Here is your weekly dose of financial wisdom. This edition is dedicated to ergodicity.
Pedro and His 100 Friends
To illustrate this concept, let me begin by telling you a story.
Like every Saturday night, Pedro sets out to the casino along with 100 friends. Pedro does not gamble, of course—he only observes.
His 100 friends each have $5,000 that they decide to gamble over the night. After four hours at the blackjack table, Morgan, friend number 40 goes bust. However, Stanley, friend number 41 does not—he keeps on gambling.
Over the past year, Pedro had observed that about 1% of his friends go bust. If one were to keep gambling, one would be expected to have about the same ratio, 1% of gamblers going bust, on average, over a night.
Pedro now notices that Morgan is crying at the bar. There is no more gambling for him. He lost everything he came with.
In fact, from Morgan’s individual perspective, going to the casino 100 days in a row with $5,000 is not a good idea. Pedro has safely calculated that Morgan’s probability of eventually going bust is 100%. If he goes bust on day 40, there is no day 41…
Once Morgan had wiped his last tears, Pedro went over to the bar and tried to explain that the probabilities of success from the group of friends do not apply to him. But, Morgan just scoffs at this remark: “Look Pedro, I was just a bit unlucky, next week I’ll borrow another $5,000 and win big. Just wait and see!”
Survival Comes First
The main lesson from this story is that too succeed, one must first survive. Indeed, sequence matters and the presence of ruin disqualifies cost-benefit analysis.
The Ergotic and Non-Ergotic
Let us now define this concept more formally.
In an ergodic scenario, the average outcome of the group is the same as the average outcome of the individual over time.
In a non-ergodic situation, the individual, over time, does not get the average outcome of the group. Observed past probabilities do not apply to future processes. This is what we saw in our story of gambling. Indeed, there is a "stop" somewhere (a.k.a. ruin/going bust), an absorbing barrier that prevents people with skin in the game from emerging from it—and to which the system will invariably tend.
For example, the outcomes of a coin toss is ergotic. If 100 people flip a coin once or 1 person flips a coin 100 times, you get the same outcome. However, the consequences of those outcomes (e.g. win/lose money) are typically non-ergodic!
To identify an ergodic situation, ask whether you get the same result if you:
Look at one individual’s trajectory across time
Look at a bunch of individual’s trajectories at a single point in time
If yes: ergodic.
If not: non-ergodic.
Two Views of the World
With this in mind, we can view events through two different lenses:
Ensemble probability: the ruin of one person does not affect the ruin of others.
Time probability: the ruin at one point in time affects all future points in time.
Implications of Ergodicity
The central problem is that we are taught to think that most systems are ergodic when in reality, most are non-ergodic. Treating non-ergodic things as if they are ergodic creates a risk of ruin, as Morgan found out in out story.
This is particularly true in financial education where ergodicity is often assumed (meaning people think time and ensemble probabilities are the same) even though it is rarely the case. This has led to a whole sub-field called “Ergodicity Economics” that challenges classical finance theory.
If you are curious about this, I invite you to peruse this research paper.
In the area personal finance, my current understanding is that effective diversification can make non-ergodic situations more ergodic. But the key is to diversify correctly.
Investing without thinking about ergodicity is like playing Russian roulette: you may win for a long time, but eventual ruin is certain.
Thus far, I have come across two ergodic diversification approaches:
Bimodal (barbell) strategy: combine extreme risk aversion with extreme risk loving. For investing, this means owning low-risk assets (treasury bonds, cash, gold…) and high-risk assets (angel investments, your own business or hobby, crypto, risky stocks, options, collectibles…) but staying clear of middle-risk assets. This is an antifragile investing strategy (i.e. it gains from volatility and disorder).
Kelly criterion: never bet everything, rather, increase your risk as you are winning and decrease it as you are losing. This assumes that markets are non-ergodic and optimizes for typical wealth as opposed to expected wealth. Essentially, this technique makes it impossible for you to go bust.
Moreover, setting up an emergency fund—3 to 12 months of expenses in cash, only to be touched in case of emergency—is an effective way to increases ergodicity.
The general key is to set up your life and finances so that you are prepared for a disaster (e.g. markets drop plus you lose your job). Volatility tends to cluster. As the saying goes, hope for the best, prepare for the worst.
To new means,