NEW YORK (CNNMoney.com) - A year ago, Bill Gross, the manager of the world's biggest bond fund, said he believed the 10-year Treasury rates could stay in the 3- to 4.5-percent range during the next three to five years.

Now, with the 10-year above 5 percent, Gross, manager of the PIMCO bond fund, admitted in his most recent forecast that he was obviously off-base.

PIMCO's Bill Gross now sees the 10-year in a 4 to 5.5% range.

"Surging global growth... has caused central banks and indeed private investors to enforce higher real yields as recompense," he wrote in a commentary on his site. "5.20% 10-year Treasuries are sort of outside of our forecasted range, wouldn't you say? 'My bad' – to use Generation Y jargon."

Still, Gross said that he believes rates will stay only slightly above inflation levels compared to historical norms, and he sees the 10-year Treasury in a range of 4 to 5.5 percent going forward.

"Having already acknowledged the partial reversal of the recent year's conundrum, it is tempting to go all the way and forecast a return to real rate normalization," he wrote. "We are reluctant to do so, however, in the face of a still-existing global savings excess, diminished as it is. Additionally, central banks have been/will likely remain cautious in their tightening cycles."

In his latest forecast, Gross is basing his new rate range on expectation of modest inflation of 1 to 3 percent on a global basis.

Gross said that his firm sees a continued weakening of the dollar and says it believes that dollar-based assets and the dollar itself should underperform global alternatives.

"When not countered by cyclical considerations, PIMCO portfolios will likely feature increasing international diversification in foreign currency terms," he wrote.

For a look at Bill Gross' typical work day, click here.