Investors who poured $1.26 trillion into bond funds in the past six years pulled out record amounts of cash last month, leaving the world’s biggest fixed-income managers struggling to stem the flow.

The funds saw $61.7 billion of withdrawals as money market mutual fund assets rose $8.17 billion in the week ended June 25, according to TrimTabs Investment Research and the Money Fund Report. Bank of America Merrill Lynch’s Global Broad Market Index dropped 2.9 percent in the past two months, the most since the inception of the daily gauge in 1996, as Federal Reserve Chairman Ben S. Bernanke laid out possibilities for reducing the $85 billion in monthly bond purchases supporting the economy.

Market bears say losses are just getting started because yields barely exceed inflation, leaving little relative value in bonds as the global economy improves. Pacific Investment Management Co., BlackRock Inc. and DoubleLine Capital LP, which together oversee about $6 trillion in assets, said the worst is already over because the securities are fairly valued.

“We are at a definite inflection point,” Richard Schlanger, who helps invest $20 billion in fixed-income securities as a vice president at Pioneer Investments in Boston, said in a telephone interview on June 28. “If this thing continues in this vein, people are going to throw in the towel and you’re going to get this pain trade. And the markets can’t take it. They’d rather see a gradual rise in short-term rates versus a precipitous rise.”

Lehman Collapse

Pioneer has held a smaller percentage of Treasuries in 2013 than is contained in the benchmark index against which it tracks performance, and is investing in short-term floating-rate notes and non-agency mortgage-backed securities, Schlanger said.

The Bank of America Merrill Lynch U.S. Broad Market index has plummeted 3.5 percent in May and June, the worst decline since a 3.9 percent dive in the two months ended October 2008 as the failure of Lehman Brothers Holdings Inc. ushered in the worst financial crisis since the Great Depression. Treasuries lost 3.3 percent in the last three months, for their third straight quarterly decline.

Record bond-fund redemptions in the month ended June 24 surpassed the previous high of $41.8 billion set in October 2008, according to TrimTabs in Sausalito, California.

In the most-recent period, investors pulled $52.8 billion from bond mutual funds, typically owned by individuals, and $8.9 billion from exchange-traded funds, or ETFs, which both institutional and private investors buy. Equity funds shrank by $2 billion, bringing their total reduction to $386 billion over the past six years.

Higher Liquidity