These exotic instruments acted as a form of insurance for the securities. In effect, A.I.G. was saying if, by some remote chance (ha!) those mortgage-backed securities suffered losses, the company would be on the hook for the losses. And because A.I.G. had that AAA rating, when it sprinkled its holy water over those mortgage-backed securities, suddenly they had AAA ratings too. That was the ratings arbitrage. “It was a way to exploit the triple A rating,” said Robert J. Arvanitis, a former A.I.G. executive who has since become a leading A.I.G. critic.

Why would Wall Street and the banks go for this? Because it shifted the risk of default from themselves to A.I.G., and the AAA rating made the securities much easier to market. What was in it for A.I.G.? Lucrative fees, naturally. But it also saw the fees as risk-free money; surely it would never have to actually pay up. Like everyone else on Wall Street, A.I.G. operated on the belief that the underlying assets  housing  could only go up in price.

That foolhardy belief, in turn, led A.I.G. to commit several other stupid mistakes. When a company insures against, say, floods or earthquakes, it has to put money in reserve in case a flood happens. That’s why, as a rule, insurance companies are usually overcapitalized, with low debt ratios. But because credit-default swaps were not regulated, and were not even categorized as a traditional insurance product, A.I.G. didn’t have to put anything aside for losses. And it didn’t. Its leverage was more akin to an investment bank than an insurance company. So when housing prices started falling, and losses started piling up, it had no way to pay them off. Not understanding the real risk, the company grievously mispriced it.

Second, in many of its derivative contracts, A.I.G. included a provision that has since come back to haunt it. It agreed to something called “collateral triggers,” meaning that if certain events took place, like a ratings downgrade for either A.I.G. or the securities it was insuring, it would have to put up collateral against those securities. Again, the reasons it agreed to the collateral triggers was pure greed: it could get higher fees by including them. And again, it assumed that the triggers would never actually kick in and the provisions were therefore meaningless. Those collateral triggers have since cost A.I.G. many, many billions of dollars. Or, rather, they’ve cost American taxpayers billions.

The regulatory arbitrage was even seamier. A huge part of the company’s credit-default swap business was devised, quite simply, to allow banks to make their balance sheets look safer than they really were. Under a misguided set of international rules that took hold toward the end of the 1990s, banks were allowed use their own internal risk measurements to set their capital requirements. The less risky the assets, obviously, the lower the regulatory capital requirement.

How did banks get their risk measures low? It certainly wasn’t by owning less risky assets. Instead, they simply bought A.I.G.’s credit-default swaps. The swaps meant that the risk of loss was transferred to A.I.G., and the collateral triggers made the bank portfolios look absolutely risk-free. Which meant minimal capital requirements, which the banks all wanted so they could increase their leverage and buy yet more “risk-free” assets. This practice became especially rampant in Europe. That lack of capital is one of the reasons the European banks have been in such trouble since the crisis began.

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At its peak, the A.I.G. credit-default business had a “notional value” of $450 billion, and as recently as September, it was still over $300 billion. (Notional value is the amount A.I.G. would owe if every one of its bets went to zero.) And unlike most Wall Street firms, it didn’t hedge its credit-default swaps; it bore the risk, which is what insurance companies do.