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· Asian shares vaulted to six-month highs on Tuesday, surpassing their July peaks, as hopes that Washington may roll back some of the tariffs it has imposed on imports from China shored up optimism on the global economic outlook.

MSCI’s broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS gained 0.5% to reach levels last seen in early May, led by gains in Chinese shares.

U.S. S&P500 futures ESc1 gained 0.2% in Asia after the Financial Times reported that the United States is considering rolling back levies on $112 billion of Chinese imports, which were introduced at a 15% rate on Sept. 1.

· Japan’s benchmark Nikkei share average leaped to 13-month highs on Tuesday after a long weekend, as U.S. and Chinese trade negotiators moved closer to sealing a preliminary deal and upbeat Wall Street stocks lifted investor sentiment.

Broad-based buying sparked a 1.8% rally in the Nikkei average to 23,251.99, its highest close since Oct. 10 of last year. The broader Topix advanced 1.7% to 1,694.16, its best finish in more than a year.

· Chinese stocks extended a rally into a third session on Tuesday, as investors cheered Beijing’s latest policy easing to boost the economy after a private survey showed sluggish growth in the domestic services sector.

The blue-chip CSI300 index ended up 0.6% at 4,002.81, while the Shanghai Composite Index added 0.5% at 2,991.56.

China’s central bank cut the interest rate on its medium-term lending facility (MLF) on Tuesday for the first time since early 2016, as policymakers work to prop up a slowing economy hit by weaker demand at home and abroad.

Some analysts said Tuesday’s reduction, though modest, may be a sign the central bank is turning more proactive.

· The pan-European Stoxx 600 hovered fractionally below the flatline in early trade, with basic resources stocks jumping out to 1% gains while utilities fell 0.9% to lead losses.

The pan-European Stoxx 600 hovered fractionally below the flatline in early trade, with basic resources stocks jumping out to 1% gains while utilities fell 0.9% to lead losses.