"To trace something unknown back to something known is alleviating, soothing, gratifying and gives moreover a feeling of power. Danger, disquiet, anxiety attend the unknown - the first instinct is to eliminate these distressing states. First principle: any explanation is better than none... The cause-creating drive is thus conditioned and excited by the feeling of fear ...." Friedrich Nietzsche

"Any explanation is better than none." And the simpler, it seems in the investment game, the better. "The markets went up because oil went down," we are told, except when it went up there was another reason for the movement of the markets. But we all intuitively know that things are far more complicated than that. But as Nietzsche noted, dealing with the unknown can be disturbing, so we look for the simple explanation.

"Ah," we tell ourselves, "I know why that happened." With an explanation firmly in hand, we now feel we know something. And the behavioral psychologists note that this state actually releases chemicals in our brain which make us feel good. We become literally addicted to the simple explanation. The fact that what we "know" (the explanation for the unknowable) is irrelevant or even wrong is not important to the chemical release. And thus we look for reasons.

The NASDAQ bubble happened because of Greenspan. Or a collective mania. Or any number of things. Just like the proverbial butterfly flapping its wings in the Amazon that triggers a storm in Europe, maybe an investor in St. Louis triggered the NASDAQ crash. Crazy? Maybe not. Today we will look at what complexity theory tells us about the reasons for earthquakes, disasters and the movement of markets. Then we look at how New Zealand, Fed policy, gold, oil and that investor in St. Louis are all tied together in a critical state. Of course, how critical and what state are the issues. It should make for a fun letter, so let's jump in.

Ubiquity, Complexity Theory and Sandpiles

We are going to start our explorations with excerpts from 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. www.Amazon.com

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. (emphasis mine)

"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."

Something only a math nerd could love? Scientists refer to this as a critical state. The term critical state can mean the point at which water would go to ice or steam, or the moment that critical mass induces a nuclear reaction, etc. It is the point at which something triggers a change in the basic nature or character of the object or group. Thus, (and very casually for all you physicists) we refer to something being in a critical state (or the term critical mass) when there is the opportunity for significant change.

"But to physicists, [the critical state] has always been seen as a kind of theoretical freak and sideshow, a devilishly unstable and unusual condition that arises only under the most exceptional circumstances [in highly controlled experiments]... In the sandpile game, however, a critical state seemed to arise naturally through the mindless sprinkling of grains."

Thus, they asked themselves, could this phenomenon show up elsewhere? In the earth's crust triggering earthquakes; in wholesale changes in an ecosystem or a stock market crash? "Could the special organization of the critical state explain why the world at large seems so susceptible to unpredictable upheavals?" Could it help us understand not just earthquakes, but why cartoons in a third-rate paper in Denmark could cause worldwide riots?

He concludes in his opening chapter: "There are many subtleties and twists in the story ... but the basic message, roughly speaking, is simple: The peculiar and exceptionally unstable organization of the critical state does indeed seem to be ubiquitous in our world. Researchers in the past few years have found its mathematical fingerprints in the workings of all the upheavals I've mentioned so far [earthquakes, eco-disasters, market crashes], as well as in the spreading of epidemics, the flaring of traffic jams, the patterns by which instructions trickle down from managers to workers in the office, and in many other things. At the heart of our story, then, lies the discovery that networks of things of all kinds - atoms, molecules, species, people, and even ideas - have a marked tendency to organize themselves along similar lines. On the basis of this insight, scientists are finally beginning to fathom what lies behind tumultuous events of all sorts, and to see patterns at work where they have never seen them before."

Now, let's think about this for a moment. Going back to the sandpile game, you find that as you double the number of grains of sand involved in an avalanche, the likelihood of an avalanche is 2.14 times as unlikely. We find something similar in earthquakes. In terms of energy, the data indicate that earthquakes simply become four times less likely each time you double the energy they release. Mathematicians refer to this as a "power law" or a special mathematical pattern that stands out in contrast to the overall complexity of the earthquake process.

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 ."

Now, let's couple this idea with a few other concepts. First, Nobel laureate Hyman Minsky points out that stability leads to instability. The more comfortable we get with a given condition or trend, the longer it will persist; and then when the trend fails, the more dramatic the correction is. The problem with long-term macroeconomic stability is that it tends to produce unstable financial arrangements. If we believe that tomorrow and next year will be the same as last week and last year, we are more willing to add debt or postpone savings for current consumption. Thus, says Minsky, the longer the period of stability, the higher the potential risk for even greater instability when market participants must change their behavior.

Relating this to our sandpile, the longer that a critical state builds up in an economy, or in other words, the more "fingers of instability" that are allowed to develop a connection to other fingers of instability, the greater the potential for a serious "avalanche."

Or, maybe a series of smaller shocks lessens the long reach of the fingers of instability, giving a paradoxical rise to even more apparent stability. As the late Hunt Taylor wrote a few months ago:

"Let us start with what we know. First, these markets look nothing like anything I've ever encountered before. Their stunning complexity, the staggering number of tradable instruments and their interconnectedness, the light-speed at which information moves, the degree to which the movement of one instrument triggers nonlinear reactions along chains of related derivatives, and the requisite level of mathematics necessary to price them speak to the reality that we are now sailing in uncharted waters.

"Next, we know things have been getting less, not more, turbulent, and that the tendency towards market serenity (complacency?) has been increasing. This is counterintuitive. It's not as though the 21st century has been lacking in liquidity-shocking events. Since the bursting of the tech bubble, we've had a disputed Presidential election, 9/11, the collapse of Enron and Worldcom, the invasion of Afghanistan, the war in Iraq, US$70 oil, the largest debt downgrade in history and the failure of Refco, to name just a few. There seems to be an inverse correlation between market complexity and market stability, for now anyway....

"I've had 30-plus years of learning experiences in markets, all of which tell me that technology and telecommunications will not do away with human greed and ignorance. I think we will drive the car faster and faster until something bad happens. And I think it will come, like a comet, from that part of the night sky where we least expect it. This is something old.

"But I have learned to trust my eyes and ears and overrule my heart, when I have to. Everywhere I look, technology is making things faster, more efficient, safer. I cannot find the law of physics or economics that says it cannot happen in financial markets as well. I think, because risk will be lower, return will be as well. And savvy investors may have to seek additional risk, and manage it well, in order to earn an excess return. This is something new.

"I think shocks will come, but they will be shallower, shorter. They will be harder to predict, because we are not really managing risk anymore. We are managing uncertainty - too many new variables, plus leverage on a scale we have never encountered (something borrowed). And, when the inevitable occurs, the buying opportunities that result will be won by the technologically enabled swift."

A second related concept is from game theory. The Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. If there is a set of strategies for a game with the property that no player can benefit by changing his strategy while (if) the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute a Nash equilibrium.

A Stable Disequilibrium

So we end up in a critical state of what Paul McCulley calls a "stable disequilibrium." We have "players" of this game from all over the world tied inextricably together in a vast dance through investment, debt, derivatives, trade, globalization, international business and finance. Each player works hard to maximize his own personal outcome and to reduce his exposure to "fingers of instability."

But the longer we go, asserts Hyman Minsky, the more likely and violent the "avalanche" is. The more the fingers of instability can build. The more that state of stable disequilibrium can go critical on us.

Go back to 1997. Thailand began to experience trouble. The debt explosion in Asia began to unravel. Russia was defaulting on its bonds. (Astounding. Was it less than ten years ago? Now Russian is awash in capital. Who could anticipate such a dramatic turn of events?) Things on the periphery, small fingers of instability, began to impinge on fault lines in the major world economies. Something that had not been seen before happened. The historically sound and logical relationship between 29- and 30-year bonds broke down. Then country after country suddenly and inexplicably saw that relationship in their bonds begin to correlate, an unheard-of event. A diversified pool of debt was suddenly no longer diversified.

The fingers of instability reached into Long Term Capital Management and nearly brought the financial world to its knees.

So, where are fingers of instability today? Where are the fault lines that could trigger another crisis? Are there any early warning signs? Matt Blackman of www.TradingEducation.com looks south at what he thinks might be the proverbial canary in the coal mine.

An Island of Deficits

Quick, which country runs the larger trade deficit, New Zealand or the United States? In percentage terms, the surprising answer is, New Zealand. The US had a record 7% (of GDP) trade deficit in the fourth quarter of 2005. But New Zealand saw its deficit hit 8.9% of GDP. Look at the chart below:

Writes Blackman: "But a quintessential star performer that has benefited from strong commodity prices in the last few years provided a warning that could be the beginning of a global market ripple effect. After 21 consecutive quarters of gains, New Zealand surprised economists both at home and abroad with the report that its economy had contracted 0.1% in Q4. The Reserve Bank of New Zealand had previously forecast a growth rate of 2.4% for the year and 0.4% for the quarter. There was little doubt that few, including the New Zealand Reserve Bank governor, expected such a rapid drop. And New Zealand was not the only trouble spot."

New Zealand has seen its currency drop more than 18% in the year ending March 2006. This should actually be expected, as large trade deficits have in the past eventually resulted in falling currency values. Everywhere, so far, except in the United States, where the dollar's reserve status and a powerhouse economy have kept the dollar higher than economic theory and history would have predicted.

There is another similarity between the US and New Zealand. "Housing prices jumped 75% between late 2001 and 2005. Even with 2-year fixed rates at 8.3% and floating rates of 9.6% as of January 2006, home prices were still appreciating at nearly 15% annually at the end of 2005."

And household debt? Household debt in NZ has risen from 100% of income in 1999 to 150% by the end of 2005, the majority of which is mortgage debt.

Rising debt. Soaring housing prices. Monster trade deficits. A rapidly falling currency. But investors are not worried. Note that the NZ stock market has risen nearly 10% in 2006.

It's a small island of 4,000,000 people (one of my favorite places in the world, by the way!). How does what happens in a country that small, with less than the population of a few counties in the Dallas/Fort Worth area, mean anything for the US?

The real and true answer is, we don't know. Maybe it means nothing. Just as we were told the problems with the Thai baht meant nothing. But it is the possible connections that we should be constantly thinking about.

What fingers of instability do I see turning red throughout the world economic sandpile? Everywhere I look, I find markets that are at very high valuations. Markets of all kinds tend to be mean reverting. Today, we diversify among nations and funds, between different types of debt and real estate. We have a diverse portfolio, we tell ourselves.

But everything is more connected than ever. If the Chinese and Japanese buy fewer dollars and US bonds, interest rates rise and the dollar falls which slows our economy and we can buy less of their stuff which slows them down and they buy less from Asia which slows their economies which affects the price of oil and commodities which (on and on). Everything is connected. It is a spider web of fingers of instability.

In a global world we have seen that things which did not correlate in the past can do so, and very quickly. The problem is that we cannot see the fingers of instability, the hidden connections, until the avalanche has started. So we have to pay attention. And we really need to hedge our portfolios. I am increasingly uncomfortable with long-only directional investments that seem to be at a trend high in terms of their valuations.

And so is good friend and market maven James Montier, global equity strategist as Dresdner, Kleinwort, Wasserstein in London. He sent this note to me a few days ago:

"Perhaps I am missing something but in my naive view of the world, peak earnings deserve discount multiples. Yet investors seem to be willing to pay pretty much top dollar for cyclically high earnings. This amounts to a display of faith in a new era. The one thing that history teaches us is that such faith has never been appropriate. Both the US and European markets are significantly overvalued.

"John Hussman has shown that US earnings have never grown by more than 6% peak to peak since 1950. Right now we are at the very top edge of this 6% limiting channel. That strongly suggests that US earnings are at a cyclical peak. The very best that we could hope for (without arguing for a new era) is that earnings crawl along the top edge of the band. Yet history suggests more often that earnings peak at the top edge of the band.

"Unsurprisingly, when earnings are close to the top edge of this 6% channel, equities tend to be priced at a discount to reflect the temporarily exalted nature of the earnings. If one excludes the bubble in the latter part of the 1990s, when US earnings are within 5% of the top edge of the band, then equities have on average traded on 9x (using a Hussman PE (price relative to peak cycle earnings) since 1950. Today with earnings at the very top edge of the band, the US market sits on a Hussman PE of 18x! Peak earnings on peak multiples.

"Nor is this situation unique to the US. A very similar picture holds for Europe. As with the US, European earnings have not managed to grow by more than 6% measured peak to peak since 1970. Current earnings are rapidly approaching the top edge of this earnings growth channel. Yet the European ex UK market is trading on a 17x peak cycle earnings. Normally (again excluding the bubble years) when earnings are within 5% of the top edge of the 6% channel, the European market would be trading on a Hussman PE of 11.5x.

"Both the US and Europe look expensive relative to peak earnings. They also look expensive on a broader range of valuation measures. For instance, across our nine measures of valuation (none of which include bonds) the US appears to be 54% overvalued. In the past when we have done a similar analysis on Europe, it has appeared to be 33% overvalued. However, this is flattered by a much shorter data set for Europe. If we take the average European valuation discount to the US since 1970, and apply it to the US long run averages we can proxy a 'long run' benchmark for Europe. When we conduct this exercise, we find that Europe is on average 63% overvalued!

"This suggests that those arguing that because Europe had a good year last year while the US went nowhere, Europe is now independent of the US, may well run into a valuation constraint far faster than they currently imagine. Neither the US nor Europe offer any value attraction. There is little to choose between them."

Today more than ever your portfolio should be targeting absolute return strategies. In a world with fingers of instability that may be connected in ways we have not seen in the past, caution is the order of the day. If we do see a slowing US economy later this year, the average complacent investor is not going to be happy as his diversified portfolio all seems to be going south at the same time.

There is the inverse relationship of connections and forces which will create a positive re-enforcement among the markets. In a later issue, we will discuss the importance of this connectivity of all things which leads to positive events. But it is time to hit the send button tonight.

Baseball, Spring and Hope

Hope, I wrote last week, is always part of Opening Day in baseball. It's a new season. Anything can happen. That new rookie could win 20 games. Sadly, the Rangers are dashing hopes rather quickly, off to a miserable 1 and 4 start. I look out my window and see the home team is losing 2-1. No, that was a home run. Now we are losing 4-1 to Detroit in the 5th inning. Oh, well. It is still baseball and spring, so we will do what Ranger fans have done for decades, which is just enjoy the ride, even if we have no expectations of getting anywhere. Maybe I am just projecting the current trend into the future. The Rangers could turn it around and go on a tear. We will see.

Oldest daughter Tiffani, who runs things around here, is in Israel this week and next. She thinks she is going to be able to work online from there. "Don't worry, Dad." I do worry. One, she might not be able to work as easily as she thinks, and things fall behind. Or, she does brilliantly and wants to travel and leave the office more. I don't see an upside for her boss (me) in this deal.

I am going to have to make sure she does not get my copy of International Living. They write about too many cool places to travel and even to live abroad. But you can get your own copy here.

Thanks to emerging hedge fund manager and chaos theory guru Chris Cooper for turning me on to Ubiquity. I don't know how I missed it. You really should think about getting your own copy. www.Amazon.com

Have a great week.

Your always in a critical state analyst,

John Mauldin

P.S. If you like my letters, you'll love reading Over My Shoulder with serious economic analysis from my global network, at a surprisingly affordable price. Click here to learn more.

• Complexity Theory
• Disequilibrium
• Ubiquity

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