Currency Wars_ The Making of the Next Global Crisis - James Rickards [108]
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