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* World shares ease back from 18-month highs
* Brent oil falls to $112 a barrel
* Dollar index hits three-week high
* Euro dips 0.3 pct to $1.3150
By Richard Hubbard
LONDON, Jan 3 (Reuters) - A global share market rally petered out on Thursday as investors focused on U.S. political battles ahead over spending cuts, halting the gains that followed a deal to avoid sharp tax hikes.
The MSCI world equity index dipped from an 18-month high to be down 0.1 percent at 346.7 points while other riskier assets such as oil and the euro also eased.
The main share indexes in Germany, Britain and France were down 0.1 to 0.4 percent, having hit multi-month highs on Wednesday when relief swept the markets after U.S. lawmakers reached a deal to prevent a fiscal crunch.
But President Barack Obama and congressional Republicans face two more months of tough talks on spending cuts and an increase in the nation's debt limit as the hard-fought deal to avert the so called "fiscal cliff" covered only taxes and delayed decisions on expenditure until March 1.
"Of the three key issues - tax increases, spending cuts and the debt ceiling - policymakers have tackled just one," said Mouhammed Choukeir, chief investment officer at Kleinwort Benson.
"The fiscal cliff issue is unresolved. This is likely to increase market volatility, supporting safe-haven assets such as gold and some commodities," he said. "Paradoxically, as the U.S. debt and deficit issues continue to make investors jittery, the dollar can be expected to remain a safe-haven asset."
The dollar was up 0.3 percent against a basket of major currencies at a three-week high on Thursday, although it slipped 0.2 percent against the yen to 87.14.
The euro, which had touched an 8-1/2 month high against the dollar on Wednesday, was down was down 0.2 percent at $1.3162, .
"The reality is that budget talks will continue for the next two months and could get sour," said Jane Foley, senior currency strategist at Rabobank. "We see the dollar index reclaiming some ground."
The dollar's strength and profit-taking pushed oil prices lower, with Brent crude slipping 0.4 percent to $112 a barrel and U.S crude futures down 45 cents to $92.67.
"After the initial excitement, reality sets in," said Victor Shum, oil consultant at IHS Purvin & Gertz. "There will be other negotiations and the (U.S.) deal is a compromise."
Gold was firm, holding near its highest level in two weeks hit on Wednesday in the wake of the initial U.S. fiscal deal. Spot gold was trading at $1,687.70 an ounce, up $1.35.
The precious metal ended 2012 with gains of around 7 percent - the 12th straight annual rise, and marking one of the longest bull runs for a commodity.
GROWTH OUTLOOK BRIGHTENS
Thursday's retreat across riskier asset markets might have been sharper but for data showing activity in China's services sector and at U.S. factories had expanded in December, brightening the outlook for global growth.
China's official purchasing managers' index (PMI) for the non-manufacturing sector rose to a four-month high in December, adding to signs of a revival in the world's second-largest economy.
Investors will now turn their attention to the December U.S. employment report on Friday. This is expected to show modest job growth of around 150,000 compared with 146,000 in November.