Pacific Investment Management Co., the world’s largest fixed-income manager, had $39 billion in net redemptions during the third quarter as investors fled bonds in anticipation of rising interest rates.

Allianz SE, the Munich-based insurer that owns Pimco, said that its other asset-management unit Allianz Global Investors had net deposits of $1.3 billion in the quarter. Pimco’s share of Allianz’s money-management assets fell by 2 percentage points this year to 84 percent as of Sept. 30, while the AGI unit’s share rose by 1.5 percentage points to 14 percent, according to a statement today announcing third-quarter earnings.

Federal Reserve Chairman Ben S. Bernanke told Congress in May that the central bank may pull back its unprecedented stimulus, prompting investors to flee bond offerings that buy traditional assets such as Treasuries, corporate bonds and mortgages, while putting money into strategies that would shield them from rising interest rates.

“While core bond categories have experienced outflows industrywide, we have continued to see inflows into our absolute return and unconstrained strategies,” Mark Porterfield, a spokesman for Newport Beach, California-based Pimco, said in an e-mailed statement. Pimco had $1.97 trillion in assets under management as of Sept. 30.

Pimco’s largest fund, Bill Gross’s Total Return Fund, lost its title as the world’s biggest mutual fund after shrinking to $248 billion following $33.2 billion in estimated redemptions this year through October, according to research firm Morningstar Inc. Investors have pulled money from its U.S. mutual funds every month since June, totaling $44 billion, based on Morningstar estimates.