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Video lecture by Ken Long (at the Statistics Problem Solvers blog) on Nassim Taleb‘s 4th Quadrant problems [1,2], i.e. a region where statistics not only don’t work but in which statistics are downright dangerous, because they lead you to make predictions as well as control systems that are unprepared for the kinds of systems shocks awaiting you.

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).”, Nassim Taleb, in [1].

[1] Nassim Nicholas Taleb, “The Fourth Quadrant: A Map of the Limits of Statistics“, An Edge Original Essay, Set., 2008. (link)

[2] Nassim Nicholas Taleb,”Convexity, Robustness, and Model Error inside the Fourth Quadrant“, Oxford Lecture (Draft version), Oxford, July 2010. [PDF paper]

Last year, at the beginning of October I decided to dedicate my second post on financial markets (I, II) to Black Swans. Swans are beautiful animals, but while white swans are vulgar and omnipresent at every pond, black swans are rare! Meanwhile, 2 days ago (June 1) the Wall Street Journal comes with this very awkward - and by all means for that precise reason - interesting article written by journalist Scott Patterson, where Mr. Taleb’s name pops-up again (image below).

Well, … let’s face it: you could put your money in the bank and have – let’s say – a 3% revenue at the end of your fiscal year. Or you could apply it to raise a new fancy gourmet restaurant at your local vicinity. Restaurants and local food stores are known to have 5-7% revenues in one year, not to speak on the immense burden they represent as well as for some associated risks – specially these days. But then you may think – better than banks, right? Right! Or, just to give you another example on this increasing scale - raising a little bit the risk -, on the other hand you could apply your money in stock markets. Main financial indexes (Dow Jones, NASDAQ, etc) are known to have an annual average revenue of 10-12% (since 1918). Not these days of course, where high volatility and entropy in the markets are installed. Well,  emergent countries like China are raising themselves at 12%/year also. We could go on and on with so many other examples. Some say that Eolic parks could achieve 40%. Normally the cost of one eolic tower is around 1 million euros, which could be paid back after one year producing energy trough wind at normal operating conditions. The rest are maintenance costs, as well as initial investment in terrains, etc. So, what’s new? Consider this. For moments imagine yourself having 100% in revenues, just last year, at this precise dramatic context. That’s 10 times what the market does in regular years, 20 times what your favorite restaurant does. Moreover, there is a substantial difference between all these examples. If you keep dropping money at the restaurant (for instance the revenue you have earned in the last year), still liquid revenues will be the same in the next year (unless you open a new dinner room next to the first one, while the awful burden keeps increasing). Some business are static and linear in time while others are exponential. As Alice in the wonderland, you will need to keep running twice as faster in order to be at the same place. Amazing those differences, no? Well, not for those “lovely” animal creatures known as Black Swans. According to Patterson, … Funds run by Universa, which is managed and owned by Mr. Taleb’s long-time collaborator Mark Spitznagel, last year gained more than 100% thanks to its bearish bets. Universa now runs about $6 billion, up from the $300 million it began with in January 2007. Excerpts from the Wall Street Journal article (Black Swan Fund Makes a Big Bet on Inflation) follow below. So, why the hell I do not feel at all surprised by this?! Really, I am not. Let me just say, I do have my own reasons:

Nassim Nicholas Taleb - Black Swan author  [...] A hedge fund firm that reaped huge rewards betting against the market last year is about to open a fund premised on another wager: that the massive stimulus efforts of global governments will lead to hyperinflation. The firm, Universa Investments L.P., is known for its ties to gloomy investor Nassim Nicholas Taleb, author of the 2007 bestseller “The Black Swan,” which describes the impact of extreme events on the world and financial markets.

Funds run by Universa, which is managed and owned by Mr. Taleb’s long-time collaborator Mark Spitznagel, last year gained more than 100% thanks to its bearish bets. Universa now runs about $6 billion, up from the $300 million it began with in January 2007. Earlier this year, Mr. Spitznagel closed several funds to new investors….

Mr. Taleb doesn’t have an ownership interest in the Santa Monica, Calif., firm, but he has significant investments in it and helps shape its strategies. The term “black swan,” which has become a market catchphrase in the last few years, alludes to the once-widespread belief in the West that all swans are white. The notion was proven false when European explorers discovered black swans in Australia. A black-swan event, according to Mr. Taleb, is something that is extreme and highly unexpected. … [...]

Many man made and naturally occurring phenomena (being inherently complex systems), including city sizes, incomes, word frequencies, internet links, social networks and earthquake magnitudes, are distributed according to a power-law distribution. One under f Zipf’s law follows the same characteristic, or pink noise. Here is a possible long list, collected year after year, since the 1910′s up to now – 2008 (which I vividly recommend). From vacuum tubes to trading activities in world financial markets. Even, we could easily found them on Pollock’s paintings (recently here). Back in 2002, I have addressed some of his painting features (mostly fractal) regarding the theme “Emergent Aesthetics in Autonomous Collective Systems“. Astonishingly, without having a clue what fractal dimension’s would be, Jackson increased his fractal signatures year over year, while getting old. Indeed, “Action painting”, has he call it, mainly using his body motion and a bucket, were largely enough. 

Financial markets are indeed complex systems, even if they are far from being self-regulated. Much after this recent black Monday, I have made here some notes regarding Self-Organization and finance, over two weeks or so. Their basic features – as I see it. However- essentially what brings me here today is-, what happens to their frequency? Are phenomena like the current financial crisis, frequent? Well, much of that depends on our knowledge on power-laws. Good news is that we know how many of them will occur in a very large time window, bad news is that, we don’t know when will they precisely occur. As in Earthquakes (check this out). Does this impel us to do nothing? Not at all. We can’t do anything about earthquakes (at least for now - except prevent them), however we can establish some ground smart rules in order to avoid financial systems to collapse in turmoil (that is, tune them in the precise physical regime). Power-laws are not only our wake-up call, as they are a signature. For good or for worse. It seems that we are all playing across the planet, a reversed El Farol Bar problem. If that’s somehow true we all should ask new questions like: In what frequency should we go to a bar ?! In other words, should we all run to the banks now, asking for our deposits?

Any polynomial relationship that exhibits the property of scale invariance is a Power-Law. Power-law implies that small occurrences are extremely common, whereas large instances are extremely rare (similarly over maps and cities - if you have time, found out the foundation of Berlin city over time). As the large quantity of small dots + low frequency of large dots we may found on Jackson Pollock paintings. The same goes for Black-Swans.

Jackson Pollock in action - As reported somehow recently by Nature magazine (Sept., 13, 2000), research suggests that the abstract works of artists such as Jackson Pollock are esthetically pleasing because they obey fractal rules similar to those found on the natural world. Pollock was known to have swung his paint back and forth like a pendulum, using a can on the end of a string with a hole punched in it. Researchers (Jensen) have found that if a swinging pendulum is hit with a hammer at just the right frequency (slightly less than the natural rhythm of the pendulum), its motion becomes chaotic and the paint traces out very convincing fake Pollocks. However, the artist had no idea of fractals or chaotic motion, while dot distribution over Pollocks paintings follow a power-law.

Jackson Pollock in action - As reported somehow recently by Nature magazine (Sept., 13, 2000), research suggests that the abstract works of artists such as Jackson Pollock are esthetically pleasing because they obey fractal rules similar to those found on the natural world. Pollock was known to have swung his paint back and forth like a pendulum, using a can on the end of a string with a hole punched in it. Researchers (Jensen) have found that if a swinging pendulum is hit with a hammer at just the right frequency (slightly less than the natural rhythm of the pendulum), its motion becomes chaotic and the paint traces out very convincing "fake Pollocks". However, the artist had no idea of fractals or chaotic motion, while dot distribution over Pollock's paintings indeed follow a power-law.

A Black Swan is a highly improbable event that has three characteristics: It is unpredictable, it has incredible impact, and after it happens we invent a reason for it that makes it seem less probable. For those of you that did not have read 2007 Taleb’s book (picture above), wondering what a Black Swan is, or question yourself from where the name arises, just jump for a quick look over here. Nassim started to wrote his book in 2003. Finished it in 2006. So, in what way this “funny” distribution regards financial markets? Well, for many of us now, it his surprising that he have wrote this, back then:

[...] Globalization creates interlocking fragility, while reducing volatility and giving the appearance of stability. In other words it creates devastating Black Swans. We have never lived before under the threat of a global collapse. Financial Institutions have been merging into a smaller number of very large banks. Almost all banks are interrelated. So the financial ecology is swelling into gigantic, incestuous, bureaucratic banks – when one fails, they all fall. The increased concentration among banks seems to have the effect of making financial crises less likely, but when they happen they are more global in scale and hit us very hard. We have moved from a diversified ecology of small banks, with varied lending policies, to a more homogeneous framework of firms that all resemble one another. True, we now have fewer failures, but when they occur ….I shiver at the thought. [...]

Were these words a Black Swan within the Black Swan book itself? Rather not. He continues directly to something we now know and face it in precise context. Please note that this was written in the period 2003-2006:

[...] Banks hire dull people and train them to be even more dull. If they look conservative, it’s only because their loans go bust on rare, very rare occasions. But (…) bankers are not conservative at all. They are just phenomenally skilled at self-deception by burying the possibility of a large, devastating loss under the rug. [...] The government-sponsored institution Fannie Mae, when I look at its risks, seems to be sitting on a barrel of dynamite, vulnerable to the slightest hiccup. But not to worry: their large staff of scientists deemed these events “unlikely”. [...] 

What about the costs, and the memory of them? Yes, indeed memory is important while playing game-theory-like games, as his mainly in our daily reality, but in one-two generations it will be probably lost (I hope not), and once again all will start:

[...]  the real-estate collapse of the early 1990s in which the now defunct savings and loan industry required a taxpayer-funded bailout of more than half a trillion dollars. The Federal Reserve bank protected them at our expense: when “conservative” bankers make profits, they get the benefits; when they are hurt, we pay the costs.

Should we be surprised? In fact, this is not new. Somehow, fallacy goes on (as George Monbiot tackle it with extreme precision over Guardian Journal very recently – Sep. 30). Not only we were not reacting to these power-law consequences, as many of those economic agents playing within the systems core itself, were thinking of something else:

[...] Once again, recall the story of banks hiding explosive risks in their portfolios. It is not a good idea to trust corporations with matters such as rare events because the performance of these executives is not observable on a short-term basis, and they will game the system by showing good performance so they can get their yearly bonus. The Achilles’ heel of capitalism is that if you make corporations compete, it is sometimes the one that is most exposed to the negative Black Swan that will appear to be the most for survival.[...] As if we did not have enough problems, banks are now more vulnerable to the Black Swan and the ludic fallacy than ever before with “scientists” among their staff taking care of exposures. The giant J. P. Morgan put the entire world at risk by introducing in the nineties RiskMetrics, a phony method aiming at managing people’s risks, causing the generalized use of the ludic fallacy, and bringing Dr. Johns into power in place of the skeptical Fat Tonys. (a related method called “Value-at-Risk,” which relies on the quantitative measurement of risk, has been spreading.) [...]

Starting with the distribution and frequency of these kind of events (among many others), all of these words were written in the period 2003-2006. Since then, you could follow Taleb’s war on “Value at Risk” over here.  Or here, at Edge.org which I highly recommend.

Meanwhile, apart from what markets are suffering and complex science may enlightened us, life goes on. Not necessarily as we supposed. As we know, reality, many times excels fiction; one single video frame could value one thousand words. Right at your neighborhood. As you may see below, consequences could be much worse than a tornado:

more about “Foreclosure Alley – SoCal Connected“, posted with vodpod

 

 

[...] People should learn how to play Lego with their minds. Concepts are building bricks [...] V. Ramos, 2002.

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