Ergodicity: Anything that can hit us will, eventually, hit us.

Ergodicity is an interesting property. 

The idea of ergodicity is that in a stochastic process, a point will eventually visit all parts of the system it moves in.

Another way of phrasing it is that given enough time, everything that can happen will happen, with a probability approaching one.

We're by no means mathematicians, and even less experts in probability theory. 

Yet, what we've understood (or misunderstood) about ergodicity might be interesting for how one looks at the world, and how one looks on investments and an investment strategy in particular.

Let's start with examples.

Two Sides of A Pet Example

And where better to start than with a gun. 

Mikhail Yuryevich Lermontov aged 33, four years before he was shot through the heart during a duel. He was, allegedly, the inventor of the morbid game of Russian Roulette.

Russian roulette is a favorite game of all amateur game theoreticians. 

1 gun, 6 chambers, 1 bullet in one of the chambers. We spin the barrel, and then the game begins.

So, in which of the following game settings of Russian roulette would we like to participate?

Game A: Ensemble probability

6 persons walk into a bar (in Novosibirsk). The first one puts the Russian roulette-gun to his head, and pulls the trigger. If he survives, he hands the gun to the next person, and so on.  

What is the a priori expected return from participating in this game?

Game B: Time probability 

Now a much more, for the individual, deadly version of the game. One person walks into a bar to play Russian roulette. In this version of the game, she puts the gun to her head, probably has an good glas of vodka, and pulls the trigger 6 times.

What is her expected return from participating in Game B?

Let's conclude that whatever the return is for game B, it's not good. 

What does this mean for us?

In life, one might easily believe that one is playing Game A. When a yearly expected return is calculated, it gives the illusion of Game A. 

It's as if we participated in one year only, and, like our six Russian Roulette-players above, we cross our fingers when we pull the trigger and hope that it's a good year.

We hear ourselves say things like 'Let's hope that the portfolio goes up this year'.

In Game A, hope is part of the equation. We can hope that we are on a good run. We can hope that we will pull out of the game before that fatal bullet. 

When we look at expected return, like in Game A - it's ensemble probability we see; an ensemble of years as if they happened at the same time, not as if they where happening one after another. 

Of course, years doesn't work the way Game A does. 

It's not ensemble probability that is a good model for designing a strategy. 

Like our unfortunate player in Game B, we must survive time probability. 

Which means acknowledging that bad events will hit us as well, due to ergodicity. What is unlikely to happen in a year might very well be very likely during a lifetime or over the timespan of our strategy, or for the unfortunate lady playing solitary Russian roulette.  

In investing, we are playing the long game, year after year. So the mechanisms of our strategy and the behavior of the game table we're at, are very important indeed. 

During a life time, a really bad year WILL hit us. Really bad events WILL happen. Then our strategy better be wiser than the one fool hoping about the average outcome of Game A above. 

Our strategy to increase and protect our wealth must be built in such a way that we don't end with a gory mess.

There's no use in having a strategy on the assumption "as long as nothing bad happens", or even worse, a strategy that leads to ruin if a bad event or year hits us. 

Then we might permanently be out of the game, and our strategy doesn't matter much anymore.

Real life examples

What does ergodicity mean for us, practically?

To sum up: if we are to stay in the game, ergodicity means that in the long run, our strategy need to be able to survive anything that can possibly happen.

Application 1. Return.

The diagram above shows the same run for the Pathfinder portfolio.Why does it look so spread out if it's the same run? We've just varied the start date with three year intervals and repeated the same series of returns on the same starting point. 

Look at the diagram again. The green, the red and the blue line all come from the same run of years. The green line sure looks lucky. But even a "lucky strike" as the green line, also has a "bad run" as can be seen around 2031 in this simulation, and what looks like hopeless laggards will overtake the initial good run. Remember that this is the same series, the variation comes from the starting year only.

The same strategy gets hit with every event; with everything that happened, and luck and misfortune even out. 

So this would be as example of a strategy that can do well both if we're lucky or unlucky with a run of years.

A side-note: Ergodicity also puts some lights on the thinking around the FIRE-number itself; the amount of money invested needed, to reliably cover one's expenses. If one hits the fire number early, one should probably be cautious. On the other hand, if one never seems to hit the fire number, one might be on a lower trajectory, with more upside potential. More about that in another article, perhaps.

Application 2. Risks.

When contemplating exiting the work life, we've set up a list of risks, consisting of things that might derail our future freedom. Socialism (this is Europe, after all), large unexpected costs, family members faring bad, our relationship taking a bad turn, and of course death. With risks, it's tempting to assign impact and likelihood and care about the high probability, high impact ones.

But ergodicity introduces something that normal risk-thinking doesn't quite comprehend. The longer a game is played, the more likely all events become. 

In the long run, we need a strategy for everything. Nothing can really be avoided.  

So we must be prepared that we will have to perform all the mitigations for all risks. We will at some point have to pay that unexpected cost. 

There will be a run of socialism with high taxes and a wealth tax during the roughly 50 years we will live from our portfolio. There will be family problems and relationship problems, illness and tragedy. And finally, one of us will die and leave the other one behind. 

Conclusion

If we at any time think it's meaningful for us to "hope" for a certain outcome, then we have probably fooled ourselves into believing that we are playing Game A.

Our strategy needs to be adopted to reality, and the long run. Amor fati; love what fate has in store for us. Or as Mark Spitznagel of Universa fame has it. He makes a parallell to Nietschze for a good investment strategy - being able to exclaim "Thus I willed it" for whatever fate throws at us. 

In real life, hope is not a good strategy.

Farewell,

//antinous&lucilius