UBS, which has been hit hard by the recent "subprime" crisis in the United States, has been struggling to regain investor confidence since posting a series of heavy losses.
Earlier writedowns had prompted shareholders to demand radical action to turn the business around.
Last month, shareholders approved the appointment of a new chairman and a capital increase of $14.9bn in the hope of turning the page on the bank's historic loss.
UBS said on Tuesday that it has reduced its exposure to subprime-related assets by 60 per cent since the third quarter of 2007.
The bank said it will cut 2,600 jobs in its investment banking arm, which was blamed for the majority of failures that have led to the record writedowns of $37.4bn since last summer.
A further 2,900 jobs will go in other parts of the business, bringing the total number of posts cut by the middle of 2009 to 5,500.
Marcel Rohner, the bank's chief executive, said: "We can see tangible effects as a result of our initial responses to the losses.
"While our exposure is still subject to swings in market conditions, we see market demand for these securities returning in certain areas and at the current level of valuations."
UBS sent a letter to its Swiss customers on Tuesday, acknowledging their "concern and disappointment" and reassuring them that "the bank remains strong" thanks to its solid capital base.
Rohner said recent data indicated that market conditions were improving, but that the financial environment was likely remain difficult for the rest of the year.