Television and blogs are filled with discussions of fat tails, although the usage often seems more like cliché than technical understanding. What is even less understood is the role of scale. The curve shown above in Figure 2 ends at some point for convenience. Yet in theory it could continue forever to the right without hitting the horizontal axis. This continuation would take the extent of possible catastrophes into unimaginable realms, like a 10.0 earthquake, something never recorded.
Is there a limit to the length of the tail? Yes, at some point the fat tail drops vertically to the horizontal axis. This truncation marks the limit of the system. The size of the greatest catastrophe in a system is limited by the scale of the system itself. An example would be an active volcano on a remote island. The volcano and the island make up a complex dynamic system in a critical state. Eruptions may take place over centuries, doing various degrees of damage. Finally the volcano completely explodes and the island sinks, leaving nothing behind. The event would be extreme, but limited by the scale of the system—one island. The catastrophe cannot be bigger than the system in which it occurs.
That’s the good news. The bad news is that man-made systems increase in scale all the time. Power grids get larger and more connected, road systems are expanded, the Internet adds nodes and switches. The worse news is that the relationship between catastrophic risk and scale is exponential. This means that if the size of a system is doubled, the risk does not merely double—it increases by a factor of ten. If the system size is doubled again, risk increases by a factor of a hundred. Double it again and risk increases by a factor of a thousand, and so forth.
Financial markets are complex systems nonpareil. Millions of traders, investors and speculators are the autonomous agents. These agents are diverse in their resources, preferences and risk appetites. They are bulls and bears, longs and shorts. Some will risk billions of dollars, others only a few hundred. These agents are densely connected. They trade and invest within networks of exchanges, brokers, automated execution systems and information flows.
Interdependence is also characteristic of markets. When the subprime mortgage crisis struck in early August 2007, stocks in Tokyo fell sharply. Some Japanese analysts were initially baffled about why a U.S. mortgage crisis should impact Japanese stocks. The reason was that Japanese stocks were liquid and could be sold to raise cash for margin calls on the U.S. mortgage positions. This kind of financial contagion is interdependence with a vengeance.
Finally, traders and investors are nothing if not adaptive. They observe trading flows and group reactions; learn on a continuous basis through information services, television, market prices, chat rooms, social media and face-to-face; and respond accordingly.
Capital and currency markets exhibit other indicia of complex systems. Emergent properties are seen in the recurring price patterns that technicians are so fond of. The peaks and valleys, “double tops,” “head and shoulders” and other technical chart patterns are examples of emergence from the complexity of the overall system. Phase transitions—rapid extreme changes—are present in the form of market bubbles and crashes.
Much of the work on capital markets as complex systems is still theoretical. However, there is strong empirical evidence, first reported by Benoît Mandelbrot, that the magnitude and frequency of certain market prices plot out as a power-law degree distribution. Mandelbrot showed that a time series chart of these price moves exhibited what he called a “fractal dimension.” A fractal dimension is a dimension greater than one and less than two, expressed as a fraction such as 1½; the word “fractal” is just short for “fractional.” A line has one dimension (length) and a square has two dimensions (length and width). A fractal dimension of 1½ is something in between.
A familiar example is the ubiquitous stock market chart of the kind shown in daily papers and financial websites. The chart itself consists of more than a single line (it has hundreds of small lines) but is less than an entire square (there is lots of unfilled space away from the lines). So it has a fractal dimension between one and two. The irregular pattern of ups and downs is an emergent property and a sharp crash is a phase transition.
A similar fractal pattern appears whether the chart is magnified to cover hours, days, months or years, and similar results come from looking at other charts in currency, bond and derivatives markets. Such charts show price movements, and therefore risk, distributed according to a power law and chart patterns with a fractal dimension significantly greater than 1.0. These features are at odds with a normal distribution of risk and are consistent with the power-law degree distribution of events in complex systems. While more work needs to be done in this area, so far the case for understanding capital markets as complex systems with power-law degree distributions is compelling.
This brings the analysis back to the question of scale. What is the scale of currency and capital markets, and how does it affect risk? If catastrophic collapses are an exponential function of scale, then every increase in scale causes a much greater increase in risk. Capital markets continually increase in scale, which is why the black swans keep coming in greater numbers and intensity.
Thinking about scale in capital markets today is like trying to measure the size of a field before the invention of the foot, the yard or the meter. There is no commonly agreed scaling metric for computing market risk using complexity and critical state dynamics. This lack is not unprecedented. Earthquakes have been known throughout history, yet the Richter scale used to measure the intensity and frequency of earthquakes was invented only in 1935. Earthquakes are phase transitions in complex tectonic plate systems, and their frequency and intensity measured by the Richter scale also correspond to a power law. The similarity of stock market charts to seismographic readings (seen in Figure 3 below) is not coincidental.
FIGURE 3: A sample seismograph reading
It will take some time for empirical work to catch up to theoretical work in this field. However, Nobel Prizes in economics likely await those who discover the best scaling metrics and accurately compute the slope of the power curve. But there is no need to wait for that work before drawing sound conclusions from the theory. Putting buildings on a known fault line was a bad idea even before the Richter scale was invented. Ignoring complexity and power laws in capital markets is a bad idea today even in the absence of empirical perfection. The edifice of capitalism may collapse in the meantime.
Even now one can make valuable inferences about the statistical properties of risk in capital and currency markets. There is no question that the scale of these markets, however best measured, has increased dramatically in the past ten years. A series of exchange mergers have created global megaexchanges. Deregulation has allowed commercial banks and investment banks to combine activities. Off–balance sheet activities and separate conduit vehicles have created a second shadow banking system as large as the visible system. Between June 2000 and June 2007, just prior to the start of the market collapse, the amount of over-the-counter foreign exchange derivatives went from $15.7 trillion to $57.6 trillion, a 367 percent increase. Between those same dates, the amount of over-the-counter interest rate derivatives went from $64.7 trillion to $381.4 trillion, a 589 percent increase. The amount of over-the-counter equity derivatives went from $1.9 trillion to $9.5 trillion in that same seven-year period, an increase of 503 percent.
Under Wall Street’s usual risk evaluation methods, these increases are not troubling. Because they consist of long and short positions, the amounts are netted against each other under the VaR method. For Wall Street, risk is always in the net position. If there is a $1 billion long position in a security and a $1 billion short position in a highly similar security, methods such as VaR will subtract the short from the long and conclude the risk is quite low, sometimes close to zero.
Under complexity analysis, the view is completely different. In complex systems analysis, shorts are not subtracted from longs—they are added together. Every dollar of notional value represents some
linkage between agents in the system. Every dollar of notional value creates some interdependence. If a counterparty fails, what started out as a net position for a particular bank instantaneously becomes a gross position, because the “hedge” has disappeared. Fundamentally, the risk is in the gross position, not the net. When gross positions increase by 500 percent, the theoretical risk increases by 5,000 percent or more because of the exponential relationship between scale and catastrophic event size.
This is why the financial system crashed so spectacularly in 2008. Subprime mortgages were like the snowflakes that start an avalanche. Actual subprime mortgage losses are still less than $300 billion, a small amount compared to the total losses in the panic. However, when the avalanche began, everything else was swept up in it and the entire banking system was put at risk. When derivatives and other instruments are included, total losses reached over $6 trillion, an order of magnitude greater than actual losses on real mortgages. Failure to consider critical state dynamics and scaling metrics explains why regulators “did not see it coming” and why bankers were constantly “surprised” at the magnitude of the problem. Regulators and bankers were using the wrong tools and the wrong metrics. Unfortunately, they still are.
When a natural system reaches the point of criticality and collapses through a phase transition, it goes through a simplification process that results in greatly reduced systemic scale, which also reduces the risk of another megaevent. This is not true in all man-made complex systems. Government intervention in the form of bailouts and money printing can temporarily arrest the cascade of failures. Yet it cannot make the risk go away. The risk is latent in the system, waiting for the next destabilizing event.
One solution to the problem of risk that comes from allowing a system to grow to a megascale is to make the system smaller, which is called descaling. This is why a mountain ski patrol throws dynamite on unstable slopes before skiing starts for the day. It is reducing avalanche danger by descaling, or simplifying, the snow mass. In global finance today, the opposite is happening. The financial ski patrol of central bankers is shoveling more snow onto the mountain. The financial system is now larger and more concentrated than immediately prior to the beginning of the market collapse in 2007.
In addition to global financial descaling, another solution to complexity risk is to maintain the system size but make it more robust by not letting any one component grow too large. The equivalent in banking would be to have more banks, but smaller ones with the same total system assets. It was not that many years ago that the current JPMorgan Chase existed as four separate banks: J. P. Morgan, Chase Manhattan, Manufacturers Hanover and Chemical. A breakup today would make the financial system more robust. Instead U.S. banks are bigger and their derivatives books are larger today than in 2008. This makes a new collapse, larger than the one in 2008, not just a possibility but a certainty. Next time, however, it really will be different. Based on theoretical scaling metrics, the next collapse will not be stopped by governments, because it will be larger than governments. The five-meter seawall will face the ten-meter tsunami and the wall will fall.
Complexity, Energy and Money
Using behavioral and complexity theory tools in tandem provides great insight into how the currency wars will evolve if money printing and debt expansion are not arrested soon. The course of the currency war will consist of a series of victories for the dollar followed by a decisive dollar defeat. The victories, at least as the Fed defines them, will arise as monetary ease creates inflation that forces other countries to revalue their currencies. The result will be a greatly depreciated dollar—exactly what the Fed wants. The dollar’s defeat will occur through a global political consensus to replace the dollar as the reserve currency and a private consensus to abandon it altogether.
When the dollar collapse comes, it will happen two ways—gradually and then suddenly. That formula, famously used by Hemingway to describe how one goes bankrupt, is an apt description of critical state dynamics in complex systems. The gradual part is a snowflake disturbing a small patch of snow, while the sudden part is the avalanche. The snowflake is random yet the avalanche is inevitable. Both ideas are easy to grasp. What is difficult to grasp is the critical state of the system in which the random event occurs.
In the case of currency wars, the system is the international monetary system based principally on the dollar. Every other market—stocks, bonds and derivatives—is based on this system because it provides the dollar values of the assets themselves. So when the dollar finally collapses, all financial activity will collapse with it.
Faith in the dollar among foreign investors may remain strong as long as U.S. citizens themselves maintain that faith. However, a loss of confidence in the dollar among U.S. citizens spells a loss of confidence globally. A simple model will illustrate how a small loss of faith in the dollar, for any reason, can lead to a complete collapse in confidence.
Start with the population of the United States as the system. For convenience, the population is set at 311,001,000 people, very close to the actual value. The population is divided based on individual critical thresholds, called a T value in this model. The critical threshold T of an individual in the system represents the number of other people who must lose confidence in the dollar before that individual also losses confidence. The value T is a measure of whether individuals react at the first potential sign of change or wait until a process is far advanced before responding. It is an individual tipping point; however, different actors will have different tipping points. It is like asking how many people must run from a crowded theater before the next person decides to run. Some people will run out at the first sign of trouble. Others will sit nervously but not move until most of the audience has already begun to run. Someone else will be the last one out of the theater. There can be as many critical thresholds as there are actors in the system.
The T values are grouped into five broad bands to show the potential influence of one group on the other. In the first case, shown in Table 1 below, the bands are divided from the lowest critical thresholds to the highest as follows:Table 1: HYPOTHETICAL CRITICAL THRESHOLDS (T) FOR DOLLAR REPUDIATION IN U.S. POPULATION
The test case begins by asking what would happen if one hundred people suddenly repudiated the dollar. Repudiation means an individual rejects the dollar’s traditional functions as a medium of exchange, store of value and reliable way to set prices and perform other counting functions. These one hundred people would not willingly hold dollars and would consistently convert any dollars they obtained into hard assets such as precious metals, land, buildings and art. They would not rely on their ability to reconvert these hard assets into dollars in the future and would look only to the intrinsic value of the assets. They would avoid paper assets denominated in dollars, such as stocks, bonds and bank accounts.
The result in this test case of repudiation by a hundred people is that nothing would happen. This is because the lowest critical threshold shared by any group of individuals in the system is represented by T = 500. This means that it takes repudiation by five hundred people or more to cause this first group to also repudiate the dollar. Since only one hundred people have repudiated the dollar in our hypothetical case, the critical threshold of T = 500 for the most sensitive group has not been reached and the group as a whole is unaffected by the behavior of the one hundred. Since all of the remaining T values are higher than T = 500, the behavior of those groups is also unaffected. None of the critical thresholds has been triggered. This is an example of a random event dying out in the system. Something happened initially, yet nothing else happened as a result. If the largest group that would initially repudiate the dollar is fixed at one hundred, this system is said to be subcritical, meaning it is not vulnerable to a chain reaction of dollar repudiation.
Consider a second hypothetical case, shown in Table 2 below. The groupings of individuals by size of group are identical to Table 1. This system of critical thresholds is identical to the syste
m in Table 1 with two small differences. The critical threshold for the first group has been changed from T = 500 people to T = 100 people. The critical threshold for the second group has been changed from T = 10,000 people to T = 1,000 people, while all the other values of T for the remaining three groups are unchanged. Put differently, we have changed the preferences of 0.3 percent of the population and left the preferences of 99.7 percent of the population unchanged. Here is the new table of thresholds with the two small changes shown in bold:Table 2: HYPOTHETICAL CRITICAL THRESHOLDS (T) FOR DOLLAR REPUDIATION IN U.S. POPULATION
Now what happens when the same one hundred citizens repudiate the dollar as in the first case? In this second case, one hundred rejections will trigger the critical threshold for one thousand people who now also reject the dollar. Metaphorically, more people are running from the movie theater. This new rejection by a thousand people now triggers the critical threshold for the next one million people, and they too repudiate the dollar. Now that one million have repudiated the dollar, the next threshold of one hundred thousand is easily surpassed, and an additional ten million people repudiate the dollar. At this point, the collapse is unstoppable. With ten million people repudiating the dollar, another one hundred million join in, and soon thereafter the remaining two hundred million repudiate at once—the rejection of the dollar by the entire U.S. population is complete. The dollar has collapsed both internally and internationally as a monetary unit. This second system is said to be supercritical, and has collapsed catastrophically.
A number of important caveats apply. These thresholds are hypothetical; the actual values of T are unknown and possibly unknowable. The T values were broken into five bands for convenience. In the real world, there would be millions of separate critical thresholds, so the reality is immensely more complex than shown here. The process of collapse might not be immediate from threshold to threshold but might play out over time as information spreads slowly and reaction times vary.
Currency Wars: The Making of the Next Global Crisis Page 24
