ABNormal Distribution

Last week’s Economist mag contained a killer special section on the inner-workings, failures, and future of modern finance.  This article on mathematical modeling of risk was particularly rad.  The highlight for me was this graph, which demonstrates a simple and common way that risk is modeled in regards to various investment vehicles …


The author points out that the normal distribution (dark blue line) has and should continue to be used to model  simple classes of risk, like those associated with a sector of an equities market, a type of bond, etc.  However, more complex types of investment structures (for instance, the nightmarish mortgage-backed securities) cannot be modeled with a normal distribution, and this has now been proven by mathematician Benoit Mandelbrot.

“…if the Dow Jones Industrial Average followed a normal distribution, it should have moved by more than 3.4% on 58 days between 1916 and 2003; in fact it did so 1,001 times. It should have moved by more than 4.5% on six days; it did so on 366. It should have moved by more than 7% only once in every 300,000 years; in the 20th century it did so 48 times.”

Looks like the normal distribution completely failed to reflect reality.  My favorite part is the mention that a former CFO from a major investment bank is on the record in 2007 as saying that they had seen 25 standard deviation movements in some markets for several days in a row!  So much for the “no one could have seen this coming” excuse.  They knew exactly what that meant.  Statistically, a shift that large should be a once in a millennium type of movement.  If each of those days is considered an independent event, then either the probabilistic laws of the universe were imploding or the model was complete garbage.

Mandelbrot basically found that the tails of the distribution need to be raised way above the normal (broken light blue line), suggesting a much higher-than-previously-thought probability of massive gains (see: 2006-7) or catastrophic loss (2008).

If the risk had been properly modeled, then maybe this crisis wouldn’t be quite so severe.  Unfortunately, there was money to be made …


~ by jazzychaz on February 3, 2009.

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