KBW Inc.'s Keefe, Bruyette & Woods Inc. cut its price targets for Fannie Mae and Freddie Mac to zero Monday, saying the government should recapitalize the two and wipe out what remains of shareholders' equity.

"The only viable option to limit taxpayer expense and recapitalize Fannie Mae and Freddie Mac is to set up a Bad Fannie and Bad Freddie," the KBW analysts wrote in a research note to clients.

Their previous price target was $1 a share.

The government could spin off new companies, the KBW analysts wrote, that are cooperatively owned by mortgage lenders such as Wells Fargo & Co. and Bank of America Corp. that sell loans to Fannie and Freddie, mirroring the Federal Home Loan Bank system.

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