Investing To Make Time Your Friend!

"Ergodicity" is a funny word. A very old-school and sciency word, but a foundational bedrock of modern investing.

First, what is it?

Think of ergodicity as the operational cousin of the physics concept called 'entropy.' You are much more likely to recall entropy from high school science class. Entropy, also known as the second law of thermodynamics, means that nature naturally moves toward disarray. Our Sun is a glowing blob, or a disarray of hydrogen and helium. The Sun is in a relatively high entropy state. Humans are unique, highly structured beings with skeletons and many unique organs; while living, we are in a low-entropy state. Sadly, nature pulls us humans toward a high-entropy state - called death.

The Bible even makes references to our natural likelihood to move toward higher entropy:

"For dust thou art, and unto dust shalt thou return."

- Genesis 3:19

Other practical examples of entropy:

• Defrosting Dinner: When you take a frozen meal out of the freezer, ambient heat naturally flows into the cold food until it reaches room temperature. Without entropy, your dinner would stay frozen forever!

• Pouring Cream in Coffee: When you pour cream into hot coffee, it naturally diffuses and mixes throughout the mug. Without entropy, the cream would sit separated in a tight blob at the bottom!

So entropy is all around us! But how does ergodicity "operationalize" entropy, and what does that have to do with investing? Great question!

In our lives, we are exposed to various environments, such as schools, businesses, apps, games, investments, etc. We often have choices about whether and how we will engage with these environments. Importantly, those environments can have radically different outcomes. These outcomes are based on their relative Ergodicity.

Let's take 2 environmental extremes. Russian Roulette and Coin Flipping.

A non-ergodic game - Russian Roulette

Let's say you have the choice of playing a russian roulette game. If you play, you will win $1million. If you lose, you die with no payout. The chamber has 6 potential bullet locations. In russian roulette, one bullet is randomly placed in a chamber. You place the gun to your head. You do not know if the chamber is holding a bullet or not! This is an extreme game!

Winning can sound great: $1 million. But there is a 1 in 6 chance you will die a gruesome death.

But there is a bigger problem: this game is non-ergodic. Its long-term outcome for playing it multiple times converges toward an almost certain death! So even if you survive the first game, subsequent games probabilistically move toward death or high entropy.

In a non-ergodic game, while a cross section ("CS") of 100 people would win about 83% of the time, 1 person playing 100 times ("TS") would essentially have a 100% chance of death. Thus, probability in non-ergodic systems: CS is NOT EQUAL to TS.

An ergodic game - Coin Flipping

But now, let's discuss the opposite kind of game. This is a coin-flipping game. To play, you need to give $1. If you get heads, you get the $1 back + 15 cents. If you lose, you only get 95 cents back. Heads you win, tails you lose. So, over time, you converge on about a 5-cent gain. But there could be times when you have extended 'tails' losses. The key is staying in the game.

So if you played 1 million times, you would make about $50k over time. But you need to invest $1 at a time and consistently play the game over time.

This game is called an ergodic game. Its long-term outcome converges toward a positive outcome, but it has to be played over time, and sometimes long periods of time, to achieve the more modest outcome.

In an ergodic game, a cross section ("CS") of 100 people will combine to make a gain; 1 person playing 100 times ("TS") will very likely make the same average rate of gain. Thus, probability in ergodic systems: CS is EQUAL to TS.

So what does this have to do with investing!?

The most important part of investing is avoiding ruin (non-ergodic outcomes). If you go bankrupt or otherwise fall into a financial abyss you cannot return from, that is "game over." So if you invested all your money in a single company, and that company went bankrupt, you would lose it all. No refunds. No return.

Diversified investing, like investing in a robo-advisor or an ETF, is the ultimate expression of ergodic investing. If a company in a diversified portfolio goes bankrupt, no big deal! It will be replaced by another. Also, since robo-advisors' and ETFs' purpose is to regularly rebalance their portfolios, a declining company will slowly be worked out of the portfolio anyway. You hardly even notice, unless you read the disclosures!

So this is pretty cool! We have connected physics to investing! It is nice when science supports how we get wealthy.

Be an ergodic investor!

Resources For The Curious

Ludwig Boltzmann, Vorlesungen über Gastheorie (Leipzig: J. A. Barth, 1896–1898).

John von Neumann, "Proof of the Quasi-Ergodic Hypothesis," Proceedings of the National Academy of Sciences 18, no. 1 (1932): 70–82.

George David Birkhoff, "Proof of the Ergodic Theorem," Proceedings of the National Academy of Sciences 17, no. 12 (1931): 656–660.

Nassim Nicholas Taleb, Skin in the Game: Hidden Asymmetries in Daily Life (New York: Random House, 2018).

Ole Peters and Alexander Adamou, Ergodicity Economics Lecture Notes (London Mathematical Laboratory, 2018), https://ergodicityeconomics.com/lecture-notes/.

Luca Dellanna, Ergodicity: Definition, Examples, and Implications (Independent Publishing, 2020).

Morgan Housel, The Psychology of Money: Timeless Lessons on Wealth, Greed, and Happiness (Harriman House, 2020).

Jeff Hulett, "Fight Entropy: Living Your Best Life by Using the Practical Physics of Time," The Curiosity Vine, October 11, 2022, https://www.thecuriosityvine.com/post/fight-entropy-the-practical-physics-of-time.

About the author: Jeff Hulett leads Personal Finance Reimagined, a decision-making and financial education organization. He teaches personal finance at James Madison University and provides entrepreneurial services. Check out his book -- Making Choices, Making Money: Your Guide to Making Confident Financial Decisions.

Jeff is a career banker, data scientist, behavioral economist, and choice architect. Jeff has held banking and consulting leadership roles at Wells Fargo, Citibank, KPMG, and IBM.