No other investor has played the bailout trade as often and as successfully as the Fairholme funds manager. Will he be able to do it again?

FORTUNE --Ever since the government began bailing out banks and others a few years ago, we have had a debate about who should benefit. The economy? Yes, that's the point. Borrowers? Eventually. Taxpayers? Always, except in the case of small banks and automakers, then no. Executives? Never. Investors? I don't know. Maybe, yes, but we won't like it.

We're headed for another round in the debate. Fannie Mae and Freddie Mac, which had to be bailed out by the government in late 2008, are making some serious money again. And that's raising the prospect that like AIG and others before them, the two giant mortgage guarantors might soon be able to pay back the government and reemerge as fully private companies. Hedge funds and other investors are lining up to ride the government's coattails. Shares of Fannie (FNMA) and Freddie (FNCC), which were de-listed from the NYSE in 2010 and until recently traded for pennies, are up 607% and 523% in the past six months in over-the-counter transactions.

Other investors are suing the government saying the recent turnaround shows that Uncle Sam unfairly seized their shares back in 2008. But that seems to ignore the fact there wouldn't have been a turnaround if not for the government's intervention, so good luck with that one.

MORE: The rebirth of Fannie and Freddie

Between them, Fannie and Freddie now guarantee 80% of the mortgage market in the U.S., or roughly double their combined market share before the housing crash. As Shawn Tully explains in the current Fortune, the government's policy decisions while managing Fannie and Freddie have had the unintended consequence of freezing out private capital.

That hasn't stopped private investors from circling Fannie and Freddie. Earlier this month, Bruce Berkowitz, who runs mutual fund firm Fairholme Capital Management, said that his funds had accumulated preferred shares in the two mortgage giants that are worth $2.4 billion at par value. Those shares now trade for about 20% of that original value, which means Berkowitz has bet around $500 million on the revival of Fannie and Freddie.

Perhaps no other investor has played the bailout trade as often and as successfully as Berkowitz, though even he has mistimed some bets. He made money on AIG (AIG) and Bank of America (BAC). But Berkowitz bought Citigroup (C) too early and sold too soon in early 2012, about five months before the shares' recent climb began. Fairholme had impressive performance in 2012, but only after a lackluster 2011, and Berkowitz lost investors along the way. Still all told, Berkowitz's flagship fund has produced annualized return of 12.6% in the past five years. But in Fannie and Freddie there is some indication that this time Berkowitz's bailout bet has much lower odds of paying off.

MORE: The Fed's other trillion dollar problem

Much of the discussion around Berkowitz and others' bet on Fannie and Freddie has been about whether they really think the government would reprivatize the companies, or whether they are just buying the mortgage guarantors' shares because they have been going up. But another part of the debate is just how much investors should be able to benefit from bailouts.

Berkowitz, through a spokesman, declined to comment on his Fannie and Freddie investment, saying the fund was in a "quiet period."

But Berkowitz appears to believe that Fannie and Freddie will be reborn, or at least should be. In a statement posted on his firm's website, Berkowitz predicted that taxpayer money extended to Fannie and Freddie will be paid back in full. As a result, he argues that there should also be equitable treatment for Fannie and Freddie's "taxpaying" shareholders as well, including "community banks, insurance companies, and mutual funds," which now includes Berkowitz's firm. "It's the American way," says the statement.

Some would disagree. The government put Fannie and Freddie into conservatorship nearly five years ago, eventually pumping $189 billion into the two companies and taking on the risk of any failure. Berkowitz and others have only showed up on the scene in the last few months, now that the companies are minting money again.

Bert Ely, a veteran Washington, D.C.-based banking consultant, says regulators tell him there is no plan to make any payouts to shareholders. So he sees the claims of investors that Fannie and Freddie could soon live off the government's dole as disingenuous. "It's bullshit," says Ely. "I've been told that the terms of the conservatorship are that the perferreds will never have any real value."

Still, Senators Bob Corker (R-Tenn.) and Mark Warner (D-Vir.) have been working on a bill that would wind down the mortgage guarantors, and replace then with a new type of private insurance. Fannie and Freddie's remaining portfolios would be put into what's called run-off, meaning they wouldn't back any new loans, but they would be able to collect a steady stream of profits from what they already have outstanding. As such, some see the plan as paving the way for investors to share in whatever profits are generated by the process.

MORE: Bruce Berkowitz is back

Others argue that Fannie and Freddie shareholders deserve the same treatment as those of AIG, Citigroup, or any of the other banks that got money from the government. Investors, like Berkowitz, who bet on those companies' rebounds have made money. And you could make the case that investors who are buying in now will make it easier for the government to exit Fannie and Freddie, and are therefore serving a useful purpose.

The difference is in all of those other bailouts the benefits to shareholders were more backdoor. They happened because the firms didn't collapse, the economy improved, and the shares that had been left for dead eventually rebounded. In the case of the Fannie and Freddie preferreds, Congress would have to pass a law that would specifically reinstate the dividends, directly and publicly rewarding hedge funds that have bet on the turnaround. And that kind of thing can be palatable if everyone in the economy is doing better. But how long until we can say that?

Putting the politics aside, there's still the question of whether there would be money left for private shareholders once the government is paid back, or at least enough to make a current investment worth it. Fannie got $117 billion from the government. By the middle of this year, the mortgage guarantor expects to have paid the government $95 billion. But a good deal of those payments come because of a one-time $60 billion tax benefit that Fannie got in the first three months of the year. Exclude that and Fannie made just $8 billion in the first quarter.

Originally, Fannie was supposed to pay a 10% dividend to the government on its preferred shares. But the deal was altered last year. The government now gets whatever profits Fannie produces as a divided. So technically, even though Fannie has paid the government 80% of what Fannie received, it still owes Uncle Sam $117 billion.

If Fannie was to go back to the original deal, to consider a hypothetical scenario, and was given a five-year window to repay the government, it would owe roughly $35 million in the first year in dividends and debt repayment. Based on its current profits that wouldn't leave any money left over for preferred shareholders. (It would actually still be in the red a bit, but let's ignore that for now.) By the second year, because its government debt would be reduced, Fannie would break even on its government payments, still leaving no money for a dividend to private shareholders.

By the third year, Fannie would have roughly $1.5 billion to pay out to preferred shares, of which there are roughly 785 million or around $2 a share. The payment would roughly double the next year. By that math, Berkowitz is likely to see a $1 dollar return on his recent $5 dollar investment four years from now, or about 5% a year. Not the type of returns Berkowitz and his investors are looking for.

So Berkowitz must be factoring in an improvement in Fannie's operations in his model, which does make some sense given that the housing market is improving. But, if Fannie is truly put in run-off mode, it's not clear how much it would benefit from the real estate rebound. Still, Berkowitz could be betting on the government refloating the company. But that would have to involve some write-down of Fannie and buildup of capital, which would significantly dilute Berkowitz's shares, if not wipe them out.

"In any assessment that I have done, I don't see how there will be much value left for its shareholders once the government is paid back," says Ed Mills, a Washington policy analyst at FBR Capital Markets.

And neither do I, even if we thought it was OK to do so. And that's a big if.