PIMCO's flagship Total Return Fund
was hit hard by investor redemptions in 2011, but this year it is a less famous fund at the world's biggest bond shop that is bleeding the most.

The PIMCO Unconstrained Bond Fund
, the firm's go-anywhere bond fund, which seeks to minimize risk from systemic shocks, saw an estimated net outflow of $1.69 billion in the first quarter, according to data compiled by Morningstar.

The investor redemptions at the Unconstrained Fund are nearly five times as much as the outflow at the JPMorgan Strategic Income Opportunities Fund, a comparable fund.

In fact, it's been a bad stretch for the Unconstrained Bond fund with $14.1 billion in assets under management. Morningstar says the fund has suffered the largest cash outflows in its category in each of the past three quarters.

My impression is that returns haven't been as strong as people had hoped and so some investors might be getting out, said Eric Jacobson, director of fixed-income research at Morningstar.

In the second half of 2011, PIMCO Unconstrained saw estimated net outflows of $2.47 billion.

All told, the PIMCO Unconstrained fund has not performed poorly.

In 2011, the fund landed in the top quartile of its category with returns of 0.64 percent, according to Morningstar, which added that its category posted negative returns of 1.29 percent.

So far this year, PIMCO Unconstrained is posting returns of 1.81 percent. Its peers are outperforming with average returns of 3.14 percent. PIMCO, which stands for Pacific Investment Management Co., oversees more than $1.77 trillion in assets.

Jacobson said: Investors expected this fund to be the perfect investment and not suffer when rates rise, but hoping too that it would thrive in every other environment. It is impossible to be that perfect.

As its name implies, the PIMCO Unconstrained Bond Fund includes a bond selection that is unconstrained by maturities, credit quality or region, and the ability to protect against rising interest rates. But last year and during some periods this year, Europe's debt crisis has driven investors worldwide to the safety of U.S. Treasuries, pushing down interest rates and hurting managers who expected rates to climb.

Jacobson of Morningstar said the fund held relatively short duration and took on other kinds of risks, so it did not rally with Treasuries last year.

He added: There is nothing fundamentally wrong with the fund. I think expectations were so high that investors have been taken aback by any down quarters. Investor thinking has been that the fund would rally no matter what.

On its website, PIMCO said Unconstrained's investment approach may lead to concentrated exposure in areas of the bond market that entail greater risks.

For example, it may invest up to 40 percent of total assets in below-investment-grade securities, which carry a higher degree of credit risk, and may be speculative and more volatile; it may also invest without limitation in securities denominated in foreign currencies and in U.S. dollar-denominated securities of foreign issuers, and can assume up to 35 percent exposure in non-U.S. currency.

PIMCO did not respond to interview requests.

Last year PIMCO's giant $252 billion Total Return Fund saw about $5 billion in redemptions. It was the first time in many years that the Bill Gross-led fund saw net outflow in a given year.

This year, however, money is flowing back into the Total Return Fund. In the first quarter, it took in $1.7 billion in new money, as performance rebounded.

(Reporting By Jennifer Ablan and Matthew Goldstein; Editing by Andrew Hay)