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MBIA provided insurance to issuers of these (junk) mortgage securities. Since MBIA had a triple A rating, investors felt anything it insured was a safe bet. However, after the mortgage security crash, MBIA learned it was way overextended.
AIG also had insured these high-risk securities, and issued loan equivalents which backed them.
Now, my question is, why did the US really bail out AIG, a company which does most of its business abroad, and which largely evades US taxation? And why was the deal structured to avoid control by the US? Yes, AIG is still run by its executives under the bailout plan.