INVESTED: In Markets, in the Future, and in Society.

Here Be Dragon Kings

Patterns and structure can be found everywhere in the world around us. From the symmetries in snowflakes to the self-similarity of Romanesco broccoli, we really can’t get away from it. However, while these examples are drawn from the natural world, the result of human enterprise can also show a surprising level of unintended organization. Consider, for instance, the population size of all cities in Canada (or any country for that matter). If we were to build a list of all Canadian cities and order them from largest (Toronto) to smallest (Saint-Louis-de-Gonzague-du-Cap-Tourmente, a Quebec municipality with only two residents), and then create a chart of how the city size changed from Toronto to Saint-Louis-du-Gonzague-du-Cap-Tourmente, we would find a surprisingly consistent dropoff in population from large to small cities. There would be very few large cities, but many small cities. Mathematically, this dropoff follows what is known as a ‘power-law’, and this case is well-described by something called Zipf’s law—A mathematical relationship between the size and ranking of objects that applies in more situations than you may think. For instance, similar power-law behaviours can be seen in financial markets, where asset drawdowns have been shown to roughly follow a power-law relationship [1].

Interestingly, in many situations there are outlying data points that deviate significantly from the power-law trend. While statistically classified as outliers, these events tend to be unique and of significant importance. For instance, if we were to make a similar categorization of all French cities, Paris would not follow the same pattern as the others. However, Paris is an exceptionally important city in the historical and present context of France as a country and shouldn’t simply be ignored [2]. Additionally, outlying data points for financial market drawdowns are representative of significant market crashes, such as the great financial crisis, or the bursting of the dot-com bubble. Due to the outsized impact that such events can have, they have been dubbed by the French physicist and financial researcher Didier Sornette as ‘Dragon Kings’, indicating their deviation from power-law trends (the wealth of Kings relative to the populations they rule is a similar ‘power-law-breaking’ data point) and their uniqueness (Dragons are unique beasts, beyond the typical) [3]. Interestingly, the fact that these points deviate from typical trends signifies that there is a different mechanism underlying their formation, offering the potential for predicting or observing their formation in real time.

As a brief aside, this discussion might be reminding the attentive reader of the ‘black swan’ concept often thrown around in finance. Put simply, black swans are events that are unpredictable because we have no historical record of similar occurrences: it was thought by Europeans that all swans were white, until the first black swan was discovered in Australia. Operationally, if we can’t predict or don’t even know about a specific type of event, then there isn’t much we can do to protect ourselves against it. While this may be true of black swans, it is not so for dragon kings. The very fact that dragon king events are so significantly unique from the general trend suggests that different mechanisms underly their formation and they could, in principle, be identified in advance.

Inspired by this tantalizing possibility, Sornette and others established the financial crisis observatory (FCO) in the wake of the 2008 financial crisis, where they scientifically applied mathematical models to identify the presence of bubbles in financial markets across the globe and predict beforehand when markets would be subject to corrections. Here, the researchers at the FCO publish predictions of where bubbles form and when they are likely to correct—which doesn’t necessarily mean to crash, but rather to change into a different regime. To varying success, the FCO has provided predictions of several market regime shifts, and even publishes a regularly updated ‘bubble watch’ to quantify the presence of financial bubbles in various markets*.

While this discussion has seemingly been far removed from the current state of financial markets, it is worth dwelling for a moment on how exactly these dragon king events come about. Ultimately, they emerge from the hidden feedback loops endemic in global financial markets. It is these same feedback mechanisms that can transmit a currency or economic crisis in a foreign country into large-scale compounding losses for the global economy. In times of crisis and uncertainty, the dragon king theory prompts us to remain vigilant and attentive to the behaviour of financial markets; even seemingly disconnected events and entities may be riding the same economic dragon.

References:
[1] A Johansen & D. Sornette, Stock market crashes are outliers, European Physical Journal B, 1998, 141-143
[2] J. Laherrere & D. Sornette, Stretched Exponential distributions in nature and economy: Fat tails with characteristic scales, European Physical Journal B,1999, 525-539
[3] D. Sornette, Dragon-Kings, Black Swans and the Prediction of Crises, SSRN, 2009

* For the interested reader, Sornette has a TED talk on the topic: CLICK HERE.