"Students cannot understand the value of "this is what we don't know"—they think it is not information, that they are learning nothing. "

I'm a big Taleb fan, and partly this derives from the fact that he sounds to me, both in his views and his style, like Paul Feyerabend. Here's a post he did:

"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)."

I see trial and error as the core of knowledge, and statistics as one way or method of relating to reality. The main failure of any explanation involving Human Agency is viewing it Mechanistically. What blew up the system was risk taking, but it was quite clearly informed.

"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. "

I'm really quite amazed that my main point of reference for this crisis, namely, the S & L Crisis, is seldom mentioned.

Here's something about what Taleb might also be talking about:

"The Brady Plan, the principles of which were first articulated by U.S. Treasury Secretary Nicholas F. Brady in March 1989, was designed to address the so-called LDC debt crisis of the 1980's. The debt crisis began in 1982, when a number of countries, primarily in Latin America, confronted by high interest rates and low commodities prices, admitted their inability to service hundreds of billions of dollars of their commercial bank loans. Because many of these countries' economies were then dependent on commercial bank financing, continued debt reschedulings and the resulting perception of uncreditworthiness led to a "lost decade" of economic stagnation, during which voluntary international credit and capital flows to these nations and their private sectors were severely interrupted.

From 1982 through 1988, debtor nations and their commercial bank creditors engaged in repeated rounds of rescheduling and restructuring sovereign and private sector debt, in the belief that the difficulty these nations experienced in meeting their debt obligations was a temporary liquidity problem that would end as the debtor nations' economies rebounded. However, by the time the Brady Plan was announced, it was widely believed that most debtor nations were no closer to financial health than they had been in 1982, that many loans would never be entirely repaid, and that some form of substantial debt relief was necessary for these nations and their fragile economies to resume growth and to regain access to the global capital markets.

The basic tenets of the Brady Plan were relatively simple and were derived from common practices in domestic U.S. corporate work-out transactions: (1) bank creditors would grant debt relief in exchange for greater assurance of collectability in the form of principal and interest collateral; (2) debt relief needed to be linked to some assurance of economic reform and (3) the resulting debt should be more highly tradable, to allow creditors to diversify risk more widely throughout the financial and investment community.

Because the rescheduling process evolved on a case-by-case basis, each Brady issue was unique, but most Brady restructurings included at least two basic options for debt holders: the exchange of loans for either Par Bonds or Discount Bonds. Par Bonds resulted from an exchange of loans for bonds of equal face amount, with a fixed, below-market rate of interest, allowing for long-term debt service reduction by means of concessionary interest terms. Discount Bonds resulted from an exchange of loans for a lesser amount of face value in bonds (generally a 30-50% discount), allowing for immediate debt reduction, with a market-based floating rate of interest. The principal of both Par and Discount Bonds was secured at final maturity by a pledge of zero-coupon instruments which, in the case of Par and Discount Bonds denominated in U.S. dollars, were U.S. Treasury securities. A portion of the interest payable on Par and Discount Bonds (generally from 12 to 24 months coverage) was also secured by the pledge of high-grade investment securities.

While both Par and Discount Bonds were 30-year collateralized bonds, a number of nations also issued uncollateralized bonds with shorter tenors (e.g., "Floating Rate Bonds" and "Front Loaded Interest Reduction Bonds"). Some nations also issued bonds in exchange for unpaid interest on defaulted loans (e.g., "Past Due Interest Bonds" or "Interest Arrears Bonds"). Each Brady country negotiated the specific terms and details of its Brady restructuring during discussions with its commercial bank creditors, who were offered a resulting 'Menu of Options' for their exchange of eligible debt.

Mexico, the first nation to begin negotiating with its commercial bank creditors (August 1982), was also the first nation to restructure under the Brady Plan (1989-90). In addition to Mexico, Brady bonds were issued (in an aggregate face amount of over US$ 160 billion) by Argentina, Brazil, Bulgaria, Costa Rica, the Dominican Republic, Ecuador, Ivory Coast (Cote d'Ivoire), Jordan, Nigeria, Panama, Peru, the Philippines, Poland, Russia, Uruguay, Venezuela and Vietnam. The large issue size of many Brady bond issuances helped to provide the Brady bond market with substantially greater liquidity than is found in many other financial marketplaces.

The Brady Plan was very successful in several important respects. First, it allowed the participating countries to negotiate substantial reductions in their overall levels of debt and debt service. Second, it succeeded in diversifying sovereign risk away from commercial bank portfolios more widely throughout the financial and investment communities. Third, it encouraged many Emerging Markets countries to adopt and pursue ambitious economic reform programs. Finally, the Brady Plan has enabled many Emerging Market countries to regain access to the international capital markets for their financing needs.

This is not to say, of course, that the Brady Plan succeeded in solving all economic problems throughout the Emerging Markets. The road to greater economic development and democratization has been a bumpy one for some countries. But the Brady Plan did facilitate a return from the rescheduling mode of the LDC debt crisis to a more normalized, market-oriented relationship between Emerging Markets countries and their creditors.

With these successes and the subsequent re-access to international capital markets by Emerging Markets countries, the dominance of Brady bonds in the Emerging Markets debt markets was gradually eroded, as they were essentially replaced by a wide variety of even more market-friendly instruments. By mid-2006, most Brady debt had been exchanged or bought back by debtor nations in public or private secondary market transactions. While Brady bond trading accounted for 61% of total Emerging Markets debt trading in 1994 (U.S. $1.68 trillion), EMTA's Debt Trading Volume Survey showed that Brady bond market share had declined to approximately 2% of total trading by 2005. "

I threw this in because we also talked recently about Brady Bonds. Anyway, you get the point. We've been through this kind of misallocation of resources and debt crisis before. Recently.

"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."

It would be nice if we could see some malpractice suits filed.

"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)."

(How can a rare event immediately occur? That takes real skill to predict that incorrectly. Don )

"Are we using models of uncertainty to produce certainties? "

That can't be done.

"This masquerade does not seem to come from statisticians—but from the commoditized, "me-too" users of the products. Professional statisticians can be remarkably introspective and self-critical. Recently, the American Statistical Association had a special panel session on the "black swan" concept at the annual Joint Statistical Meeting in Denver last August. They insistently made a distinction between the "statisticians" (those who deal with the subject itself and design the tools and methods) and those in other fields who pick up statistical tools from textbooks without really understanding them. For them it is a problem with statistical education and half-baked expertise. Alas, this category of blind users includes regulators and risk managers, whom I accuse of creating more risk than they reduce."

( You know, that has to be correct, otherwise, it's not possible for a rare event to occur immediately. They were obviously increasing the risk and provoking it. Don )

"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."

Okay. What were the first three quadrants?

"So the principal value of the map is that it allows for policy making. Indeed, I am moving on: my new project is about methods on how to domesticate the unknown, exploit randomness, figure out how to live in a world we don't understand very well. While most human thought (particularly since the enlightenment) has focused us on how to turn knowledge into decisions, my new mission is to build methods to turn lack of information, lack of understanding, and lack of "knowledge" into decisions—how, as we will see, not to be a "turkey"."

There isn't a map that makes for easy policy making, which includes values. My method of learning how to live in a world I don't understand very well is called agoraphobia.

"This piece has a technical appendix that presents mathematical points and empirical evidence. (See link below.) It includes a battery of tests showing that no known conventional tool can allow us to make precise statistical claims in the Fourth Quadrant. While in the past I limited myself to citing research papers, and evidence compiled by others (a less risky trade), here I got hold of more than 20 million pieces of data (includes 98% of the corresponding macroeconomics values of transacted daily, weekly, and monthly variables for the last 40 years) and redid a systematic analysis that includes recent years."

Sorry Taleb, I don't believe that you can hold more than 10 million pieces of data. Tops.

What Is Fundamentally Different About Real Life

"My anger with "empirical" claims in risk management does not come from research. It comes from spending twenty tense (but entertaining) years taking risky decisions in the real world managing portfolios of complex derivatives, with payoffs that depend on higher order statistical properties —and you quickly realize that a certain class of relationships that "look good" in research papers almost never replicate in real life (in spite of the papers making some claims with a "p" close to infallible). But that is not the main problem with research."

That's a fairly large problem in my book.

"For us the world is vastly simpler in some sense than the academy, vastly more complicated in another. So the central lesson from decision-making (as opposed to working with data on a computer or bickering about logical constructions) is the following: it is the exposure (or payoff) that creates the complexity —and the opportunities and dangers— not so much the knowledge ( i.e., statistical distribution, model representation, etc.). In some situations, you can be extremely wrong and be fine, in others you can be slightly wrong and explode. If you are leveraged, errors blow you up; if you are not, you can enjoy life."

I don't like leverage either, but then, I'm not an investor or banker.

"So knowledge (i.e., if some statement is "true" or "false") matters little, very little in many situations. In the real world, there are very few situations where what you do and your belief if some statement is true or false naively map into each other. Some decisions require vastly more caution than others—or highly more drastic confidence intervals. For instance you do not "need evidence" that the water is poisonous to not drink from it. You do not need "evidence" that a gun is loaded to avoid playing Russian roulette, or evidence that a thief a on the lookout to lock your door. You need evidence of safety—not evidence of lack of safety— a central asymmetry that affects us with rare events. This asymmetry in skepticism makes it easy to draw a map of danger spots."

( That doesn't sound correct. You need to be afraid, and then you'll ask for evidence. The reason you lock your door or don't play with guns is called prudence, meaning not taking undue risk:

noun

1.	the quality or fact of being prudent.

2.	caution with regard to practical matters; discretion.

3.	regard for one's own interests.

4.	provident care in the management of resources; economy; frugality.

I don't know, but I like my description better.

"The Dangers Of Bogus Math

I start with my old crusade against "quants" (people like me who do mathematical work in finance), economists, and bank risk managers, my prime perpetrators of iatrogenic risks (the healer killing the patient). Why iatrogenic risks? Because, not only have economists been unable to prove that their models work, but no one managed to prove that the use of a model that does not work is neutral, that it does not increase blind risk taking, hence the accumulation of hidden risks."

Can't these guys read a philosophy of math book? If your model or theory is wrong, you might fall off the edge of the earth or be poisoned. I don't think that risks are hidden, but ignored. Also, induction works differently in math and the world:

"The problem of induction exists within the philosophy of science, but not within the philosophy of mathematics, which may seem puzzling. However, scientific induction and mathematical induction are very different. Scientific induction relies on generalizing a set of observations in a non-deductive manner, while mathematical induction relies on axioms to make deductive arguments. For example, proving general theorems about the natural numbers requires appealing to the axiom of induction. The epistemic question of why mathematician are allowed to use these arguments is sidestepped by making induction a part of the systems they are investigating. To over-simplify the issue, it could be said that mathematics replaces the question "Why should we use inductive arguments at all?" with "What conclusions do we reach if we allow certain kinds of inductive arguments?"

Figure 1 My classical metaphor: A Turkey is fed for a 1000 days—every days confirms to its statistical department that the human race cares about its welfare "with increased statistical significance". On the 1001^st day, the turkey has a surprise.

Figure 2 The graph above shows the fate of close to 1000 financial institutions (includes busts such as FNMA, Bear Stearns, Northern Rock, Lehman Brothers, etc.). The banking system (betting AGAINST rare events) just lost > 1 Trillion dollars (so far) on a single error, more than was ever earned in the history of banking. Yet bankers kept their previous bonuses and it looks like citizens have to foot the bills. And one Professor Ben Bernanke pronounced right before the blowup that we live in an era of stability and "great moderation" (he is now piloting a plane and we all are passengers on it).

Figure 3 The graph shows the daily variations a derivatives portfolio exposed to U.K. interest rates between 1988 and 2008. Close to 99% of the variations, over the span of 20 years, will be represented in 1 single day—the day the European Monetary System collapsed. As I show in the appendix, this is typical with ANY socio-economic variable (commodity prices, currencies, inflation numbers, GDP, company performance, etc. ). No known econometric statistical method can capture the probability of the event with any remotely acceptable accuracy (except, of course, in hindsight, and "on paper"). Also note that this applies to surges on electricity grids and all manner of modern-day phenomena.

Figures 1 and 2 show you the classical problem of the turkey making statements on the risks based on past history (mixed with some theorizing that happens to narrate well with the data). A friend of mine was sold a package of subprime loans (leveraged) on grounds that "30 years of history show that the trade is safe." He found the argument unassailable "empirically". And the unusual dominance of the rare event shown in Figure 3 is not unique: it affects all macroeconomic data—if you look long enough almost all the contribution in some classes of variables will come from rare events (I looked in the appendix at 98% of trade-weighted data)"

Didn't Hume already talk about this?

"The problem of induction is the philosophical question of whether inductive reasoning is valid. That is, what is the justification for either:

1. generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (for example, the inference that "all swans we have seen are white, and therefore all swans are white," before the discovery of black swans) or
2. presupposing that a sequence of events in the future will occur as it always has in the past (for example, that the laws of physics will hold as they have always been observed to hold).

The problem calls into question all empirical claims made in everyday life or through the scientific method. Although the problem dates back to the Pyrrhonism of ancient philosophy, David Hume introduced it in the mid-18th century, with the most notable response provided by Karl Popper two centuries later. A more recent, probability-based extension is the "no-free-lunch theorem for supervised learning" of Wolpert."

"Now let me tell you what worries me. Imagine that the Turkey can be the most powerful man in world economics, managing our economic fates. How? A then-Princeton economist called Ben Bernanke made a pronouncement in late 2004 about the "new moderation" in economic life: the world getting more and more stable—before becoming the Chairman of the Federal Reserve. Yet the system was getting riskier and riskier as we were turkey-style sitting on more and more barrels of dynamite—and Prof. Bernanke's predecessor the former Federal Reserve Chairman Alan Greenspan was systematically increasing the hidden risks in the system, making us all more vulnerable to blowups."

( Imagine no more- Don )

"By the "narrative fallacy" the turkey economics department will always manage to state, before thanksgivings that "we are in a new era of safety", and back-it up with thorough and "rigorous" analysis. And Professor Bernanke indeed found plenty of economic explanations—what I call the narrative fallacy—with graphs, jargon, curves, the kind of facade-of-knowledge that you find in economics textbooks. (This is the find of glib, snake-oil facade of knowledge—even more dangerous because of the mathematics—that made me, before accepting the new position in NYU's engineering department, verify that there was not a single economist in the building. I have nothing against economists: you should let them entertain each others with their theories and elegant mathematics, and help keep college students inside buildings. But beware: they can be plain wrong, yet frame things in a way to make you feel stupid arguing with them. So make sure you do not give any of them risk-management responsibilities.)"

There's also the problem of:
1) Relying on experts
2) Anybody can be wrong

In a way, Taleb is confusing himself, by expecting people to be infallible, like Greenspan and Bernanke, and then admitting that they can't be. All anyone on earth does it try their best. I'm not sure that he's refuted induction, by the way. The Turkey isn't conscious in the way that we supposedly are. If it was, it wouldn't be looking forward to Thanksgiving. If something happens a lot, it's reasonable to expect that it will continue to happen, until it doesn't. I would say that there were two main problems:
1) Accepting an incorrect relationship between math and the world
2) Not getting enough data or the appropriate data to make decent predictions with
The third, the predisposition to look the other way or ignore risk for a possible payoff, effected more than the quants. I actually like my prudence explanation better. I mean, once the facts are in, making fun of the people who got things wrong is fun, but not really profound.

"Bottom Line: The Map

Things are made simple by the following. There are two distinct types of decisions, and two distinct classes of randomness."

I don't believe this. His map or rules are just that, and are useful or not based on whether or not we can actually use them to our benefit.

"Decisions: The first type of decisions is simple, "binary", i.e. you just care if something is true or false. Very true or very false does not matter. Someone is either pregnant or not pregnant. A statement is "true" or "false" with some confidence interval. (I call these M0 as, more technically, they depend on the zero^th moment, namely just on probability of events, and not their magnitude —you just care about "raw" probability). A biological experiment in the laboratory or a bet with a friend about the outcome of a soccer game belong to this category"

Okay.

"The second type of decisions is more complex. You do not just care of the frequency—but of the impact as well, or, even more complex, some function of the impact. So there is another layer of uncertainty of impact. (I call these M1+, as they depend on higher moments of the distribution). When you invest you do not care how many times you make or lose, you care about the expectation: how many times you make or lose times the amount made or lost. "

This looks like this from Derivative Dribble:

"A Closer Look At Risk

As stated here, my own view is that risk is a concept that has two components: (i) the occurrence of an event and (ii) a magnitude associated with that event. This allows us to ask two questions: What is the probability of the event occurring? And if it occurs, what is the expected value of its associated magnitude? We say that P is exposed to a given risk if P expects to incur a gain/loss if the risk-event occurs. As is evident, under this rubric, that whole conversation above was grossly imprecise. But that’s ok. Its import is clear enough. "

"Probability structures: There are two classes of probability domains—very distinct qualitatively and quantitatively. The first, thin-tailed: Mediocristan", the second, thick tailed Extremistan. Before I get into the details, take the literary distinction as follows:

In Mediocristan, exceptions occur but don't carry large consequences. Add the heaviest person on the planet to a sample of 1000. The total weight would barely change. In Extremistan, exceptions can be everything (they will eventually, in time, represent everything). Add Bill Gates to your sample: the wealth will jump by a factor of >100,000. So, in Mediocristan, large deviations occur but they are not consequential—unlike Extremistan.

Mediocristan corresponds to "random walk" style randomness that you tend to find in regular textbooks (and in popular books on randomness). Extremistan corresponds to a "random jump" one. The first kind I can call "Gaussian-Poisson", the second "fractal" or Mandelbrotian (after the works of the great Benoit Mandelbrot linking it to the geometry of nature). But note here an epistemological question: there is a category of "I don't know" that I also bundle in Extremistan for the sake of decision making—simply because I don't know much about the probabilistic structure or the role of large events."

Let's keep going:

"The Map

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").

The four quadrants. The South-East area (in orange) is where statistics and models fail us.

Tableau Of Payoffs

I think that the map is pretty straightforward. It's an attempt to assign the value of statistics and probablity in various delineated realms.

"Two Difficulties

Let me refine the analysis. The passage from theory to the real world presents two distinct difficulties: "inverse problems" and "pre-asymptotics".

Inverse Problems. It is the greatest epistemological difficulty I know. In real life we do not observe probability distributions (not even in Soviet Russia, not even the French government). We just observe events. So we do not know the statistical properties—until, of course, after the fact. Given a set of observations, plenty of statistical distributions can correspond to the exact same realizations—each would extrapolate differently outside the set of events on which it was derived. The inverse problem is more acute when more theories, more distributions can fit a set a data.

This inverse problem is compounded by the small sample properties of rare events as these will be naturally rare in a past sample. It is also acute in the presence of nonlinearities as the families of possible models/parametrization explode in numbers"

We absract and organize the events that we observe.

"Pre-asymptotics. Theories are, of course, bad, but they can be worse in some situations when they were derived in idealized situations, the asymptote, but are used outside the asymptote (its limit, say infinity or the infinitesimal). Some asymptotic properties do work well preasymptotically (Mediocristan), which is why casinos do well, but others do not, particularly when it comes to Extremistan.

Most statistical education is based on these asymptotic, Platonic properties—yet we live in the real world that rarely resembles the asymptote. Furthermore, this compounds the ludic fallacy: most of what students of statistics do is assume a structure, typically with a known probability. Yet the problem we have is not so much making computations once you know the probabilities, but finding the true distribution."

Even with Mechanics, the models or theories or math are not exact, but work well enough for us to find them useful. If they don't work for us, then they're not useful. What's going on in math and other such endeavors is a different, although related, question.


"The Inverse Problem Of The Rare Events

Let us start with the inverse problem of rare events and proceed with a simple, nonmathematical argument. In August 2007, The Wall Street Journal published a statement by one financial economist, expressing his surprise that financial markets experienced a string of events that "would happen once in 10,000 years". A portrait of the gentleman accompanying the article revealed that he was considerably younger than 10,000 years; it is therefore fair to assume that he was not drawing his inference from his own empirical experience (and not from history at large), but from some theoretical model that produces the risk of rare events, or what he perceived to be rare events."

That does seem a bizarre statement, assuming it has to do with human culture in some way.

"Alas, the rarer the event, the more theory you need (since we don't observe it). So the rarer the event, the worse its inverse problem. And theories are fragile (just think of Doctor Bernanke)."

( You would certainly need a better explanation for why you believe as you do- Don )

"The tragedy is as follows. Suppose that you are deriving probabilities of future occurrences from the data, assuming (generously) that the past is representative of the future. Now, say that you estimate that an event happens every 1,000 days. You will need a lot more data than 1,000 days to ascertain its frequency, say 3,000 days. Now, what if the event happens once every 5,000 days? The estimation of this probability requires some larger number, 15,000 or more. The smaller the probability, the more observations you need, and the greater the estimation error for a set number of observations. Therefore, to estimate a rare event you need a sample that is larger and larger in inverse proportion to the occurrence of the event. "

You could certainly use it.

"If small probability events carry large impacts, and (at the same time) these small probability events are more difficult to compute from past data itself, then: our empirical knowledge about the potential contribution—or role—of rare events (probability × consequence) is inversely proportional to their impact. This is why we should worry in the fourth quadrant!"

( Of course, if you have less data, it's harder to make a prediction- Don )

"For rare events, the confirmation bias (the tendency, Bernanke-style, of finding samples that confirm your opinion, not those that disconfirm it) is very costly and very distorting. Why? Most of histories of Black Swan prone events is going to be Black Swan free! Most samples will not reveal the black swans—except after if you are hit with them, in which case you will not be in a position to discuss them. Indeed I show with 40 years of data that past Black Swans do not predict future Black Swans in socio-economic life.

Figure 4 The Confirmation Bias At Work. For left-tailed fat-tailed distributions, we do not see much of negative outcomes for surviving entities AND we have a small sample in the left tail. This is why we tend to see a better past for a certain class of time series than warranted.

Surely the S & L Crisis and Tech Bubble could have added up to an attitude and disposition to prudence. Is that really so hard to imagine?

"Fallacy Of The Single Event Probability

Let us look at events in Mediocristan. In a developed country a newborn female is expected to die at around 79, according to insurance tables. When she reaches her 79th birthday, her life expectancy, assuming that she is in typical health, is another 10 years. At the age of 90, she should have another 4.7 years to go. So if you are told that a person is older than 100, you can estimate that he is 102.5 and conditional on the person being older than 140 you can estimate that he is 140 plus a few minutes. The conditional expectation of additional life drops as a person gets older."

You are more likely to die, over a certain age.

"In Extremistan things work differently and the conditional expectation of an increase in a random variable does not drop as the variable gets larger. In the real world, say with stock returns (and all economic variable), conditional on a loss being worse than the 5 units, to use a conventional unit of measure units, it will be around 8 units. Conditional that a move is more than 50 STD it should be around 80 units, and if we go all the way until the sample is depleted, the average move worse than 100 units is 250 units! This extends all the way to areas in which we have sufficient sample."

A human being is a living organism, the price of a stock is not. For one thing, one can go in either direction on a continuum, while the other cannot.

"This tells us that there is "no typical" failure and "no typical" success. You may be able to predict the occurrence of a war, but you will not be able to gauge its effect! Conditional on a war killing more than 5 million people, it should kill around 10 (or more). Conditional on it killing more than 500 million, it would kill a billion (or more, we don't know). You may correctly predict a skilled person getting "rich", but he can make a million, ten million, a billion, ten billion—there is no typical number. We have data, for instance, for predictions of drug sales, conditional on getting things right. Sales estimates are totally uncorrelated to actual sales—some drugs that were correctly predicted to be successful had their sales underestimated by up to 22 times!"

Same point.

"This absence of "typical" event in Extremistan is what makes prediction markets ludicrous, as they make events look binary. "A war" is meaningless: you need to estimate its damage—and no damage is typical. Many predicted that the First War would occur—but nobody predicted its magnitude. Of the reasons economics does not work is that the literature is almost completely blind to the point."

That's hard to believe, but maybe it's true.

"A Simple Proof Of Unpredictability In The Fourth Quadrant

I show elsewhere that if you don't know what a "typical" event is, fractal power laws are the most effective way to discuss the extremes mathematically. It does not mean that the real world generator is actually a power law—it means you don't understand the structure of the external events it delivers and need a tool of analysis so you do not become a turkey. Also, fractals simplify the mathematical discussions because all you need is play with one parameter (I call it "alpha") and it increases or decreases the role of the rare event in the total properties"

It's still a model, however.

"For instance, you move alpha from 2.3 to 2 in the publishing business, and the sales of books in excess of 1 million copies triple! Before meeting Benoit Mandelbrot, I used to play with combinations of scenarios with series of probabilities and series of payoffs filling spreadsheets with clumsy simulations; learning to use fractals made such analyses immediate. Now all I do is change the alpha and see what's going on."

He likes fractals. They can generate large increases or decreases.

"Now the problem: Parametrizing a power law lends itself to monstrous estimation errors (I said that heavy tails have horrible inverse problems). Small changes in the "alpha" main parameter used by power laws leads to monstrously large effects in the tails. Monstrous."

Small changes can generate large effects, which is why non-linearity is also used in chaos theory, I believe.

"And we don't observe the "alpha. Figure 5 shows more than 40 thousand computations of the tail exponent "alpha" from different samples of different economic variables (data for which it is impossible to refute fractal power laws). We clearly have problems figuring it what the "alpha" is: our results are marred with errors. Clearly the mean absolute error is in excess of 1 (i.e. between alpha=2 and alpha=3). Numerous papers in econophysics found an "average" alpha between 2 and 3—but if you process the >20 million pieces of data analyzed in the literature, you find that the variations between single variables are extremely significant.

Figure 5—Estimation error in "alpha" from 40 thousand economic variables. I thank Pallop Angsupun for data.

Now this mean error has massive consequences. Figure 6 shows the effect: the expected value of your losses in excess of a certain amount(called "shortfall") is multiplied by >10 from a small change in the "alpha" that is less than its mean error! These are the losses banks were talking about with confident precision!

Figure 6—The value of the expected shortfall (expected losses in excess of a certain threshold) in response to changes in tail exponent "alpha". We can see it explode by an order of magnitude.

What if the distribution is not a power law? This is a question I used to get once a day. Let me repeat it: my argument would not change—it would take longer to phrase it.

Many researchers, such as Philip Tetlock, have looked into the incapacity of social scientists in forecasting (economists, political scientists). It is thus evident that while the forecasters might be just "empty suits", the forecast errors are dominated by rare events, and we are limited in our ability to track them. The "wisdom of crowds" might work in the first three quadrant; but it certainly fails (and has failed) in the fourth."

The "rare" events involve massive results. My problem isn't with the massive events or results, but the word "rare". In other words, there are two predictions:
1) How likely?
2) How large?

It seems that in Extremistan both are terribly misjudged. But they are, by definition, more complex than his earlier binary decisions and probablities to begin with. The math doesn't seem to be helping us out with the difficulties inherent in the very definition of the domain. It merely puts it into graph form.

"Living In The Fourth Quadrant

Beware the Charlatan. When I was a quant-trader in complex derivatives, people mistaking my profession used to ask me for "stock tips" which put me in a state of rage: a charlatan is someone likely (statistically) to give you positive advice, of the "how to" variety.

Go to a bookstore, and look at the business shelves: you will find plenty of books telling you how to make your first million, or your first quarter-billion, etc. You will not be likely to find a book on "how I failed in business and in life"—though the second type of advice is vastly more informational, and typically less charlatanic. Indeed, the only popular such finance book I found that was not quacky in nature—on how someone lost his fortune—was both self-published and out of print. Even in academia, there is little room for promotion by publishing negative results—though these, are vastly informational and less marred with statistical biases of the kind we call data snooping. So all I am saying is "what is it that we don't know", and my advice is what to avoid, no more.

You can live longer if you avoid death, get better if you avoid bankruptcy, and become prosperous if you avoid blowups in the fourth quadrant.

Now you would think that people would buy my arguments about lack of knowledge and accept unpredictability. But many kept asking me "now that you say that our measures are wrong, do you have anything better?"

I used to give the same mathematical finance lectures for both graduate students and practitioners before giving up on academic students and grade-seekers. Students cannot understand the value of "this is what we don't know"—they think it is not information, that they are learning nothing. Practitioners on the other hand value it immensely. Likewise with statisticians: I never had a disagreement with statisticians (who build the field)—only with users of statistical methods.

Spyros Makridakis and I are editors of a special issue of a decision science journal, The International Journal of Forecasting. The issue is about "What to do in an environment of low predictability". We received tons of papers, but guess what? Very few addressed the point: they mostly focused on showing us that they predict better (on paper). This convinced me to engage in my new project: "how to live in a world we don't understand".

This is what I really like about Taleb. He focuses on what we don't know. We do need to live in a world that we cannot understand.

"So for now I can produce phronetic rules (in the Aristotelian sense of phronesis, decision-making wisdom). Here are a few, to conclude. "

I don't like the word "rules". I would say "guidelines" or "rules of the road" or "tricks of the trade".

"Phronetic Rules: What Is Wise To Do (Or Not Do) In The Fourth Quadrant

1) Avoid Optimization, Learn to Love Redundancy. Psychologists tell us that getting rich does not bring happiness—if you spend it. But if you hide it under the mattress, you are less vulnerable to a black swan. Only fools (such as Banks) optimize, not realizing that a simple model error can blow through their capital (as it just did). In one day in August 2007, Goldman Sachs experienced 24 x the average daily transaction volume—would 29 times have blown up the system? The only weak point I know of financial markets is their ability to drive people & companies to "efficiency" (to please a stock analyst’s earnings target) against risks of extreme events.

Indeed some systems tend to optimize—therefore become more fragile. Electricity grids for example optimize to the point of not coping with unexpected surges—Albert-Lazlo Barabasi warned us of the possibility of a NYC blackout like the one we had in August 2003. Quite prophetic, the fellow. Yet energy supply kept getting more and more efficient since. Commodity prices can double on a short burst in demand (oil, copper, wheat) —we no longer have any slack. Almost everyone who talks about "flat earth" does not realize that it is overoptimized to the point of maximal vulnerability.

Biological systems—those that survived millions of years—include huge redundancies. Just consider why we like sexual encounters (so redundant to do it so often!). Historically populations tended to produced around 4-12 children to get to the historical average of ~2 survivors to adulthood.

Option-theoretic analysis: redundancy is like long an option. You certainly pay for it, but it may be necessary for survival."

( 1 ) Save

"2) Avoid prediction of remote payoffs—though not necessarily ordinary ones. Payoffs from remote parts of the distribution are more difficult to predict than closer parts.

A general principle is that, while in the first three quadrants you can use the best model you can find, this is dangerous in the fourth quadrant: no model should be better than just any model."

( 2 ) Take the money

"3) Beware the "atypicality" of remote events. There is a sucker's method called "scenario analysis" and "stress testing"—usually based on the past (or some "make sense" theory). Yet I show in the appendix how past shortfalls that do not predict subsequent shortfalls. Likewise, "prediction markets" are for fools. They might work for a binary election, but not in the Fourth Quadrant. Recall the very definition of events is complicated: success might mean one million in the bank ...or five billions!"

( 3 ) Stick to what you know and understand

"4) Time. It takes much, much longer for a times series in the Fourth Quadrant to reveal its property. At the worst, we don't know how long. Yet compensation for bank executives is done on a short term window, causing a mismatch between observation window and necessary window. They get rich in spite of negative returns. But we can have a pretty clear idea if the "Black Swan" can hit on the left (losses) or on the right (profits).

The point can be used in climatic analysis. Things that have worked for a long time are preferable—they are more likely to have reached their ergodic states."

( 4 ) Look at past results, but going forward base rewards on future proven results

"5) Beware Moral Hazard. Is optimal to make series of bonuses betting on hidden risks in the Fourth Quadrant, then blow up and write a thank you letter. Fannie Mae and Freddie Mac's Chairmen will in all likelihood keep their previous bonuses (as in all previous cases) and even get close to 15 million of severance pay each."

This is my most important one for this crisis:
( 5 ) Do not give implicit or explicit guarantees without tying the people involved to personal responsiblity for the results or severely circumscribing their performance

"6) Metrics. Conventional metrics based on type 1 randomness don't work. Words like "standard deviation" are not stable and does not measure anything in the Fourth Quadrant. So does "linear regression" (the errors are in the fourth quadrant), "Sharpe ratio", Markowitz optimal portfolio, ANOVA shmnamova, Least square, etc. Literally anything mechanistically pulled out of a statistical textbook."

( 6) Forget mechanistic explanations

"My problem is that people can both accept the role of rare events, agree with me, and still use these metrics, which is leading me to test if this is a psychological disorder.

The technical appendix shows why these metrics fail: they are based on "variance"/"standard deviation" and terms invented years ago when we had no computers. One way I can prove that anything linked to standard deviation is a facade of knowledge: There is a measure called Kurtosis that indicates departure from "Normality". It is very, very unstable and marred with huge sampling error: 70-90% of the Kurtosis in Oil, SP500, Silver, UK interest rates, Nikkei, US deposit rates, sugar, and the dollar/yet currency rate come from 1 day in the past 40 years, reminiscent of figure 3. This means that no sample will ever deliver the true variance. It also tells us anyone using "variance" or "standard deviation" (or worse making models that make us take decisions based on it) in the fourth quadrant is incompetent."

He's describing weakness of the will, which is a very old problem.

"7) Where is the skewness? Clearly the Fourth Quadrant can present left or right skewness. If we suspect right-skewness, the true mean is more likely to be underestimated by measurement of past realizations, and the total potential is likewise poorly gauged. A biotech company (usually) faces positive uncertainty, a bank faces almost exclusively negative shocks. I call that in my new project "concave" or "convex" to model error.

( 7 ) Try and figure out where your weaknesses are.

"8) Do not confuse absence of volatility with absence of risks. Recall how conventional metrics of using volatility as an indicator of stability has fooled Bernanke—as well as the banking system.

Figure 7 Random Walk—Characterized by volatility. You only find these in textbooks and in essays on probability by people who have never really taken decisions under uncertainty.

Figure 8 Random Jump process—It is not characterized by its volatility. Its exits the 80-120 range much less often, but its extremes are far more severe. Please tell Bernanke if you have the chance to meet him.

( 8 ) Be prepared for surprises

"9) Beware presentations of risk numbers. Not only we have mathematical problems, but risk perception is subjected to framing issues that are acute in the Fourth Quadrant. Dan Goldstein and I are running a program of experiments in the psychology of uncertainty and finding that the perception of rare events is subjected to severe framing distortions: people are aggressive with risks that hit them "once every thirty years" but not if they are told that the risk happens with a "3% a year" occurrence. Furthermore it appears that risk representations are not neutral: they cause risk taking even when they are known to be unreliable."

( 9 ) Always be conservative with risk

"Technical Appendix to "The Fourth Quadrant"—Click Here"

Okay. I made up my own rules from his rules. So sue me. Read him yourself. It's fun.