Stock markets in the US and Europe have experienced turbulence in recent weeks, a by-product of Greece’s debt crisis and concerns about similar problems in Portugal, Ireland, Italy and Spain.

Each of these fiscally troubled countries counts the euro as their national currency; the possibility of a sovereign default has raised questions about the euro’s viability. Investors are also concerned about the European Central Bank’s lack of comprehensive authority in monetary matters; in the EU, central banks of member states dictate monetary policy at the national level, though they can’t print additional currency.

That’s led to heavy criticism of the single-currency union, particularly from fiscally conservative member states, many of which resent having to rescue other nations from their own fiscal irresponsibility. And support for the currency is waning, even in Central and Eastern European countries that had anxiously sought EU membership.

I expect the EU will ultimately cobble together a bailout; allowing a member state to default on its debt or exit the union would call the organization and its currency into question. It is also in the EU’s best interest to nip this crisis in the bud before other fiscally weak members find themselves in the crosshairs.

Although the macroeconomic picture is ugly, savvy investors have an opportunity to gain exposure to high-quality European companies on the cheap.

We screened for mutual funds with broad European exposure and managers who have been through at least one full economic cycle in the region, either with their current funds or in another capacity. All three of our picks sport low expense ratios and excellent track records, plus they carry little to no exposure to the unfortunately named PIIGS (Portugal, Ireland, Italy, Greece and Spain). We’ve arranged our findings from the riskiest to the most conservative.

A Shepherd’s Guide to Europe

Mark Yockey has helmed Artisan International (ARTIX) for 15 years but boasts over 20 years of experience in international investment. Over that period, he’s endured numerous regional downturns and has consistently turned them to his advantage.

The fund falls into the growth category because of Yockey’s propensity for holding onto winners that he believes can support higher valuations. But management’s methodology is a bit more value-sensitive, seeking growth at a reasonable price.

Yockey views the current European crisis as an opportunity rather than an obstacle and increased the fund’s stake in European markets to 67.1 percent in the fourth quarter. Financial-services names account for 31.7 percent of the fund’s investable assets, and management has upped its stakes in HSBC Holdings (NYSE: HBC) and BNP Paribas (France: BNP). This emphasis has weighed heavily on the fund’s performance in 2010 but should pay off as the economic situation improves. The fund traditionally hasn’t hedged its currency exposure, so any bounce in the euro will be a positive.

The fund’s exposure to the PIIGS amounts to 5.6 percent of the portfolio and consists primarily of higher-risk names. However, given the relatively light weighting of these individual names and the fund’s positions in emerging markets, these holdings aren’t cause for concern.

William Kennedy has managed Fidelity International Discovery (FIGRX) since its inception in 1986 and has successfully navigated several economic cycles.

The fund took a hit after Kennedy loaded up a bit too early on financial stocks. That misstep left him a bit gun shy on the sector, though he has increased the portfolio’s exposure to roughly a quarter of its investable assets over the past few months. HSBC is the fund’s top holding, but the portfolio also includes smaller stakes in Banco Santander (NYE: STD) and several Asian banks.

Kennedy currently favors consumer goods and health care names in Europe, along with a smattering of utilities such as Telefonica (NYSE: TEF).

This approach has enabled the fund to generate solid returns relative to its peers. The fund is down 7.6 percent on a three-year annualized basis and up 3.5 percent over the last five years. That ranks the fund in the top 33 percent and 28 percent of its category, respectively, and the top 14 percent on a 10-year basis.

The Fidelity fund allocated 2.1 percent of its assets to Italian equities and 3.3 percent to Spanish stocks. But most of these holdings are large multinationals whose businesses aren’t directly tied to the fortunes of their nations.

Finally, the most conservative way to gain exposure to Europe is through Homestead International Value (HISIX), which allocates 64 percent of its assets to the region. A much smaller fund than our other two picks, it has the lowest expense ratio of the bunch at just 0.98 percent. The fund also maintains a smaller portfolio, currently holding just 55 names.

Homestead International Value has the lowest exposure to financials at just 22 percent, and none of these names are major European banks. Its largest regional financial-services name is AXA (NYSE: AXA), a large insurance outfit in France. With an emphasis on consumer goods and business services, the fund’s portfolio is geared more toward a recovery in household spending. Management also favors the relative stability of the UK and French markets.

Homestead International Value allocates 7.2 percent of assets to Italian names, but these holdings are disproportionately blue chips such as the energy outfit Eni (NYSE: E) and electric utility Enel (Italy:  ENEL).