Does Chaos Theory teach us anything about financial markets?
Does Chaos Theory teach us anything about financial markets?
How earthquakes, arcade games and financial markets are related
Chaos Theory can explain some of the general properties of financial markets and explain at a high level why certain phenomena occur. At the same time, Chaos Theory is pretty much useless in helping you predict the specific timing of anything.
But even knowing what something isn’t can be useful too. For example, knowing that financial markets are very hard to predict in the short run can help you avoid spending too much time and brainpower trying to predict day-to-day price movements! [1]
In general, I have found Chaos Theory to be a useful mental model to set out basic rules that could make you a better investor as well as helping you avoid some potentially very costly mistakes.
How Earthquakes, Arcade Games and Financial Markets are Related
I am by no means an expert on Chaos Theory — especially all of the detailed mathematics behind it — but I know enough to know that financial markets demonstrate similar characteristics common to chaotic systems like earthquakes.
(1) Dynamical systems whose “state” can be represented by a set of variables at any given point in time:
For earthquakes, this is the amount of seismic energy that is released at any given point in time. [2]
For financial markets, these are asset prices that reflect the values at which buyers and sellers transact at any given point in time.
(2) There is an external “power source” that provides energy that feeds into and drives the system:
Earthquakes: natural tectonic plate activity.
Financial Markets: decisions on the prices of securities based on new information; human emotions like fear and greed.
(3) Small differences in the initial condition of these systems can lead to a wide range in outcomes because the variable(s) representing system state are merely rough approximations:
Earthquakes: it is hard to predict when the next earthquake will happen.
Financial Markets: it is hard to predict when the next market crash or bubble will happen.
(4) Chaotic systems can show pattern repetition:
Earthquakes: Periodic release of seismic energy.
Financial Markets: Boom and Bust cycles.
(5) Chaotic systems can stay in equilibrium for long periods of time:
Earthquakes: centuries where there is little seismic activity.
Financial Markets: low volatility in stock prices, e.g. U.S. markets in 2017.
(6) The systems feature scale invariance and can be measured in terms of something called a power law:
Earthquakes: Gutenberg–Richter law
Financial Markets: Power Laws in Economics
How can two seemingly unrelated systems display some similar behavior? I try to think about it by boiling it down to simple models.
For earthquakes, think about that game in the arcade where you drop quarters onto a big pile of quarters to try to make a whole lot of them fall into a bin where you can collect them. It has “pushers” that move back and forth to supply the “energy” for the system.
Piles of quarters are not exactly the same as stone and sand formations that make up tectonic plates but both systems are governed by the similar forces (i.e. the laws of physics).
It looks like this:
Most of the time, nothing happens. The quarter falls into the pile but does not push a single quarter off the edge — even ones that seem like they are right about to fall off. Indeed, this seems like the most common outcome. The system is in a state of equilibrium i.e. no earthquake.
Sometimes you drop a quarter and a few quarters fall off the first edge but then land in the second pile and nothing happens. This is analogous to a small tremor. It falls out of equilibrium for a second, undergoes a small “chaotic event” and then returns to a new state of equilibrium.
And every once in a while, an entire avalanche of quarters falls into the bin. This event is equivalent to a large earthquake.
The reason that this happens is that there are connections [3] between the quarters (the “initial condition”) and when you apply energy to the system (adding a new quarter), the way that it translates into a series of actions cannot be predicted — even by the most sophisticated super computer and state-of-the-art measurement equipment.
In each state of equilibrium, there may be a hidden network of these connections where if you upset one that is very far away from the edge, it may still cause the quarter to fall, and perhaps trigger even more to fall in a massive wave. These network connections can be represented like this in Stuart Kauffman’s “button” model and helps abstractly visualize the phenomenon of the “Butterfly effect”:
Source: Deep Simplicity: Bringing Order to Chaos and Complexity by John Gribbin (page 177). An excellent read on this topic and one I highly recommend.
Now think about a financial market as if it were a number of investors that are connected to each other in some way whether it is by relationship, the same sources of information, or similar patterns of human behavior and emotion.
When new information is introduced, it works its way through these networks and each node makes a decision on whether to change its opinion about the price of a specific security. There are many correlations in the way decisions are made. Investors that follow similar investment philosophies tend to react similarly (e.g. value vs. momentum investors). The human emotions of fear and greed play an ever-present role in decision-making. And in the modern era technology is playing an increasing role in decision-making, often reinforcing many of these existing correlations.
Infinitely Small, Infinitely Large
One cool property of chaotic systems is something called self-similarity. This is like when you zoom into one of those Mandelbrot fractals and notice that, as you zoom in, it looks very similar down below. Financial markets exhibit some of this behavior as well. To illustrate this, look at the following price charts where I have stripped out the values and the dates. Each of these were some famous market crashes. Now try to figure out which famous market crash each chart represents as well as its time period:
Unless you are really into financial history and charts, this is really hard to figure out:
Scenario 1 was the May 2010 Flash Crash. This chart of the DJIA takes place in a four-hour period.
Scenario 2 was the October 1929 Crash. This chart of the DJIA takes place over a thirty-year period (1925 to 1955).
Scenario 3 was the October 1987 Crash. This chart of the DJIA takes place over a six-month period (July 1987 to January 1988).
Scenario 4 was the 2008 Financial Crisis. This chart of the S&P 500 takes place over a 12-month period over calendar year 2008.
This would be even harder to figure out if I took random stock price trading over different periods of time and used the same chart formatting and tick-interval to make them look the same.
Seeking Wisdom out of Chaos
Accepting the idea that financial markets are chaotic systems, there are several interesting observations and conclusions that one can draw:
Chaos Theory explains the somewhat paradoxical idea that stocks might be extremely unpredictable in the short run but quite predictable in the long run. In other words, it is very hard to predict where the price of Apple stock will head in the next hour or next day (short of having true insider information) but over the long run you can predict where it will go based on Apple’s business fundamentals.
Predictability over the long run is based on an understanding of what drives long-term equilibrium in the system. I believe that long-run equilibrium state for individual stocks eventually maps to the real-world fundamentals of a business. Therefore, understanding real-world fundamentals of a business is the most important factor in my investing approach. For me, investing is about understanding how businesses work (and don’t) in the real world.
At the same time, Chaos Theory explains why you do find recurring patterns in asset prices.
The occurrence of these patterns is one of the fundamental bases for why much of the quantitative hedge fund industry exists. Many of these firms employ statisticians to look for these patterns to exploit via arbitrage.
Of course, over time these strategies themselves feed their energy back into the system and the arbitrage opportunities fade away over time. Some persist longer than others.
Chaos Theory also helps explain why “Six Sigma” events seem to occur at a much higher frequency than would be implied by “standard” models.
In the middle of the 2008 Financial Crisis, the frequency of Six Sigma events — scenarios that are supposed to occur once every 6,849 years — was off-the-charts.
The problem is that the “Six Sigma” concept (i.e. six standard deviations above the mean) is based on a normal distribution of probabilities (i.e. the “standard model”) which is how a lot of financial models that underpinned the global financial system were built.
Chaotic systems do not follow normal distributions but power law distributions and have “fat tails”. In other words, a lot of these models were simply wrong and that invariably contributed to the fragility of the overall system, ultimately leading to the biggest market crash and financial crisis since the 1920s.
Chaos Theory explains how outwardly calm markets (e.g. low volatility) can hide extreme structural fragility down below. Drawing on the “button” model from up above, deep fault lines of hidden connections and correlations could develop underneath the surface among participants in the marketplace. Random events (whether "Black Swan" type events like 9/11 or something as small as a simple "fat finger" mistakes) could set in motion a series of events that, accelerated by these connections and correlations, results in a market crash.
A good example of this was Black Monday in 1987 when stock markets suddenly crashed in tandem around the world. The benchmark Dow Jones Industrial Average (DJIA) crashed by 23%. When people investigated what had happened, some blamed the rise in the use of “innovative” portfolio insurance hedges. These contracts would trigger automatic program trading if the markets fell too much. Combined with relatively low liquidity, this resulted in a vicious cycle that overwhelmed markets. This market crash was analogous to a massive earthquake (8+ on the Richter scale).
As an aside, I see correlations in today’s equity markets, particularly in the United States. While the market seems extremely calm on the surface, there are some “connections” that have been built up over the years that may lead to a future market crash. For example, the rise in passively traded Exchange-traded funds (ETFs) that merely reinforce existing market weightings — while very positive for investors overall in the effect they have had on lowering fees — have probably increased the level of connections/correlation amongst equity investors. And who knows what sort of random event in the future triggers the a cascading series of events — reinforced by these structural correlations — that results in the next market crash.
Finally, Chaos Theory teaches me the importance of being conservative with debt, particularly callable margin loans from unpredictable counter-parties that are tied to the price of stocks.
“Earthquakes” can happen at any time in financial markets at unpredictable levels of volatility.
If you take out a 50% margin loan and the market is cut in half (this has happened many times before), you are wiped out — as in permanent capital loss.
However, if you remain conservatively leveraged and can withstand a 50% drawdown, you live to fight another day.
Survival (i.e. avoiding “permanent capital loss”) is extremely important as an investor: Absent a complete collapse in the American system (at which point I would be worrying about a lot more than my stock portfolio), I am confident U.S. equities will thrive over the very long run — because I believe in American prosperity over the very long run.
Notes
[1] This advice is geared more at the general investing public. Large trading firms with access to capital and expertise can build advantages that allow them to generate attractive risk-adjusted returns predicting day-to-day price movements or exploiting structural inefficiencies in the market.
[2] There is always seismic energy being released at any given point in time; you just cannot feel it 99.99999% of the time (in the case of a once-in-a-hundred-years earthquake situation; add one digit for each additional order-of-magnitude). Earthquakes occur on a geological time-scale which is several orders of magnitude higher than human time-scale.
[3] An example of a connection is the overlap between two quarters, including the specific angle at which they touch each other and the the positioning of one quarter relative to another that is teetering on the edge.
This was originally published on Quora in January 2018.