A lot of people have been asking that question, for obvious reasons. The short answer is that no one quite knows, and that's the problem.
During the Lehman failure, the Federal Reserve and other agencies put quite a lot of effort into making sure that the ripple effects didn't spread too far in the markets where Lehman was a major counterparty. They were successful: the unwinding of Lehman's positions has actually been rather smooth, though slow and not particularly happy for the counterparties. What they hadn't known, and indeed, couldn't really have known, was that the effect on Lehman debt would cause the value of a smallish money market fund aimed at institutional investors would break the buck. And because breaking the buck is so rare--the last major one had occurred in 1994--they certainly didn't see what would happen next, which is that the commercial paper market would completely freeze up, threatening massive effects in the real economy, like firms not being able to make payrolls.
What hidden issues like this lurk in a Citigroup bankruptcy? Compared to Citigroup, Lehman was a simple entity; it borrowed some money, it issued some securities, it bought and sold some other securities. Citigroup is a bank, a trading operation, an insurer . . . and it has commercial banking operations in something like 119 countries, all of whom have their own opinion about what should happen to the company, and regulatory authority over at least a piece of it. It's tempting to think that the Lehman bankruptcy has already exposed the potential problems from any collapse
Then there are the effects we can predict. If we really let Citigroup go bust--wipe out everyone except the depositors up to the FDIC insured limit--there are some fairly predictible effects. Being an economics writer, and therefore prizing gains from trade, I will outsource my explanation to another blog:
Remember back to last September. What was the lesson of Lehman Brothers? The most important asset a bank has is confidence. If people are confident in a bank, it can continue to do business; if not, it can't.
For the last six months, where has that confidence been coming from? Not from the banks' balance sheets, certainly. And not, I would argue, from the dribs and drabs of capital and targeted asset guarantees provided by Treasury and the Fed. It has been coming from a widespread assumption that the U.S. government will not let the creditors of large banks lose money, out of fear of repeating the Lehman debacle.
The story goes something like this. Let's say that Citigroup were restructured - via bankruptcy, or via government conservatorship - in such a way that creditors did not get all their money back. (None of this applies to FDIC-insured deposits or to recently-issued senior debt that is explicitly guaranteed by the government.) They might be forced to convert debt for equity, or they might be stiffed altogether. The first-order concern is that this would have ripple effects that could take down other financial institutions. According to Martin Wolf, bank bonds comprise one quarter of all U.S. investment-grade corporate bonds; losses would be spread far and wide, hitting other banks, pension funds, insurance companies, hedge funds, and so on. If Citigroup did not support its derivatives positions, then institutions that bought credit default swap protection from Citi would face further losses. (I believe that most U.S. banks were net buyers of CDS protection, however.) The fear is that it will be impossible to predict how these losses will be distributed and who else might go down.
The second-order concern is bigger. After all, Lehman did not seem to force any major financial institution into bankruptcy, although it may have twisted the knife that AIG had already stuck in itself. Once investors figure out that bank debt is not safe, they will refuse to lend to any banks, and we are back in September all over again. Or almost: it is possible that the Federal Reserve's massive efforts to provide liquidity to the banking system will be enough to keep banks functioning. But who wants to take that risk?
This is why, for the last five months, the government has been doing everything it can to imply that bank creditors (at least for "systemically important" banks) will be protected, without saying so explicitly, because that would suddenly increase the potential liabilities of the government by trillions of dollars.
Would the cost of letting the bank fail exceed the cost of bailing them out? Impossible to say. But the cost of implying you won't let the bank fail is definitely smaller than either actually bailing it out, or letting it go to the devil. Geithner et al. are hoping that the implication will be enough to make the actual act unnecessary.