Merck

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. And while the drugmaker may not seem like an obvious defensive choice in light of its legal headaches over Vioxx, Hilton says the liability is overblown and the franchise is not dead by any means. He also bought the stock after it blew up. His average price is $29, while the stock recently traded above $33.