Value at Risk Formula

Gordon Crovitz had a very interesting article in the Wall Street Journal the other day. Link to it here. Now I am not an economist and don't pretend to have full comprehension of the algebra involved. I will try to deliver the basic concept in a nutshell. His fundamental question is - how did the financial system collapse? We have extremely sophisticated modeling and analytic tools and they all got mowed down like an old levee in Louisiana. Where did the system fail?

Crovitz looks back to a 2004 paper by Yale mathematician Benoit Mandelbrot:

Benoit Mandelbrot pointed out the shortcomings of the VaR model in his "The (Mis)behavior of Markets," published in 2004. He noted that bell curves work for, say, disparities in the height of people. In markets, instead of flat tails of rare events at either end of the bell curve, there are "fat tails" of huge upsides and huge downsides. Markets are more complex than the neat shape of bell curves.

He also refers to a book written last year by ...former trader Nassim Nicholas Taleb, "The Black Swan" that pointed out that extreme outcomes are actually common, warning that financial engineers -- "scientists," as he calls them -- ignore these unlikely outcomes at their peril. But today's credit panic was not entirely unpredictable. Mr. Taleb was prescient in writing, "The government-sponsored institution Fannie Mae, when I look at their risks, seems to be sitting on a barrel of dynamite, vulnerable to the slightest hiccup. But not to worry: Their large staffs of scientists deemed these events 'unlikely.'"

Likewise, the financial engineers at once high-flying hedge fund Long-Term Capital Management thought they had taken all risks into account, but the Russian financial crisis of 1998 blew their model. Last week the former general counsel of LTCM, James Rickards, reflected on how an incomplete VaR model undermined his firm. "Since we have scaled the system to unprecedented size, we should expect catastrophes of unprecedented size as well," he wrote in the Washington Post. "We're in the middle of one such catastrophe, and complexity theory says it will get much worse."

I think that this is very interesting stuff. In a random dynamic universe, it would seem to me unlikely not to experience these 1% eventualities. I once read an interesting interview with Robert Hunter, the writer, talking about coincidence. In this big world of ours, numbers fall into coincidental patterns all the time. Oftentimes when these events happen we imbue them with mythic causal overtones but the reality is that probability says that in an infinite universe they have to occur. What would be truly unusual is if they did not. Objects (or markets) in motion tend to stay in motion or stasis, but as we have seen in the last month, they can also swing on a dime.

Chaos Happens.