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By Dan Wilchins

NEW YORK, May 22 (Reuters) - Lehman Brothers Holdings Inc LEH.N has not written down bad assets enough, and should raise large amounts of capital to support its assets, short-seller David Einhorn said in a presentation to investors.

The presentation was the latest volley from Einhorn, who has sold Lehman's shares short in a bet they will decline, against the fourth-largest U.S. investment bank.

Lehman for its part has said it is cooperating with regulators that are looking at whether short-sellers are spreading market rumors.

A spokesman for Lehman declined to comment on Einhorn's latest remarks.

Speaking at the Ira W. Sohn Investment Research conference, Einhorn said Lehman Brothers only wrote down a $6.5 billion collateralized debt obligation portfolio by about $200 million in the first quarter, when most investment banks were recording much bigger drops in the value of those assets.

That small write-down is surprising given that Lehman said in a footnote to its quarterly filing with regulators that about 25 percent of the CDOs were junk rated, Einhorn said. The CDO portfolio in question does not have subprime mortgage exposure, but does have exposure to small business loans, consumer loans, and other assets.

Einhorn said that when asked about the magnitude of this write-down, Lehman Chief Financial Officer Erin Callan did not explain the first-quarter write-down, but said Lehman would expect to record further write-downs in the second quarter on the assets.