You couldn't have asked for a better environment for stocks than what investors have seen over the past several years. Finding companies with rising share prices hasn't taken much more than randomly picking a ticker symbol out of the newspaper. And when it comes to investing overseas, throwing darts at a world map would have served you pretty well.

Yet all good things must come to an end. Despite our increasingly globalized economy, investors can be sure that at some point, the entire world economy will stop rising in tandem. Some countries will continue to do well, but others will struggle to hold onto their gains. When that happens, you'll need to know how to distinguish a successful leader in the global economy from followers who have been riding on coattails. Will the prospect of seeing your investments actually go down throw you into a panic?

Going beyond American thinking
When you're on unfamiliar ground, it's only natural to try to relate your own experiences to a new situation. So in evaluating how foreign stock markets will react to a crisis, an easy assumption to make is that they'll behave a lot like stock markets in the U.S. As a simple example, if you see a stock trading at a multiple to earnings that's high by American standards, you might just dismiss it as being too expensive.

But assuming that the rest of the world behaves like the U.S. is extremely naive and bad news for your portfolio. Foreign currencies and differing interest rates make comparing price-to-earnings ratios across countries complicated. For instance, the Japanese market routinely trades at P/E levels that would make any American think about a coming crash.

From a macroeconomic perspective, even as the world's economy becomes increasingly interconnected, economic conditions in different parts of the world still vary greatly. Countries in Asia and the Far East have done particularly well in recent years, while European economies have only caught fire more recently, especially among the more industrialized countries. And when the next downturn hits, those different conditions will likely show that stocks in some places -- though not everywhere -- have risen too high.

Pick your comfort level
In addition, economies come in different sizes. Just as large-cap stocks offer greater stability at the cost of slightly lower prospective returns, developed industrialized countries like Japan, England, France, and Germany are relatively safe places for international investors to put their money. You'll find companies like Sony (NYSE:SNE), GlaxoSmithKline (NYSE:GSK), Alcatel-Lucent (NYSE:ALU), and Deutsche Bank (NYSE:DB) among the top stocks in those countries -- companies that you're familiar with and whose products you probably use everyday.

Conversely, major emerging markets like India, China, and Brazil offer the same risk-reward characteristics that stocks of smaller companies have -- they're less established and have greater risks of failure, but they also have a lot further to grow before they attain fully mature status. And the smallest economies, like micro caps and small private companies, can bring huge successes to investors -- or they can cost you your entire investment.

Over the past couple of years, it hasn't mattered much where you were invested -- you've probably done well. But with many international markets at or near all-time highs, now is the perfect moment to reevaluate your risk tolerance for international stocks. In the same way that diversifying among companies of different sizes can help dampen losses in down markets, diversifying across different countries can help you manage the risk of specific events that might disproportionately affect one particular country or region of the world.

Where to start
To learn more about the world of international investing, consider trying out the Fool's international investing newsletter, Motley Fool Global Gains. Unlike other publications that simply throw stock picks at you without explaining why you should invest in them, Global Gains makes an effort to educate you about how international investing works and the business conditions you'll experience around the world.

The bottom line is that even if global markets start to fall, some will fall less than others -- and others may even buck the trend and keep going up. Now more than ever, you need to know how to find the most promising investments in the parts of the world that will best survive a global economic downturn. With Global Gains, you'll find the confidence you need to navigate the turbulent waters of international investing successfully.

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You can try out Motley Fool Global Gains right now with a free 30-day trial. There's a world of investments out there waiting for you, and you can try it out with no obligation.

Fool contributor Dan Caplinger has sent his money abroad for investing for a very long time. He doesn't own shares of the companies mentioned in this article. GlaxoSmithKline is an Income Investor recommendation. Baidu.com is a Rule Breakers selection. The Fool's disclosure policy is good everywhere you want to go.