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GLOBAL MARKETS-Shares, bonds rally as markets bet on glacial Fed

* Investors relieved as Yellen sounds less-than hawkish

Asia shares ex-Japan reach highest since mid-2015

* Bonds rally as market prices in gradual Fed tightening

* Canadian dollar surges as BoC hikes, opens door to more

By Wayne Cole

SYDNEY, July 13 (Reuters) - Asian shares scaled a two-year top on Thursday as investors wagered policy tightening in the United States would be glacial at best, lifting Wall Street to record peaks and lowering bond yields almost everywhere.

The star performer was the Canadian dollar, which rocketed to 11-month highs after the country's central bank hiked rates for the first time in seven years and left the door wide open to further moves.

Yet the overall mood was one of relief that Federal Reserve Chair Janet Yellen had not sounded more hawkish in her appearance before Congress, a green light for risk taking.

MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.45 percent to its highest since mid-2015.

Japan's Nikkei firmed 0.4 percent and Australia's main index jumped 1 percent.

On Wall Street, the Dow rose 0.57 percent, while the S&P 500 gained 0.73 percent and the Nasdaq 1.10 percent. The rate-sensitive S&P 500 real estate index jumped 1.3 percent, its biggest gain in about four months.

Equities were underpinned by a drop in bond yields as Yellen sounded cautious on inflation and noted the Fed would not need to raise rates "all that much further" to reach current low estimates of the neutral funds rate.

"The market did perceive a greater degree of anxiety over inflation at the margin," said Westpac's U.S. economist, Elliot Clarke. "To our mind, this is unlikely to get in the way of another hike this year."

"Two further hikes in 2018 will likely be justified by conditions. However, the case for additional hikes thereafter is nowhere near being made."

Indeed, markets doubt even that modest tightening will ensue and imply only a 50-50 chance of a rise by December. Treasuries rallied in reaction, with yields on two-year notes falling to three-week lows, as did bonds in Europe.

The odd man out was Canada, where yields hit their highest since late 2013 after the Bank of Canada raised rates a quarter point saying the economy no longer needed as much stimulus.

The Canadian dollar notched its biggest percentage gain since March 2016 and was last trading near one-year peaks at C$1.2748.

Moves elsewhere were mixed, with the dollar gaining ground on the euro only to lose on the yen. In early trading Thursday, the euro had steadied at $1.1418 while the dollar sat at 113.32 yen.

Against a basket of currencies, the dollar was holding just above nine-month lows at 95.793.

The drop in U.S. yields benefited gold, which pays no interest, and nudged the precious metal up to $1,218.35 and away from its recent trough of $1,204.45.

Oil prices faded as a report showing hefty drawdowns in U.S. crude inventories was offset by data pointing to lacklustre gasoline demand.

Brent crude futures were off 13 cents at $47.61 a barrel, while U.S. crude lost 10 cents to $45.39.

(Editing by Shri Navaratnam)