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Black Swan, Dragon King, Greek Tragedy – Lessons from a “Diplomatic Debate”


In his Ted Talk Dragon King beats Black Swan in June 2013 Didier Sornette contrasted his ideas of market predictability to Nassim Taleb’s concept of a Black Swan. As Sornette explained a black swan is a rare bird. Seeing a black swan shatters all beliefs that swans should be white. The Black Swan stands for the idea of unpredictability and extreme events that are “fundamentally unknowable”. Sornette compared this idea with his concept of a Dragon King which is “exactly the opposite”. According to his view, most extreme events are actually knowable and – at least to a certain extent – predictable.

In May 2014, there was a very stimulating ETH-sponsored debate between Nassim Taleb and Didier Sornette which threw further light on their “Diametrically Opposite Approaches to Risk & Predictability”, so the title of the meeting. The following video is an edited version of what Nassim Taleb called a “diplomatic debate”. To him this is a conversation in which one looks for synthesis as opposed to one in which one is trying to win an argument by all means. This is surely benefitting the audience who, if they had not read their books, may know Didier Sornette and Nassim Taleb mainly from their highly technical scientific papers here and here.

For an outside observer it is hard to take sides after these 45 minutes. To me, there seems to be no “right” or “wrong”. There are valid arguments on either side and on second sight Taleb’s Black Swan turns out to be one of several possible crisis scenarios in Sornette’s framework.

Nassim Taleb’s focus is on risk management of exposures. He starts with the example of a china cup which is fragile because “it doesn’t like volatility and has very specific attributes.” (0:43) On the other side, there are other things with other attributes which like volatility. The same holds in risk management. Knowledge about these attributes allows to adjust exposures respectively and benefit from volatility without identifying and predicting a concrete event.

Taleb draws attention to three mistakes which in his view people make in managing risk:

(1) They study random variables as sources of risk instead of exposures (1:06). He argues that very often risk, or the source of risk, is extremely hard to compute. He can avoid this wasting of time, as he calls it, by changing his exposure instead. (1:20)

(2) People tend to adjust to the worst past. (This is the example of the high-water mark at 1:51) But, as Taleb argues, if you look at natural things, they don’t adjust in the same way. They adjust to something higher and “overcompensate”. But the brain doesn’t. This explains why in his view when people study risk they are not as good as when they act based on their perception of risk.

(3) People neglect that the response of their exposures to a source of risk is nonlinear. In Taleb’s concept, exposure to the source of risk may be concave or convex, and concavity – an accelerated harm or negative response to risk – and fragility are related. A single item may be fragile. “If you’re fragile than you’re necessarily concave to the source of risk.” (3:35) Take again the china cup. There are more downsides than upsides from earthquakes in this case. In contrast, Taleb’s exposure is symmetric.

Didier Sornette’s approach is indeed “diametrically opposite” to this concept. While Nassim Taleb accepts the world’s inherent uncertainty, and abstains from trying to predict the course of random events, Didier Sornette and his Financial Crisis Observatory in a sense are searching for “patterns”. According to Sornette extreme events such as the French revolution in 1789 or the “Spanish” worldwide flu of 1918, but also the dotcom crash in 2000 and the financial crisis in 2008, go through dynamical processes that make them knowable and to some degree predictable before they occur (6:20).

Focusing on financial time series and studying the distribution of peak-to-valley losses Sornette shows that a large part of these losses can be represented by a power law (6:39). However, some of them, which are associated with great crashes in the past, are outliers. They occur much more frequently than predicted by the law. These are the Dragon Kings.

As Sornette wrote in his book Why Stock Markets Crash: “Large financial crashes … form a class of their own that can be seen from their statistical signatures. … They are special and thus require a special explanation, a specific model, a theory of their own.” (p.xvi)

In the debate, Sornette then goes on arguing how these extreme events result from a progressive maturation towards an instability or bifurcation. He takes water levels at different temperatures as an example (7:53). The fact that at the boiling point the nature of the water changes can be inferred from the past although “macroscopic linear extrapolation” is no longer possible.

Note in this context what Nassim Taleb wrote in his textbook on Probability and Risk in the Real World (p. 13): “The risk of breaking of the coffee cup is not necessarily in the past time series of the variable; in fact surviving objects have to have had a “rosy” past.” This may hold for the coffee cup, but not for water. In Didier Sornette’s example, the past of the observed variable was “rosy”, too. Nevertheless, he argues that it is possible to draw conclusions from the past dynamics of the water about its entirely different behaviour in the future.

Sornette considers financial market crashes as the result of the collective behaviour of herding agents that ends up destabilizing the system (“a single molecule does not boil at 100°”). But, he continues that there is good news: From the theory of bifurcations and dynamical systems he has learned about the Fundamental Reduction Theorem. It says that most of the time, the system is too complex to predict its behaviour. But, close to bifurcation there is a window of visibility (9:10).

Sornette continues explaining how „generally, close to a regime transition, a system bifurcates through the variation of a single (or a few) effective “control” parameter”. This brings him to two questions:

Can predictability be implemented in practice? Can the process be influenced?

As an example he presents the activities of the Financial Crisis Observatory developed at ETH Zurich since 2008. There are two hypotheses:

Hypothesis 1: Financial (and other) bubbles can be diagnosed in real-time before they end.

Hypothesis 2: The termination of financial (and other) bubbles can be bracketed using probabilistic forecasts, with a reliability better than chance (which remains to be quantified).

Passionately, Sornette states that never again will we “go through the process of these extremely damaging crises where the policymakers, analysts and so on conclude that … this was not knowable in advance.

Furthermore, this type of knowledge should empower the researcher to go to the next stage which is control. “Of course the control system is not of the scale of the full financial market but … in some circumstances, when we understand this system shows this power distribution of events with a Dragon King, by very tiny perturbations at the right moment we can actually control and slay this Dragon King.

Sornette finishes his presentation by summarizing his view in a kind of predictability diagram where he distinguishes two dimensions (13:25). One is heterogeneity or diversity of the different elements in the system and the other is the level of coupling or interaction. “By classifying a system in a given regime, we can assert its degree of predictability.” In this framework, non-predictability is part of a larger picture. Sornette concedes that there are Black Swans, but most crises are Dragon Kings:

This Financial Crisis Observatory that we have developed, for me was really a reaction to the disgust that developed from the often heard statement that the financial crisis of 2008 was a big surprise, was a Black Swan. It was no Black Swan, it was clearly visible – not in detail. But it was clearly visible that something was going to happen.

And, according to his findings it is about to happen again (see also at the end of this article the extract of an interview Sornette gave to Finanz und Wirtschaft in September 2013). Right now, a crisis has been looming for many years and once the bubble bursts nobody can pretend that this was not knowable in advance. As Sornette said: Not the details, but the broad picture. And we feel that he is right in that policymakers and analysts foreseeably will come up exactly with the Black Swan argument that this is coming as a surprise – and we will know simply from watching from outside that this cannot be true. Whether the dynamics can be captured in mathematical detail early enough to prevent the bubble from bursting is another matter. But it is encouraging to see that in Zurich efforts are made in this direction.

What has the Greek tragedy mentioned in the title to do with all this? It is not the form of theatre I had in mind, but the drama which is currently unfolding in the Eurozone. Both Taleb and Sornette stress that bubbles and crises are part of our lives. They will happen again and again. On January 25, Greece could become a trigger – as could any other minor or major event before and after. Then again analysts and policymakers will tell us that this is a Black Swan.

Do not believe them. They could have known.


The following is a short extract from a German-language interview with Didier Sornette by Gregor Mast und Mark Dittli, Finanz und Wirtschaft, September 19 2013:

„Die Notenbanken pumpen neue Blasen auf“

Herr Sornette, fünf Jahre sind seit dem Zusammenbruch von Lehman Brothers vergangen. Ist das globale Finanzsystem heute sicherer als 2007?
Nein, im Gegenteil. Die Situation ist schlimmer als zuvor. Die zehn bis fünfzehn grössten Banken sind heute noch grösser und von noch höherer systemischer Wichtigkeit als vor fünf Jahren. Sie bilden als sogenannte Superspreader das Zentrum des globalen Finanznetzwerks. All die falschen Anreizsysteme innerhalb der Banken sind intakt, da wurde nichts geändert. Das wissen die Banker, die Regulatoren und die Notenbanker ganz genau. Alles, was in der Zwischenzeit getan wurde, all die Stresstests, die Massnahmen der Notenbanken, diente bloss dazu, das Vertrauen ins System wieder herzustellen. Die grundsätzlichen Probleme wurden nicht angepackt.
Wir tanzen eine Art Tango aus ¬Manie und Crash. Und die Notenbanken reagieren auf jeden Crash damit, dass sie eine neue Blase aufpumpen.

Tun sie das auch jetzt wieder?
Ja und nein. Unbestritten ist: Wir sehen heute eine enorme Blase im Bondmarkt, im gesamten Kreditvolumen. Mit ihren riesigen Bilanzen führen die Notenbanken ein einzigartiges Experiment durch. Generell kann gesagt werden, dass eine Unmenge an Geld gegenwärtig nach Anlagemöglichkeiten sucht. Wir identifizieren am Financial Crisis Observatory an der ETH heute eine ganze Reihe blasenähnlicher Übertreibungen in verschiedenen Märkten. Es blubbert überall. Das Finanzsystem ist viel fragiler als früher.

Sie führen die vierjährige Hausse an den Börsen auf die Politik des Fed zurück?
Wir sehen auf jeden Fall eine hohe Korrelation zwischen dem Bilanzvolumen des Fed und dem amerikanischen Aktienmarkt. Jedes Mal, wenn ein Quantitative-Easing-Programm startete, stiegen die Kurse. Und jedes Mal, wenn eines stoppte, kam es zu einer Korrektur.

Wie wird das alles dereinst enden?
Die Frage ist furchteinflössend. Wir wissen, dass diese Geldpolitik nur kurzzeitig den Schmerz lindert, die grundsätz¬lichen Probleme aber nicht löst. In den USA haben wir einen dreissigjährigen kreditgetriebenen Boom gesehen. In Europa, um ein anderes Beispiel zu -nennen, haben wir mit dem Euro ein ¬unfassbares Monster geschaffen, eine politische Kreatur, ohne jeden ökonomischen Verstand. Das kann die EZB nicht ewig überdecken.“
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