FORGET the banks and the carmakers. The biggest bets that American taxpayers have made are on three less famous firms: American International Group (AIG), an insurer, and Fannie Mae and Freddie Mac, two mortgage-finance agencies. The state now owns about $170 billion of shares in banks. It has so far invested over $160 billion of equity in the toxic trio, and this number is likely to rise towards $300 billion. Include other kinds of help, such as loans, and the total pumped into the three firms could eventually reach $800 billion (see table), or 6% of GDP. “I had no idea what I was in for,” admitted Edward Liddy this month as he stepped down after a gruelling year running AIG. Americans must feel the same way.

The case that was made to taxpayers last year for bailing out the three is intact. Through its derivatives activities and giant insurance business, AIG was so entangled in the financial system that it could have brought it down. Fannie and Freddie, which own, guarantee and help securitise about half of American mortgages, were judged as vital to a healthy housing market. Banks and foreign governments held buckets of their paper, too, in the belief it had implicit state backing. Defaults would have badly hurt relations with China, the largest foreign-government creditor.

What has changed is the size of the bill. AIG’s bail-out has been revised upward four times as its losses have mounted. “They tried to put on a band aid and then realised they needed a tourniquet,” says Rob Haines of CreditSights, a rating firm. When the government first began to help the two mortgage agencies in July 2008, it said capital injections were “not something we expect”. That looks like a bad joke now. The question is no longer whether the trio will receive vast sums, but whether taxpayers will get any money back.

Of the three firms, AIG represents their best hope, even though its credit spreads are still at levels that suggest a real risk of default. The government fired a blunderbuss of money at it, with six different categories of intervention (see table). Safest are probably the direct loans from the Federal Reserve, the commercial paper that the Fed has guaranteed and the loans that it is likely to make that are secured by life-insurance policies. These instruments are fairly high up the pecking order if the firm goes bust. The $25 billion preferred-equity stake that the Fed owns in two of AIG’s insurance subsidiaries is also pretty safe: they may be worth as much as double that sum.

The danger to taxpayers comes in two forms. First, the Fed has lent $44 billion to two special-purpose vehicles, into which many of AIG’s flakiest securities have been dumped, including derivatives written on structured-credit instruments. At the end of March these vehicles were $5.4 billion in the red: unless prices recover taxpayers will ultimately take the hit. Second, the Treasury has $43 billion of preferred shares in AIG itself. So far the firm’s core book value (the value of its assets) is about equal to that, suggesting that the investment is covered.

The Fed has around 25 full-time staff sitting in AIG now, so its accounts should be more reliable. But even though AIG made a small profit in the second quarter, more losses are possible. It still has a giant portfolio of credit-default swaps that European banks use to game capital rules. These have not lost money yet, but remain a black box. And the government’s long-term plan to raise cash by spinning off or selling the traditional insurance businesses could crystallise losses. Several AIG assets sold so far have ended up fetching less than book value.

These risks, though, pale into insignificance compared with Fannie and Freddie. The two have racked up colossal losses. As Wall Street ate into their securitisation business, they branched into buying debt securities worth some $1.6 trillion. Of this about $230 billion turned out to be toxic, with losses of almost $90 billion at market prices. Future pain will come from the traditional guarantee business. The pair have underwritten $4.8 trillion of mortgages between them and delinquency rates are rising along with unemployment. Impairments are likely to be only 4-5% of the total but that would be more than enough to sink the two agencies.

The government has agreed to fund these losses with equity injections of up to $400 billion. It has invested $98 billion so far, and Rajiv Setia of Barclays Capital thinks the total cumulative capital required will be $160 billion-200 billion. It could turn out worse. The book value of the two firms, using market prices and excluding the existing equity from the state as well as tax assets, showed a capital shortfall of $280 billion at the end of June. This sum is a proxy for how much taxpayers will lose unless prices recover.

Such massive insolvency makes it hard to restructure the two agencies. Right now they are staggering on in “conservatorship”, a form of direct state control. The Treasury is backstopping their capital and the Fed is helping them refinance their debts by buying up to $200 billion of their bonds in the open market. Over time their holdings of securities will probably be wound down. The guarantee business will be harder to kill. The government plans to decide on Fannie’s and Freddie’s futures by February, but the agencies are likely to survive under state control or as co-operatives with state guarantees.

This extraordinary resilience reflects the widespread political lust in America for subsidising housing. Anyone who doubts this should look at Ginnie Mae, another fully state-owned agency which guarantees and bundles mortgages, usually of below-average quality, that are insured by the government. Fannie and Freddie are now being conservative about writing new business, but Ginnie is enjoying its own bull market, issuing guarantees at a furious rate. It is expected to have a trillion dollars outstanding by next year. “We are seeing a gravitation of the subprime universe from Fannie and Freddie to Ginnie”, says Mr Setia. It will be a miracle if taxpayers get their money back from Fannie and Freddie. Worse, there is a chance the disaster will be repeated.