Asian markets were mixed in quiet trading Tuesday, following another record day on Wall Street.

The Dow Jones Industrial Average

DJIA, +0.34%

  and S&P 500

SPX, +0.09%

  closed at record highs for a third consecutive day, while the Nasdaq Composite

COMP, +0.23%

  notched a record ninth-straight record close.

Traders have been buoyed by the pending phase-one trade deal between the U.S. and China, which announced Monday plans to open its oil, telecom and power markets wider to private competitors.

On Tuesday, leaders from China, Japan and South Korea were meeting against the backdrop of increasing threats from North Korea’s nuclear and missile programs. The trilateral summit aims to smooth some regional frictions, and discuss furthering regional cooperation on the economy.

Japan’s Nikkei

NIK, +0.02%

  was about flat and Hong Kong’s Hang Seng Index

HSI, -0.15%

  fell 0.2%. The Shanghai Composite

SHCOMP, +0.42%

  advanced 0.3% while the Shenzhen Composite

399106, +0.94%

  rose 0.7%. South Korea’s Kospi

180721, -0.46%

  fell 0.5%, while stocks inched up in Singapore

STI, +0.24%

  but fell slightly in Taiwan

Y9999, -0.38%

 . Australia’s S&P/ASX 200

XJO, +0.13%

  rose 0.2%. Markets in Australia and Hong Kong were set to close early for Christmas Eve. Many global markets will be closed Wednesday for the Christmas holiday.

Read: Here’s when markets will be closed for the Christmas and New Year holidays

Among individual stocks, Fuji Electric

6504, +1.19%

  and tech-equipment maker Advantest

6857, +0.98%

  gained in Tokyo trading, while Dai-ichi Life Holdings

8750, -1.64%

  and Nikon

7731, -1.45%

  fell. In Hong Kong, casino operator Sands China

1928, +1.13%

  rose while stock-market operator Hong Kong Exchanges & Clearing

388, -0.94%

  and China Construction Bank

939, -0.75%

  declined. Samsung

005930, -0.90%

  slipped in South Korea, and Beach Energy

BPT, +3.17%

  surged in Australia.

The market’s latest gains came on a day of mostly muted trading as investors kicked off a holiday-shortened week. U.S. markets were scheduled to open for only a half day on Tuesday and then close Wednesday for Christmas.

“Right now, a lot of people have gone home for the year and the path of least resistance is higher,” said Sameer Samana, senior global market strategist at Wells Fargo Investment Institute. “It’s hard to see any kind of meaningful trend change between now and the end of the year.”

Momentum for stocks has been clearly upward for months, driving the major stock indexes to record highs. The benchmark S&P 500 index has finished with a weekly gain in 10 out of the past 11 weeks.

Fears about a possible recession have also faded since the summer after the Federal Reserve cut interest rates three times, and the central bank appears set to keep them low for a long time.

Benchmark U.S. crude oil


  lost 3 cents to $60.49 per barrel. Brent crude

BRNG20, +0.20%

 , the international standard, was down 2 cents at $65.40 per barrel.

The dollar

USDJPY, +0.02%

  to Japanese yen was flat at 109.39 yen.

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