Tuesday, January 6, 2009

TBD=there be dragons

I saw an interview on TV once with evolutionary biologist and noted baseball fan Steven Jay Gould in which he explained his enthusiasm for Joe DiMaggio's legendary 1941 56-game hitting streak. Gould's argument -- informed by his deep understanding of statistics -- turned on the enormous difference between DiMaggio's accomplishement and the mean (average) hitting streaks of all other players in the major leagues. In a later piece in the New York Review of Books, Gould described the statistical research of a scientific colleague into the probabilities of other stand-out baseball accomplishments that showed they constituted no significant violation of what was to be expected in terms of their probabilities. But then he wrote:
But "treasure your exceptions," as the old motto goes. There is one major exception, and absolutely only one—one sequence so many standard deviations above the expected distribution that it should not have occurred at all. Joe DiMaggio's fifty-six–game hitting streak in 1941.

Here's a simple example of a bell curve marked to indicate standard deviations:

(Image from here)

Investopedia defines standard deviation thus:
A measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance.
It's a measure of difference in numeric value of some sort within a class of like events and it's a measurement of the general likelihood of any member of the class holding that value. What made DiMaggio's streak so fantastic, Gould insisted, was that in terms of probability it never should have happened. Nothing lies that far off the curve. Except Joe DiMaggio.

This came to mind today when I got around to reading a long piece published last weekend in the NY Times Magazine about a risk model called Value at Risk, which is commonly used by financial professionals in their dealings. The author, Joe Nocera, describes VaR as a set of mathematical models which (it was believed) could assess the likelihood an investment would lose money in a given period of time.
Built around statistical ideas and probability theories that have been around for centuries, VaR was developed and popularized in the early 1990s by a handful of scientists and mathematicians — “quants,” they’re called in the business — who went to work for JPMorgan. VaR’s great appeal, and its great selling point to people who do not happen to be quants, is that it expresses risk as a single number, a dollar figure, no less.

VaR isn’t one model but rather a group of related models that share a mathematical framework. In its most common form, it measures the boundaries of risk in a portfolio over short durations, assuming a “normal” market. For instance, if you have $50 million of weekly VaR, that means that over the course of the next week, there is a 99 percent chance that your portfolio won’t lose more than $50 million. That portfolio could consist of equities, bonds, derivatives or all of the above; one reason VaR became so popular is that it is the only commonly used risk measure that can be applied to just about any asset class. And it takes into account a head-spinning variety of variables, including diversification, leverage and volatility, that make up the kind of market risk that traders and firms face every day.
Systems theorist and Black Swan author Nassim Taleb shows up quickly in the article to argue against such a model-based strategy. It's "a fraud," he says. As I understand it, his "Black Swan" concept is a lot like somebody hitting safely in 56 successive major league baseball games. It can't happen until it does.
“Any system susceptible to a black swan will eventually blow up,” Taleb says. The modern system of world finance, complex and interrelated and opaque, where what happened yesterday can and does affect what happens tomorrow, and where one wrong tug of the thread can cause it all to unravel, is just such a system.
Or to put in the words of a risk consultant also quoted in the article:
[Marc]Groz has his own way of illustrating the problem: he showed me a slide he made of a curve with the letters “T.B.D.” at the extreme ends of the curve. I thought the letters stood for “To Be Determined,” but that wasn’t what Groz meant. “T.B.D. stands for ‘There Be Dragons,’ ” he told me.
I have no idea whether Taleb is right in his crusade against models like VaR. But we all know that the bell curve had monsters at its extreme ends, monsters the smart guys didn't even imagine. They shouldn't even exist, according to the financial experts' thinking over the past few years.

Joe, Joe DiMaggio, we want you on our side.

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