* Japan allocation back to flat - BoFA Merrill's survey
* Nikkei drops off 4-week high on profit-taking
* Cosmetic firms, other China-related shares hit hardest
* Limited reaction to Brexit saga
By Ayai Tomisawa and Hideyuki Sano
TOKYO, Jan 16 (Reuters) - Japanese shares retreated from a four-week high on Wednesday as investors took profits on firms exposed to China's economy a day after they enjoyed a boost from Chinese stimulus hopes.
Despite small gains on Wall Street the previous day, the Nikkei share average dropped 0.6 percent to 20,442.75, after briefly touching a four-week high of 20,580.25.
Bank Of America Merrill Lynch said in its fund manager survey that as the dollar-yen was sold off and global investors became more concerned about prospects for the global economy, their Japan equity allocation fell to net minus 1 percent in January, the first minus figure since 2016.
Market analysts said that although overly pessimistic views for the global economy have receded somewhat compared to last month, there are still underlying concerns.
"The market has rebounded from its low last month as investors look to positive catalysts, such as developments in U.S.-Sino trade talks," said Yutaka Miura, a senior technical analyst at Mizuho Securities.
"But people are cautiously focused on the dollar, U.S. economic growth and the impact from U.S. government shutdown on the private sector. So they are careful about taking positions."
The New York Federal Reserve's business activity index declined more than expected to its lowest level since May 2017 in another sign of troubles in the manufacturing sector.
On Wednesday, as with most equity markets, Japanese stocks shrugged off British lawmakers rejection of Prime Minister Theresa May's Brexit deal.
Companies that are seen as dependent on Chinese demand met heavy selling, as investors tried to take advantage of their gains made the previous session after Beijing signalled more stimulus measures to come.
Among them were cosmetic firms, with Shiseido tumbling 2.4 percent, nearly offsetting Tuesday's 2.7 percent gains.
Rival Kose dropped 3.5 percent despite a local media report that its April-Dec profits are seen hitting a record for that period.
Shippers dropped 1.2 percent while Murata Manufacturing, a big supplier to Apple, dropped 3.0 percent, after a 5.3 percent jump the previous day.
Investors also took profits from other recent gainers. Hitachi fell 2.6 percent after a 16 percent surge in the previous two days, helped by a media report the firm is considering withdrawing from nuclear plant business.
The broader Topix fell 0.3 percent to 1,537.77. (Editing by Simon Cameron-Moore)