LONDON — Speculators are buying gold faster than the world’s biggest producers can mine it as analysts forecast a 26 per cent rally that may extend the longest run of annual gains since at least 1920.

Exchange-traded products backed by bullion added 42.5 metric tons in the week to May 14, the most in 14 months, according to data from UBS. China, Australia and the 16 other largest mining nations averaged weekly output of 42.3 tons last year, researcher GFMS Ltd. estimates. Even though prices have fallen 4.8 percent to $1,189.75 from a record $1,249.40 an ounce May 14, the median in a Bloomberg survey of 23 traders, analysts and investors shows it will reach $1,500 by the end of the year.

Buying accelerated as the MSCI World Index of 23 developed nations’ stocks tumbled as much as 16 percent since mid-April and the euro weakened to a four-year low against the dollar. Holders of ETPs, including George Soros and John Paulson, accumulated a record 1,921 tons by May 14, eclipsing all but four of the biggest central-bank holdings.

“You could see gold go up another $1,000,” said Evan Smith, who helps manage $2 billion at U.S. Global Investors Inc. in San Antonio and in 2006 correctly predicted that gold would reach $700 within two years. “All of the turmoil and problems we’ve seen in Europe is just another reminder that there’s a lot of value in gold as a safe haven.”

The risk to gold bulls lies in economic growth, which should buoy the prospects of metals linked to industrial demand, such as copper and silver. The world economy will expand 4.2 percent this year, the International Monetary Fund said April 21, raising its January projection from 3.9 percent.

While gold is favored by investors when the dollar weakens and inflation gains, the metal can also advance at other times. Gold rose 5.8 percent in 2008 as U.S. consumer prices gained 0.1 percent. The metal added 18 percent in 2005 when the U.S. Dollar Index, a measure against six counterparts, advanced 13 percent. Gold rose 8.5 percent this year as the U.S. Dollar Index jumped 10 percent. U.S. consumer prices dropped in April.

“People are afraid of the debasement of all the currencies,” said Peter Schiff, president and chief global strategist for Euro Pacific Capital, whose clients have more than $2 billion in assets. “What’s surprising is that gold is still as low as it is,” he said, predicting $5,000 to $10,000 an ounce in the next five to 10 years.

Gold is still at half the peak set in 1980, after adjusting for inflation. Then, prices rose to $850, equal to $2,266 today, according to a calculator on the website of the Federal Reserve Bank of Minneapolis.

Supply from mines, which peaked in 2001, fell in five of the last eight years, data from London-based GFMS show. Companies are digging deeper to extract dwindling reserves, with mines in South Africa extending as far as 2.35 miles down.