By Christopher Whittall

U.S. investors, prepare for a new high-stakes geography test.

Europe's recent decision to import the U.S. strategy for economic stimulus could give share prices on the Continent the same kind of boost that has made many Americans wealthier in recent years. European stocks already are outracing U.S. counterparts so far this year, with Germany's benchmark index up 9.5% and France's up 8.4%, through Thursday, while the Dow Jones Industrial Average is down 2.3%.

Yet stocks in many countries across the Atlantic still look alluringly inexpensive. European stocks are selling at the steepest discount ever to U.S. equities based on one popular valuation measure, according to an analysis by Morgan Stanley of data going back to late 1979.

How much foreign stock you should own can depend on many factors, including your personal comfort level. Europe is a major part of non-U.S. markets, and experts say typical U.S. investors should consider having at least 20% to 30% of their stock portfolios in foreign firms.

But the opportunity comes with risks for anyone investing with U.S. dollars, because some of the same policies that could boost European asset values could weaken the common European currency, the euro, relative to the greenback. That would eat into any gains when converted into dollars.

"What you gain on the stock price you may lose on the currency," says Graham Secker, head of European equity strategy at Morgan Stanley.

The European Central Bank announced in mid-January that it plans to spend more than a trillion euros buying bonds in an effort to fend off the risk of deflation and give the Continent's anemic economies a shot in the arm. European stocks rallied in recent weeks in anticipation of the move.

Loading up on European stocks now is a bet that the ECB's move will help things go right on a continent where so much has gone wrong for investors in recent years. Other problems include potential clashes between the new Greek government and the country's beleaguered creditors, and ongoing conflict on the eurozone's doorstep in Ukraine.

European economies also face serious structural problems that rising share prices wouldn't solve--and could, in fact, obscure--including government commitments to spending on social programs that could be difficult to sustain.

Investors tempted by the prospect of another rally fueled by loose monetary policy should consider taking a few basic steps to protect against possible pitfalls.

Here is how to map out your European portfolio:

The Case for Europe

One recent sign of hope for European investors was the calm response to the recent triumph of the left-wing Syriza party in Greece, which wants to ease the terms of the European bailout.

Greece's Athex Composite Share Price Index plummeted 15% in the first three trading days following the vote. But investors elsewhere shrugged, bidding the Stoxx Europe 600--akin to the S&P 500--to a fresh seven-year high in the days that followed.

There are other reasons for optimism.

The euro already has tumbled 19% against the dollar since March, and many analysts believe it has further to fall, particularly when the Federal Reserve raises interest rates, which could happen later this year. A weaker currency should make European exports more competitive abroad and boost revenues in euro terms.

European firms also are able to borrow on favorable terms due to low interest rates, and plunging oil prices have reduced energy costs in countries that often rely on imported fossil fuels.

"Recently, we seem to be running out of reasons to dislike Europe, and for us that signals that it's time to buy," says John Manley, the New York-based chief equity strategist at Wells Fargo Asset Management, a unit of Wells Fargo that oversees about $490 billion.

European stocks also are less richly valued than U.S. equities, which have appreciated more sharply in the aftermath of the financial crisis. European stocks currently trade at nearly a 40% discount to U.S. equities, according to Morgan Stanley, based on the cyclically adjusted price/earnings ratio--a valuation measure popularized by Nobel Prize-winning economist Robert Shiller that uses average inflation-adjusted earnings over the prior 10 years. The long-term average discount is 10%.

Morgan Stanley forecasts that European corporate earnings will outpace the U.S. for the first time since 2008, with 10% growth in 2015 compared with 6% to 8% in the U.S.

For many U.S. investors, the simplest and most convenient way to own European stocks is to buy a mutual fund or an exchange-traded fund offered by a major investment firm that focuses on Europe or includes a chunk of European stocks among its holdings.

The Currency Effect

For an investor in Berlin, Paris or Rome, the case for European stocks in 2015 may look particularly strong.

For an investor in Chicago, Los Angeles or New York, the analysis is more complicated because of the potential impact of currency fluctuations.

Jens Nordvig, a currency strategist at Tokyo-based Nomura Holdings, expects that one euro will cost $1.05 by year-end, down from $1.13 on Thursday. Other analysts think the euro could become even cheaper compared with the dollar.

While that could boost the prospects for European companies that can sell goods to Americans at lower prices, it would hurt U.S. shareholders of those firms that tally gains in dollar terms.

The impact could be significant, as a comparison between two similar exchange-traded funds shows. The iShares MSCI EMU ETF--which holds an array of European companies--lost 4.6% over the past 12 months, through Thursday, including dividends, according to Chicago-based investment researcher Morningstar. The fund charges annual fees of 0.49%, or $49 on a $10,000 investment. It doesn't hedge against changes in the exchange rate between the euro and the dollar.

By contrast, the WisdomTree Europe Hedged Equity Fund, an ETF which hedges the impact of currency moves and which has many of the same top 10 holdings as the iShares fund, is up 19% over the same period. The fund charges annual fees of 0.58%.

There are other differences between the iShares and the WisdomTree funds, but the divergence in their fortunes broadly illustrates how hedging and not hedging the effect of currency movements can have an impact on returns.

Diversify or Wager?

Investors should first figure out what they are looking for when they invest abroad. If diversifying your portfolio is the goal, then you may choose to view currency swings as a valuable way to hedge against uncertainty.

At the same time, the prospect of a rise in the dollar and a decline in the euro is real given the different policy signals officials in the U.S. and Europe are sending to the markets.

So if you want to bet on near-term gains in European stocks, consider a fund that tries to limit the impact of the euro, such as the WisdomTree Europe Hedged Equity Fund, which has $8.9 billion in assets.

Consider focusing on European companies that are in a good position to benefit from a weaker euro as well. In general, larger European companies with international exposure should outperform smaller companies that tend to be more focused on domestic markets, according to Société Générale, the Paris-based investment bank.

The WisdomTree ETF, for example, focuses on European companies worth more than $1 billion that generate at least half of their revenue outside of Europe.

Another option is the Deutsche X-trackers MSCI Europe Hedged Equity ETF, says Gregg Wolper, a senior analyst at Morningstar. The fund aims to hedge against fluctuations in the euro against the dollar and holds shares in European companies with an average market capitalization of $18.6 billion. The fund charges annual fees of 0.45% and has $1.1 billion in assets.

Don't assume that the stocks in all European countries will perform the same way, especially those that don't use the euro. The FTSE 100 index in the U.K. is up 4% over the past year, through Thursday, for example, while Germany's DAX index is up 15% over the same period.

Similarly, companies in the eurozone won't benefit equally from the ECB's efforts. Companies in the eurozone overall should see a 7% bump in earnings if the euro falls 10%, Société Générale said in a note on Jan. 20 (as of Thursday, the euro had fallen 3% since the note was published). But French companies, which tend to be more export-oriented, should see a 9% increase, compared with a 4% increase in Italy, according to the bank.

Investors can get broad exposure to European stocks through funds such as the Vanguard FTSE Europe, which had nearly a third of its holdings in the U.K. at year-end, while stocks in Switzerland, France and Germany each comprised about 14% of the portfolio. The fund doesn't hedge against changes in the euro/dollar exchange rate.

There also are a number of funds that focus on single countries, some of which hedge and some of which don't. For example, investors who want to invest in German stocks in a fund that hedges against the euro/dollar exchange rate can buy the Deutsche X-trackers MSCI Germany Hedged Equity ETF, which charges fees of 0.45% and has assets of $53 million. The fund tracks 54 German companies.

Analysts at major investment banks believe that some companies and sectors are in a particularly strong position. For example, Société Générale strategists say aircraft maker Airbus Group and luxury-goods retailer LVMH Moët Hennessy Louis Vuitton will each see earnings per share rise 29% if the euro falls 10%.

Goldman Sachs Group, meanwhile, favors luxury retailers that cater to U.S. consumers, such as Burberry Group, Christian Dior and Salvatore Ferragamo, as well as banks that should benefit from a recovery in the eurozone, such as Intesa Sanpaolo and Banco Bilbao Vizcaya Argentaria, which are based in Italy and Spain, respectively.

Continental Drift

Investors who are placing such bets should keep in mind the possibility that Europe's economy could keep drifting. Economists have predicted a European revival in recent years, only to be disappointed by persistently anemic growth.

Peter Westaway, chief European economist at Vanguard Asset Management, a unit of Vanguard Group, says that major eurozone countries such as France and Italy need to enact significant structural changes to remove obstacles to growth. Those efforts will "determine the success of Europe going forward," he says.

Similarly, sectors that may look well-positioned could end up being vulnerable to disappointment, as could investors who wager on them. Banks, which make up 22% of European stock indexes based on market capitalization, could benefit from new economic stimulus but also could suffer from low bond yields, which tend to limit their profitability, says Andrew Sheets, head of cross-asset strategy at Morgan Stanley.

"If banks continue to disappoint, that's a pretty large sector of equity markets," he says.

Investors should view the current situation in Europe as an opportunity to determine a comfortable level of international exposure. Stocks in Europe comprise about a quarter of the value of stock markets around the world, Mr. Westaway says.

For most investors, that should be seen as an upper limit for how much of your stock portfolio to bet on a renaissance in European stocks. But don't be surprised if the investing world turns out to be more difficult to navigate than it appears to be on a map.

Josie Cox contributed to this article.

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