Managing Financial Risk wIth Fractal Geometry

By Sorkin, Jay; Buyer, Shera | Modern Trader, August 2001 | Go to article overview

Managing Financial Risk wIth Fractal Geometry


Sorkin, Jay, Buyer, Shera, Modern Trader


Emotions as much as supply/demand factors are behind the moves in markets. One reliable reflection of such emotions is money flow. Here's one systematic approach to analyzing this key market factor.

Life itself is a complex adaptive system, as is a self-organizing economy or political entity. The first attempts at using complexity theory for market analysis were little more than brute-force exercises in number crunching. Predictably, these were unsuccessful; numbers alone can't provide the information needed to make market decisions. Human behavior, the decision-making processes of market participants, is critical and too often overlooked. How else can you explain the times when the Fed lowers (raises] interest rates, yet the capital markets go down (up) or some similar example? Human interpretation of information, not the information itself, drives market decisions.

While obvious to some, professional recognition has been long in arriving. However, Matthew Rabin recently received the biennial John Bates Clark medal, given to the most outstanding economist under the age of 40, for his work on the incorporation of psychology into standard economic theory. Markets can be viewed as complex adaptive systems to be studied in the context of their total environment, just as people must be studied in theirs to make sense of their actions. While this may sound a little farfetched initially, consider there are currently more physicists than economists on Wall Street payrolls.

Complexity theory has gone mainstream. Urbanologist Jane Jacobs in her recent book The Nature of Economies writes, "Economic life is ruled by processes and principles we didn't invent and can't transcend...." These processes include fractals, entropy, feedback loops and many other characteristics of complex adaptive systems. Complex adaptive systems self-organize to amass, distribute and react to the collective behavior of many interacting units. Financial markets are distributors of goods and services. Markets incorporate new information to make decisions that, in turn, create newer information and newer decisions in an endless loop. The key is market participants must interpret and react to this information individually before a collective market decision can emerge.

Toward complex analysis We combine complexity theory with firsthand experience in the Chicago Board of Trade's (CBOT) Treasury bond option pit and research being done at the exchange to produce a new market analysis tool, the Cash Flow Analysis Series (CFAS). This graphic market model uses fractal geometry, a staple of complexity analysis, to make the interaction between the market's natural organization and human behavior visible and available to risk managers.

The CFAS was developed over eight years of research and had to meet two criteria for acceptance. First, the conceptual framework had to cover all market situations. Second, the market had to confirm the numbers selected in advance by the model. The premise is if you can see how price relates to the market's natural organization in the present, you can use this information to anticipate prices. Of course, the CFAS is a tool, not a "magic bullet" trading system.

A CFAS is illustrated in "Sierpinski waltz" (right). This chart organizes Treasury bond futures data over the July 2000 through February 2001 period. The vertical axis is the price scale. The horizontal axis represents "market time," the time it takes for market participants to reach a consensus on value. The dated rectangles represent the first standard deviation of trading volume for that date. They are organized sequentially, opposite the appropriate price area, according to a simple set of rules. The concepts of expended effort and market value may remind some of point-and-figure charts and Market Profile analysis, respectively.

To find value, market participants establish a range and then test various outcomes within that range. …

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