Ergodicity Economics – Applications to Financial Markets

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Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.

Ergodicity Economics is a relatively new field of study that challenges traditional economic theories.

It offers a new perspective on how individuals make decisions under uncertainty while considering time dynamics.

At its core, it emphasizes the importance of time and the dynamics of individual experiences in economic decision-making.


Key Takeaways – Ergodicity Economics

  • Ergodicity Economics challenges conventional economic theories, emphasizing the dynamics of individual experiences and the importance of time in decision-making rather than the neoclassical focus on expected utility.
  • Unlike traditional models, Ergodicity Economics recognizes that individuals make decisions based on the trajectory of outcomes over time, leading to more nuanced risk perceptions and choices.
  • This perspective has broad applications, from explaining investor behavior in financial markets to influencing public policy decisions, highlighting the significance of considering time dynamics in complex systems.


The Traditional Economic View

Traditional economic theories often assume that individuals make decisions based on expected utility.

This means that people weigh the potential outcomes of their choices and select the one that offers the highest expected benefit or expected value.

However, this approach has been criticized for not accurately reflecting real-world decision-making processes.


The Concept of Ergodicity

Ergodicity is a concept borrowed from statistical mechanics and thermodynamics.

In simple terms, it refers to the idea that over time, the average behavior of a system will reflect the behavior of a typical individual in that system.

For economics, this means that the average outcome for a group of individuals over time should be the same as the average outcome for a single individual repeated over time.


How Ergodicity Economics Differs

Ergodicity Economics argues that traditional models fail to account for the non-ergodic nature of individual experiences.

It suggests that people don’t just consider the average outcome, but also the trajectory of outcomes over time.

This means that individuals might make decisions that seem irrational in traditional models but make sense when considering the dynamics of time and personal experience.


Investing is a classic example. Instead of immediate reward, people invest for a future stream of income.


Implications for Decision-Making

Under the ergodicity framework, individuals are more risk-averse than traditional models suggest.

This is because they consider the potential long-term impacts of their decisions, rather than just the average expected outcome.

For example, a person might avoid a gamble or calculated risk that has a high expected return but also a high risk of losing a lot, even if the odds are in their favor.


An example might be starting a business.

People generally like having a guaranteed income that enables them to support themselves.

Even if the expected value of starting a business is a lot more than being an employee, the downside of having nothing to show for it is too daunting for many.

Also, many at some point might want to switch from being an employee to entrepreneurship.

However, they might have a fixed expense base that is too high and they can’t risk it at that point.

So, they might value stability. Moreover, they may fear that if the gamble doesn’t pay off, the gap in experience might impair their ability to return to what they were doing.

Example Game

For example, let’s say someone is playing a game and they have the following options:

  • Option A: A guaranteed reward of $100 with no risk.
  • Option B: A 30% chance of a $1,000 reward (e.g., business success) and a 70% chance of a -$100 penalty (e.g., business failure).

The expected value of Option A is simply the guarantee of $100.

The expected value of Option B is: 0.30 * $1,000 – 0.70 * -$100 = $300 – $70 = $230.

So we have different pros and cons:

Expected Odds of Success

  • Option A: 100%
  • Option B: 30%

Expected Value

  • Option A: $100
  • Option B: $230

How would you make this decision?

To make an informed decision between these options, one would weigh the higher expected value of option B ($230) against the guaranteed payout of option A ($100).

Considering one’s risk tolerance is critical.

If willing to take a higher risk for a potential greater reward, option B might be the choice.

Conversely, if one prefers stability and a sure gain, option A would be the safer bet.

It’s essentially a choice between a guaranteed payout and a gamble with a higher upside but a significant chance of loss.

One might also consider various other angles, such as what option A gives them (e.g., following boss orders) versus option B (e.g., more autonomy).


Real-World Applications

Ergodicity Economics has implications for various fields, from finance to public policy.


In finance, it can help explain why investors might be more conservative than traditional models predict.

Public Policy

In public policy, it can offer insights into how individuals respond to incentives and risks, leading to more effective interventions.

Public Sector vs. Private Sector

It can also shed insight into what role the public or private sector should play in various projects.

For example, infrastructure projects have long lead times.

And they are also not always profitable.

Because of the private sector’s desire for it to be profitable (at a high enough rate of return relative to competing investments) and as soon as possible, risk in infrastructure (i.e., the analogous equivalent of who the common stockholders would be) is more commonly taken on by the public sector than the private sector.

However, in terms of public benefit, even if a project is not profitable it doesn’t necessarily mean it was a bad decision thinking through the multi-order effects.

Governments don’t get squeezed for money (they can create it) and don’t have to worry about market losses causing them financial problems.

Example of Ergodicity Considerations in the Real World

Following from the above, let’s say a city built a train system with the following characteristics:

  • System has a 25-year lifespan
  • It costs $2 billion
  • Financed with debt to be paid back from revenue

Let’s say in the real world this happens:

  • Economics are worse than expected – only 50% of the expected revenue comes in
  • Debt has to be written down by 50% accordingly

Should the train system have been built?

In this scenario, even though the train system project did not meet its financial targets and had to write down 50% of its debt, it can still be considered a valuable investment from a broader societal perspective.

When assessing the value of public infrastructure projects, it is important to not only to look at profitability but also at the long-term benefits it can bring to the community and the broader economy.

Here – if you frame the problem a different way – even though the subway system costs $1 billion more than initially anticipated, this investment might still be justified considering the potential benefits it could bring to the community over a 25-year lifespan.

The introduction of a subway system can:

  • facilitate easier and faster transportation for the residents
  • possibly alleviating road congestion
  • reducing carbon emissions, and
  • promoting better connectivity between different parts of the city

These factors can, in turn, spur economic development and improve the quality of life for residents, making the city more attractive to potential newcomers and investors.

Moreover, at the end of the expected 25-year lifespan, some parts of the infrastructure may last longer (e.g., the rails) and some parts of it (or blueprints) may be able to be resold to other municipalities.

It can also create know-how, which has value, and can add another layer of tail benefits.

So there are many other economic and non-economic benefits beyond ticket sales.

Additionally, the 2% increase in annual costs ($1 billion shortfall divided by 25 years = $40 million per year; $40 million / $2 billion = 2%) could be perceived as a reasonable trade-off for these community benefits.

If this debt shortfall can be spread out and monetized, then it helps alleviate the problem.

When seen from this perspective, the subway system project represents not a failure, but a potentially wise investment in the city’s future growth and development, underscoring the principle that the success of public infrastructure projects can’t be measured by profitability alone.

Therefore, policymakers should consider a range of factors, including societal benefits and improvements to quality of life – and evaluate these benefits over time – when evaluating the success of such projects.

It also underscores why the public sector tends to be a better fit for some projects relative to the private sector.


Ergodicity Economics vs. Classical Economics (Expected Utility)

Ergodicity Economics (thinking of effects through time) and reach a different conclusion about certain economic problems than Classical Economics, which relies heavily on the concept of expected utility.

Let’s consider a simple gambling scenario:


  • You’re offered a gamble where you can flip a coin.
  • If it’s heads, you gain 50% of your current wealth.
  • If it’s tails, you lose 40% of your current wealth.

Would you take this gamble?

Classical Economics (Expected Utility)

  1. Calculate the expected value of the gamble.
  2. Heads: Gain 50% (0.5 * 0.5 = 0.25 or 25%)
  3. Tails: Lose 40% (0.5 * 0.4 = 0.20 or 20%)
  4. Expected value = 25% – 20% = 5% gain.
  5. Classical economics suggests that since the expected value is positive, a rational individual should take the gamble.

Ergodicity Economics

  1. Consider the time dynamics of this scenario over repeated plays.
  2. If you start with $100 and win the first round, you’ll have $150. But if you lose the next, you’ll have $90 (a loss of 40% of $150). Do another round, you’re down to $81.
  3. Repeated plays will, over time, erode your wealth due to the multiplicative nature of the gamble, even though the expected value from one round is positive.
  4. Ergodicity Economics would argue that it’s not rational for an individual to take the gamble repeatedly, as the time average growth rate is negative.

In this example, while classical economics focuses on the average outcome from a single play (ensemble average), ergodicity economics emphasizes the long-term effects on an individual’s wealth over time (time average).

The two approaches can lead to vastly different conclusions about the rationality of the decision.


Ergodicity Economics Applications in Financial Markets

Understanding Financial Markets Through Ergodicity

Financial markets are complex systems where participants make decisions under uncertainty.

Ergodicity Economics provides a different lens to understand these decisions.

Traditional Financial Theories

Traditional financial models, like the Efficient Market Hypothesis, assume that market participants make decisions based on expected utility (expected value).

These models suggest that traders/investors weigh potential outcomes and choose strategies that maximize expected returns.

However, real-world observations often deviate from these predictions.

Ergodicity and Risk Perception

Ergodicity Economics posits that investors don’t just consider average outcomes.

Instead, they focus on the entire distribution of potential outcomes and their trajectories over time.

This perspective can explain why many traders/investors are more risk-averse than traditional models predict.

An investor might avoid a high-risk investment not because of its expected return but because of the potential for significant losses over time.

Portfolio Management

From an ergodic perspective, portfolio management becomes more than just maximizing expected returns.

It involves considering the time dynamics of investments and the potential for long-term impacts on wealth.

This can lead to more diversified portfolios or higher-returning portfolios over time, as investors seek to minimize the risk of large drawdowns and ensure sustainable growth over time.

Market Anomalies and Behavioral Finance

Ergodicity Economics can help with various market anomalies that traditional theories struggle to explain.

For instance, why do bubbles and crashes occur?

By considering the non-ergodic nature of individual experiences, we can better understand these behaviors as rational responses to the dynamics of time and uncertainty.

Pricing Models and Asset Valuation

Asset pricing models that incorporate ergodic principles might offer more accurate valuations.

By accounting for the time dynamics of returns and the non-ergodic nature of individual experiences, these models can capture the true risk and reward profiles of assets.


FAQs: Ergodicity Economics – Applications to Financial Markets

What is Ergodicity Economics?

Ergodicity Economics is a relatively new approach to economic theory that challenges traditional economic models by focusing on the time dynamics of individual agents rather than ensemble averages.

It emphasizes the difference between ensemble averages (averages taken over a group of entities at a single point in time) and time averages (averages taken over the trajectory of a single entity over time).


Ergodicity Economics differentiates between ensemble and time averages.

For instance, consider a gamble:

  • if half of people raise their wealth by 50%, and
  • the other half lose 50%…
  • …the ensemble average shows no gain or loss.

However, for an individual repeatedly taking the gamble, the time average reveals they’ll eventually lose most of their wealth playing that game (up 1.5x, down 0.5x, up 1.5x, down 0.5x, etc.), as losses compound more than gains.

How does Ergodicity Economics differ from traditional economic theories?

Traditional economic theories often assume that the average outcome for a group of individuals will be the same as the average outcome for an individual over time.

However, Ergodicity Economics highlights that this assumption may not always hold true, especially in complex systems like financial markets.

Instead, it suggests that the behavior of individual agents over time can differ significantly from the average behavior of a group.

Why is Ergodicity Economics relevant to financial markets?

Financial markets are inherently dynamic and involve a multitude of individual agents making decisions over time.

Ergodicity Economics provides a framework to better understand the behavior of individual agents in these markets, leading to more accurate predictions and better risk management strategies.

How can Ergodicity Economics improve investment strategies?

By focusing on the time dynamics of individual agents, Ergodicity Economics can offer insights into how individual traders/investors might behave in different market conditions.

This can lead to the development of trading/investment strategies that are more aligned with the actual behavior of investors, rather than relying solely on ensemble averages.

Are there any real-world examples of Ergodicity Economics being applied to financial markets?

Yes, there have been several studies and papers that have applied the principles of Ergodicity Economics to financial markets.

These studies have explored topics such as the optimal leverage for individual investors, the dynamics of wealth distribution, and the impact of non-ergodicity on financial derivatives.

What are the criticisms of Ergodicity Economics?

Like any emerging theory, Ergodicity Economics has its critics.

Some argue that while the theory provides interesting insights, it may not be universally applicable to all economic systems.

Others believe that the traditional models, while not perfect, are sufficient for most practical applications.

How does Ergodicity Economics impact risk management in financial markets?

Ergodicity Economics offers a different perspective on risk, emphasizing the importance of understanding the time dynamics of individual agents.

This can lead to better risk management strategies that account for the potential divergences between individual and ensemble behaviors.

What does ergodic and non-ergodic mean?

“Ergodic” means a system’s time average and ensemble average are the same.

“Non-ergodic” indicates they differ, so individual trajectories can’t be inferred from ensemble behavior and vice versa.

In non-ergodic systems, long-term individual outcomes can differ significantly from short-term average outcomes.

What’s an example of the differences between ergodic and non-ergodic?

Consider a casino roulette game:


If every number on the roulette wheel has an equal chance of landing, over many spins, the average outcome for any single spin (ensemble average) will match the long-term average outcome for a specific number (time average).


Now imagine a person’s winnings change over time, so initially they win often, but later they lose more (e.g., playing poker and the skill of their opponents changes).

The average winnings of all players at one moment (ensemble) won’t predict this individual’s long-term winnings trajectory (time average), as their ability to win changes over time.



Ergodicity Economics offers a perspective on economic behavior.

By considering the dynamics of time and individual experiences, it provides a more accurate and nuanced understanding of decision-making under uncertainty.

As the field evolves, its goal is to deepen our understanding of economics and economic systems and inform more effective policies and strategies.