VIEW 5 Systemic risk: The catataxic shift

5. Systemic risk: The catataxic shift

Earlier, in View #4, we explained the difference between specific and systemic risk. The former can be mitigated by diversification. Strictly defined, systemic risk is ‘undiversifiable risk’, in other words, the risk that cannot be mitigated through diversification, though in an insurance context the term is used more loosely. But to divide risk into these two categories is misleadingly simple because it assumes a static environment. As we know, particularly in the cyber world, the environment is always changing (See View #13). So, let’s look at a dynamic model in which systemic risk can emerge over time.

Imagine an experiment in which there are 20 buttons and 20 threads. The ideas behind this approach were first put forward in two papers: On Random Graphs by Erdos & Reyni (1958) and The Origins of Order by Stuart Kauffman (1993) although they were applied in a biological context to explain how life might have originally emerged on earth.

5. Systemic risk: The catataxic shift

A sudden change
At the start of the experiment, one thread is randomly attached to two buttons, one at each end. After five threads have been attached randomly in this way, if you were to close your eyes and pick up a thread at random, you would probably pick up two buttons with it. Continuing in this way, after you have added 10 threads picking up a random thread might also lift up three or four buttons. You can see that at some point picking up a thread will pick up all the buttons. The question is when does this point happen?

5. Systemic risk: The catataxic shift

The answer is when the ratio of buttons to threads is 0.5, in other words very soon after 10 threads have been added to the 20 buttons. Please refer to the original papers for the mathematical proof. You may think “more threads, more buttons, so what?”. The important thing is that it happens very suddenly, in a step function change. At one moment you are picking up a few buttons, the next moment you are picking up the whole thing. This sudden change - the catataxic shift - marks the point that you can no longer view the system as a set of independent elements. You must view all the elements as a single entity. This is analogous to a phase change. In a gas, you can view the particles as independent elements. When the temperature changes and the substance becomes solid you must view all particles as a single object.

Systemic risk arises when the degree of connectivity reaches a certain point. You may have assumed you have a diversified portfolio with all your eggs in different baskets. But a change in the environment, such as temperature or the ‘threads to button ratio’ in these examples, forces you to realise that all your eggs are in fact in the same basket - one big global basket that we call the internet.