If Shinzo Abe and Mario Draghi were being compensated by investment banks rather than taxpayers, they would both be looking forward to some pretty hefty year-end bonuses.

Mr. Abe, the prime minister of Japan, and Mr. Draghi, the president of the European Central Bank, were responsible for policies that helped deliver huge gains to stock market investors during the last year.

How many hedge fund managers can boast 56.7 percent gains? That was how much Tokyo's Nikkei average rose in 2013, thanks in large part to Mr. Abe's aggressive stimulus policies intended to shake Japan out of its economic torpor. It was the Nikkei 225's best performance in 40 years.

And who would have thought a year ago that the best-performing stock markets in Europe would include Greece, up 28.1 percent during the year, and Ireland, up 33.6 percent? Much of those gains, in countries that have been among Europe's most troubled, can be attributed to Mr. Draghi's success in convincing investors that the European Central Bank would not allow the euro zone to break apart — though improvement in the Irish economy and signs of stability in Greece also played a big role.

"This year has marked the end of the financial crisis," said David Thébault, head of quantitative sales trading at Global Equities in Paris. "Now we're beginning to see recovery in the real economy. The U.S. is growing and the European economy is stabilizing."

Yet the unexpected swiftness of the rebounds in equity markets, which far outpace actual economic performance, has also created a palpable nervousness among investors. Gains that robust will be almost impossible to repeat in 2014, and could easily be reversed, analysts say.

To many investors, the list of bad things that could happen in the year ahead is long. It includes a resurgence of the sovereign debt crisis in Europe and global repercussions from the withdrawal of monetary stimulus in the United States.

Analysts are particularly concerned about the potential for disappointment in Japan if the government does not follow up with measures intended to make the economy perform better, such as allowing more competition in the energy business.

"The verdict on Abenomics is still out," Holger Schmieding, chief economist of German bank Berenberg, said in a note to clients, referring to Mr. Abe's economic policies. "Without serious reforms, Abenomics will be little more than another flash in the pan, a brief footnote in Japan's long slide into fiscal oblivion."

China provides a reminder of how a onetime star performer can disappoint. Though it is the world's fastest-growing major economy, China can also lay claim to a more dubious superlative: home of the worst performing stock market in Asia.

The benchmark Shanghai Composite Index ended 2013 on a low note, closing at 2,115.98 points, a decline of 6.8 percent from a year ago.

In general, emerging markets lost some of the glamour they have enjoyed in recent years, when they often made stocks in developed countries look staid and boring. The Shanghai stock market's performance was slightly worse than the 6.7 percent annual decrease of the main share index in Thailand, where street protests have seized the nation's capital for weeks. In Indonesia, the main index finished down 0.98 percent from a year earlier, as investors grew concerned over lofty stock valuations amid signs that growth was slowing.

Other Asian markets followed Japan higher during the year, however.

The slump in Chinese stocks came despite signs that the country's policy makers have been acting to rejuvenate the country's languid financial markets. On Tuesday, five companies announced that they had received approval to conduct public share offerings — the first batch of deals to be approved since regulators announced on Nov. 30 that they would resume share sales after a yearlong ban.

Next to Japan, Europe was the surprise gainer of the year. But, like Japan, the gains threaten to evaporate if early signs of recovery prove ephemeral or if policy makers lose their will to make politically unpopular changes.

The Stoxx 600, a pan-European equity benchmark, was trading on Tuesday at its high for the year, racking up a gain of just over 17 percent. The DAX in Germany ended the year up 25.5 percent, while France's CAC 40 rose 18 percent despite many doubts about the competitiveness of the French economy. The FTSE 100 in London was ahead 14.4 percent.

Many investors remain optimistic about prospects for euro zone indexes, in part because of increased exports of products like German cars or French luxury goods to the resurgent United States. Analysts surveyed by Reuters expect European shares to gain about 14 percent in 2014.

Hugues Le Maire, managing director of Diamant Bleu Gestion, an asset manager in Paris, said that growth in gross domestic product across the developed world would replace central bank stimulus as the impetus for stock market gains in 2014, saying, "It will be the G.D.P. growth year, the economic results year."

Mr. Le Maire expressed concern at signs of continued fragility in Europe. Lending to consumers and businesses, for example, continues to decline. Many economists warn of the potential for deflation, a broad, sustained decline in prices that can destroy corporate profits and jobs.

Faced with resistance from Germany, the European Central Bank has been more restrained than its counterparts in Japan and the United States in taking measures to head off such threats. As a result, Mr. Le Maire tempered his generally upbeat outlook with a warning: "Be very careful about any risks that could occur."