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# Critical States Revisited

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In reading through John's mailbag response regarding GM, I was struck by a particularly telling anecdote:

"I was on the phone with one of our biggest clients talking about things when the news hit that the LBO for UAL was failing. The customer without missing a beat told me to sell something. I asked him what and he said, "it doesn't matter, just sell anything now"...He understood how everything was tied together, mostly through psychology. This one event could/would change that psychology and change it quickly...Market declines are normally accompanied by a dramatic increase in correlation between stocks."

In our piece last week (entitled "Critical States") we wrote about how complex systems - which we posit the stock market is - have two important characteristics: self-organization and criticality. We provided a standard example of what a critical state is by using water at 0 degrees Celsius:

"It can be both a liquid and a solid at that temperature. Somehow, at that precise temperature, water can, depending on the internal and external forces affecting the sample, change between a solid and a liquid instantaneously: all molecules act as "one" in this critical state. In this state, only a small change (say a small heat source on one side of the sample) can instantly propagate throughout the sample size, turning it into a liquid from a solid. And further, the heat decays only algebraically rather than geometrically. This contrasts radically with a sample of liquid water at 25 degrees Celsius: if you were to heat it up, that heat would only affect the molecules of liquid closest to the heat source. And that energy would propagate slowly from one molecule to its nearest neighbors and from them to their nearest neighbors. And the heat effect would decay geometrically. At water's critical state of 0 degrees Celsius however, that propagation takes place instantly, affects all molecules throughout the sample, and decays algebraically. There is something special about that critical state."

"...all molecules act as "one" in this critical state."
" only a small change...can instantly propagate throughout the sample..."
"...the heat decays only algebraically rather than geometrically."

And John's comments that struck me were:

"...He understood how everything was tied together, mostly through psychology..."
"...This one event could/would change that psychology and change it quickly..."
"...Market declines are normally accompanied by a dramatic increase in correlation between stocks..."

One of the most remarkable aspects of equity markets around the world in the last several years has been how tightly correlated they have been. The U.S. market goes up, European bourses go up. The U.S. market goes down, Asian markets swoon. The same is true for Latin American markets: as the U.S. goes, they go. Below is a list of the specific correlations between the S&P 500 and the respective worldwide indices listed.

UK FTSE: +0.95 correlation over last 2 years, +0.90 correlation over the last decade.
German DAX: +0.98 over last 2 years, +0.92 over the last decade.
French CAC 40: +0.98 over last 2 years, +0.93 over the last decade.
Spanish IBEX: +0.96 over the last 2 years, +0.97 over the last decade.
Italian Milan 30: +0.93 over the last 2 years, +0.95 over the last decade.
Japanese Nikkei: +0.88 over the last 2 years, -0.21 over the last decade.
Hong Kong Hang Seng: +0.95 over the last 2 years, +0.59 over the last decade.
Korean Kospi Index: +0.92 over the last 2 years, +0.01 over the last decade.
Australian Index: +0.87 over the last 2 years, +0.72 over the last decade.
Mexican Bolsa: +0.94 over the last two years, +0.55 over the last decade.
Brazil Bovespa: +0.95 over the last 2 years, +0.65 over the last decade.

There are two things to note here. (1) Over the last two years, there has been a remarkably (incredibly really) tight correlation between worldwide stock markets and U.S. markets and, (2) the 2 year correlations have in almost all cases increased meaningfully over the 10 year correlations.

One could debate the macroeconomic causes of such correlations; perhaps globalization, coordinated central bank policies, or the dominance of the U.S. dollar as the world's reserve currency are the causa proxima? The cause is unimportant for the point we are trying to make, and that point is this

Global equity markets - global risk premia of all sorts really - are in a 'critical state'. For the last two years they have all been "act[ing] as one" as complex systems do at important junctures of state change. Given how complex systems behave in their critical states, notably how "only a small change...can instantly propagate throughout the sample...", makes John's comment that "...This one event could/would change that psychology and change it quickly..." all the more insightful at our current juncture. How many times have you heard from me, from John, from Stephen Roach, that only a small financial failure could cause a cascade that produces systemic risk to the entire financial firmament? Well, complex systems and critical state analysis suggest the same thing: risks are high and only a small perturbation could give rise to the "instant propagation" of a reduction of risk throughout financial markets worldwide.

The propagation of the current diminished risk premia - how it has spread through the world's equity markets over the last several years - has parallels in our water example above too. Recall that "...the heat [energy] decays only algebraically rather than geometrically" in a water sample in its critical state. Hasn't this been exactly the case over the last several years? The desire to take on risk has built up slowly but steadily across markets and financial instruments, much to the chagrin of those macromancers who recognized the risks of such a 'grab for yield' for what it was: long term dangerous.

Of course, once equilibrium systems come out of their critical state, their behavior is vastly different: the characteristics of the system change dramatically. Algebraic propagation gives way to geometric: where the desire to take on risk may have built up algebraically over the last several years, the desire to reduce that risk will likely be geometric. The fact that all equity markets are "acting as one" given their tight correlations, suggests that the change from a slow, algebraic acceptance of risk to a rapid, geometric disposal of it, could come from some relatively small and unimportant event.

Maybe GM's announcement yesterday isn't that "small change" event this time. But complex systems and critical state theory suggest it could be something even less obvious.
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