Some 16 percent of the investors polled by the bank for its monthly fund manager survey, said they were underweight U.K. equities. Looking ahead, 14 percent of the group said the U.K. is the region they most want to underweight in the coming 12 months.
Furthermore, a fifth of the investors surveyed by the bank also says the U.K. has the least favorable profit outlook, up from 12 percent last month.
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"The U.K. has entrenched its status as the world's least popular region among asset allocators this month," said BofA ML chief investment strategist, Michael Hartnett.
"Allocation to U.K. equities has fallen to its lowest level since February 2013 and this is the fourth consecutive month of decline," Hartnett said.
The 202 panelists, running a total of $556 billion of assets under management polled by the bank, are not the only ones nervous of the upcoming referendum.
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Hedge fund managers are also looking to protect their portfolios, and are trimming their long positions on sterling against the dollar, as sterling has weakened in the weeks leading up to the vote.
On average, investors have cut their positions from 5 percent of their net assets at the end of May to -1.3 percent in early September, according to French asset management group Lyxor.