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Managing risk and avoiding ruin: The Ergodicity View

Updated: Jan 2

The difference between risk and ruin is significant. Their nuanced differences are also critical to managing risk and uncertainty in our lives. One of my favorite related quotes is from one of my favorite authors:

“One may be risk loving yet completely adverse to ruin.”

- NN Taleb

A critical aspect of understanding the differences between risk and ruin is found in the study of a peculiar and not well-known word. That word is: "Ergodicity"

Table of Contents:

  1. What is Ergodicity?

  2. Ergodicity as related to investing

  3. Ergodicity as related to gambling

  4. Ergodicity as related to economics and physics

  5. Conclusion and Notes

We even provide an example of a famous scientist confusing ergodicity. It is easy to do!

To start: Most human systems are non-ergodic. This is code for - most human systems may lead to ruin.

1. What is Ergodicity?

Ergodicity is the degree to which probabilistic outcomes of systems are the same regardless of how the systems are engaged over time. If a system is perfectly ergodic then the outcome is the same regardless of whether many system participants engage in the system simultaneously or whether one participant engages in the same system over time. The degree of ergodicity relates to comparing probabilistic outcome differences between cross-sectional and time-series distributions.

For Example:

A coin-flipping game (with a fair coin and consistent flipping conditions) is ergodic. Regardless if 100 people flipped a coin at the same time or 1 person flipped a coin 100 times, the outcome is expected to be approximately a 50% probability of heads or tails.

A Russian roulette game (with a fair bullet chamber) is decidedly non-ergodic. If 100 people play Russian roulette at once, 1/6th (or 17%) of them will likely die. If I alone try to play Russian roulette 100 times, there is an almost 100% chance I will be dead long before I get to 100 attempts.

The degree of ergodicity generally relates to the degree to which a system is subject to entropy. Because humans will die at some point, human systems are generally non-ergodic. How quickly a system is subject to entropy generally defines the degree of ergodicity. The slower the entropy, the higher the degree of ergodicity.

2. Ergodicity as related to investing

Investing is a good example of where ergodicity confusion may create significant risk.

Most companies eventually fail. Credit Suisse and CNBC demonstrate the average life of companies is shortening, down from an average of 60 years in 1958 to an average of 20 years in 2012. The average life trend shortens as technology disrupts older companies. It would seem, the scaffolding needed to support companies as they grow from small to large may become a source of fragility. Thus, disruption reveals a company’s lack of adaptability to changing markets. So investing in one company, no matter how good it is today, may at some point lead to a loss of value. Statistically, a good company is likely to become a victim of its own success as it grows. To manage this risk, a best practice is to invest in portfolios of companies and periodically rebalance holdings. This recognizes that investing, by its very nature, is a non-ergodic activity. If investing was ergodic, we would only need to invest in one company.

Companies promoting their own employee stock ownership plans may expose their employees to undesired risks. A company, because it is likely to fail at some point, is non-ergodic. As such, stock ownership plans are very risky. Just look at what happened to the GSEs (the Government Sponsored Enterprises, Fannie Mae and Freddie Mac), resulting from the Financial Crisis and Great Recession.

After they went bankrupt and were ordered into conservatorship, the employees lost their company stock value. The employees of the GSEs had accumulated stock via various company stock ownership plans. At the time, the GSEs were backed by an implied guarantee from the U.S. Government. So if GSE employees and retirees lost value in their company stock ownership plans, imagine the risk of companies without the backing of the U.S. Government!

Fannie Mae’s workers had $116 million in the employee stock ownership plan at the end of 2006. [In 2008], it’s more like $17.5 million. Ouch.

- New York Times article and this was before they went bankrupt!

Company stock ownership plans expose employees to diversification risk. If a company fails and its employees are deeply invested in the company stock, then they lose both income and wealth. It is a best practice to diversify that risk by separating sources of income and wealth.

To be clear, I’m certainly not suggesting company stock ownership plans are intrinsically bad. Like any other tool, my concern relates to usage. In this case, my concern relates to a potential lack of diversification. Single-company stock ownership should only be considered in the context of a well-diversified investment portfolio. Complicating the considerations, some companies provide significant incentives for their employee, especially executives, to participate in employee stock ownership plans. For executives, SEC public disclosure requirements and tax liabilities may create a disincentive to divest employee stock.

3. Ergodicity as related to gambling

This is similar to investing but has a “staying power” characteristic that helps us understand the degrees of ergodicity. Gambling generally has two primary agents, the bettor and the house. The bettor places the bet, the house makes the bet. The odds are the chances the bet will pay off, once the bet is made. Both agents are aware of the odds. However, in most cases, the house is more ergodic than the bettor. That is, the house has higher relative ergodicity. This means the house can absorb more losses until the payoff makes them whole. On the other hand, the bettor has much lower staying power. The bettor is more likely to run out of money before the house. Thus, the bettor’s ability to absorb risk is lower, even though they are operating under the same odds as the house. Keep in mind, losses and gains are inversely related between the house and the bettor. That is, the bettor’s loss is the house’s gain and vice versa.

In fact, the house depends on this relative ergodicity principle as the source of revenue. There is a higher chance a bettor will leave before they realize a payoff than the house will not be able to absorb additional losses before the payoff. The house, like a bank, is much better capitalized than the bettor. That difference is how the house makes money.

4. Ergodicity as related to economics and physics

Economics: See the following link for a good explanation concerning ergodicity in the context of economics.

“Much of classical economics assumes that human behaviour is founded on the expected average outcome of the group (see Expected Utility Theory). This works under the assumption that most environments or situations are ergodic, when in fact this is not the case.”

This statistical mechanics approach works well when describing gases and entropic behavior. However, in the world of human affairs, very few activities are ergodic. So the underlying assumption of ergodicity in the Paul Samuelson branch of economics is problematic and is the basis of the behavioral economics revolution to improve the formulations with the ergodicity assumption. (E.g., Expected Utility Theory, Efficient Market Hypothesis)

Physics: Relating to entropy, if entropy is the ultimate definition of ruin, then perhaps the human struggle against entropy is actually a search for ergodic systems. At least, the human struggle against entropy relates to building resilience in known non-ergodic systems.

See the following link for a nice article on ergodic systems and economics in Nature:

Birkhoff’s Ergodicity equation:

Basically, an individual performing the same activity over time (left side of the equation) has the same probabilistic outcome as many individuals performing the same activity at the same time. (Right side of the equation). This is an ergodic system.

Also, a gas being released from a closed container would have an ergodic relationship to its surroundings. Meaning the gas would have an equal distribution across the new container. In effect, time becomes meaningless as a descriptor of the gas distribution in the new space. The gas would have a uniform distribution after the initial transition.

The key here is the gas movement to the new space is aligned with the Second Law of Thermodynamics (entropy). The gas outcome (I.e., a uniform distribution in the new space) is the expected entropic outcome.

Most people want to avoid ruin. (that is, entropy) As such, many human activities that are non-ergodic, if properly managed, may avoid ruin.

5. Conclusion

It is easy to confuse risk and ruin. System ergodicity is a key determinant of system outcomes. As our examples showed, ergodicity differences are critical to understanding and appropriately managing risk. Most systems impacting our lives are non-ergodic. This means we must consistently manage our risk of ruin. This may seem obvious. However, people could significantly improve personal life decisions by managing risks via a non-ergodic lens.

Please see the article Our investment barbell strategy for an investment strategy that implements ergodicity principles. The strategy embraces risk and avoids ruin.



Physicist Ludwig Boltzmann first theorized ergodicity in the 1870s. His theory related to the equalizing atomic nature of gases over time and across space. In the 1930s, John Von Neumann, along with George Birkhoff, proved Boltzmann’s ergodicity conjecture.

As a suggested reading: NN Taleb, in his book Skin In The Game, does a nice job applying Ergodicity principles across a number of disciplines.

In Richard Dawkins’ book, The Selfish Gene, the author uses a probability-based evolution comparison example that misses the mark from an ergodicity standpoint.

"At some point a particularly remarkable molecule was formed by accident. We will call it the replicator. It may not necessarily have been the biggest or the most complex molecule around, but it had the extraordinary property of being able to create copies of itself. This may seem a very unlikely sort of accident to happen. So it was. It was exceedingly improbable. In the lifetime of a man, things that are that improbable can be treated for practical purposes as impossible. That is why you will never win a big prize on the football pools. But in our human estimates of what is probable and what is not, we are not used to dealing in hundreds of millions of years. If you filled in pools coupons every week for a hundred million years you would very likely win several jackpots."

As it relates to ergodicity, the football pool/evolution probability comparison is like comparing apples and oranges:

  • A football pool is non ergodic. Eventually, the pool player will run out of money. Thus, there is a different probability of ruin the longer the game is played.

  • A natural system like the earth and evolution is ergodic. In effect, the probabilistic evolution game can be played forever with little impact on probability.

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