Securities and Exchange Commission investigators discovered in 2006 that Bernard Madoff had misled the agency about how he managed customer money, according to documents, yet the SEC missed an opportunity to uncover an alleged Ponzi scheme.

The documents indicate the agency had Mr. Madoff in its sights amid multiple violations that, if pursued, could have blown open his alleged multibillion-dollar scam. Instead, his firm registered as an investment adviser, at the agency's request, and the public got no word of the violations.

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