NEW YORK — Former Fannie Mae chief executive Daniel Mudd must face a lawsuit in which the Securities and Exchange Commission accuses him of misleading investors about the entity’s exposure to risky loans.

US District Judge Paul Crotty in New York Friday rejected a request to dismiss the case by Mudd and Enrico Dallavecchia and Thomas Lund, two other ex-Fannie Mae executives.

The SEC alleged that Fannie Mae underrepresented its exposure to subprime and so-called Alt-A loans, which require little or no documentation from borrowers.

“The SEC has plausibly alleged that Mudd, Dallavecchia, and Lund consciously assisted the venture to misstate FNMA’s subprime and Alt-A exposure in an active way,” Crotty wrote.