April 23, 2012

As Delicate as a Butterfly

We live in an unstable world. The probability of what used to be thought as improbable is becoming more and more likely. The old definition of a statistical outlier as a "1 in a 100 years" event has morphed into the now famous "Black Swan" event. Using Didier Sornette's term, "Dragon Kings" are now becoming more likely.

Put it probability distribution terms, the distribution of all possible outcomes is becoming more bimodal (tails are "fatter", as shown in the graph below). It appears that reality is abandoning the familiar Normal probability distribution shape, depriving us of the standard tools we used to rely on to estimate the future. The comfort of saying that there is a 95% probability that an event will be within 2 standard deviations from its mean is gone, leaving analysts and futurologists clueless.

Sornette (2011): Scaled Distribution of Runs of Gains (Right) / Losses (Losses) for 30 major US stocks. 
Notice the fat tails of the distribution

"Dragon Kings" are crises which are exacerbated due to the combination of a series of elements that reinforce each other, creating a singularity that cannot be explained by the parameters of past events. Think of the potential energy contained in a mass of snow until a tipping point is combined with gravity, mountain inclination, and absence of vegetation to create a huge avalanche; or the epileptic attack, where a neuron firing barrage is unleashed when the inhibitory and excitatory mechanisms in the human brain fall out of balance. The shocking magnitude is caused by the interaction of amplifier forces built in their own system. Real life examples: the flash crash of May 2010 was the result of high frequency trading algorithms combined with stop orders; the Venezuela megaflood of December 1999 was the consequence of persistent orographic winds blowing from a relatively warm ocean surface meeting the coast.

Notice the importance of the meeting of the reinforcing elements. Without the interconnection of these elements, amplification doesn't occur. In human systems, interconnection amongst people allows imitative (herding) behavior that helps reinforce an event. We have all been witnesses of the effect of interconnectedness on social causes, like The Arab Revolutions. Here, potentially reinforcing elements (people willing to do something about a common problem) are interconnected thanks to a platform (the social networks) that exacerbate an event (social discontent) to create a "Dragon King" (simultaneous revolutions that have overthrown decades-old regimes). Once social discontent reaches a tipping point, all it takes is a trigger (Mohamed Bouazizi setting himself on fire) and interconnectedness fuels the fire.

Are we headed for a Dragon King in the global financial markets?

If we are looking for the orographic winds or the critical mass of snow in the global economy, by now it should be clear (thanks to the hyper-coverage in the media) that they are in the banks' high levels of leverage. Specifically, in the assets denominated in USD held by foreign banks (see graph below). Yes, those at the very center of the European debt crisis [gasp]. The critical mass for the snow avalanche or the orographic conditions for a Venezuelan flood are silently setting in.
Shin (2011). Global Banking Glut & Risk Premium.
Interconnectedness, following our framework, is in international trade. Trade synchronizes economic cycles of countries around the world (see graph below). Unfortunately, Harry Markowitz' Nobel Prize winning idea of putting your eggs in different baskets is of no use if the baskets are on a table at risk of imploding.

with world Bank Figures
Normally, "Dragon Kings" are not triggered by a shocking event. It is often an innocuous event that sets the wheels of the full system in motion and unleashes the potential energy contained in the reinforcing elements. Very much like the butterfly effect. With so many potential financial triggers lingering in the air (Spain and Italy's unsustainable yields, France's election, Holland's political crisis) any of them could unleash the next Dragon King.

Our sky is filled with butterflies, and they are flapping their wings. Hard. Which one will create the next big hurricane? Who knows. No wonder people are nervous.


  1. ...good read & plausible "dragon king" scenario is disconcerting...having said that, the first image makes one want to say "lay off the bong chinonomist"...

    1. Its ugliness conveys fear, doesn't it?
      (btw, I am not the author of that graphic representation).
      Thanks for reading.