Ergodicity in Action: A Story of Ski Racing and Investment

During their recent episode, Taylor, Carlisle, and Luca Dellanna discussed Ergodicity in Action: A Story of Ski Racing and Investment, here’s an excerpt from the episode:

Luca: Yeah. So, the trick is to avoid defining it and make an example first. Because when people hear the story, they understand it immediately. And in the book, I’m talking about the story of my cousin, who was a great skier since very, very young age. He made it even to the World Championship for his age bracket. But then, sadly, one leg injury after the other, he had to quit professional skiing before he even turned 18.

From him, I’ve learned a lesson, that it is not the fastest skier who wins the race, but the fastest skier amongst those who make it to the finish line. [Tobias laughs] Here, I’m not making the banal point that survival matters for performance, but I’m showing that it matters more than performance, especially over the long-term. And so, I’m bringing this numerical example, which is a very quick riddle. It goes like this.

Imagine that my cousin is a very good skier. He participates in a ski championship consisting of 10 races. My cousin, excellent skier, he has a 20% chance of winning each race, but he also takes a lot of risks, so he has a 20% chance of breaking his leg in each race. The question is, how many races is he expected to win over a championship of 10 races? The naive answer is two races. Because we think 10 races, 20% chances of winning each, 10 times 20% makes 2. However, if you crunch the numbers, you get to only 0.71. This big difference between 2 and 0.71 is due to the fact that if my cousin breaks his leg in one race, not only he loses that race but also all the following ones, because he cannot participate to that.

So, this is the principle that irreversibility absorbs future gains. We see this in skiing, we see it investing. If you have $1,000 and you lose 50%, not only you lost $500 but you also lost all the future gains that those $500 could have produced. This principle that irreversibility absorbs future gains is the core of Ergodicity. In particular, we say that when a context is ergodic, there is non-irreversibility, we call it ergodic, and you can use averages. But in most of the real world, if not in all of the real world, losses are irreversible, which means that you cannot use averages, you cannot rely on averages, and these are contexts that we call non-ergodic.

Jake: Beautiful. That’s surprising. I think it’s probably one of the least appreciated concepts and yet most important to understand in the financial world.

Luca: Yeah, exactly. I think that it’s terrible that it has such a bad name. The name ergodicity is terrible to-

Jake: Yeah, the marketing team.

Luca: -understand. To market.

Jake: It’s getting fired for sure on that.

Luca: [laughs] Exactly. And then the problem is that everyone tries either to define it or to explain in mathematical terms, which is terrible idea, to get the idea understood. What I did in the book was that I had two constraints for myself. The first one, I won’t use any mathematics at all. And the second one, I will not define the concept until we get in the second– Oh, my God, what’s happening? until we get into the–

[laughter]

Luca: Sorry. Until we get into the second half of the book. Yeah.

You can find out more about the VALUE: After Hours Podcast here – VALUE: After Hours Podcast. You can also listen to the podcast on your favorite podcast platforms here:

Apple Podcasts