What Is Ergodicity? Ergodicity In A Nutshell

Ergodicity is one of the most important concepts in statistics. Ergodicity is a mathematical concept suggesting that a point of a moving system will eventually visit all parts of the space the system moves in. On the opposite side, non-ergodic means that a system doesn’t visit all the possible parts, as there are absorbing barriers

Understanding ergodicity

Suppose you are writing a restaurant travel guide and want to determine what the popular restaurants are in your home city. One strategy involves taking a momentary snapshot, where you visit ten restaurants and count how many patrons are eating in each. 

Another strategy involves choosing one patron and following them for a predetermined amount of time. For the purposes of this article, let’s say twelve months. During this time, you observe their eating behavior and whether they dine at a particular restaurant repeatedly.

With two different strategies, you will obtain two different results. The first strategy is a statistical analysis of the entire ensemble of restaurant diners at a given moment in time. The second strategy is a statistical analysis for one person for a certain period of time. 

While the first strategy may not be representative of popular restaurants over a long period of time, the second strategy may not be representative of popular restaurants for all restaurant diners.

If both strategies determine that the same ten restaurants are the most popular in the city, the ensemble of diners is said to be ergodic. In reality, however, most ensembles of human populations are not ergodic.

Why is ergodicity important?

Ergodicity is important in explaining how individuals make conclusions about something while having information about something else. Fundamentally, ergodicity helps determine whether the generalizations people make are correct or incorrect. If the generalization is directed at an ergodic ensemble, there is a good chance it is correct.

To explain this concept in more detail, consider a newspaper reader. One day, the reader notices that the newspaper has printed inaccurate information. Based on this observation, they generalize that the newspaper will print inaccurate information in the future. This generalization is more or less ergodic and thus correct. If someone determines how many mistakes appear in one issue of a newspaper and then compares that number with how many mistakes the editor makes over time, the results are almost identical. 

Ergodicity in finance

Many theories of finance and investment assume ergodicity. These assumptions are particularly prevalent in modern portfolio theory, aggregate macroeconomic models, and discounted cash flow (DCF) models, among others.

However, these models often fail to account for large deviations caused by debt crises, financial crises, and other systemic risks associated with the banking system. Author Nassim Nicholas Taleb suggested finance and investment were non-ergodic since an even statistical distribution where the system returns to every possible state infinite times is simply not possible. 

The reasons for this are caused by what Taleb called absorbing states, where ruin such as bankruptcy, death, or the devolution of a country or legal regime occurs. Ruin then results in absorbing barriers, which Taleb defines as “anything that prevents people with skin in the game from emerging from it, and to which the system will invariably trend.

Given the possibility of ruin in finance and investment, cost-benefit analyses are no longer possible and the system is non-ergodic. In other words, traditional models based on probabilistic data fail to account for extreme, atypical scenarios that end in ruin.

To grasp this concept you need to understand the difference between ensemble probability and time probability.

In an ensemble probability, we pretty much take all the possible outcome from a group of people, and sort of average it out. A completely different story applies to time probability.

Source: Nassim Nicholas Taleb at The Logic of Risk Taking

As Taleb explains:

The difference between 100 people going to a casino and one person going to a casino 100 times, i.e. between (path dependent) and conventionally understood probability. The mistake has persisted in economics and psychology since age immemorial.

Ensemble probability vs. time probability

In short, modern economics, finance, and cognitive psychology often fall into the trap of mistaking time probability for ensemble probability, where an outcome is judged based on all the possible paths that the players in the system can take. Instead of taking into account that in the real world, there is an absorbing barrier (a point o non-return and ruin), thus making most of the endevoirs “path-dependent.”

From there we develop naturally something that Taleb would define as “BS detector” which is a natural defense in a complex world. Whereas instead, with the claimed “rationality” modern psychologists want us to act against this natural tendency to avoid ruin, as if we were living parallel lifes, all together. When instead we have a natural filter to ruin, and we do undersant risk in the real world.

Modern behavioral psychologists, instead assign humans a growing list of biases, claiming the “irrationality” of individuals, rather than aknowledging (as Taleb would say over and over) they do not understand the real world.

This has huge implications, as it cancels out most of the work proposed in modern financial theory, and behavioral economics. In fact, as already explained in biases and what we got wrong about them, this also invalidates many of the findings of the last decades related to behavioral economics and psychology.

Key takeaways:

  • Ergodicity is a mathematical concept suggesting that a point of a moving system will eventually visit all parts of the space the system moves in.
  • Ergodicity helps explain how individuals make conclusions about something while having information about something else. More specifically, ergodicity helps determine whether the generalizations people make are correct or incorrect.
  • In finance and investing, ergodicity forms the basis of DCF and macroeconomic modeling. However, the industry is non-ergodic because of the presence of ruin events and the failure of probabilistic data models to properly account for them.

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Gennaro Cuofano

Gennaro is the creator of FourWeekMBA which reached over a million business students, executives, and aspiring entrepreneurs in 2020 alone | He is also Head of Business Development for a high-tech startup, which he helped grow at double-digit rate | Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy | Visit The FourWeekMBA BizSchool | Or Get The FourWeekMBA Flagship Book "100+ Business Models"