If you own shares of Fannie Mae (FNM) or Freddie Mac (FRE), you're sitting on a whole lot of nothing, according to analysts at Keefe, Bruyette & Woods.

The analysts cut the price target on both stocks to zero and downgraded them to underperform.

In order for these mortgage giants to survive, the analysts said, they need to be recapitalized from the banking industry. But even if that happens, their common and preferred stocks will be worthless.

The government has funneled $98 billion in capital into Fannie and Freddie, according to MarketWatch.

Both stocks dropped after the analyst note came out. Fannie Mae shares were down 21.9% to $1.14 and Freddie shares were down 21.5% to $1.35.

Fannie and Freddie buy mortgages from lenders and bundle them into securities, according to MarketWatch. They also guarantee payment, and accounted for 68% of all mortgage originations in 2009.

The KBW analysts suggested the government separate out the Bad Fannie and Bad Freddie from the good. That way, the government can cut its losses and create an exit strategy from the industry.