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The Incerto Podcast
Nassim Taleb & Benoit Mandelbrot - A Focus On The Exceptions That Prove The Rule (EXTREMISTAN VS MEDIOCRISTAN)
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Within a few days of publishing this episode, Tim Ferriss will release a podcast with Nassim Taleb and Scott Patterson. You may have noticed that the most previous guest on this podcast was the very same Scott Patterson, because he had authored this incredible book that looks into the worldview of the likes of Nassim Taleb and other people that he refers to calls Chaos Kings. In the Chaos Kings book, there was an anecdote that really stood out to me, and that was Taleb's introduction to this fella, Benoit Mandelbrot. And the Black Swan was in fact dedicated to Benoit. It was extremely influential in the Sim Taleb's worldview. And something that Scott had said is that they'd only produced one piece of work together and that was an essay or, or an academic paper. I'm not sure what you would class it as, but it was written back in 2006 and I found it online and that is what I'm just reading verbatim here for this podcast. But before we do it, I just want to remind you all that this podcast is an absolute side hustle to what my main podcast is, which is a curious worldview. There you will find the very same interviews that are featured on this podcast, but then as well many, many more. For instance, even last week Desmond Shum, a Chinese billionaire who had to flee out of fear of being disappeared, he just tells his entire story on the podcast. Many other examples like that. So it's the top link in the description. I would encourage you all to go over there, follow it and just give it a chance. Because let's assume that we have more interests in common and if we had to take that assumption to its logical conclusion, then hopefully you will also enjoy a curious worldview. But here is the essay. It is called A Focus on the Exceptions that Prove the Rule by Benoit Mandelbrot and the Simta Lab Conventional studies of uncertainty, whether in statistics, economics, finance or social science, have largely stayed close to the so called Bell curve, a symmetrical graph that represents a probability distribution used to great effect to describe errors in astronomical measurement by the 19th century mathematician Carl Friedrich Gauss. The Bell curve or Gaussian model has since pervaded our business and scientific culture, and terms such as sigma variance, standard deviation, correlation, R square and the Sharpe ratio are all directly linked to it. If you read a mutual fund prospectus or a hedge fund's exposure, the odds are that it will supply you with, among other information, some quantitative summary claiming the measure risk. That measure will be based on one of the above buzzwords that derive from the Bell Curve and its kin. Such measures of future uncertainty satisfy our ingrained desire to simplify by squeezing into one single number matters that are too rich to be described by it. In addition, they cater to psychological biases and our tendency to understate uncertainty in order to provide an illusion of understanding the world. The Bell Curve has been presented as normal for almost two centuries, despite its flaws being obvious to any practitioner with empirical sense. Granted, it has been tinkered with using such methods such as complementary jumps, stress testing, regime switching, or the elaborate methods known as Garch. Garch. But while they represent a good effort, they fail to address the Bell Curve's fundamental flaws. The problem is that measures of uncertainty using the Bell Curve simply disregard the possibility of sharp jumps or discontinuities and therefore have no meaning or consequence. Using them is like focusing on the grass and missing out on the gigantic trees. In fact, while the occasional and unpredictable large deviations are rare, they cannot be dismissed as outliers because cumulatively, their impact is long term and so dramatic. The traditional Gaussian way of looking at the world begins by focusing on the ordinary and then deals with exceptions or so called outliers and ancillaries. But there is also a second way which takes the exceptional as a starting point and deals with the ordinary in a subordinate manner, simply because that ordinary is less consequential. These two models correspond to mutually exclusive types of randomness, mild or Gaussian on the one hand, and wild fractal or scalable power laws on the other. Measurements that exhibit mild randomness are suitable for treatment by the Bell Curve or Gaussian models, whereas those that are susceptible to wild randomness can only be expressed accurately using a fractal scale. The good news, especially for practitioners, is that the fractal model is both intuitively and computationally simpler than the Gaussian, which makes us wonder why it has not been implemented before. Let us first turn to an illustration of mild randomness. Assume that you round up 1,000 people at random among the general population and bring them into a stadium. Then add the heaviest person you can think of to that sample. Even assuming he weighs 300kg more than three times the average, he will rarely represent more than a very small fraction of the entire population, say 0.5%. Also, FYI, this is mediocristan. Similarly, in the car insurance business, no single accident will make a dent in a company's annual income. These two examples follow the law of large numbers, which implies that the average of a random sample is likely to be close to the mean of the whole population in a population that follows a mild type of randomness. One single observation, such as a very heavy person may seem impressive by itself, but will not disproportionately impact the aggregate or total. A randomness that disappears under averaging is trivial and harmless. You can diversify it away by having a large sample. There are specific measurements where the Bell curve approach works very well, such as weight, height, calories consumed, death by heart attacks, or performance of a gambler at a casino. An individual that is a few million miles tall is not biologically possible, but an exception of equivalent scale cannot be ruled out with a different sort of variable, as we will see next. And here is where he must introduce for the first time the concept of extremistan. Whether he uses that language or not, we will see. All right, back to the piece. Wild Randomness what is wild randomness? Simply put, it is an environment in which a single observation or a particular number can impact the total in a disproportionate way. The Bell curve has thin tails in the sense that large events are considered possible, but far too rare to be consequential. But many fundamental quantities follow distributions that have fat tails, namely a higher probability of extreme values that can have a significant impact on the total. One can safely disregard the odds of running into someone several miles tall or someone who weighs several million kilograms. But similar excessive observations can never be ruled out in other areas of life. Having already considered the weight of 1,000 people assembled for the previous experiment, let us now consider wealth. Add to the crowd, or 1,000 of the wealthiest people to be found on the planet. Bill Gates, the founder of Microsoft. Assuming that his net worth is close to $80 billion, how much would he represent of the total? Wealth? 99.9. And by the way, this as an aside I think I read over the weekend, Elon was up to $250 billion, making him the richest person on the planet, which is four times what Bill's clocked in here. Just shows you how much more into the odorous bowels of extremists than we are plunging back to the text. Indeed, all of the others would represent no more than the variation of his personal portfolio over the past few seconds. For someone's weight to represent such a share, he would need to weigh 30 million kilograms. Try it again with book sales. Line up a collection of 1,000 authors, then add the most read person alive, J.K. rowling, the author of the Harry Potter series with sales of several hundred million books. She would dwarf the remaining 1,000 authors who would collectively have only a few hundred thousand readers. So while weight, height and calorie consumption are Gaussian wealth is not, nor are income market returns, size of hedge funds, returns in financial markets, number of deaths in wars or casualties in terrorist attacks. Almost all man made variables are wild. Furthermore, physical science continues to discover more and more examples of wild uncertainty, such as the intensity of earthquakes, hurricanes or tsunamis. Economic life displays numerous examples of wild uncertainty. For example, during the 1920s the German currency moved from 3 to a dollar to 4 billion to a dollar in a few short years. And veteran currency traders still remember when, as late as the 1990s, short term interest rates jumped several thousand percent. We live in a world of extreme concentration where the winner takes all. Consider for example how Google grabs much of Internet traffic, how Microsoft represents the bulk of PC software sales, how 1% of the US population earns close to 90 times the bottom 20%, or how half the capitalism of the market at least 10,000 listed companies is concentrated in less than 100 corporations. Another aside from this text that I must point out here, which is something Taleb has been hark on more and more and more recently, is how all of these examples are just further exacerbated by our global interconnectedness. Taken together, these facts should be enough to demonstrate that it is the so called outlier and not the regular that we need to model. For instance, a very small number of days account for the bulk of stock market changes. Just 10 trading days represent 63% of the returns of the past 50 years. I'm going to say that one again for emphasis. Extremistan power laws just 10 trading days represent 63% of THE returns of the past 50 years. 10 singular days let us now return to the Gaussian for a closer look at its tails. The sigma is defined as a standard deviation away from the average, which could be around 0.7 to 1% in a stock market, or 8 to 10% in a. Oh sorry. Or 8 to 10 centimeters for height. The probabilities of exceeding multiples of sigma are obtained by a complex mathematical formula. Using this formula, one finds the following values to be one sigma away. The probability of exceeding 6.3 times and it goes all the way down to 10 sigmas is 1.1 in 130, I don't know, 16 zeros and then 20 sigmas away 1 in 36 plus maybe 100 zeros. That's just the eye test. It might not be 100 zeros, but it's it's insane. By the way, you'll be able to see There's a link to this in the podcast description so you'll be able to see the things that you know. I can't communicate well just through words Back to the text soon after about 22 sigmas, one hits a Google which is one with 100 zeros behind it. With measurements such as height and weight, this remote probability makes sense as it as it would require a deviation from the average of more than 2m million. The same cannot be said variables such as financial markets. For example, a level described as a 22 Sigma event has been exceeded with the stock market crashes of 1987 or the interest rate moves of 1992, or variables such as financial markets. For example, a level described as a 22 Sigma event has been exceeded with stock market crashes in 1987 and the interest rate moves of 1992. The key here is to note how the frequencies in the preceding list drop very rapidly in an accelerating way the ratio is not invariant with respect to scale Let us now look more closely at a fractal or scalable distribution using the example of wealth. We find that the odds of encountering a millionaire in Europe are as follows. Richer than 1 million 1 in 62.5 than the bottom value richer than 320 million 1 in 6.4 million. This is simply a fractal law with a tail exponent or alpha of 2, which means that when the number is doubled, the incident goes down by the square of that number, in this case 4. If you look at the ratio of the moves, you will notice that this ratio is invariant with respect to scale. If the alpha were 1, the incidence would decline by half when the number is doubled. This would produce a flatter distribution whereby a greater contribution to the comes from the low probability events. We have used the example of wealth here, but the same fractal scale can be used for stock market returns and many other variables. Indeed, this fractal approach can prove to be an extremely robust method to identify a portfolio's vulnerability to severe risks. Traditional stress testing is usually done by selecting an arbitrary number of worst case scenarios from past data. It assumes that whenever one has seen in the past a large move of, say 10%, one can conclude that a fluctuation of this magnitude would be the worst one can expect for the future. This method forgets that crashes happen without antecedents. Antecedents. I don't know what that word means. Before the crash of 1987, stress testing would not have allowed a 22% move using a fractal method, it is easy to extrapolate multiple trajectory scenarios. If your worst case scenario from the past data was, say, a move of 5% and you assume that this happens once every two years, then with an alpha of two, you can consider that a 10% move happens every eight years and add such a possibility to your simulation. Using this model, a 15% move would happen every 16 years and so forth. This will give you a much clearer idea of your risks by expressing them as a series of possibilities. You can also change the alpha to generate additional scenarios. Lowering it means increasing the probabilities of large deviations and increasing its means. And increasing it means reducing them. What would such a method reveal? It would certainly do what sigma cannot do, which is to show how some portfolios are more robust than others to an entire spectrum of extreme risks. It can also show how some portfolios can benefit inordinately from wild uncertainty. Despite the shortcomings of the Bell Curve reliance on its accelerating and widening the gap Reality and standard tools of measurement the consensus seems to be that any number is better than no number, even if it is wrong. Finance academia is too entrenched in the paradigm to stop calling it an acceptable approximation. Any attempts to refine the tools of modern portfolio theory by relaxing the Bell Curve assumptions or by fudging and adding the occasional jumps will not be sufficient. We live in a world primarily driven by random jumps, and tools designed for random walks address the wrong problem. It would be like tinkering with the models of gases in an attempt to characterize them as solids and call them a good approximation. While scalable laws do not yield precise recipes, they have become an alternative way to view the world and a methodology where a large deviation and stressful events dominate the analysis instead of the other way around. We do not know of a more robust manner for decision making in an uncertain world. And that's it. If you want to hear a little bit more about this, one of the middle episodes of this podcast called Extremistan vs Mediocrity Stan, I think it's potentially my favorite thing I ever learned from the Simta Lab. This is him, I suppose, chipping away the first couple of indents into the sculptor that eventually becomes mediocre. Stand versus Extremistan. Because once you do internalize it, you start to see it everywhere. You really do start to see it everywhere. So check that out if you're interested. Otherwise, I'm sorry if that was hard to follow. As I was reading it, I realized it probably was hard to follow. But as well, a reminder. Go check out a curious worldview. I think you'll like it. All the best. Bye. Bye.