"Year after year, economic theorists continue to produce scores of mathematical models and to explore in great detail their formal properties; and the econometricians fit algebraic functions of all possible shapes to essentially the same sets of data without in any way being able to advance, in any perceptible way, a systematic understanding of the structure and the operation of a real economic system." - Wassily Leontief, 1982

Have we improved since 1982? Was Wassily being a little harsh? Are our current models any better?

Today we again turn to our exploration of the implications of complexity theory and the critical state and their applications to the market. Can we find some explanation for the seeming decrease in market volatility and an increased appetite for risk and leverage? The more I meditate on this, the more implications and explanations for market behavior seem to come to mind. What I hope to do is give you a way to understand the markets apart from the usual easy bromides.

A Return to Critical States

Two weeks ago, we started to explore the implications to the markets of a very important book by Mark Buchanan called Ubiquity, Why Catastrophes Happen. I HIGHLY recommend it to those of you who like me are trying to understand the complexity of the markets. Not directly about investing, although he touches on it, it is about chaos theory, complexity theory, and critical states. It is written in a manner any layman can understand. There are no equations, just easy-to-grasp, well-written stories and analogies. For those who are looking for a better way to grasp the seemingly inexplicable manner in which the world behaves, this is critical reading.

We have all had the fun as kids of going to the beach and playing in the sand. Remember taking your plastic buckets and making sand piles? Slowly pouring the sand into ever bigger piles, until one side of the pile started an avalanche?

Imagine, Buchanan says, dropping one grain of sand after another onto a table. A pile soon develops. Eventually, just one grain starts an avalanche. Most of the time it is a small one, but sometimes it builds up and it seems like one whole side of the pile slides down to the bottom.

Well, in 1987 three physicists named Per Bak, Chao Tang and Kurt Weisenfeld began to play the sandpile game in their lab at Brookhaven National Laboratory in New York. Now, actually piling up one grain of sand at a time is a slow process, so they wrote a computer program to do it. Not as much fun, but a whole lot faster. Not that they really cared about sandpiles. They were more interested in what are called nonequilibrium systems.

They learned some interesting things. What is the typical size of an avalanche? After a huge number of tests with millions of grains of sand, they found out that there is no typical number. "Some involved a single grain; others, ten, a hundred or a thousand. Still others were pile-wide cataclysms involving millions that brought nearly the whole mountain down. At any time, literally anything, it seemed, might be just about to occur."

It was indeed completely chaotic in its unpredictability. Now, let's read this next paragraph slowly. It is important, as it creates a mental image that helps me understand the organization of the financial markets and the world economy.

"To find out why [such unpredictability] should show up in their sandpile game, Bak and colleagues next played a trick with their computer. Imagine peering down on the pile from above, and coloring it in according to its steepness. Where it is relatively flat and stable, color it green; where steep and, in avalanche terms, 'ready to go,' color it red. What do you see? They found that at the outset the pile looked mostly green, but that, as the pile grew, the green became infiltrated with ever more red. With more grains, the scattering of red danger spots grew until a dense skeleton of instability ran through the pile.

"Here then was a clue to its peculiar behavior: a grain falling on a red spot can, by domino-like action, cause sliding at other nearby red spots. If the red network was sparse, and all trouble spots were well isolated one from the other, then a single grain could have only limited repercussions. But when the red spots come to riddle the pile, the consequences of the next grain become fiendishly unpredictable. It might trigger only a few tumblings, or it might instead set off a cataclysmic chain reaction involving millions. The sandpile seemed to have configured itself into a hypersensitive and peculiarly unstable condition in which the next falling grain could trigger a response of any size whatsoever."

Fingers of Instability

So what happens in our game? "... after the pile evolves into a critical state, many grains rest just on the verge of tumbling, and these grains link up into 'fingers of instability' of all possible lengths. While many are short, others slice through the pile from one end to the other. So the chain reaction triggered by a single grain might lead to an avalanche of any size whatsoever, depending on whether that grain fell on a short, intermediate or long finger of instability."

Now, we come to a critical point in our discussion of the critical state. Again, read this with the markets in mind (again, emphasis mine):

"In this simplified setting of the sandpile, the power law also points to something else: the surprising conclusion that even the greatest of events have no special or exceptional causes. After all, every avalanche large or small starts out the same way, when a single grain falls and makes the pile just slightly too steep at one point. What makes one avalanche much larger than another has nothing to do with its original cause, and nothing to do with some special situation in the pile just before it starts. Rather, it has to do with the perpetually unstable organization of the critical state, which makes it always possible for the next grain to trigger an avalanche of any size."

The Importance of Power Laws

In the preceding paragraph Buchanan refers to something called a power law. While the strength of avalanches in the sandpile game is basically random, there is a certain uniformity to them.

In a real-life example, if earthquakes of level "A" of energy on the Richter scale release twice as much energy as those at level "B," then level A quakes happen four times less frequently. This simple pattern - a power law - holds for quakes over a tremendous range of energies.

There is no way to know if the next earthquake, whether in our sandpile or in the real world, will be the "Big One" or just another minor tremor. We simply have no way to measure or calculate the stresses in the earth. It all depends on what level of "critical state" that the system is in as to whether the roof caves in or we don't even notice.

These power laws show up in a lot of places. Forest fires, the distribution of wealth, the size of cities, the destruction of wars (in terms of the number of people killed), the importance of a particular piece of research, all sorts of physical phenomena and, yes, the markets.

What this suggests is that there is a critical state behind these events, something on the order of our sandpile game. What starts a revolution? Why does the death of an archduke really matter? Why would a cartoon in an obscure Danish magazine set off worldwide protests when other more serious events fail to make a mark?

The clear direction that complexity theory points us to is that there is some sort of critical state in human organization that builds fingers of instability into our world. And then we attempt to explain it. Let's look at how the Wolf Blitzer of the Sandpile Evening News would report about the latest catastrophe:

"The trouble began a week ago in the remote West, where in the early evening a single grain of sand fell on a portion of our pile that was already very steep. This triggered a small avalanche, as a few grains toppled downhill toward the East. Unfortunately, the pile hasn't been managed properly in the West, and these few grains entered into another region of the pile that was also already steep. Soon more grains toppled, and throughout the night the avalanche grew in size; by the next morning, it was well out of control. In retrospect, there is nothing surprising. One fateful grain falling a week ago led to a chain of events that swept catastrophe across the pile and into our own backyard here in the East. Had the Western authorities been more responsible, they could have removed some sand from the initial spot, and then none of this would have happened. It is a tragedy that we can only hope will never be repeated."

Does that not sound like any number of reporters trying to explain Iraq or a market event or forest fires?

What we can be certain of is that a critical state is continually building in our economic system. Are we as investors then simply doomed to wait until yet another even bigger crash than 1929 or 1987 heaves itself upon our shores? Hardly. And now we depart from Buchanan's lucid description into my own less solid meditation. I think there are some lessons we can learn from the Sandpile Game. To set the stage for those lessons, let's think some about the nature of risk.

Against The Gods

I am quite often asked what books I think investors should read. Most often, the first book that comes to mind is my good friend Peter Bernstein's Against the Gods: The Remarkable Story of Risk. If you don't understand how we got here, you don't have a chance at discerning where we are. Peter has written the definitive history of how humans have dealt with risk. My friend and CPA Art Bell recommended this book to me years ago, and I will always be grateful. Let me be your friend and tell you to buy this book if you have not already read it.

It is hard to imagine, but Leonardo da Vinci would have trouble with third-grade math. Drop any of us back into the Middle Ages, and we would be the premier mathematician of the day. Gamblers had no understanding of probability, as each throw of the dice was determined by the gods. We could make our way to the gaming tables and soon own the house. Let's look at this brief section from the introduction to Against the Gods (emphasis mine):

"The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature...

"The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on quantification and numbers, determined by the patterns of the past, and those who base their decisions on more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved.

"The issue boils down to one's view about the extent to which the past determines the future. We cannot quantify the future, because it is an unknown, but we have learned how to use numbers to scrutinize what happened in the past. But to what degree should we rely on the patterns of the past to tell us what the future will be like? Which matters more when facing a risk, the facts as we see them or our subjective belief in what lies hidden in the void of time? Is risk management a science or an art? Can we even tell for certain precisely where the dividing line between the two approaches lies?

"It is one thing to set up a mathematical model that appears to explain everything. But when we face the struggle of daily life, of constant trial and error, the ambiguity of the facts as well as the power of the human heartbeat can obliterate the model in short order. The late Fischer Black, a pioneering theoretician of modern finance who moved from M.I.T. to Wall Street, said, "Markets look a lot less efficient from the banks from the Hudson than from the banks of the Charles."

"Over time, the controversy between quantification based on observations of the past and subjective degrees of belief has taken on a deeper significance. The mathematically driven apparatus of modern risk management contains the seeds of a dehumanizing and self-destructive technology. Nobel laureate Kenneth Arrow has warned, "Our knowledge of the way things work, in society or in nature, comes trailing clouds of vagueness. Vast ills have followed a belief in certainty." In the process of breaking free from the past we may have become slaves of a new religion, a creed that is just as implacable, confining, and arbitrary as the old."

Now, let's go back to our Sandpile Game and drill down to the grain of sand John Q. Sandman is perched on. He watches as all around him a sea of red begins to emerge, with fingers of instability creeping closer. What does he do? Move? Shore up the basement? Or, maybe, decide to change the color of the risk around him from red to green? How does he do this remarkable thing? He buys insurance.

From ancient times, shipping was a risky business. If the boat went down, or was captured by pirates, the loss was total. Lloyd's of London was started in a bar, where shipowners would "buy" insurance against total loss. International commerce increased because risk-taking was shared.

We now buy insurance for a wide variety of risks. If our car is wrecked, our home burns down, we face an illness, or we lose our job, we are (hopefully) covered with some form of insurance which helps us weather our own personal moment with instability.

Islands of Stability

Insurance does not get rid of risk. It merely spreads the damage to other participants for a fee. Now, follow me here. Derivatives are a form of insurance in their simplest form. As a farmer, I sell my grain on the futures market knowing I can make a profit at $3.85 a bushel. Kellogg's buys my grain at $3.85, locking in a price so they can know they will make a profit. And speculators get into the game, thinking they can find an advantage and make a profit off the risk aversion of both the farmer and the cereal buyers.

The same thing goes for credit swaps and all manner of fancy derivatives. One market participant says they want to offset some risk and another wishes to take the risk.

We are all trying (or should be!) to turn our particular portion of the sandpile into green islands of stability, protected from the fingers of instability that roam throughout the markets. As an example, instead of taking long-only market risk in periods of high valuations (like now), we find a long-short equity hedge fund that offers lower volatility and pair it with other noncorrelated assets in an effort to increase yield but reduce risk for our overall portfolio.

Has overall market risk been decreased? No. But our personal exposure to risk has. This form of "insurance" has been a clear and growing choice among larger investment portfolios at pension and high-net-worth individuals for the last 10 years.

But not just investment portfolios. More and more businesses are increasingly using sophisticated techniques to stabilize their income streams, reduce their volatility, and manage their risks.

The Global Association of Risk Professionals (GARP) tells us that credit derivatives have doubled in size every year this decade to a current market size of over $12 trillion. Other derivative markets have seen the same type of explosive growth.

If you buy hurricane insurance, does it change the actual risk of there being a hurricane? In the same way, fire insurance or health insurance does not change your odds of being sick or your house burning down.

Neither does buying some form of credit insurance reduce the risk of a credit problem. It simply spreads the financial impact of the risks to other market participants.

One of the more remarkable features of today's financial scene is the seeming drop in volatility and a simultaneous increased appetite for risk. As Rob Arnott noted in his recent editor's corner in the Financial Analyst's Journal: "...[the use of] leverage for improving returns is the only one that assuredly increases portfolio risk. If the cost of borrowing is less than the rewards for our investment strategies, our returns will improve. But leverage increases risk faster than it increases returns."

Brave New World, Revisited

Let's look at some of the implications. The growth of all forms of risk control, whether derivatives, hedge funds, fixed annuities, etc. is increasing exponentially. The move in the markets by players at all levels to build their own islands of stability may in fact be changing the historical nature of the market sandpile game. But it does not decrease the risk. It transfers it.

Charles and Louis-Vincent Gave and Anatole Kaletsky of GaveKal postulate that we are in a Brave New World - that we have shifted risk such that the world can see increased amounts of debt and leverage without the risk that might have been historically associated with it.

There is a certain logic to that argument. Perhaps by distributing risk we have mitigated the chance of the types of meltdowns that we have seen in the past. But that begs the question of where now do the fault lines of the new critical state arise?

It is not a question, at least to me, of a critical state or no critical state. Just as we cannot repeal the business cycle, we cannot stop the formation of a critical state in our collective economic world. We as humans organize ourselves along the lines of a critical state, ala the Sandpile Game. We have done it for millennia. Those fingers of instability are going to develop. The question is where? And when? From time to time, the nature of the rules changes, but another new set of rules for yet another critical state arises.

But from time to time, we see the results of a critical state in breakdown. We see a NASDAQ in 2000-2002. A market crash in 1987. This week's meltdown in the silver market, as silver broke from $14 an ounce to $12 an ounce in less than five minutes yesterday. Sadly, more than a few people saw their own personal crisis as the margin clerks picked up the phone.

The clear imperative to me is that as investors we should be working to create our own islands of stability. We need to learn to recognize the signs of a critical state breakdown. Overvaluations, manias, rookies coming to the party, people saying "this time it's different" are all signs of an impending problem.

We are in an era when it is as important to manage uncertainty as it is to manage risk. That most definitely does not mean we pull our heads into our shells. There are wonderful opportunities in today's world. But it does mean we need to look at our own personal situations and make sure our exposure to the fingers of instability in our own area of the world are limited.

Sadly, for many people Congress has limited their choices, with the pernicious accredited investor and private placement rules. Why the rules permit the average investor to buy volatile mutual funds, futures, options, leveraged real estate, and any other form of risk but limit their ability to hedge their portfolios like the "rich" is one of the great travesties of our time. Only after the next real bear market, as hedge funds demonstrate their advantages as they did in 2000-2002, will there maybe be some demand for change.

And so as not to close on a totally bearish note, there are also the reverse implications for the Sandpile Game. Because in a very true sense, the Sandpile Game I described does not show the whole picture. You can have positive actions which change the nature of the critical state. For instance, new technologies, such as the internet, change the nature of human organization. It is a very complicated, complex dance, but one in which if you are careful in your management of personal risk you can be a clear winner.

There is a lot more to say, but this letter is growing overly long and it is time to hit the send button.

John Mauldin is president of Millennium Wave Advisors, LLC, a registered investment advisor.  Contact John at John@FrontlineThoughts.com.

Disclaimer
John Mauldin is president of Millennium Wave Advisors, LLC, a registered investment advisor. All material presented herein is believed to be reliable but we cannot attest to its accuracy. Investment recommendations may change and readers are urged to check with their investment counselors before making any investment decisions.