Nassim “Black Swan” Taleb writes on Edge about an unwillingness or consider and remember extreme events leads to financial disaster in The Fourth Quadrant: A map of the limits of statistics.

Statistical and applied probabilistic knowledge is the core of knowledge; statistics is what tells you if something is true, false, or merely anecdotal; it is the “logic of science”; it is the instrument of risk-taking; it is the applied tools of epistemology; you can’t be a modern intellectual and not think probabilistically—but… let’s not be suckers. The problem is much more complicated than it seems to the casual, mechanistic user who picked it up in graduate school. Statistics can fool you. In fact it is fooling your government right now. It can even bankrupt the system (let’s face it: use of probabilistic methods for the estimation of risks did just blow up the banking system).

The current subprime crisis has been doing wonders for the reception of any ideas about probability-driven claims in science, particularly in social science, economics, and “econometrics” (quantitative economics). Clearly, with current International Monetary Fund estimates of the costs of the 2007-2008 subprime crisis, the banking system seems to have lost more on risk taking (from the failures of quantitative risk management) than every penny banks ever earned taking risks. But it was easy to see from the past that the pilot did not have the qualifications to fly the plane and was using the wrong navigation tools: The same happened in 1983 with money center banks losing cumulatively every penny ever made, and in 1991-1992 when the Savings and Loans industry became history.

It appears that financial institutions earn money on transactions (say fees on your mother-in-law’s checking account) and lose everything taking risks they don’t understand. I want this to stop, and stop now— the current patching by the banking establishment worldwide is akin to using the same doctor to cure the patient when the doctor has a track record of systematically killing them. And this is not limited to banking—I generalize to an entire class of random variables that do not have the structure we thing they have, in which we can be suckers.

And we are beyond suckers: not only, for socio-economic and other nonlinear, complicated variables, we are riding in a bus driven a blindfolded driver, but we refuse to acknowledge it in spite of the evidence, which to me is a pathological problem with academia. After 1998, when a “Nobel-crowned” collection of people (and the crème de la crème of the financial economics establishment) blew up Long Term Capital Management, a hedge fund, because the “scientific” methods they used misestimated the role of the rare event, such methodologies and such claims on understanding risks of rare events should have been discredited. Yet the Fed helped their bailout and exposure to rare events (and model error) patently increased exponentially (as we can see from banks’ swelling portfolios of derivatives that we do not understand).

Are we using models of uncertainty to produce certainties?

…So the good news is that we can identify where the danger zone is located, which I call “the fourth quadrant”, and show it on a map with more or less clear boundaries. A map is a useful thing because you know where you are safe and where your knowledge is questionable. So I drew for the Edge readers a tableau showing the boundaries where statistics works well and where it is questionable or unreliable. Now once you identify where the danger zone is, where your knowledge is no longer valid, you can easily make some policy rules: how to conduct yourself in that fourth quadrant; what to avoid.

…

Now it lets see where the traps are:

First Quadrant: Simple binary decisions, in Mediocristan: Statistics does wonders. These situations are, unfortunately, more common in academia, laboratories, and games than real life—what I call the “ludic fallacy”. In other words, these are the situations in casinos, games, dice, and we tend to study them because we are successful in modeling them.

Second Quadrant: Simple decisions, in Extremistan: some well known problem studied in the literature. Except of course that there are not many simple decisions in Extremistan.

Third Quadrant: Complex decisions in Mediocristan: Statistical methods work surprisingly well.

Fourth Quadrant: Complex decisions in Extremistan: Welcome to the Black Swan domain. Here is where your limits are. Do not base your decisions on statistically based claims. Or, alternatively, try to move your exposure type to make it third-quadrant style (“clipping tails”).

Below I’ve redrawn Taleb’s figure.  His article provides a fuller picture.

Similarly, Scientific American reprints Benoit Mandelbrot’s 1999  How Fractals Can Explain What’s Wrong with Wall Street:

Individual investors and professional stock and currency traders know better than ever that prices quoted in any financial market often change with heart-stopping swiftness. Fortunes are made and lost in sudden bursts of activity when the market seems to speed up and the volatility soars. Last September, for instance, the stock for Alcatel, a French telecommunications equipment manufacturer, dropped about 40 percent one day and fell another 6 percent over the next few days. In a reversal, the stock shot up 10 percent on the fourth day.

The classical financial models used for most of this century predict that such precipitous events should never happen. A cornerstone of finance is modern portfolio theory, which tries to maximize returns for a given level of risk. The mathematics underlying portfolio theory handles extreme situations with benign neglect: it regards large market shifts as too unlikely to matter or as impossible to take into account. It is true that portfolio theory may account for what occurs 95 percent of the time in the market. But the picture it presents does not reflect reality, if one agrees that major events are part of the remaining 5 percent. An inescapable analogy is that of a sailor at sea. If the weather is moderate 95 percent of the time, can the mariner afford to ignore the possibility of a typhoon?