Asian shares started the week mostly higher, following Wall Street’s gains last week, with Japanese shares hitting a fresh 15-year high.
US stocks rose last week after the dollar weakened following the Fed’s vow of a cautious approach to lifting interest rates.
In Japan, the benchmark Nikkei 225 index closed up 1% at 19,754.36 – its highest level since April 2000.
The dollar was at 119.89 yen, down from 120.11 yen in New York on Friday.
Chinese shares also rose. Hong Kong’s Hang Seng index closed up 0.5% at 24,494.51, while the Shanghai Composite rose 1.95% to 3,687.73.
Hong Kong-listed shares of Asia’s largest oil refiner Sinopec fell 2.1% after the company posted its first quarterly loss since becoming a public firm in 2000.
Sinopec reported a fourth-quarter net loss of 5.3bn yuan ($854m; £571m) against a net profit of 13.8bn yuan for the same period a year earlier. The company attributed the loss to the tumble in oil prices since the middle of last year.
Australian shares closed lower, but the country’s benchmark index had a earlier come close to touching the 6,000 level last seen more than seven years ago.
The S&P/ASX 200 hit an intraday high of 5,995, but then lost ground and finished down 0.3% at 5956.14, ending a three-session winning streak.
In South Korea, the Kospi index closed flat at 2,036.59 points.
Meanwhile, Singapore-listed shares of Noble Group rose 2.9% after the commodities trader said it was launching legal action against allegations made by little known research firm Iceberg over its accounting practices.
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