The Black Swan Problem. Håkan Jankensgård

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The Black Swan Problem - Håkan Jankensgård


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in melting ice sheets. In the end, there are too many variables and too many complicated feedback loops in these highly dynamic systems. On top of that there is human civilization itself. While once rudimentary and mostly local, over time society has become complex beyond imagination. Technical innovations have made possible advanced systems that increasingly connect people across different parts of the globe. It is fundamentally unknowable what outcomes these vast and interconnected systems of interacting people and technologies will produce. Human agency by itself ensures why the future keeps bringing so many surprises, as the 9/11 attack illustrates. It should be clear that we are up against a complexity that is beyond our ability to predict successfully.

      Once we capitulate to the fact that we cannot predict the future, the next best thing would be to be able to characterize randomness itself, i.e. describe it. In that way, we would have some idea about the scope for deviations from what we expect. A description of randomness would involve some degree of quantification of things like the range within which the values of a variable can be assumed to fall and how the outcomes are distributed within that range (frequencies). We might occasionally find such descriptions of random processes to be practically relevant insofar as they help us make informed decisions and our future wellbeing depends on the outcome of the variable in question. They are potentially helpful, for example, in coming up with a reasonable analysis of the trade‐off between risk and return in different kinds of investment situations.

      Whenever data exists, it is of course possible to try to use it to come up with descriptions of the randomness in a stochastic process. Chances are that we can ‘fit’ the data to one of the many options available in our library of theoretical probability distributions. Once we have, we have seemingly succeeded in our quest to describe randomness, or to turn it into something resembling known odds. This is the frequentist approach to statistical inference, in which observed frequencies in the data provide the basis for probability approximations. Failure rates for a certain kind of manufacturing process, for example, can serve as a reasonably reliable indication of the probability of failure in the future.

      While the normal distribution is often highlighted in discussions about ‘well‐behaved’ stochastic processes, many other theoretical distributions appear to describe real‐world phenomena with some accuracy. There is nothing, therefore, in the concept of benign uncertainty that rules out deviations from the normal distribution, such as fat tails or skews. It merely means that the data largely fits the assumptions of some theoretical distribution and appears to do so consistently over time. It is as if we have a grip on randomness.

      The crucial aspect of wild uncertainty is precisely that the tails of the distributions are in flux. In other words, the historically observed minimum and maximum outcomes can be surpassed at any given time. I will refer to the idea of an ever‐changing tail of a distribution as The Moving Tail. With wild uncertainty, an observation may come along that is outside the established range – by a lot. Such an event means that the tail of the distribution just assumed a very different shape. Put another way, there was a qualitative shift in the tail. Everything we thought we knew about the variable in question


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