Financial crises always seem to come out of nowhere. Despite the best guesses of economists, it seems that every few decades another one turns every prediction on its head. How could there possibly be a way of predicting the unpredictable?
One French academic, however, has made it his mission to do just that — predict the supposedly unpredictable. Didier Sornette, a professor of entrepreneurial risks at the Swiss Federal Institute of Technology, has helped developed a theory that he calls “dragon-kings” that could help economists plan for potential financial catastrophes before they ever happen.
So, what are “dragon-kings?” To explain, Sornette provides as an example the distribution of city sizes in France, which, he says, follow the traditional power law; France, like most nations, has many small cities and just a few larger ones. “On a log-to-log scale, this distribution gives a straight-line,” Sornette says, but there’s one exception. “Paris,” Sornette notes, “is an outlier and many times larger than it ought to be if it were to follow the power law,” per the MIT Technology Review.
“Paris is an outlier because it has been hugely influential in the history of France and so has benefited from various positive feedback mechanisms that have ensured its outsize growth,” Sornette notes. “London occupies a similarly outlying position in the distribution of cities in the United Kingdom.”
Sornette describes a number of outliers that deviate from traditional power law, outliers that he says are the result of positive feedback mechanisms, which make them much larger than their peers. Such outliers, Sornette says, can be used to describe everything from extreme weather events, to financial collapses, to epileptic seizures, to human birth. These are dragon-kings. They are entirely unaccounted for by current ideas about power law, since they are “absolutely non-linear,” as Sornette says.
Dragon-Kings vs. Black Swans
Sornette emphasizes that the primary characteristic of dragon-king events is the presence of a positive feedback mechanism that “creates faster-than-exponential growth, making them larger than expected.” But just because dragon-king events are extreme, doesn’t mean they’re infrequent, Sornette cautions. Dragon-kings, he says, are not a gussied up version of a “black swan” event.
“Black swan” or “black swan event” is a term originally coined by Nassim Nicholas Taleb, a professor of Risk Engineering at the New York University Polytechnic School of Engineering, which describes highly influential and yet unpredictable events that seemingly come “out of nowhere.” Black swan events are considered rare and extreme outliers; indeed, the term “black swan” is a fitting euphemism.
In contrast, Sornette says he and his fellow researchers chose the term “dragon-king” carefully. “I also like to refer to these exceptional events as ‘dragons’ to stress that we deal with a completely different kind of animal, beyond the normal, which extraordinary characteristics, and whose presence, if confirmed, has profound significance.”
These, dragon-kings, Sornette says, “represent extreme events which are a class of their own. They are special. They are outliers,” and perhaps most importantly, unlike black swans, “they are generated by specific mechanisms that may make them predictable, perhaps controllable.”
According to more classical power laws, extreme events are rare. Yet Sornette’s reserach suggests that this isn’t true; another deviation from the “black swan” idea, which stresses the rarity and infrequency of those events. “The seemingly ubiquitous presence of these dragon-kings in all kinds of data sets means that extreme events are significantly more likely than power laws suggest,” Sornette says, per the MIT Technology Review. That’s the reason why we’ve experienced two or three “once in a century” financial crises in the last couple of decades.
Since these events are significantly more common than they were originally thought to be, understanding how they form and, more importantly, how they can be prevented, are of crucial importance. Sornette believes that dragon-kings could be the key to preventing collapses like the one which shook the world at the end of 2008, and which we’re still recovering from today. Even more optimistic: he believes it’s possible.
Are extreme events predictable?
When Sornette’s dragon-king theory was first published in 2009 — smack in the middle of the most devastating recession in the history of the U.S. since the Great Depression — his work was well-received, yet considered far from applicable. Later that year, the MIT Technology Review covered the publication of his theory and commented that Sornette’s idea could be “hugely influential” but, the publication added, Sornette’s “contention that these outliers are in some way more easily predictable than other events smacks more of wishful thinking than of good science.”
It’s easy to understand readers’ skepticism. Sornette’s theory is all very romantic when you think about it. Even the name “dragon-kings” sounds fantastical, almost as though it’s the stuff of Dungeons & Dragons or Game of Thrones rather than a new, academic theory in risk-management and prediction.
Nowadays, however, researchers think that Sornette may be on to something. Daniel Gauthier, a physicist at Duke University as well as his co-authors have found ways to detect telltale signs that a dragon-king event is approaching, and thereby stop it from happening. “A chaotic system may be in flux,” Gauthier told Wired, “but maybe there’s some internal structure we can identify that leads to destabilizing events,” he added.
If Gauthier’s assessment still sounds shaky, that’s probably because it is. Even years after it was first published, Sornette’s theory is still a ways off from informing practical tools for predicting extreme events. Yet, Sornette remains optimistic. “These processes provide clues that allow us to diagnose maturation of a system towards a crisis.” In his original research, he notes that theories like his are necessary if we are ever to manage extreme, “dragon-king” events.
“In many of the pressing issues for our future welfare as well as for the management of our everyday life, will need such a systemic complex system and multidisciplinary approach. This view tends to replace the previous ‘analytical’ approach,” which, Sornette asserts, focused on deconstructing a system into its respective parts; his view, instead, is more holistic.
It’s important to note that dragon-kings don’t just apply to financial crises, either. They describe events in many different complex systems, such as rogue waves in the ocean, extreme weather in the climate, or as Sornette suggested years earlier, the variation in size of cities in France. While we may still be years or even decades away from successfully applying the dragon-king theory to any of those systems, Sornette’s research does offer a small glimmer of light at the end of the tunnel. “The dragon-king theory gives hope,” Sornette said, ending a Ted Talk he presented at the global conference last year. “We learn that most systems have pockets of predictability.”
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