The restructuring of Fannie Mae and Freddie Mac will hinge on who gets to control their credit guarantee businesses, where they buy newly originated mortgages from banks, assemble them into pools of mortgage-backed securities (MBS), stamp them "guaranteed," and then sell them to investors.

For providing this function, Fannie and Freddie earn guarantee fees, and until recently, they had experienced modest losses.

The credit guarantee business is not only valuable, but also provides crucial liquidity to the mortgage and housing markets — thus the political and economic stakes are high. Who should control Fannie and Freddie's credit guarantee businesses? The choices are: investors, the government, or big banks.

How can the MBS business be "valuable" when the institutions have failed?

In normal times, Fannie and Freddie earn wide margins on their $4.6 trillion portfolio of guaranteed MBS, thanks to what is a natural monopoly (or "duopoly," to be precise).

Fannie and Freddie dominate the MBS market because their securities trade with superior liquidity that other financial issuers cannot match. The liquidity reflects their enormous market share as well as special advantages. For example, banks can hold Fannie and Freddie's MBS without concentration limits.

Not only is the credit guarantee business profitable, but it also provides significant liquidity to the capital markets.

Fannie and Freddie MBS help put a lot of American voters in houses at reasonable cost. I don't think many people want to shut down this business, especially right now while the housing market is still wobbling.

The firms got into trouble with their MBS in part because they stretched too far, guaranteeing risky loans like "alt-A" mortgages.

Even if they hadn't stretched, it would have been difficult for them to survive the recent crash, given their mortgage focus, modest capital cushions, and aggressive housing goals.

Looking ahead, unless we experience another housing boom, the credit guarantee business should return to steady profitability for many years to come.

So who should control this valuable, important business?

Fannie and Freddie have operated under a mixed public-private model, where private capital funds a public mission.

I believe investors would recapitalize Fannie and Freddie in a heartbeat, as they well understand the value of the MBS business — provided they could get comfortable with the continuation of this mixed model.

However, the mixed model has become too controversial and is no longer workable.

Regulators have long worried about the moral hazard of the mixed model.

Competitors have long claimed the model is unfair.

There are no longer any comparables. And now people blame the mixed model for the two GSE's expensive failures.

As an alternative to private investors, the government could take over Fannie and Freddie, explicitly guarantee their obligations, and operate them as a direct lender, much like the Federal Housing Authority.

But this would add nearly $5 trillion to the federal government's debt load. And a policy of permanently nationalizing the U.S. mortgage market has few supporters.

This leaves us with the big banks, which would be delighted to take over Fannie and Freddie's credit guarantee business.

This option, too, would be unpopular. But perhaps there is a "horse trade" that could make this a workable political solution.

• For starters, according to an idea whose supporters includes Alex Pollock of the American Enterprise Institute, the government could auction one or more charters to operate an MBS securitization franchise with all the special advantages of Fannie and Freddie's securities.

The purchase price for these charters would help offset some of taxpayers' losses from recent bailouts.

• With the MBS business now operated by big banks, the government could place Fannie and Freddie into run-off, which would eliminate $1.5 trillion in outstanding U.S. agency debt — a helpful move at a time when our country's debt load is mounting.

The government could also wind down Fannie and Freddie's cousin, the Federal Home Loan Bank system, eliminating another $900 billion in U.S. agency debt.

• Finally, the government could introduce new programs to provide mortgages to certain segments of the market, like low-income and first-time homebuyers — — although these should be small and targeted, so that they promote strong communities without fueling a future boom and bust.

Kenneth A. Posner is the author of "Stalking the Black Swan: Research and Decision-Making in a World of Extreme Volatility" (Columbia University Press, 2010) and a former analyst who covered Fannie Mae and Freddie Mac.