Submitted by Christopher Cole via Artemis Capital Management [9],
The extraordinary market intervention by China in response to their declining market, coupled with further ‘kick the can down the road’ policies by the EU regarding Greece, resulted in the greatest collapse in the history of the VIX index (which is still ongoing as I write). Over the past five days and counting the VIX has fallen -40% from 19.97 to 12.11. To gain perspective on moves in volatility Artemis ranks consecutive drawups and drawdowns (peak-to-trough or trough-to-peak % moves by day) in the VIX index and models them as a power law distribution. While the concept may be obscure to grasp at first the ramifications of the analysis are enlightening.
What is a power-law distribution? The distributions of a wide variety of physical, biological, and human phenomena follow what is known as a power-law distribution. Examples include earthquakes, deaths in war and terrorism, populations of cities, solar flares, word frequencies in language, movie box office receipts… and financial asset price movements up and down over multiple days.
Supernormal Power-Law Violations: When you rank events from the above natural and human phenomena the vast majority of observations follow the power-law distribution perfectly- however the violations of the function are the most interesting. Power-law violations are true black swans or supernormal observations because their results contain a degree of reflexivity that outside the boundary of what would be expected from an exponential growth function. Examples of supernormal violations in power laws across other phenomena include death counts in WWII ranked among all wars, box office receipts of the movie Titanic, the 9.2 Magnitude 1960 Chilean Earthquake, the population of Tokyo, the 1987 Black Monday Crash, and the 9/11 terror attack in NYC.
For volatility we define a Supernormal Volatility Collapse (Drawdown) as a multi-day decrease in spot-VIX index that violates power law distribution and is indicative of self-reflexivity in markets and unknown unknown events. These occur 1 out of every 920 drawdowns or 0.1087% of the time. Supernormal VIX collapses show returns below an expected power law distribution line since the extreme speed of collapse meets the fact that volatility is bounded by zero.
The graph below shows data points representing the rankings of VIX peak-to-trough declines (y-axis = % drawdown in vol over consecutive days & x-axis = ranking ).
[10]
As with most natural events – the vast majority of VIX drawdowns neatly follow the power law distribution function represented by the white line. The supernormal vol drawdowns to the lower left of the graph represent the most extreme violations of that power law (black swans) whereby the speed of collapse meets price constriction of implies due to the zero bound of volatility. They are the 9.2 earthquakes, 9/11s, and Titanics of VIX drawdowns.
We would like to highlight:
- The ongoing decline in the VIX starting last week (and still going) is the largest supernormal volatility collapse in VIX history
- 3 of the largest supernormal VIX collapses have occurred in the last year alone
- The top 7 ranked power law violations have ALL occurred during the regime of monetary easing between 2010 and today
In summary, over the past 2 years, we have been experiencing a quantifiable ‘outlier’ or ‘black swan’ decline in the VIX every 6 months as evaluated against history.
I can only point to government intervention as the core reason. I firmly believe that this moral hazard produces a hidden leverage and “shadow market gamma” that at some point will result in a sustained volatility outlier event in the opposite direction.
