Please note that none of the four options discussed should give false hope to holders of the common stock.
The AEI being the AEI favors the privatization option. in which case my best guess is the shareholders would end up with some warrants or an equity stub as a residual claim on the future cash flows of the former GSE's.
From the American Enterprise Institute for Public Policy Research:
The renewed interest in Fannie Mae and Freddie Mac is premature. They are currently the mainstays of the U.S. housing market--more important now than they were before being placed in a government conservatorship in September 2008. Many observers do not believe the two government-sponsored enterprises (GSEs) can survive the immense losses they will cause taxpayers, but this is far from true. For Fannie and Freddie to be eliminated, a new mortgage-financing system must take their place, but there is not even a hint of a replacement on the horizon. Once the housing market recovers, the GSEs will still be the only game in town, and supporting them will continue to be the course of least resistance for Congress. Moreover, it will not be easy to implement any of the alternatives to reestablishing Fannie and Freddie as GSEs. Nationalizing or reorganizing them as public utilities would both have significant drawbacks, while privatizing the GSEs--the most sensible approach--would require a major change in public attitudes about securitization. Sadly, in the absence of viable alternatives, their restoration as GSEs seems the most likely outcome....MORE (8 page PDF)HT: EconBlog Review who writes:
...When talking heads comment on debt-to-GDP ratios and similar metrics, they are often shilling for their own interests. Not only do they generally ignore unfunded liabilities such as Social Security, they assign a present value of zero to this sort of GSE obligation.
The U. S. once had a Federal Government that was serious about financial responsibility. Those days are long gone. One way or another, however, bookkeepers and accountants have their day. The road down which cans get kicked is not smooth, straight and downhill forever.