Re: [MLUG - DISCUSSION] What is a CDO?

[Mike Miller <EMAIL:PROTECTED>]

On Wed, 5 Dec 2007, Jonathan King wrote:

> This gives you a flavor of what's going on in the mortgage securities 
> markets:
>
> http://www.portfolio.com/interactive-features/2007/12/cdo


> From a statistical/probabilistic perspective, I think they are saying that 
the investors were implicitly assuming independence of the elements of 
their portfolio, thus they had achieved diversity and a degree of 
protection afforded by the central limit theorem, but they were mistaken. 
They were mistaken because all of these diverse elements were correlated 
and the effective diversity (like effective sample size) was much smaller 
than they thought.

Another example of failure due to dependence comes from the Challenger 
space shuttle (or so I'm told).  The O-rings failed due to cold 
temperature, but this was not expected because people had been thinking 
that they had sufficient redundancy in the system and the failure of one 
or a few O-rings would not cause the shuttle to fail.  If you have 90% 
reliability, and 10 O-rings, and you need 6 to be working, the probability 
that 5 or more O-rings will fail at once is given (they thought) by a 
binomial distribution:

1 - binomial_cdf(4, 10, .1) = .0016

But that assumes independece of failures.  If the stressor (cold in this 
case) affects all O-rings equally and simultaneously, they become 
completely dependent and the probability of catastrophic failure (5 or 
more failing at once) is 10%, not 0.16% (that is, about 60 times greater 
than predicted by the independence model).  Oops.

Mike

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