The rarer the pricer or the deadly: If you look at the graph with the magnitude of earthquakes on the x-axis plotted
against the frequency of the earthquakes on the y-axis. You can see that as
earthquakes get stronger they get rarer. The way the frequency of earthquakes
varies as a function of their size is characterized by an exponent - or a power
- of the frequency. The enormously powerful Tohoku and Sumatra earthquakes,
more than magnitude 9, are many times less frequent than magnitude 4
earthquakes. The other thing about power-law phenomena is called
scale-invariance - otherwise known as fractals. Earthquakes have no
characteristic size or scale - so even though large earthquakes are rare they
are no different than small earthquakes. Think of a coast line or cauliflower:
as you zoom in the patterns will repeat themselves at each scale.Power-law distributions have been
found in many phenomena: the sizes of cities for example follows a power-law.
In addition to the frequency-size function, there is frequency-rank: which is
that the frequency of something is inversely proportional to its rank. For
cities the biggest city is about twice the size of the second biggest city,
three times the size of the third biggest city, etc. So you have very rare huge
cities like New York City, and thousands of small cities with 50,000 or fewer
people. This is also known as Zipf's law, who discovered the same pattern for
word frequency. The second most common word in a text is half as common as the
most common word in a text.
What does all this have to do with
extreme income inequality? Well we can see that income inequality follows a
power-law, so that people with very large incomes are very rare, and people
with very small incomes are very common. These kinds of distributions can arise
from what is called self-organized criticality. These are nonlinear systems that
manage to stay stable by adapting their internal dynamics in subtle ways to
their environments. The idea was introduced using very simple models of this
kind of behavior: forest-fires and avalanches in sand piles.
Sand piles are often used to
illustrate how self-organized systems stay on the edge of order and disorder,
and illustrate the concept of a nonlinear threshold. Imagine a completely
flat surface on which you pour grains of sand at some constant rate. The grains
of sand fall randomly to either side of the pile as it builds up. At first the
pile is small and so the angle of its slope is very shallow. You can keep
adding sand and the pile will just get taller. At a certain point the angle of
the pile will become steep enough so that adding more sand causes small
avalanches. After a time the angle of the pile and the frequency of the
avalanches will converge to form a balance so that the overall shape of the
pile is maintained. However, the key to this is that there is an open
dissipation of sand running off the pile to compensate for the new sand being
poured on to the pile. If you keep adding sand and it cannot dissipate the pile
angle will become so steep that when you add just one more grain of sand, it
will cause a catastrophic avalanche that flattens the whole pile.
So actually you can estimate how
often catastrophic sand pile avalanches will occur based on how often smaller
avalanches occur: and crucially you can maybe prevent catastrophic
avalanches by causing smaller avalanches.
While I don't have this rigorously
worked out because a) I probably couldn't do the math and b) I just thought of
all this today after seeing the YouTube video (if someone wants to try I think
it would be very interesting): in hazard research for example, small controlled
forest fires are used to prevent enormous disastrous fires. If we could,
causing small scale earthquakes in critical regions might actually prevent
Sumatra or Tohoku-type earthquakes. And just as in the sand pile case in which
there are extreme situations where adding only one grain of sand causes a
catastrophic avalanche: are we now in such an economic situation of steep
inequality teetering on the threshold of a catastrophic event? Where one tiny
seemingly insignificant "grain of sand" causes our entire economy to
collapse? The super-rich would do well to heed the lessons of nonlinear
dynamics and power-law distributions: it might only require them to give up
small portions of their wealth to prevent a convulsive social upheaval.
In these situations the stable
dynamics of the systems (forest, sand pile, earth's seismic activity, society)
are maintained by small crises: small fires, small avalanches, small
earthquakes; but catastrophic disasters are no different from these smaller
ones. When these systems go too far from this stability they become vulnerable
to massive catastrophes: what are called Dragon-Kings. The Tohoku earthquake
for example was so powerful that it's even an outlier in a power-law
distribution. And likewise: the super-wealthy are so rich they are outliers
even in a power-law distribution. So the term dragon-kings serves a nice
double-purpose: an apt name for the super-wealthy and the mathematical
description of their outlier status. More ominously, dragon-kings can also
refer to rare catastrophic events.
“While financial crashes, recessions, earthquakes and other extreme events appear chaotic, Didier Sornette’s research is focused on finding out whether they are, in fact, predictable. They may happen often as a surprise, he suggests, but they don’t come out of the blue: the most extreme risks (and gains) are what he calls “dragon kings” that almost always result from a visible drift toward a critical instability. In his hypothesis, this instability has measurable technical and/or socio-economical precursors. As he says: “Crises are not external shocks.”
Stability breeds instability.
1. A type of strategy or mindset becomes prevalent (Momentum, Don’t Fight Fed)
2. The winners become more successful, attracting imitators
3. Crowding in the strategy makes out-performance more difficult, without increasing risk/leverage
4. The stability & low-volatility meltup usher in a new paradigm for risk as VaR models encourage levering (today, selling vol)
An interesting insight that I took away from a recent comparable reading “Forecast” – markets tend to tip into the “unstable” (crash-prone) when:
1. Momentum/Short-term strategies and market participants become increasingly powerful/wealthy and garner a larger share of the market (ownership, volume, etc.)
2. The number of competing strategies shrinks, leading to erosion of profits, or increasingly risky behavior to maintain profits – more leverage, turnover, etc.
3. Let the first domino fall……
Especially troubling is his view that up until the mid 1980’s, GDP growth was the result of real productivity and since then it’s artificial due to the rise of the financial sector. Yet, even he notes, that the longest bubble in the S&P 500 was in the 1955-1975 period. However, he then describes the great crashes the late 1990’s and 2008 as resulting from debt, ignoring that the fall from 1964 to 1968 was as large as the late 90’s fall, and then it kept going, so that the market in 1982 was only 22% of it’s peak, while the post dot-com low was 45% of it’s peak. He doesn’t say what measure of CPI he uses, but I use CPIAUCSL, and with this the all time normalized market highs are around 1958 and 1962 while his figure shows the 1998 peak slightly higher than the earlier ones.
Much of the rest is equally troubling. He constantly uses some measure of debt/gdp or similar, but never takes into consideration that the actual share of economic flows servicing this debt is a small fraction of what it was earlier. And he fails to note that the fluctuations in the actual economy and the markets were large and frequent pre 1980’s.
In Forecast, physicist and acclaimed science writer Mark Buchanan answers these questions and more in a master lesson on a smarter economics, which accepts that markets act much like weather. While centuries of classical financial thought have trained us to understand “the market” as something that always returns to equilibrium, economies work more like our atmosphere — a loose surface balance riding on a deeper torrent of fluctuation. Market instability is as natural — and dangerous — as a prairie twister. With Buchanan’s help, we can better govern the markets and weather their storms.
Any economy operating above the sustenance minimum is unstable. Some version of the fundamental economic equation is always valid, and in fact debt does not appear in it. Even with zero debt, if people save more (spend less), businesses invest less, and government spends less, the economy contracts.
Does Sornettes’s track record of predicting
so-called unpredictable events not speak to the value in his work (i.e
Chinese equities in 2007, oil in 2008, the Swiss Franc vs. the Euro in
2011 and bitcoin this year)–regardless of his view of debt?
“Games are fundamentally different from decisions made in a neutral environment. To illustrate the point, think of the difference between the decisions of a lumberjack and those of a general. When the lumberjack decides how to chop wood, he does not expect the wood to fight back; his environment is neutral. But when the general tries to cut down the enemy’s army, he must anticipate and overcome resistance to his plans. Like the general, a game player must recognize his interaction with other intelligent and purposive people. His own choice must allow both for conflict and for possibilities for cooperation.
The essence of a game is the interdependence of player strategies. There are two distinct types of strategic interdependence: sequential and simultaneous. In the former the players move in sequence, each aware of the others’ previous actions. In the latter the players act at the same time, each ignorant of the others’ actions.”
Title:
|
A review of power laws in real
life phenomena
|
Source:
|
Pinto, Carla. Communications In
Nonlinear Science And Numerical Simulation Volume: 17 Issue: 9
(2012-09-01) p. 3558-3578. ISSN: 1007-5704
|
Title:
|
Black swans, power laws, and
dragon-kings: Earthquakes, volcanic eruptions, landslides, wildfires, floods,
and SOC models
|
Source:
|
Sachs, M. The European Physical
Journal Special Topics Volume: 205 Issue: 1 (2012-05-01) p. 167-182.
ISSN: 1951-6355
|
