The bank's analysis of the views of 255 managers overseeing $664 billion (£409bn) of assets found that their anxieties about issues such as the so-called fiscal cliff in the United Sates and the debt problems of the European Union have eased.
Global growth expectations are at their highest since March 2011, as optimism about China's prospects has surged.
Worries over the eurozone debt crisis fell for the seventh month in a row. Just 22% of fund managers see it as the number one tail risk, an unlikely but potentially devastating event, down from 65% in June.
But 31% of asset managers see France as the biggest risk to European Union stability, ahead of Spain, Italy and Greece.
This is despite political turmoil in Italy given the looming resignation of technocrat prime minister Mario Monti.
John Bilton, European investment strategist at BofA Merrill Lynch Global Research, said: "I think the reason France is being cited is we are waiting to see what some of the French government's policies will mean."
He said as France is one of the two largest eurozone economies, "it is going to cause some problems" across the continent and would be too large for a bail-out using existing structures.
This would be of concern to companies in the UK who export to other EU states and have seen demand subdued by the eurozone sovereign debt crisis.
BofA Merill Lynch is focusing on three investment themes for the coming year: the recovery stage of the global cycle, European stabilisation and cash returns by companies.
This has seen it highlight sectors such as basic materials to harness global growth, banking stocks to benefit from stabilisation and pharmaceuticals for the cash.
Investors are becoming increasingly optimistic about the eurozone and have a stronger position in eurozone equities than those of the US for the first time since November 2010.
The number of investors viewing the US fiscal cliff, a set of tax rises and spending cuts that will begin in the absence of a spending agreement, as the biggest tail risk has fallen to 47%, down from 54% in November.
But the fiscal cliff remains the number one worry of investors.
A large majority of investors expects China's economy to strengthen in the coming year.
"The bulls are back in China, while policy makers elsewhere put bears onto the back foot," said Michael Hartnett, chief investment strategist at BofA Merrill Lynch.