SYDNEY - Asian sharemarkets started the last month of the year on a cautious note after recent strong gains, though growing expectations Europe and the U.S. are poised to cut rates should help ease pressure on local currencies and central banks.

Global oil prices extended losses after a drop of more than 2% overnight as voluntary oil output cuts by OPEC+ producers for the first quarter next year fell short of market expectations.

MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.5% after a surge of 7.3% last month, the most since January. Japan's Nikkei was flat, having also jumped 8.5% in November in the best month in three years.

Chinese bluechips dropped 0.6% and Hong Kong's Hang Seng index fell 0.4%.

"Our sense is that quite a lot of the good news is already in the price. A little bit of profit-taking and rebalancing have probably played in the month-end, obscuring the messaging we typically get from the price action," said Rodrigo Catril, a senior FX strategist at the National Australia Bank.

Regional surveys of purchasing managers showed mixed results in November. Japan's factory activity shrank at the fastest pace in nine months, South Korea's factory activity steadied and China's manufacturing industry returned to expansion, based on a private survey.

Overnight, data showed that both U.S. and European inflation are cooling as desired. The Federal Reserve's preferred gauge of inflation - the personal consumption expenditures (PCE) price index - stood unchanged for October, while consumer spending also pulled back.

The major surprise was with euro zone inflation, which missed expectations by a large margin, triggering a slide in the euro and prompting markets to price in rate cuts of about 110 basis points next year, commencing as early as April.

Traders are now waiting for Fed Chair Jerome Powell's Q&A appearance on Friday, with bulls betting the central bank chief will accommodate their early and aggressive U.S. policy easing bets for next year. Fed funds futures imply rate cuts of 115 basis points.

"We suspect this will be a very tightly choreographed session and will stick to the pre-Waller script of caution when it comes to further hikes but with no hint of easing," said Robert Carnell, regional head of research, Asia-Pacific, at ING.

Fed Governor Christopher Waller, deemed a hawk, this week hinted at lower interest rates in the months ahead if inflation continued to ease.

Declining interest rates in Europe and the U.S. would be good news for Asia, greatly easing the pressure on emerging market currencies and allowing room for Asian central banks to ease monetary policy.

Investors are turning more bullish on Asian currencies, a Reuters poll found. Bullish bets on the South Korean won , Taiwanese dollar and Philippine peso were at their highest since early February.

The dollar index hovered near a five-session high at 103.28 against its peers, drawing some support from a sliding euro overnight. That came after a staggering loss of 3% for November, the worst in a year.

The euro rose 0.2% to $1.0907, after tumbling 0.7% overnight to a one-week low of $1.0879.

U.S. Treasuries also eased a little after the best month since 2011. The yield on 10-year Treasury notes slipped 3 basis points in Asia to 4.3264%, on top of a plunge of 52.2 basis points for the month.

Two-year Treasury yields fell 4 basis points to 4.674%.

In the oil market, Brent crude futures slipped 0.4% at $80.56 a barrel while U.S. West Texas Intermediate futures also fell 0.3% to $75.77 a barrel.

Gold prices was 0.3% higher at $2,042.49 per ounce.

(Reporting by Stella Qiu; Editing by Jamie Freed)