The Australian share market was flat in quiet trading before a US holiday and the outcome of a two-day policy meeting of the Bank of Japan.

US markets were due to be closed for Martin Luther King Day.

The benchmark S&P/ASX 200 rose 0.1 per cent to 4777.5 points after being confined to a narrow range of 4762.6 to 4779.7. The index hit a 20-month high of 4787.2 last week having risen 10 per cent since mid-November.

The market was cautious after pricing in expectations of further policy stimulus from the BOJ as well as an improved world-wide growth outlook stemming from recent better-than-expected economic data in China and the U.S.

"I remain bullish equities but I wouldn't be buying now because a lot has been priced into the market," IG chief market strategist Chris Weston said. "Valuations are still reasonable but we've had a good run and domestic earnings season is coming up.