"Thanks to the ECB, people now expect that if you buy a government bond you'll get paid back in full on time and in the right currency," says David Kelly, chief global strategist at J.P. Morgan's money-management group. Before the central bank hatched the plan, bond buyers weren't entirely sure if their Greek bonds would be paid back in euros or in newly printed Greek drachmas.

Since then, Government borrowing costs in Greece, Italy and other struggling countries have dropped from dangerously high levels. European finance ministers have given Greece another two-year financial lifeline, and made strides toward shoring up the continent's banking system. In December, the rating agency Standard & Poor's gave Greece a better credit rating.

All these signs of progress propelled stock markets up. The Athens market surged 32 percent for the year, Italy's 8 percent. Germany's DAX index reached a five-year high this month. Hedge funds and other big money managers from around the world have started warming up to the region, putting billions into European stock funds for all but one of the past eight weeks, according to fund tracker EPFR.

Even after those recent gains, stock markets across Europe still appear cheap by standard measures. The typical company trades at less than 12 times its earnings over the next year and 6 times its cash flow. For U.S. companies, the same averages are 13 and 8.

To Kelly, there's a good reason European companies sell for a discount: The economic crisis is far from over. Europe's financial markets may look stable but the region's overall economy is shrinking. It's likely to keep shrinking, Kelly says, as long as European officials demand struggling countries cut spending on government services in exchange for aid.

"Austerity to fix a debt crisis doesn't work," Kelly says. "It only makes things worse. There's no evidence Europe's leaders really understand that."

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