"The Approximate Present Does Not Approximately Determine The Future"

Chaos Theory turns 50 years old this year, celebrating half a century of flapping butterfly wings in Brazil creating tornadoes in Texas.  That most famous example is especially appropriate, since it was a meteorologist named Edward Lorenz who first outlined why seemingly consistent and knowable systems can still go wildly wrong.  As it turns out, as ConvergEx's Nick Colas reminds us, small errors in measurement or observation at the start of a time series can significantly change how things look at the end.  In the current low volatility, one-variable central bank driven global equity markets, Chaos Theory may seem a quaint relic of past crises.  However, its central lesson – that complex interrelated systems create unexpected outcomes from seemingly benign inputs – is still relevant.  Students of economics like to think of their discipline as scientific, just like physics or other hard sciences.  They would do well to embrace the intellectual honesty neatly encapsulated by the central lessons of Chaos Theory.


Via ConvergEx's Nick Colas:

If I asked you to name a famous weatherman, I doubt you’d come up with Dr. Edward Lorenz of the Massachusetts Institute of Technology.  No, he’s no Al Roker or Jim Cantore in terms of fame or fortune.  He never stood in the middle of a hurricane to report for the Weather Channel or walked through a devastated trailer park after a tornado.

Dr. Lorenz’s contributions, however, have a far wider reach because he is the researcher who came up with what we know today as ‘Chaos Theory’.  Here’s brief history of the man and his discovery:

  • Edward Lorenz was born in West Hartford Connecticut in 1917, attending Dartmouth (BA 1935) and Harvard (Master’s 1940).  He served as a meteorologist for the U.S. Army Air Corp. during World War II and earned two degrees from the Massachusetts Institute of Technology during and after the war.
  • At the time, weather forecasting was considered pretty simple stuff.  Take enough inputs from today’s climate and you should be able to forecast tomorrow’s weather pretty closely.  Simple, but not especially effective.  And potentially deadly for an air force during times of war, even the “Cold” one which followed the armistices of 1945.
  • Lorenz thought that the linear approach was wrong, and started working on non-linear algorithms to forecast the weather from his new seat as a MIT professor.  In the mid 1950s, he started to use an early computer – the Royal McBee LGP-30 – to help with the calculations.  Its clock speed was 120 kHz, about 100,000 slower than an iPhone 5.  It weighed 740 pounds.  But it was better than doing thousands of calculations by hand.
  • To speed up the calculations of the many iterations required for his research, Lorenz truncated the number of decimal places for the inputs to his model.  He then went back and added more detail to those same inputs – 2.212 became 2.212175 – to see if he got a more fine-tuned response.  To his surprise, those little tweaks created very different outcomes in his models.  Small changes to the “Base state” – today’s weather conditions, for example – could result in radically different expectations for the weather in just a few days time.
  • Lorenz published a paper on this phenomenon in 1963 – 50 years ago – titled “Deterministic Nonperiodic Flow.”  Yeah, not a very catchy name…  And according to a summary about the 50th anniversary of the paper in Physics Today, it garnered fewer than 20 citations in the dozen years after its publication. 
  • Lorenz’s observations begin to catch real traction only in the mid-1970s, when a paper titled “Period Three Implies Chaos” (Li and Yorke, 1975) gave his ideas a catchy name and a new audience: mathematicians and physicists.

In 1972, Lorenz gave a talk which he titled “Predictability: Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”  This famous observation is almost as well-known as the term “Chaos Theory” itself, and serves to explain the basics of Lorenz’s discovery.  Three quick points here:

  • Lorenz’s 1962 paper summarized his findings this way: “For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly different initial states can evolve into considerably different states.”
  • He later summarize “Chaos” more concisely as “When the present determines the future, but the approximate present does not approximately determine the future. 
  • In totally laymen’s language, Chaos Theory says that if you want to forecast the future you need to know everything about the present.  And by “Everything” we mean all knowable characteristics of today, in infinite detail.  Even if you have a great set of formulas in a comprehensive model about how those many variables interrelate, your predictions will run afoul of ‘Chaos’ – the ability of an overlooked (and typically small) characteristic of the starting point to have a large effect on the outcome.


In the world of economics and capital markets, Chaos Theory clearly resonates.  The Financial Crisis of 2007-2008 and its follow-on travails all have the gentle flutter of the butterfly’s wings somewhere at their core.  Small issues – a marginal residential development in Scottsdale, a deal by Greek monks for some Athenian commercial real estate – quickly cascade to become the tornado in Texas.   Or New York, or London, for that matter.

What I find most striking is the current market psychology that seems to think all the butterflies are dead, or at least safely in their pupae.  Observed volatility for stock prices, as measured by the S&P 500 Index, are trending lower over the last 10 and 20 days, even as the market itself reaches new highs.  Implied volatility in options contracts are trending lower as well.

It not just the math of volatility that I find most puzzling, but the notion that central bank policy is all that matters to economic and market outcomes.  I get the fact that the last few years have been humbling for everyone from risk-averse investors (who missed the move in risk assets) to policymakers who shovel liquidity into an economic system which still struggles to create jobs or growth.  But it seems very much like commentators and market participants desperately want to believe the world behaves according to simply rules.  “Just buy the equity market whose central bank has the largest bond buying program” is essentially the only piece of investment wisdom needed for the last 48 months.  And counting…

I keep coming back to Lorenz’s statement that "The approximate present does not approximately determine the future."  We know our approximate present very well, at least in the U.S.:

  • A slow growth economy
  • An accommodative central bank
  • Only one other large economy (Japan) with the appetite to follow our lead in buying large quantities of long dated bonds
  • A seemingly “Self sustaining” rally in stocks, where there is enough momentum to pull at least a few new buyers into the mix.  And low enough interest rates to provide few alternatives to investors.

At the same time, Chaos Theory is clear: this does not approximately determine the future.  There are more than enough variables out there – the butterflies flapping away – which can change outcomes.   Don’t get me wrong – this is not meant to be a doom and gloom closing thought.   If stock markets exhibited ‘normal’ volatility, it would be far easier to defend current price levels.  You could leave the butterfly net at home.  The problem is that current market price action –that slow steady grind higher – indicates marginal buyers don’t fret very much about the future.  No matter how little we really know about it.


Additional Reading

Original 1963 paper: http://eaps4.mit.edu/research/Lorenz/Deterministic_63.pdf

50th Anniversary in Physics Today: http://www.physicstoday.org/resource/1/phtoad/v66/i5/p27_s1?bypassSSO=1


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