Chaos Theory and Risk Management

Summary This essay tells the story of chaos theory and its importance in finding order where there was only chaos before—and then applies chaos theory to the practice of risk management—thereby turning uncertainty into
a harbinger of opportunity.

Quotation  Chaos theory is a branch of mathematics focused on the behavior of dynamic systems that are highly sensitive to inputs. 

Wikipedia A young professional having breakfast might decide to eat another piece of toast and risk missing the bus. She runs for the bus but, alas, just misses it. Then, as she waits for the next bus, an old friend comes along and offers her a ride. On the way to the office the friend tells her of a new movie production company he has formed and that he is looking for a partner. She has always wanted to make movies and so she accepts his offer of partnership on the spot.

Systems.  The systems approach views the world as a complex organization of interconnected parts. The universe is a system. One scopes a system by defining its boundary and identifying which elements are inside the system
and which are outside the system. One can make simplified models of systems in order to understand and to predict the impact of future behavior. These models may define the structure and behavior of systems. Consider a simple example of a system as a box with an input and output. By varying the input, we can see how the output is affected. When outputs are highly sensitive to inputs the system is said to be chaotic.

Chaos Theory.  Research has shown that many simple nonlinear systems act chaotically and unpredictably. Chaos theory has broad implications for many disciplines. In risk management it suggests that rather than trying to
control several smaller basins of risk, it is best to define a larger basin boundary and allow the smaller risk basins to spill into each other. Chaos theory is a new science based on the principle that order can be found in disorder. It is the result of classical physics’ inability to predict the movement of subatomic particles beyond a certain quantum level. Werner Heisenberg foreshadowed chaos theory in 1927 with his uncertainty principle, which states that the position and momentum of a subatomic particle cannot be known simultaneously. Since its inception in the 1970s, chaos theory has become one of the fastest-growing areas of research in theoretical physics. Chaos theory may eventually prove more useful than quantum theory in accounting for some aspects of particle behavior. Chaos theory attempts to understand the rules of disorder rather than the rules of order, as is the case with traditional science. It relies as much on faith and intuition as it does on cold, hard science. Chaos theory picks up where conventional thinking leaves off and endeavors to comprehend phenomena that seemingly defy rational description. Consider the four chaotic subjects discussed below that relate to risk management:

1) The Butterfly Effect; 2) Universality; 3) Inner Rhythms; and 4) Fractals.

1) The Butterfly Effect refers to the cause and effect relationship between seemingly small disturbances in air flow caused by the flapping of a butterfly’s wings which can ultimately cause severe changes in weather patterns thousands of miles away. The butterfly effect refers to systems that are highly sensitive to inputs. Small changes in one state of a deterministic nonlinear system may result in much large differences in the following states. It is impossible to foresee all of the twists-and-turns in life and in business. All that we can do is have a clear set of values and objectives, and then make the best of every situation. Risk management, like chaos theory as described by the butterfly effect, must concern itself with outcomes rather than with pathologies. For example, a risk manager is not so much interested as to whether an increase in revenue comes from an increase in price or a decrease in the foreign exchange rate, as she is in predicting revenue for the following year. Consider a system that has 1 as an input and 10 as an output. If the input is increased slightly to 1.01, the output might shoot up to 10,000. In this case, outputs are chaotic and highly sensitive to inputs—and thus embody the butterfly effect.

2)Universality  in chaos theory argues that common ground exists between otherwise divergent phenomenon. With statistics, universality is the view that the properties of a large class of systems are independent of the contents of the system. Universality exists in chaos when a large number of moving parts come together. Traditional scientific theories stop at the edge of the forest, unable to penetrate the dense underbrush of apparent randomness. At a certain point the quantification of phenomena breaks down and further understanding can only take place by observing the emergence of patterns common to parallel systems. A physicist studying the movements of planets around the sun as a way of further understanding the movement of electrons around the nucleus of an atom is an example of using parallel systems to understand divergent phenomena. Chaos theory focuses on phenomena that are unpredictable, but yet have obscure connectedness to other seemingly unrelated phenomena. The edge that chaos theory holds over traditional science is that it does not focus on specific outcomes, but instead observes obscure subtle tendencies and patterns common to different systems that had previously gone unnoticed. As far as risk management is concerned, the key tenet of universality is that all risks share a good number of common traits. Consider that out-of-the-money put options function in exactly the same way as property insurance, with the deductible being the difference between the current price and the exercise price. Furthermore, because of their similarities, individual risk elements should be assessed in aggregate as a way of understanding how they interact with each other and how they impact the whole organization.

3)Inner Rhythms describe the workings of systems and how they tend to steady or unsteady states. Chaos theory addresses the conditions necessary for a system to reach and maintain a steady state. Inner rhythm is an exploration of the inner landscape. We can see inner rhythms in terms of biological systems. Equilibrium represents a state of total control, whereas a steady state is a balance between chaos theory and control. When a biological system reaches equilibrium, it is dead. A certain amount of chaos is healthy in a system. Inner rhythms are the practice of surrendering to the moment and to our body’s wisdom. It is an opportunity for allowing, feeling, and expressing all the emotional qualities and textures that make up the human experience. I dare ask the question of what it is like to welcome inner chaos? Also, what is it like to be firmly rooted in our own center, true to ourselves, while sharing space and interacting with others? And what unfolds when we carry this embodied truth
and freedom beyond the dance floor, into our daily lives? The risk management parallel of inner rhythms is represented by the trade-off between risk and return. The state where firms are most likely to meet their corporate objectives are those where risk and return are optimally balanced. A system is considered robust if it can both withstand jolts and function well over a wide range of economic conditions. Too much control leaves companies unable to react to unexpected changes, whereas too much chaos theory leaves companies out of control. Mode locking in chaos theory refers to the natural tendency of systems to harmonize with each other. Pendulums on wall clocks next to each other tend to swing in synchronicity. Mode locking also explains why the light side of the Moon always faces the Earth. There is a natural tendency for risk elements to acquire a degree of synchronicity and become correlated with other elements.

4) Fractals are natural phenomena exhibiting self-similar patterns at every scale. They stem from chaos theory and are fractions of dimensions that include everything from clouds to oil prices to galaxy clusters.
Consider a coastline viewed from both space and a person walking along it. The coastline is neither one nor two-dimensional but is a fractal dimension somewhere in between. Fractals tell us that the fractal dimension is the
same for both the astronaut and the pedestrian. Metaphorically speaking, there is no difference between looking through a microscope and looking through a telescope. Fractals prove there is no inherent scale to the
universe—and link the macrocosmos of relativity theory (Einstein’s Moon) with the microcosmos of quantum theory (Schrödinger’s Cat) which tells us consciousness determines perceived reality in both cases. If one compares
minute-to-minute oil prices to month-to-month prices, fractals tell us that the probability of big jumps stays relatively the same (ie. micro equals macro). Fractal basin boundaries refer to the natural tendencies of systems
to gravitate to particular basins. It is a question of chaotic elements choosing one basin over another. In risk management, the objective is to delineate the basin boundary and therefore determine the characteristics of
the risk elements within the basin. Chaos theory suggests that rather than trying to control several smaller basins of risk, it is best to define a larger basin boundary and allow the smaller risk basins to spill into each
other. Corporately, the risk basin boundaries define both by a firm’s exposure to risk and by the objectives, values and risk preferences of the firm. This postmodern approach to risk management ties all risk elements
into the very heart of corporate policy.

Conclusion. This essay tells the story of chaos theory and its importance in finding order where there was only chaos before in risk management and many other disciplines. Chaos theory teaches us to expect the unexpected. When one comes across a chaotic system, most people just give up. Instead, we can turn disorder into order by simply applying the extensive methods of chaos theory.