Sensitivity to original conditions is a key characteristic of complex deterministic systems, but a system may change dramatically without a change to initial conditions, but rather as the result of moving beyond critical tipping points, or points of no return. Within systems theory and complexity science, around the boundaries of chaos theory, the field focusing on dramatic transformations into disorder is catastrophe theory, which attempts at isolating global properties for systems drifting into disorder beyond certain critical thresholds. Tipping point analysis is more relevant to our analysis of financial markets today.

French mathematician René Thom is the father of catastrophe theory; growing beyond certain critical thresholds in a nonlinear system can cause equilibria to appear or disappear, or morph, leading to large and sudden changes of the behaviour of the system. It may lead to abrupt ruptures, such as the unpredictable timing and magnitude of a landslide. The subject is so fascinating that even captured the attention of Salvador Dalí, who would dedicate its last painting to one of the catastrophe-types categorized by Thom, The Swallow's Tail.
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The question then becomes one of identification of such critical tipping points, or ‘bifurcation events’. What is the level beyond which a small change can provoke a large swing, a big transformation? What is the last grain of sand on the pile that the system can take in before transformation? How to predict when a system collapses?

The relevance of a tipping point is clear to the human mind when associated to a simple element. Too many people on the side on a boat, at some tipping point the boat flips. Or the pushing of a chair out of balance, at some tipping point the chair flips. However, we struggle with the concept when it comes to complex systems, ecosystems, societies, climate change, forests and fisheries, human immune system and brain, and financial markets.

Mathematical biologist Marten Scheffer of Wageningen University studies social-ecological tipping point dynamics . He argues that there may be several critical switching points, not just one, on one key variable. The resilience of the system may degrade to some tipping point where a small perturbation can push it into another state. The loss of resilience makes it flip, eventually, at a point. There are jumps, discontinuities beyond certain tipping points for key variables, where the system snatches to a totally different equilibrium / attractor, into an alternative stable state. The loss of resilience will eventually be reflected in a critical slowing down in getting back to original positions after disturbances. Such critical slowing down has got to do with very fundamental mathematical properties of systems that are close to a tipping point. His analysis focuses on lakes and ecological domains, but can be applied broadly across complex systems

  

How does the system degrade? How is resilience lost? How does it happen? One such way is with a change in feedbacks. It happens when self-correcting negative feedback loops weaken, and self-amplifying positive feedback loops arise.

Feedback loops are essential forces in the build-up of any ecosystem. They are mutual causal interactions between the elements of the system. The natural world is full of it. Negative feedback loops are the internal stabilizing forces of a system, as they bring the system back into balance early on after small perturbations.

As negative feedback loops get impaired or lose relevance within a system, the system degrades, and the basin of attraction becomes smaller, flatter, less convex, to the point where new small disturbances can push the equilibrium out of the basin. Resilience falls and the system nears a critical transition zone. The system stands at an unstable equilibrium, from where it can flip at any time on closing up to the tipping point.

In the words of Brian Walker of the Stockholm Resilience Centre, ‘if you never burn a forest the species in there who are capable of putting up with fire eventually go out-competed; the only way to make a forest resilient to fire is to burn it. The only way to make children resilient to the environment is to expose them to it (‘sheltered kids do not make for capable adults’ Lythcott-Haims). Resilience is maintained by probing the boundaries of the basin, otherwise the basin becomes smaller and smaller. That’s how the body maintains a body temperature of 38 degrees (at 41 you die). We had 10 million years to develop the feedbacks we needed to adapt. Our earlier versions extinguished/ got extinct.’

Resilience in a system is the ability to absorb shocks and to retain the same structure functions and feedback as before. It implies persistence, adaptability, transformability of the system. It requires a wide basin of attraction, a good balance between order and disorder. Essential to resilience is the presence of negative feedback loops.

Dr. Walker argues that one should manage feedbacks to reach resilience. You lose your feedback, you lose resilience. The essence of resilience is then to understand the feedbacks in the system that keep it self-organized, stable, robust.

On the contrary, positive feedback loops are amplifiers, amplifying loops, as they exacerbate a particular set of conditions of a system. As such, they can ultimately be harmful, and lead to an unstable balance, towards a critical tipping point.

We can never predict the exact point at which the system transforms. We live in a stochastic world and the final little push out of equilibrium may happen randomly. But what we can say is when the system has become inherently unstable, fragile, vulnerable, ready for small perturbations to trigger critical transitions, in phase transition zone. If we have reasons to suspect the possibility of a critical transition, the analysis of generic early warning signals may be a significant step forward when it comes to judging whether the probability of a transition is increasing.

In relation to financial markets, this is the subject of our next thematic research to be presented during our upcoming INVESTOR PRESENTATION. Please get in touch to register.

In conclusion of the theoretical section, it can be argued that the dynamics of positive feedback loops acting on an unstable equilibrium at the edge of chaos are one likely precursor of a regime shift. Sooner or later, at some critical tipping point in close reach.

The analytical tools of ‘complexity theory’ can be used to understand phenomena as diverse as biological ecosystems, climate change, forests, lakes, brain and ... financial markets. Features typical of complex systems include the broad inter-connectedness of global markets - only increased with globalization, the vast network of factors at play, the flipping correlation between assets over time, the non-linear relationship between the various elements in the system. The endogenous crises, broad discontinuities and sudden ruptures experienced by financial markets over history also do resemble far-from-equilibrium phenomena in complex systems.

'Complex means non-linear, as there is more in them than purely direct relationships of cause and effect, showcasing deterministic chaos. Adaptive means evolving, dynamical. In ecosystem species evolve, in financial systems people will change their behavior. Systems mean very broad, operating over a range of scales', in the words of Dr Walker.

Financial markets shares the three characteristics of complex dynamical systems, as defined by the Stockholm Resilience Centre: (i) highly unpredictable, due to their non-linear relationships / interactions, it is hard to say what the state of the system might be some time in the future. (ii) contagio effect, things can spread very quickly and (iii) modularity, although the whole system is well connected parts of the system are more connected within than between, which may help its resilience, or the ability for the system to return to equilibrium after turbulence.

In a military parlance later adopted by the business world, financial markets are typical VUCA (acronym for Volatility, Uncertainty, Complexity, Ambiguity): they are interconnected, interdependent, non-linear and a structurally volatile complex system. In markets is visible the non-linear interactions between the elements in the complex system, as they co-evolve over time to adapt to local events.


Financial Markets Are On The Edge Of Chaos

When analyzed through the prism of complexity theory, today’s markets exhibit the signatures characteristic of criticality, lack of resilience, flipping feedback loops and likely proximity to critical tipping points. In other terms, markets are unstable, while stationing on the edge of chaos.

Such signatures characteristics include:

The list can be longer, but it does not need to be any longer to draw conclusions on the sustainability of the current setting. If unsustainable and unstable, a transformation may loom ahead. How severe a transformation depends on how big an anomaly was built beforehand. From the look of things, the anomaly is bigger than at any point in history, thus making the potential shift potentially large and disruptive.

As we learn in complexity theory, resilience is lost when positive feedback loops arise and are held constant for long enough, while on the edge of chaos. Then, it becomes more probable to be nearing critical thresholds for transformation. The biggest change in markets over the last few years has been exactly that: the formation of positive feedback loops between QE/NIRP policies and the private investment community. Private flows followed public flows, exacerbating valuations, leverage, debt levels, concentration of positions, correlation amongst strategies, life-dependence on low levels of volatility. The structure of the market itself morphed, and is now dominated by passive or quasi-passive investors, that incorporated the ‘ trend factor ’ or the ‘volatility factor’ within their constructs.

On the edge of chaos, it does not take much to flip, no need for a major catalyst. The flapping of a butterfly’s wings may do. As we heard in a recent show: ‘remember: it was not Holyfield or Lewis to knock Tyson out in 1990, but Buster Douglas. A mostly unknown, to remain unknown, second-tier boxer. It doesn’t take much to take you down when your time is up.’

If this analysis is correct, and tipping points are near, markets are in an uncomfortable spot, where not much escape is available via new lending, not much escape via higher valuations, not much escape with new QE, not much escape with more leverage, not much escape with more cash to deploy. No escape, no further rise does not necessarily imply a crash. However, treading water on the edge of chaos is dangerous, as any small perturbations can trigger a critical transformation. An exogenous or endogenous trigger can easily push the equilibrium out of its small basin of attraction. A new equilibrium may be waiting to assert itself, nearby, through chaos.

Thanks for reading us today! We remain at your disposal for data, questions and feedback. If you have contrasting or confirming data or arguments please get in touch, would be great to compare notes. Portfolio-wise, a list of shorts, convex-rich, long vol instruments is locked and loaded for deployment. Our time is currently spent on closely monitoring critical tipping points and evaluating the merit of different general early warning signals for each.