Altogether, a quarter of the staff at this division of the US investment bank could be made redundant, particularly in London and to a lesser degree in New York, the newspaper said, quoting people familiar with the matter.
The debt market is declining mainly because of lower interest rates, which have led many banks to cut staff.
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Two weeks ago Colm Kelleher, president of Morgan Stanley's investment banking and securities businesses, said it was grappling with the size of its fixed-income branch in the face of a shrinking supply of trading business.
Morgan Stanley posted a 42 per cent fall in fixed-income trading revenue in the third quarter.
Steven Chubak, an analyst with Nomura Holdings, told the Journal that Morgan Stanley's fixed-income division would post a five percent return on equity this year, compared to nine percent for the company overall.