Ergodicity in Action: Betting on Skiers with Risk & Reward Trade-offs

During their latest episode of the VALUE: After Hours Podcast, Taylor, Carlisle, and Huber discussed Ergodicity in Action: Betting on Skiers with Risk & Reward Trade-offs. Here’s an excerpt from the episode:

Jake: Well, he’s run lots of marathons. Yeah, he’s going to run Boston. So, I have a little sports segment here that’s on downhill skiing. So, it’s not quite running. So, just a little fun background on downhill skiing. It has ancient origins. Like, they trace back even to prehistoric times in Russia, and Finland, Sweden, Norway, these cold northern latitudes. And it’s been an integral part of transportation in colder countries for thousands of years at this point.

And in the 1760s, skiing was recorded as being used in military training. So, that’s all the way back to revolutionary times, basically. There was a Norwegian legend named Sondre Norheim, who was the first downhill ski champion in 1868. But the first slalom competition, which I think is what we all think of when we’re thinking of this downhill skiing was occurred in Switzerland in 1922. So, we’re well into more than 100 years’ worth of this. And the term slalom is from Norwegian dialects. Meaning, trail on a slope. It’s kind of a portmanteau of that.
A recent study showed that there’s more than 114,000 alpine related injuries per year. And in alpine skiing, for every 1,000 people that are skiing in a day, between two and four will require medical attention. So, there’s a bit of danger in this, which you’ll see what I’m going– [crosstalk]

Tobias: [unintelligible 00:32:01] pickleball.

Jake: Yeah, I think there are more acute injuries in skiing and more repetitive injuries in pickleball. I don’t know. So, who’s the greatest downhill skier of all time? You guys have any guesses?

Tobias: Eddie the Eagle.

John: I can’t name– Well–

Tobias Carlisle Name a skier, John. [laughs] [crosstalk]

John: I can picture some great Winter Olympics and some of the great faces of these American downhill skiers, but I can’t tell you who it is.

Jake: All right. Well, it’s probably Mikaela Shiffrin. She’s a US skier still actively skiing. 17 global medals, 6 consecutive world championships, winning gold. In 270 starts, she’s had 95 World cup wins. She’s got like a 35%-win rate. And just for reference, like, Hall of Famer Lindsey Vonn, who’s like a household name, she won 21% of her races. So, it’s possible that Michael Jordan is the Mikaela Shiffrin of basketball.

[laughter]

Jake: So, however, in during the 2022 Olympics in Sochi, she was the odds-on heavy favorite to really clean up. And yet, during the games, she had three failures to reach the bottom of the course, which matched her total number of DNS, did not finishes, over the previous four years of racing. And it was just like a complete disaster. She ended up closing the Olympics without winning anything.

So, right now, we’re going to reintroduce our old friend, Ergodicity, to the discussion. we’ve done some segments on this before. I’m actually borrowing an example here from researcher and author, Luca Dellanna. I don’t know if you guys have ever followed any of his stuff, but he’s got–

Tobias: He wrote the book, right? He’s Ergodicity. He’s made ergodicity into a black swan.

Jake: Kind of. Yeah. I think I would probably say that Ole Peters might be a little bit ahead of him on that front, but fair enough. So, imagine this little scenario. You’ve got two different skiers, and one has a 20% chance of winning any race that she enters and a 10% chance of breaking her leg. And then we have a second skier who takes fewer risks, and she doesn’t push as hard, and so she’s only going to win about 15% chance of winning. But because she’s less aggressive, she only has a 1% chance of breaking her leg in any one race. So, which skier would you want to bet on in this scenario, so basically like a 20% winner and a 15% winner?

Tobias: To bet on at any given rates?

Jake: Yeah, who do you want to bet on given those–? [crosstalk]

Tobias: I’ll take the one with a better win rate.

Jake: It’s 20%? Yeah. John–

John: Give me the numbers again. So, the win rate is 20% and 15% between the two skiers?

Jake: Yeah.

John: And the other was accident rate?

Jake: 10% chance of crashing, and 1% chance of crashing for the other one.

John: Ah, I guess I would take the 20% winner. Yeah.

Jake: So, you guys are right. However, it completely depends on how long the championship is, how many races. If it’s a single race, you want to bet on the risk-taking skier. She has an 18% expected chance of winning, which is just 90% chance of finishing times 20% chance of winning when she does finish. That’s 0.18. The other safer skier has a 15% expected win rate. Like, 99% chance of finishing times a 15% chance of winning rounds up to 15%. So, you have 18% versus 15%. However, the more races in the championship, the higher the chances that the riskier skier will break her leg and have to forfeit the remaining races after that.

John: Right.

Jake: This is where it’s a non-ergodic at that point. This is what ergodicity is all about, really. And in this little scenario, anything longer than five races means that the more conservative approach has a higher expected payoff. So, the payoffs completely depend on time horizons. If you’re a professional money manager and your LPs have you on a, let’s say a, three-year shot clock, which I think probably accurately describes most of the industry even if everyone says they’re long-term, you may be forced to take risks that you otherwise wouldn’t really want to, and maybe even a lot of it happens at a subconscious level.

And if you’re part of a portfolio of other managers like in an institutional allocator sense, they may really want you to press your bets in a way and go all out for the win like that 20% chance skier. And if you crash and break your leg, so be it, like, they have other racers in the field. But for you, you’re done from the race now. And so, you personally as a manager are in a terrible spot. So, you really can’t base your decisions on a payoff that is computed on a time horizon that doesn’t match your time horizon. I think so much of, like, you have to know what your time horizon is and be on the same page with everyone who’s involved with your investment style, including if it’s for family members or whatever, if you’re a smaller investor or if you’re professional, like your LPs, you have to all be on. This is why it’s so important. I think probably mismatched time horizons might be the number one biggest flaw in the investment universe to solve for.

And as we see with our two-skier example, different strategies are optimal over different time horizons. It depends on the number of races that you’re aiming for. So, there really is no one size fits all in these non-ergodic systems like this. And Dellanna makes the point that catastrophic losses can absorb future gains. So, when you get taken out, your ability to win the future races after you break your leg disappears, and the math of winning the championship completely changes and skews, and then towards being more conservative at that point.

So, shorter-term optimization is to push hard and win, which I think you see that a lot in the investment world, but the longer-term optimization of not breaking your leg, you have a lower win percentage is more optimal over that. And this always brings me back to that Niki Lauda quote that I love, which is “The secret—” And he was a race car driver, right? “The secret is to win going as slowly as possible.” Over longer-term horizons, I think the math proves that out. Whereas over shorter horizons, you have to theoretically push harder and risk breaking your leg.

John: Yeah, that’s really interesting. Yeah, if you’re picking one race, you want the 20% winner. But if you’re drafting like a downhill skiing fantasy league, you’re going to take the one that gives you the most likelihood of finishing.

Tobias: The other complication though is, as Jake points out, if you’re the allocator and you have 30 downhill races, then you want them all going as hard as they possibly can. It doesn’t matter to you if a handful of them break their legs, even though for them it’s catastrophic. I guess you got to work out which where you are.

Jake: So, that type of system is ergodic for the allocator and non-ergodic for the individual manager. And a lot of times, there’s a mismatch there where people are facing very, very different setups in the consequences of chances of winning versus failure.

John: Yeah, that scenario is not unlike the VC world, where a VC is going to make a bunch of different bets and try to achieve that ergodic type result, where you’re going to have maybe 1 winner out of 100, or 2 or 3 winners out of 100. Many of the startups aren’t going to make it. But yeah, the point on time horizon is, to me, it’s the biggest advantage, I think, in today’s market. We were talking about smaller companies, and there are some unloved and hated companies. But even there, it’s less of an informational thing. It’s more of just, “I can’t own this thing right now, or I don’t want to own this thing right now, or the stock hasn’t done well, so I don’t want to own it for the next couple of years. I’m going to wait for it to do this or that.”

I think you just got to look at the last two years to see even the biggest and the best companies in the world and look at their stock prices, how they have fluctuated violently up and down. It’s remarkable. There’s a lot going on with those companies fundamentally, but the intrinsic value is not fluctuating nearly as much as the stock price. And so, that’s the real time arbitrage opportunity it seems like there.

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