Diversification Explained: The Farmers Fable and the Math Behind Risk & Reward

During their latest episode of the VALUE: After Hours Podcast, Taylor, Carlisle, and Brewster discussed Diversification Explained: The Farmers Fable and the Math Behind Risk & Reward. Here’s an excerpt from the episode:

Jake: Oh, it’s the worst. [chuckles] Shall we do some vegetables?

Tobias: Let’s do some veggies. It’s top of the hour. Let’s do it.

Bill: What do veggies cost these days? It’s a lot.

Jake: They’re kind of expensive. Yeah, surprisingly, given that–

Bill: Has it taken you longer to do veggie segments with inflation or not so much, does that not apply?

Jake: There’s a little bit of inflation.

Tobias: It’s the margins.

Jake: It’s just purely ego, I think is the–

Tobias: The input cost is low relative to what he sells them for. Good margins.

Bill: Productivity increased.

Jake: You know what it is there’s diminishing marginal utility from them as I scrape the bottom of the barrel for ideas.

[laughter]

Bill: Yeah, you’re learning about the oil industry. You’ve mined your good wells first.

Jake: Yeah, definitely.

Bill: I don’t know, that’s not true. You come up with good stuff, so let’s get it.

Jake: Let’s get it. This is called the Farmers Fable, and it’s a story about a farmer named Bill. And in a good season, he’ll harvest 150 seeds for every 100 seeds that he plants. So, it’s a 50% growth rate. Not bad. And if Bill plants these seeds every year, this business will grow exponentially. But at last, farming is not so easy. And sometimes there’s a bad harvest. And when that happens, Bill only gets 70% of his original seed count. So, it’s a 30% loss. So, where Bill lives in Florida, it’s random coin flip–

Bill: You should have given me a trigger warning, Sir.

Jake: [laughs] I’m not going to. I wanted to get you off here, like on tilt here. So, where he lives in Florida, it’s a random coin flip between a good season and a bad season. So, we’re still looking at a pretty good bet with a positive expected outcome. Half the time, it’s plus 50%. The other half of the time, it’s minus 30%. On average, we can expect a 10% outcome.
And Bill has an edge here.

Given all this, we could run simulations on what Bill might expect to happen over the next 100 years of his farming. And in the first run that I did of this, Bill fared pretty well. Things started choppy, good season, bad season, back and forth. But then he had a run of good luck, and he ended up with over 100x his original seed count. He’s the man. And then the next time I ran it, he started with a run of bad luck, and he lost 90% of his seeds before bouncing back and finishing with ten times the original amount after 100 years.

Bill: He didn’t stick with it. That Bill blew out at the bottom after a 90% drawdown, [Jake laughs] started selling itself on the corner.

Jake: He did.

Bill: Went broke.

Jake: The next time I ran it, Bill started hot, but then he hit a rough patch, lost his confidence, and he finished with actually less than he started with, which is bad luck. And so, even with an average of a 10% expected return, Bill ended up with 100x in the first scenario, 10x in the next, and then a loss in the last one. So, there’s a lot of luck involved here. So, maybe farming maybe isn’t as good a business if it’s so random.

But here’s where things start to get interesting. Bill has his friend named Toby, and he’s also a farmer. And they happen to live on opposite sides of the country from each other, so their weather is [Tobias laughs] completely unrelated. It’s random who will have a good year and who will have a bad year.

So, let’s run another 100-year simulation with both Bill and Toby farming alone. This time, Bill ends up with a relatively lucky outcome, and he has 16 times his original seeds. And Toby’s unlucky, and he ends up at just barely break even. So, maybe Toby is a bad farmer, I don’t know.

However, what if these friends decide to make a deal? And at the end of every season, Bill and Toby agree to pool their harvest and then split it equally. So, here’s a little of the math behind it. And it’s actually quite counterintuitive. So, I would urge you, if you’re listening to this, to go to farmersfable.org, which is where I got this from, and click through the little animations that it has. And that’s fable with an F, it’s not table. Click through the animations yourself to follow along.

And honestly, I’ve had to run this multiple times before it really made sense to me, it’s that counterintuitive. But eventually, I’ve started to wrap my mind around it. And honestly, it blows your mind a little bit, and so that’s why I’m sharing it with you guys now.

So, I’ll try my best here to keep it simple of what’s going. So, imagine that Toby starts with– We’re going to change it to like one bundle of wheat, okay? And in the first harvest, it’s a great year, and Toby triples his bundle to three, all right? Awesome, right? Then he has a second harvest, but it’s not so good and he merely breaks even. So, Toby finishes after two years with three bundles of wheat. All right, we’re following along so far?

At the same time, running along with this, Bill also starts with one bundle of wheat. He breaks even in his first year, and then triples in his second. So, both Bill and Toby started with one bundle and finished with three after two runs of the simulation, right? Simple enough.

Now, let’s imagine that they pooled and shared and it’s the exact same weather patterns held over this. Just like in the first example, in the first year, Bill finished– sorry, Toby finished with three and Bill finished with one, okay? But before we moved to the second season to run it, they pool their bundles and then split them up. So, three plus one totals to four. They split it, and now they each have two for the next harvest season.

In this next season, Toby breaks even and keeps his two. Bill triples his two, which then takes him to six, okay? What a stud. They pool again and split it, and this time, it’s six plus two equals eight, so they split it in half, and now they arrive at each at four bundles. So, that’s one more each than when they were farming by themselves. So, there’s actually this free lunch that occurs from diversification and pooling, and that’s maybe what everyone has been talking about when they talk about this free lunch.

So, anything that grows exponentially like this in a multiplicative series, there’s an advantage to sharing. It pays to redistribute after each step moving forward, because you only take a partial step backwards when you share. And so, this luck becomes more of a certainty over the long run with this pooling and sharing. And so, you’re actually, interestingly reducing risk and increasing the growth for everyone involved, because it’s reducing the fluctuations. It’s this variance strain that we’ve talked about.

There’s actually ways you can demonstrate this mathematically that that someone who is objectively better farmer than the person that they’re pooling with will benefit from a pooling arrangement, although, there are some limits to it. If I was paired up with Warren Buffett of farming and then I was totally dead weight for them, that would not be a good arrangement. But there is allowance for a little bit of delta there. So, it really shows you the importance of avoiding those big downs that the variants drain as much as possible, which, of course, is why probably Buffett has rule number one is don’t lose money.

And this whole Farmers Fable was inspired by a 2019 research paper from Ole Peters and Alexander Adamou, I believe, is how he said, called an evolutionary advantage of cooperation, if you wanted to read the more scientific treatment of it. But they’re basically able to prove that this cooperative transactions in a multiplicative series, where you have to multiply things out like geometrically, there’s a real advantage to be had for pooling arrangements. So, I find that to be very interesting. And if you click through that farmersfable.org, it’ll help do a better job of what I just said orally, which is not as good of a way of teaching this as probably looking at little bundles of wheat.

Tobias: Yeah, good call. Tyler Pharris got there again with Shannon’s Demon before he got very far into that story again.

Jake: Correct.

Tobias: Shannon’s Demon is a great example of that, which is why you want the uncorrelated or anticorrelated. Ray Dalio says. “Get 10 uncorrelated series.” That’s a good way of doing it if you can find them.

Jake: Yes. That diversification of being able to limit the downside, which allows you to catch that bigger upside with a larger pool of capital.

Tobias: Evidently, we’ve crashed farmersfable.org. Dozens of people went there.

[laughter]

Tobias: Couldn’t handle a lot.

Jake: I didn’t think about that. Sorry, guys.

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