INVESTED: In Markets, in the Future, and in Society.

The Greek myth of Icarus and Daedalus tells the story of a son and his father in their attempts to escape the island of Crete by crafting wings from wax and feathers, enabling them to fly away. While their engineering prowess was enviable, and they succeed in constructing a functioning set of wings, the fate of Icarus is undesirable, plunging to his death after the hot sun melted the wax holding the wings together. The idiom ‘don’t fly too close to the sun’ has since become a well-known fixture in the English language, typically meant to express a foreboding tone about greed or overambition. Ultimately, however, the wings of Icarus were an astounding success, and the engineering marvel of a millennia’s pre-flight-era father and son team was unfairly marred by a poor understanding of the limitations of its design.

In the eons since the time of Ancient Greece, the field of control theory has provided a strong record of success in teasing apart the fundamental aspects and limitations of control and observation in physical systems. In homage to the tale of Icarus, control theory has been the driving force behind our understanding and commercialization of flight. In the 1900s, the formalization of this general field of study had astounding success, with its ‘modern era’ exemplified by the physical marvel of ‘stabilizing the unstable’ and creating functioning rockets for the space program[i]. If you think about it, the design of a rocket is far removed from the antiquated wax wings of Icarus, largely doing away with the animalistic inspiration of traditional aircraft. Inherently, rockets are an example of an unstable system. Absent any clever design of systems to control them, a cylinder filled with fuel attached to a persistent explosion doesn’t seem like it would work as an effective mode of flight. There’s a reason that paper rockets are much less popular than paper airplanes.

The problem of providing stability to an otherwise unstable system is a surprisingly pervasive issue. In fact, this is what your own internal control system is doing whenever you’re standing up. As humans, we are an example of an unstable system: when we stand upright our brains must constantly provide feedback—both from our visual system, as well as our inner ear—on what corrections need to be made for us to continue standing. In fact, it is the failure of these regulatory systems in old age (and not simply carelessness or muscular fatigue) that lead to many falls. One simple example of an analogous unstable system that most of us surely have experience with is an inverted pendulum. While that name may not immediately recall your memories from school, I’m sure visions of the class clown balancing a meter stick on his open hand will. An inverted meter stick (or any long stick, for that matter) in an outstretched hand is a perfect example of an unstable system. Try balancing one upright on the floor alone, while it may stand upright for a moment or two, eventually, it will topple over onto the ground. However, if you place the meter stick standing upright in your open hand, it’s possible—through feedback you provide by moving your hand—to stabilize the system in a state where it stands upright for as long as your attention remains focused. Like a rocket, feedback is necessary for the system to remain stable.

While this simple example may seem trivial, it really isn’t, and there has been a breadth of academic research on the topic[ii]. For instance, in trying to understand exactly what information you use to stabilize the stick, or even inferring the signal delay time between seeing the stick move and responding by moving your hand. Interestingly, this latter experiment provides a limit on how short of a stick you can balance in your hand based on how fast your nervous system can process information and respond (just try balancing a pen on your hand in the same way and you will see how much more difficult it can be).

While this discussion has been far removed from the world of finance so far, much like the problem of unstable systems, the management of a financial portfolio itself represents a controlled system: we control financial portfolios and provide feedback by adjusting exposures to different asset classes, updating leverage in response to changing volatility, and monitoring the risk and relationships between financial instruments. Much like the tale of Icarus, our ignorance to the limitations of a particular technique or strategy (or unwillingness to acknowledge such limits exist) could vaporize the wax holding together any tenuous portfolio of financial assets in the wrong circumstances. A better strategy would be to understand what the limitations of control are in all cases, and to design a robust system in the same way that modern control theory suggests; so that a shock to any given component does not compromise the system as a whole. Put in the language of portfolio theory, build robustness through diversification.

[i] J. Bechhoefer, “Control Theory for Physicists”, Cambridge University Press, 2021

[ii] T. Insperger & J. Milton “Stick Balancing with Feedback Delay, Sensory Dead Zone, Acceleration and Jerk Limitation”, Procedui IUTAM, 2017, 22