Undernews is the online report of the Progressive Review, edited by Sam Smith, who covered Washington during all or part of one quarter of America's presidencies and edited alternative journals since 1964. The Review has been on the web since 1995. See main page for full contents

June 30, 2009


This is just a short excerpt from an interesting article in Plus on how mathematics got Lehman Brothers into a big mess

Plus, UK - CDO is a lot riskier than bank deposits, but Lehman Brothers, like many investors, didn't seem to know that. Let's go back to our original model. The first source of error is that we have assumed that each investor has a 3% chance of defaulting. How do we know that? It must be from historical data. The problem is, there hasn't been a national drop of housing price since the great depression in the 1920s, so the chance that a borrower defaults was calculated on the basis of a good period when the housing prices surged. However, the housing market crashed in 2007. Many borrowers' properties are now worth even less than the loan they have to pay in the future, so many of them refuse to pay. To worsen the situation, 22% of these borrowers are the so-called subprime borrowers - those who had little income and had little hope of returning money. Banks were not afraid of lending money to them because even if they defaulted, the insurance would pay them back. The participation of the subprime borrowers makes lending much riskier than before.

In fact, the default probability in the US has quadrupled from the 3% as assumed in the model to 12% since 2007, making it four times riskier. This means that investors like Lehman Brothers will be hit four times harder than they have anticipated. . .

There is also a second and more subtle source of error. Whether you can make money from selling the CDO insurance for the bank depends on whether the borrowers return the money, which in turns depends on the economy. So if the economy goes down, you are a lot more likely to lose money. If you are an active investor, then you probably have invested in the stock market as well. Now if the market crashes you lose both the money invested in the stock market and in the CDO. Suppose, on the other hand, that instead of spending the money on CDO, you bet on whether Manchester United will win the European Champion League. This time in order to lose all your money you need both the market to go down and Manchester United to lose their match - this is less likely than just having the market go down. Therefore, investing on CDO is a riskier choice than betting for Manchester United. The error in our model is that we have not taken into account this extra risk due to its dependence of CDO on the market.

These two errors were sufficient to mask the risk in CDO. In fact, the errors are so serious that 27 out of 30 of the CDOs issued by Merril Lynch were downgraded from AAA (the safest investment) to "junk" when the errors were spotted.

Lehman Brothers, unaware of the hidden risks, decided to invest big on CDO. It even had a 35 to 1 debt to equity ratio, that is, it only owned $1 out of every $36 in its bank account - the other $35 were borrowed from somewhere. This meant that a loss of just 3% of the money on its balance sheet, would have meant the loss of all the money it owned. After suffering heavy losses (more than 3% of the money in its balance) from CDO, borrowers began to lose confidence and called back the loans. As Lehman had always relied on short-term loans, its lenders were able to pull their cash back quickly. Now the bank was in trouble. It borrowed much more than it was able to return and soon found itself unable to pay back. On 15th September 2008, the world's fourth biggest investment bank was gone, forever.


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