Odd Lots - 52: What Math Models of Herding Cows Can Teach Us About Markets

Episode Date: October 28, 2016

Investors are often said to exhibit herding behavior when they follow each other into crowded positions — creating market bubbles that are susceptible to sudden pops when everyone begins stampeding for the exit. This week we take the analogy literally and speak to three professors who have created a mathematical model to examine why cows synchronize their behavior and — crucially — why they stop. Jie Sun, Erik Bollt, and Mason Porter, the authors of "A Mathematical Model for the Dynamics and Synchronization of Cows," extrapolate their findings to humans and modern markets. This episode is co-hosted by our resident bovine expert, Lorcan Roche-Kelly.See omnystudio.com/listener for privacy information.

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slash audio. That's vanguard.com slash audio. All investing is subject to risk vanguard marketing Corporation Distributor. Put knowledge to work and grow your business with CIT. From transportation to health care to manufacturing, CIT offers commercial lending, leasing, and treasury management services for small and middle market businesses. Learn more at cIT.com. Put knowledge to work. Hello and welcome to another episode of the Odd Lots podcast. I am Tracy Allaway, executive editor of Bloomberg Markets. And let me just say that I, I think what you are about to hear is probably the most random edition of odd lots that we've done so far. And just to give you an idea of how random it is, I have with me a special co-host.

It is Lorkin Roche Kelly. He is our resident cow expert. That's how random this is. Say hello, Lorkin. Hi, Tracy. How's it going? I think a cow expert, I think, I'll definitely think that one as a compliment. cow owner, if not in else.

It's meant to be a compliment, Morgan. We don't have a lot of cow experts, so that's pretty special. You're reducing the compliments straight away, Tracy. I should say that my normal co-host, Joe Wisenthal, is still on his epic business trip. And he's left me to do this podcast. How do I intro this podcast? All right, so a couple weeks ago, I noticed a mathematical paper. It was called, quote, a mathematical model for the dynamics and synchronization of cows.

Lorkin, I think I sent it to you at the time. Yeah, I think you said to you with this email subject was, can you believe this exists? I think may have been something online with what the email subject was. I was very excited to see it, I must say, because anything to do with cows excites me. Right. How many cows do you have now, Lorkan? I think you ever ask a farmer how many cows he has because it's a way of working out what his income is. But I think enough to keep me busy is the standard answer, I think that.

I'm sorry, I just made a bovine faux paw, I guess. All right, enough to keep you busy. That's good enough for this podcast. Okay, so we got this paper, a mathematical model for the dynamics and synchronization of cows. It's written by, let's see, one, two, three, four mathematicians at various universities. and it talks about herding behavior in cows and sort of mathematical models used to analyze that behavior. And I know you're all thinking, what in the world does this have to do with markets and

investment and finance? But if you'll remember, we often talk about investors acting in markets like a herd. We often talk about herding behavior, people crowding into the same types of investments, the same positions, basically, following each other, seeking the safety of numbers. So it's not totally off the wall. Lorkin, am I stretching that a bit? I think that's fair.

I don't think it's stretching it at all. I think I'm like, I suppose I spend a lot of my time looking at markets and some of my time looking at cows. And while the similarities don't immediately jump out to me, I must say, when I'm working in either of both, there is generally feeling that markets gain momentum. And the more, I suppose, more people talk about the trades, the more like, likely people are to get on a trade or to have an opinion on a trade anyway. And much like with cows, if one cow finds good grass, the rest of the cows will see the good grass and run over and get some for themselves.

So on the high level, the herding idea, I think, it's being well established within markets and it's, it comes from animals, it comes from herds of animals. That's where the word comes from. So I'd imagine to examine what cows do should tell us something about herding in markets or at least give us a way of modelling herding in markets, which is why I fund. paper very interesting. Do you ever look out your window on your farm in Ireland and watch your cows and like ponder them as you think about markets? I have this image of you doing that. I can see my cows from my window depending on what field they're in. Whether what I'm doing

is pondering them or pining to be with them rather than staring as some unfinished coffee in front of me. I'm not sure. All right, without further ado, we are going to bring in the authors of this paper. We have three of them with us. And because we have three guests, and it's the first time I think we've ever had a trio of guests on this podcast, I'm going to ask them to quickly introduce themselves so that you all know who they are. Why don't we start with Jay? Jay, can you say hello and intro yourself? Hey, hello, this is Jay. Last name is Son. I actually, I'm currently assistant professor in the master's department at Clarkson University. It is in Potsdam, New York, upstate New York. I work with a lot of the complex systems, networks, nonlinear dynamics, and more recently,

studying the information flow in those complex systems. By the way, the time the paper was written, I actually was a graduate student visiting with at the time my advisor, Eric Bolt, who is here also today, and was a very exciting journey for me to be on this project. Fantastic. Eric, why don't you say hello? Hello, I'm Eric Bolt, also Clarkson University. I'm John Harrington Professor of Mathematics. So like Rio, we do a lot with non-linear dynamics. I'd also like to add, in years past, we'd call it chaos theory.

But in recent years, we do a lot also with large-scale complex systems, which is something we're developing a center for a Clarkson. And this is also non-liter dynamics. And then finally, we have Mason Porter joining us, I think from L.A. Yeah, I'm Mason Porter. I'm currently a professor of mathematics at UCLA. I just moved over from University of Oxford a few weeks ago. I'm also a specialist in complex systems and networks and nonlinear dynamics. And one of the things I wanted to mention, you were talking about similarities between herding in animals and herding in markets. In fact, one of the things that we specialize in is exactly collective behavior in complex systems, which can be. things like hurting in all sorts of context or ideas becoming viral and so on. So we actually take an abstract point of view and very specifically study these sorts of things in many different types of systems. Exactly. We've all worked together in these different sorts of things, including swarming, schooling, if it's fish, and then also human behaviors when they work in groups.

Well, maybe that's a good jumping off point. So we have collective behavior and there's been a lot of study of collective behavior, whether it's in animals or humans or systems and that sort of thing. What made you decide to focus on cows specifically for this paper? Okay. So maybe I should answer that because the project actually started with me. And the fourth co-author is Marian Dockin. She's actually, she's a zoologist rather than a mathematician. And she and I know each other from being in the same Oxford College. And we formulated a project actually about a year or so before Eric and Jay visited. And one of the things that had predated the project was that Marion was sort of lamenting

that many people who were theorists and working on problems that come from biology were not sufficiently interfacing with biology. And at some point, the conversation turned to her work on cows and other animals. which is something that she's been doing for many years. And it seemed interesting to me, and I was interested in collective behavior in general. So we formulated a project that we did in a certain manner called an agent-based model. This was the year before Eric and Jay visited.

And then that one was attempting to be more realistic, but was a bit abstract. And so we wanted to step back and have a bare-bones project. So serendipity, I suppose, is a short version of that answer, and I tend to be interested in just about everything and I had a local expert. And so we worked on it. And then Eric visited me along with Jay the next year. And so we decided that we would pursue that further. So when we think about hurting behavior in cows and I guess other mammals like antelope,

zebra, whatever, we usually think that they all move, I guess in tandem. Like Larkin was saying, if one cow sees fresh grass, then all the cows migrate there. but also, I guess, for protective reasons to protect themselves from predators. Is that the accepted version of hurting behavior in cows? I think that's at least part of it. There's also, if they're in a pen, for instance, they actually may also want to just all be able to lie down at a similar time, especially if they're under similar sort of forces from a day-night cycle.

So, you know, some of this is actually protection, but some of it is also similar needs. Yeah. So all those elements are in our work. Actually, we have a follow-on work, which actually includes things like, why would they do that, optimizing their resilience to predators and so forth.

But the centerpiece of the model is that the cow individually has these different things that go on inside their bodies. You know, they need to eat, they need to digest, which is kind of complicated in a cow. And then they need to sleep. So it's a little bit like a several parts circadian rhythm in your own body. And for the other reason you described, then it actually turns out to be a good thing if they do it together. So that's the synchronization aspect.

And whether they're in a pen or they're in the wild, there's some aspect of they want to do it together. Now, the pen, they're not really predated anymore, but they carry on that natural behavior. Yeah, so one of the things was those interactions turn out to be really important as a determining factor of whether they could synchronize. and to what extent they do synchronize, which happened to be also related to the production, and even though we don't know how happy they are, people do say that they seem to be happier when they actually produce more and more synchronized.

Just looking from the paper, the original paper, you have, they can look at a single cow model, and then you looked at what you call coupled cows. But just for your information on the farming background, when you say cows are coupling, it means something completely different. but um i get it right but then it said in a larger herd the the the synchronicity seems to break down is this what you're seeing to be saying in the paper that um well as the as the stand-up sit-down cycle is the

one that you're looking at seems to break down so you have a mixture of cow standing up and sitting down and i'm wondering um is that a thing that you saw from observation or is something that you produce from your mathematical models yourself um our second paper actually has an aspect where um the groups can become too large for their own good and they break apart and they may sub-synchronize into smaller groups. Do you see that in your farm? Yeah, well, if I had that many cows, I'm sure I'd say it, but

I think the way I'm supposed to get back to nuts and both so farming, the way farming works here is that it is very, the synchronicity I see tends to be much more if it's going to rain in the next 20 minutes. Most of the cows are sitting down if it's very hot and most are standing up. But beyond

that, they will generally I suppose the herd is big enough that some will be sitting down and some be standing up at any time whereas if you put a small number of cows in a shed that occasionally will do if some are lame if we have cows or lame we take them out of the herd because they can't keep up to your cows

we may have three or four cows together and they will synchronise very strongly so the four will be sitting down or the four will be standing up but whether that's because they're in a shed and not out in the field it's I suppose the externalities would be very hard to calculate

within a model like this The externalities are a very big deal, and one of the things that people argue about is, you know, how much of this is from circadian rhythms and how much of it is from, say, signals from other animals that are nearby. It's a very difficult thing to disentangle from each other. One thing I want to mention, just kind of going back on your earlier comment in terms of having a larger herd, having kind of not complete synchrony, in the paper we're not actually demand. demanding complete synchrony. We're just measuring how synchronized they are and trying to do it in a sort of a quantitative way. So you can measure, and this is something that comes originally from the theory of coupled oscillators. The term coupled has a very specific meaning

in mathematics and physics that's not quite the same as the English meaning. It just means that they're interacting. So if you write down equations and you have some term that has parts of two different equations, this is a way for, this is a way for them to be coupled together. But there are some measures that are from long studies of oscillations, from biological rhythms, for example, that tries to measure how synchronized things are. And so it's not that you have a yes or no that everybody is synchronized.

You have sort of how much they are. And you can imagine doing this with animal behavior as well by just saying, okay, well, do different cows stand up at a similar time? You know, maybe there's a delay of one second versus 10 seconds. And so you would say that the delay of one second, if you're able to measure that, would be more synchronized than if it's 10 seconds apart. Whether and the extent to which that comes from cows getting signals from others by watching what others are doing and how much comes from having similar desires, that's very difficult to disentain.

I think that's first an interesting aside is the one thing that where cows completely, I suppose, desynchronized themselves from the rest of the herd is when they're about to give birth to a calf. And it's interesting that there's a product available. I don't know if I have it from my cows in my farm. It's called Moe Call, M-O-O-C-A-L-I-L-E. What it is, it is a small internet. Morgan, are you making this up? No, I'm not making those up.

You can Google it. It does exist. It's an electronic product that I attach to the cow's tail. And what it measures is how much the cow switches her tail. And before a cow gets birth, she becomes agitated. She is more tail-swishing. And this product notices the extra tail-swishing, and it sends me a text message. to say this cow is going to have in the next two hours.

And how that thing works is that you put it on the cow and it stays on the cow and it gets an idea of what the cow's rhythm is. And then it notices the change in rhythm and acknowledges that there's something big has happened there that's a change rhythm. So cows generally have a strong rhythm within themselves, I suppose it's what this company's taken advantage of,

that their stand-up, sit down, swish their tail, can be very easily predicted within a certain set of circumstances. So when the circumstances change, as in the cow is about to have a calf, it can use that information to send me a text message to say, this cow is about the calf?

Now, is there an analog of Mook cow for the market? It's on the market, yes? It's something that. No, I mean for market prediction. You can put it on the traders. Although if you could figure out what it is, I imagine you get very rich, you won't tell me about it.

I'm actually surprised that we've gotten this far and you haven't remarked that actually what does a bull market mean? We're saving that for later. First, we are going to take a short break for a word from our sponsors. Put knowledge to work and grow your business with CIT. From transportation to health care to manufacturing, CIT offers commercial lending, leasing, and treasury management services for small and middle market businesses.

Learn more at CIT.com. Put knowledge to work. Okay, and we are back. We are talking cows. hurting behavior and mathematics. Just to kick off the second half of the conversation, maybe could you just walk us through in very simple terms what you found in your paper from the mathematical model you used

and what it says about cow's hurting behavior? I think from the mathematical point of view, there are something that's very unique about this particular model because one thing about cows and some other animals are that they actually have different modes, right? It's not that they follow one type of motion or dynamics and then they just continue. For cars, there are three distinct modes. They can walk, stand, they eat, or they lie down.

And it turns out that they're very traditional and machinery in mathematics that we could use for particularly to model this behavior, as well as their interactions. So one thing we found that sort of counterintuitive is you would imagine that maybe by, interacting more or more intensively, they would necessarily synchronize more. And that wasn't the case. So what that means in reality is if you start to, you know, put them in fence and with higher density, it's not necessarily true that you make them synchronize more. They actually could break the synchrony by increasing those coupling. So when you have more cows together and they're in a crowded, confined area, they don't actually exhibit hurting behavior? Is that right?

I mean, again, it's not a yes-no question. It's the extent to which they synchronize could actually decrease when you put more in the finite physical space. And is that competition for resources or they just start to feel pressure because there's too many other cows? It's more of a pressure scenario. Yeah. Well, why don't we widen out the discussion? Because I know that you all also study network effects and chaos theory and things. things like that. So how much can we extrapolate from cow behavior into other types of behavior

and specifically humans and or human investors? So one of the things, one of the advantages of mathematics is that it's automatically massively parallel. You know, people talk about massively parallel computation. With mathematics, you can get insights on a specific system and then other systems that might have similar model equations, possibly it will teach you something about that. So Jay was talking about the fact that you could have stronger coupling in this situation leading to less synchronized behavior. So that can also potentially occur elsewhere. So if people are interacting with each other more strongly, at least this is known in mathematical models, you can have situations where they're not necessarily more synchronized as a result.

I don't know how to experimentally verify that. I mean, it's much more, reality is much more complicated than mathematical model, but it's a very general situation that one sees mathematically, not just in the specific model that we did, and others have reported similar results using other models of synchronization in the last few years. So that's one example. Another thing I say about this work is it's actually a scientific study on two levels. So it's about cows.

So we're studying the topical area of cows, and we want to make conclusions about cows. But the tool set we bring to it is actually an unique kind of tool set in the area of modeling a complex system like an animal. Because as Jay said, it's a what's called a piecewise impulsive system as we modeled it, which means it's a bit like a bouncing ball. Something continues continuously for a while, and then it reaches a threshold. It switches. So it might switch from the lying digesting state to say, okay, now I'm done with that. onto sleeping. So those states and switching between the states is actually a unique element in the area of modeling. Dynamical systems like a cow. Now if we want to bring that over to people,

then you might say, okay, great, the cow is a kind of a simple system compared to a person. And if we said a person's like this, then they would have many, many states, perhaps, because I think we would think the cow is probably somewhat a simpleton in the sense of the different kind of scenarios they would run through. So if I were to be courageous enough to advance this into human behavior, I would want a many-part scenario and switches between them. And then we can ask, do those synchronize? So we haven't done that study, but I think that's how I would roll this forward if I were to do so. We keep finding that the interaction is just as important as the, you know, individual dynamics that they follow by their own. Well, that's actually, that's a very good point.

And I want to expand on that. In the study of, you know, in traditional studies where people are reductionists, you often talk about how an individual, an individual entity behaves. And one of the things that people try to convey in the study of networks more generally is that, you know, the interactions really matter. And this is something, of course, now in the modern world we see, I would say much more than we see before. And the study of networks and complex systems really tries to focus on what effects can emerge from, interactions that you don't just see from individual components. And so things like, you know, which memes go viral, you know, there's a bunch of cat memes that go viral.

It's probably not because of the intrinsic quality, but probably because of interactions. Now we're in my area of expertise, which is, of course, cat memes. Cat videos. Yeah, exactly. Well, I mean, this idea of how things impact on each other is really interesting and it's really important in markets and finance. And we've seen various attempts over the past decades, I suppose, with different degrees of success to model that. How exactly, this has always fascinated me. Before the financial crisis, I looked at things like Gosian copulas on Wall Street, the things that

were used to try to model how, you know, one corporate or one mortgage default would impact other defaults in the same space. How difficult is it to mathematically model things that are impacting on something else? This actually is something that Eric and I have started to work on starting a few years ago. We think it's a very difficult problem, and scientists try to find this so-called causality or causation between different components in a very big system. In the financial sector, it would be like different corporations, as you said. So the challenge, comes from two means. One is you have to distangle the effect from their individual motion dynamics from the actual interactions. What you observe is the aggregated effect. So you first have to

find a way to disentangle that. And we've been using tools from information theory, which seems to be very natural for those type of analysis. The real challenge, I think, applying this to any practical situation is that depending on the environment, you know, the actual interactions might actually change, and that's something that's very difficult to predict. It's like an extreme event. You sort of have to believe that your process is sort of stationary. The underlying rules don't change in order to make those predictions, but if they do change, then you can see, you know, your model may fail to predict those situations. But people do look at those so-called early warning science, and that's an encouraging direction to go, basically by looking at it.

at the science that seems might start to change and that that's that's hope there's hope there yeah just I suppose that with that idea to go back and look I suppose at something we talked about earlier where you said a larger herd will tend to break up the synchronity will lose once a herd meet I don't know if we've got to say the herd reach the critical size but in a larger herd you've less synchronicity do we is there a chance that we can see some of that like if we look at say bubble behavior or bubbles in markets where herding becomes particularly intense in an area, like I suppose 2007, it was about property. There was a large mortgage bubble in bound property, particularly in some countries in

Europe and in the US with the mortgage markets in US. And that, I suppose the herd into that became unsustainable and had to break up. And within financial markets, a breakup of a herd like that almost always seems to be catastrophic. Am I, I suppose am I getting towards the right end of the stick or is it's something completely different? Well, for cows, I think there would be two reasons why they wouldn't want to, well, they wouldn't synchronize in large groups.

One is the difficulty if it keep them all together, right, and all synchronizing. And the other is the communication from one end of the herd to the other end of the herd at some larger scale, the information may not be going back and forth between the large group such that they can stay together. So you can maybe think more like a wave in a stadium. And then the other aspect is what there's some benefit to synchronizing on a certain scale and maybe not in a larger scale. And that second aspect, I would guess, has more to do with the market. Because in the market system, I think the communication across large scales,

you know, in distance, isn't a problem. We all just check our iPhone. Do you think, given our conversation that maybe we've enticed you to do some research on markets and hurting behavior in markets specifically? Yeah, I've been always very interested in things like bank run, because that's essentially where you study how the different banks with their customers, how they interact. And what happens in the financial crisis was there is this extra layer of coupling from the media, right? Because when the media is reporting that we have a problem, then, you know, we think there's a problem. And because we think there's a problem, this coupling leads me to, say, withdraw my deposit. And if I do that, my friend sees my doing that, they do the same. And when

everyone does that, you have a bank run and banks start to, you know, go bankruptcy. Obviously, the federal government has policies now ensure a certain amount of deposit being safe, but that in general can happen in different levels like the property market. If you see all your friends selling their houses, you're more likely to do the same. So this couple actually is not a constant. It might actually change, and I think the media is playing a very big role there to influence sort of the behavior of consumers in general. So I'm very interested in this topic. And as I said, the tools Eric and I have been developing called causation entropy.

We think we actually might want to utilize this to study data collected from those past years. Yeah, interesting. We'll have to have you on again once you've completed that project. We have to leave it for today, though. Jay, Eric, and Mason, I'd like to thank you so much for coming on and talking to us about cows, mathematics, herding, and markets. Thank you. Thanks for having us. Thank you so much.

I actually think, I thought that was really, really interesting. And if I do say so myself, I think we managed to connect it quite well to markets and financial behavior. So I'm pretty happy. I always knew there was a reason why I was attracted to markets, I think. Yes. The hurting fit. But I think it's interesting that the research that I suppose is continuing to go into is to

understand the behavior of people and particularly people in markets has been, I suppose, has been going on for hundreds of years and will continue to go on. So the more angles that it's looked at from is interesting. And if cows can prove a basis for investor behavior, I think that would be an interesting breakthrough. Right. But I mean, this is one of the most intractable problems of finance and markets and mathematics is trying to calculate this sort of network theory and connectivity and how one thing impacts the other. One thing I did think was interesting, and you brought this up, Lorcan, in the context of bubbles, was this idea that at some point the herd becomes so big that the hurting instinct or the hurting behavior starts to break down a bit.

And you see cows, and I suppose you could extrapolate to investors, but you see cows start to kind of group together and do their own thing. I thought that was interesting when we think about bubbles and markets and how they seem to go on and on and on until suddenly they don't and then they very quickly break down, as you mentioned. Yes, and I think it is that kind of view, I suppose, there always be in markets, there always be contrarians because in order to buy something,

you always need someone to sell it to you. So you always have two views, you need two views in the market. But if you get the market moving directionally in one way, like house prices up to 2000, there comes a point where the, I suppose, the herd stops wanting to buy. Or you get an imbalance in her. So I think it is interesting. And I think it is, again, the Holy Grail, like we said, it's easy for me to get a piece of technology that will predict when my cow is going to calf.

It's very hard to get a piece of technology that will predict when the market's going to turn from a bull into a cow or a bull into a bear or whatever. I can't believe you're getting text messages about when your cows are going to give birth to calves. Modern technology. So tell me, has this conversation changed your view of your cows? No, I'm very solid in my view of my cows. We go back a long way. Their view is my job is to feed them and keep them happy. So a happy cow is a productive cow.

Aw, that's nice. We are going to leave it there for now. You can follow me on Twitter. I'm at Tracy Alloway. And I'm at Lorken RK. Thanks for listening. Put knowledge to work and grow your business with CIT. From transportation to health care to manufacturing,

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