Mark Kritzman: Thank you. Thank you, Cayla, for that introduction. Good morning everybody. Thank you for being here with me. So the first thing I should say is that this is a joint research with Wiley Song and Dave Turkington. And I should also point out that Wiley actually came to Dave and me with this idea, and she also did the lion's share of the analysis. So credit goes to Wiley. So I'm going to talk about bubbles. This is a very controversial topic. I think there's a consensus, certainly in academia, that you cannot detect when a bubble has begun, nor can you sort out how far it's traveled along its path. And I think that view may also be shared by people in industry. And I think the perhaps the fiercest proponent of this position is Gene Fama. So he would go as far as to say there are no such things as price bubbles. And in fact, he's so committed to this view that this was one of the themes in his Nobel lecture a couple of years ago when he got the Nobel Prize. Well, you may some of you may have been here a couple of years ago when my predecessor this morning, Robin Greenwood, gave a paper called, bubbles for Fama. And this is a paper that was co-authored with Andrei Shleifer and Yang Yu. And what they showed. They didn't completely rebut Fama, but what they did argue. I don't know if Robin's still here and he can correct me if I'm I can't, you know, I can't see anything.

Mark Kritzman: Okay. Good. Robin. So you'll correct me if I'm wrong, but I think what you showed you and Andre and Yang showed is that, you can detect when the likelihood of a crash has become elevated and possibly add some value from that information. Well, Willie and Dave and I go a lot further. So what I'm going to argue and try to persuade you about is that we can determine the onset of a bubble, and we can also tell you how far along it is in its journey, in a way that will enable you to profit. So that's that's our that's what we're going to I'm going to try to convince you of. So anyway, let me let me show you how we do this. I guess what I should do is first just give you an overview of what we're going to do. So we're going to use this new tool. It's not new. It's new to finance, but we're going to use something called dynamic time warping. And this was I think introduced in the 1970s to aid with speech recognition. People speak at different cadences, and this was a technique that was used to help synchronize the way people speak. And it can be used broadly to synchronize any series that progress at different cadences. Now, as an aside, every year I think of what's the new buzzword? And two years ago it was cadences, right? Everybody used to use schedule or pace or whatever, and then cadence.

Mark Kritzman: Everything was a cadence two years ago and then last year. Anybody know what the word last year is the buzzword. It was performative. I didn't even know what performative meant until last year. And then that word gets used. Okay, that's an aside. I apologize, but I'm going to use cadence in a legitimate way here. So the challenge is that bubbles you know they have different durations right. Some happen over a few weeks. Some happen over a few years. And not only are their durations different, but their cadences are different. Some, you know, some have a very quick run up in a slow selloff. Some have a very I think it's more common to have a slower run up and a quicker selloff. And and they're not you know, if you look at bubbles, if you plot these prices, you'll see that they're not this smooth concave function that you know. You know that we visualize when we think of a bubble. There's lots of irregularities. So this this dynamic time warping is going to allow us to synchronize bubbles, bubble pairs into uniform time steps. Right. So we're going to we're going to examine millions of bubble pairs pair by pair. And we're going to synchronize them. And it turns out that, time when we do this time is no longer universal. It's actually specific to a particular bubble pair. So what why do we want to do that? Well, what we do is, we we then look at stock characteristics for each time step.

Mark Kritzman: There are 21 time steps. We use 5% increments. So what we do is we look at a whole bunch of characteristics of stocks for all of these, you know, so you know the first bubble synchronized with every other bubble. So we get this this very large distribution of the values of these characteristics for each time step. And then what we do is when we contemplate an out-of-sample stock, we can see, you know, which time step its, its characteristics are most similar to. And then that's how we can detect where we are. So, I think I've just said all of this. So let me give you now an example. Of this technique called dynamic time warping. So we have two series A and B. These are just sequences of nbers. And what we want to do is synchronize them. And the way we go about this is by constructing what's called a culative distance matrix. Right. So we have series A right along the colns and series B along the rows. So we want to calculate the culative distance between each of those values in in these two series. And there's the formula for doing it. We take the Euclidean distance and we add to it the minim of the prior. either the what came before either horizontally, diagonally or vertically. So if we start, if we look at the upper left, we don't have anything that precedes it.

Mark Kritzman: So it's just the Euclidean distance between, you know, 0.01 and -0.104. But as we go to some of the elements where there are preceding cells, we have to add the minim of those cells. So that's how we fill out this matrix. And then to figure out the warped sequence, we go to the lower right and we work backwards. Okay. And what we do is we just proceed and go to the adjacent cell. Right. So it could be adjacent either vertically, horizontally or diagonally that has the minim distance. So if these two series had the same cadence you know those the warped sequence would be along the diagonal right. If one of if one of the series is proceeding at a quicker pace than the other, then it has to, you know, it has to hold in place and allow the other series to catch up. And you see that occurring where you see these, you know, the 22.57 and 2.67, right. Staying in the same row. And, and then there's another instance where we were staying in the same coln. Okay. So that's that's how we do dynamic time warping. So here what you see are the original series, you know, a across the colns and B up and down the rows. And now you see the Warped Series and you see that there's an additional step because each series had to wait one period for the other one to catch up. All right, everybody with me so far.

Speaker2: Okay.

Mark Kritzman: So now what I want to show you are some, bubbles. You know, an example of two bubbles from our sample. So I should point out that we identified our sample goes back to 1973, and we identified 2638, bubbles, which gives us between 6 and 7 million pairs. Right. So this is this is computationally pretty intensive. So here are two bubbles that we identified, Perrigo Company and Zebra Technologies. And then this lower right panel is you know how they're linked in elapsed calendar time okay. So you know it's trivial to link them in a lapse time. But that's not sufficient for what we want to do because that's only linking their durations. Right. We want to we want to link. We want to synchronize their entire shapes. Right. And that's what dynamic time warping will do. And you'll see that in another slide okay. So you see these two bubbles. You know one lasted about a year longer than the other. and here they are linked in calendar time. Now what we're going to do is, warp them and, but we're still going to link them in calendar time. And what you see is if we do this right, if they're, you know, we've warped them, but we're still trying to link them in calendar time. We actually have to bend time in order to synchronize these two bubbles, which is why you don't see a straight line here. But if we actually then link them in warped time and they're both warped, you see that we get this perfect synchronization again. And the other thing to notice, let me I don't know how you go backwards, but in the, in the other I won't go backwards. In the other preceding two slides, you saw that they had different shapes, like one went up at a different pace than the other. Here they both have the same shape in warped units, approximately the same shape. All right. Maybe I should go backwards. How do you go backwards?

Speaker3: Should be a button to lower button.

Speaker4: No no no no no. There in the back there. Moving it back for you.

Mark Kritzman: Oh, good. Okay, you stop there and I'll go. Okay. So what you see is that, you know, zebra went up quickly, you know, and then the sell off was, over a longer period, whereas Perrigo had a much longer run up and a quicker sell off. So you see that the shapes are different in calendar time, but that when we link them in warped time, we warped them and linked them in warped time. You see that the shapes are much more similar, right? So they're much, you know, they're more accurately synchronized. Okay. So that's just an example that this technology actually works. So you know, what's almost as controversial as the existence of bubbles is the definition of a bubble. Is Robin still here? Robin are you still here. No. Okay good. So I can talk about him. So, you know, I showed this paper to Robin, early on, and he said that you're not using the officially sanctioned academic definition of a bubble. I didn't actually realize that there was an officially sanctioned academic definition. So, you know, the way I think about a bubble, it's you have a run up in a sell off that's disconnected from fundamentals, and it really doesn't matter whether the run up is 50% or 100%, if it's, you know, for my purposes and I think for your purposes, as long as you can profit by knowing you know, where you are in the bubble, whether it's a big bubble or a little bubble, that's a sufficient definition of a bubble.

Mark Kritzman: Okay. So anyway, here is our definition, an increase of 50% or more from its previous low point. And then subsequently it declines by 50% or more from its peak. And the bubble ends when the return index reaches a new low point prior to recovering to 30% below its prior peak. I don't even know what that means. But anyway. And then the start date of the bubble is the most recent time the index value was as low as the value at the conclusion of the bubble. And as I said, we found based on this definition, we found 2638 bubbles, from 866 different stocks. We looked at stocks. We just looked at stocks in the S&P 500 over this period, January 1st, 1973 through, mid-May of last year. Okay. So as I mentioned to you, we synchronize all these bubble pairs. More than 6 million I think closer to 7 million bubble pairs. So this is computationally very, very intensive. And as I'll show you in a little bit, we also do a lot of cross-validation. So it gets even more computationally intensive. In fact, when Huili was doing this, she lives in Hoboken. There were two blackouts during the period she was doing this. Now it could just be a coincidence, but I don't know. Maybe Huili knows. So we have for you know, we'll take one stock and it's paired with one bubble, paired with another bubble.

Mark Kritzman: And then what we do is we look at the values of all of these characteristics for that stock for time. Step one. And then we pair it with bubble three. And we do the same thing. And with bubble four. And then we start with bubble two paired with bubble one and bubble two paired with bubble three. And we go on and on, you know between 6 and 7 million times. So for each time step, for each time step, we have more than 6 million values for each of these characteristics. Okay. So does everybody. Sort of clear. So far we've identified all of the you know, we've synchronized all of these different bubbles into uniform time steps. And then we've generated a distribution of values for all of these different characteristics that I showed you. Okay. So there were there were behavior and sentiment characteristics coming from State Street information. There were price characteristics and there were fundamental characteristics. So let me talk now about training and prediction. So we select 90% of the bubbles in the full sample without replacement. And then as I mentioned we warp bubble one and bubble two into 21 time steps of 5% intervals. And then we record the vector of stock characteristics. And we we standardize them into cross sectional percentile ranks. And then we repeat the process for bubble one with every other bubble.

Mark Kritzman: Bubble two with every other bubble, and so on, recording these vectors of characteristics along the way. And we repeat the entire process for all of the other time steps. So we did time step one. Now we're going to do time step two through 21. So for each time step we have this massive distribution of values of these different characteristics. So then what we do is we have this 10% holdout sample. And those of you who know me know that I can never do research that doesn't include the Mahalanobis distance. So what we do is for an out of sample, you know, we're going to consider a stock out of sample. And one of the time steps is no bubble at all. Right. So we have the the 21 time steps of the bubbles. And then we have the the stock characteristics for periods in which there were no bubbles. And so then we consider a stock out of sample. And we measure its Mahalanobis distance to the no bubble period as well as each time step of the bubbles. And wherever we find the smallest Mahalanobis distance, then what we argue is that this is where that bubble is. It's either, well, this is where that stock is either not in a bubble or in a bubble, and this is the time step at which it is. Okay. Does everybody understand that? Good. So let me show you some results.

Mark Kritzman: So we're going to on the let's look at the left panel horizontal axis. This is warped time. And what we're saying what this is telling us is how much appreciation remains between the inception of the bubble to the peak. This is estimated from our warping. And then the vertical axis is the subsequent appreciation that actually occurred from inception to peak. So if this were perfect for zero, that what do we call these things? Box plots, you know, the middle of the box plot. You know, where it's the color separated. That's the 50th percentile. That would be right at 100%. But it's not perfect, right? So it's at just about 90%. And but what you see is that in warped time, the distribution. Of the price appreciation isn't that far from what you would expect. Especially if you contrast it to doing the same thing in calendar time, which is the right panel. Right. You see, there's the relationship. There is not nearly as good. The horizontal axis is not warp time, but it's the nber of half years since the bubble inception. So this is matching the predicted remaining price appreciation at each time step with the price appreciation that actually occurred. And then we do the same thing for the depreciation. Depreciation from peak to conclusion. And again what you see is a much better fit. If we look at this in warp time as opposed to calendar time. And the other thing to notice is that the you know, the dispersion around the 50th percentile is much smaller in warp time than it is in calendar time.

Mark Kritzman: Okay. So this is some evidence that we're, you know, we have some ability to determine how much more run up is available to us and how much more depreciation is coming. The next thing I want to show you is how these characteristics evolve when measured in warp time versus calendar time. So what you see this is what's this this EPs growth. Right. So in warp time it actually conforms somewhat to our stylistic image of what a bubble looks like. But but look at calendar time right. No one would ever say that there's a bubble. If you look at this, this characteristic in calendar time and then, you know, it's the same for these other, these other characteristics. Net margin. Right. This looks like a bubble on the left but not so in calendar time warp time. And so on. Okay. So now what I'm going to do is describe a trading rule. Two trading rules. Given the information that we can glean from warping bubble pairs. So we're going to use an expanding window and we're going to learn bubble characteristics from historical bubbles. And then we're going to predict warp signals monthly out of sample. We're going to construct two market neutral portfolios. So the first one there are two rules. One is we call it the run up trading rule.

Mark Kritzman: And the other one is the overreaction trading rule. So the run up rule has us purchasing bubble stocks cap weighted, that are estimated to be between 20 and 80% of the elapsed warp time from the bubble inception to the peak. So, you know, we're not buying the stock right at the initial time step of the bubble. But, you know, a couple of time steps in and we're not trying to exit right at the peak. That would be a bit heroic, but a little bit before the peak peaks are the peak. It turns out that the bubbles are a little less stable around the peaks. So that's the run up trading rule. And so we go along these stocks that are within that, within those time steps. And we go short the S&P 500. And then the overreaction rule is it's based on our observation that when the selloff occurs, investors overreact and they drive the price down further than it should go. Which means that when you believe you're sort of near the conclusion of the bubble, that's a good time to buy the stock, right? So we have this overreaction rule where we purchase these bubble stocks again, cap weighted, that are estimated to be between 80 and 100% of the elapsed warp time from the bubble peak to the bubble. Conclusion. And again, we make it market neutral by selling the S&P 500. So those are our two trading rules.

Mark Kritzman: And here's the obligatory culative return graph that we have to have when we talk about trading rules. So you see there. The return and risk and information ratio for the run up trading rule the overreaction rule and then combining them. And what you see is that overreaction has the highest return. But it also has the highest risk. But it has a pretty good information ratio. And combining them gives us a really good information ratio 0.74. So you think about that. This is market neutral. This just this doesn't require any capital. You just follow these rules and you just plop this on top of whatever your underlying portfolio is, whether it's treasury bills, your policy portfolio or the S&P index, for example. So what you'll notice is that the combined. run up and overreaction strategy seems to match more closely the run up strategy. And the reason for that is that, you know, the run ups. Take a lot longer, much more time than the overreaction when the overreaction occurs. So it's so the combined strategy is dominated by the run up. But what you see is that. This is, you know, this is a pretty good result. Now, we thought that maybe we should try this at a more macro level. So we're going to do the same thing, right? We're going to identify characteristics for industries groups of industries and sector bubbles. And we're going to consider them all in combination.

Mark Kritzman: So it's actually possible that you can make a double bet by betting on an industry. And then, you know, an industry group that has that industry and then a sector that could be a triple bet, but it's unlikely that, you know, an industry group or a sector is going to be in a bubble of just one industry is in a bubble. So same exact trading rule and very similar results, right? The combination, we get a pretty decent information ratio. Again, market neutral. This can be just, add it to this is incremental to without any additional capital to whatever your underlying portfolio is. And then finally we wanted to see if there's information here that can tell us something about the overall stock market. And what we're what we do here is we look at the bubble count. So we calculate the fraction of bubbles that are estimated to be between 20 and 80% of elapsed warp time from inception to peak, and also those that are estimated to be between 0 and 20% of elapsed warp time from bubble bubble peak to bubble. Conclusion. And and then we calculate. So we look at. You know we consider when. The nber of bubbles is in the top quartile historically. Okay. So this is sort of in-sample. So this is not like a back test. But this is something this is information that you can use going forward. Right.

Mark Kritzman: So if it's in the top quartile of the bubble count historically, you see over on the right what the S&P return was in the following month. So the way to think about this is if there's a lot of if there are a lot of bubbles. Then the S&P has an abnormally high return in the following month, and if there are few bubbles relative to historical norm, then the S&P return is is significantly below average annualized in the following month. And then near peak we get the reverse, which you would expect, right. So if we're near the peak, if there are, if you're in the top quartile of being near the peak, then the S&P return is below average. And but if you're in the bottom quartile it's above average. Okay. So this is just to show you that this methodology allows us to potentially add value by picking individual stocks by picking or Overweighting or Underweighting sectors. Sector industries, industry groups and sectors. And also it gives us information about the aggregate stock market. So to conclude. What we're doing is we're showing you how to rescale stock price bubbles that evolve at different paces into synchronized steps. And this allows us to observe characteristics that coincide with different stages of a bubble. And it you know, what we've shown, I think, is that we can detect the onset of a bubble and where it is along its journey. So I'll stop there.

Speaker4: Great. Thank you.

Cayla Seder: So we do have some time for questions. I'm afraid of that. I have a couple of things coming in, and we also have folks in the back with mikes too. So if for some reason, the QR codes or QR codes aren't working, that's an option too. Okay, so the first question that we have coming in is, what's the false positive rate of detecting a bubble that isn't a bubble?

Mark Kritzman: I don't know the answer to that.

Speaker4: Okay. It's a good. That's honest.

Mark Kritzman: No, it's a good question. Really may know the answer. So I would encourage you to address that question to Huili later on.

Cayla Seder: Perfect. And then.

Speaker4: Also this may be.

Mark Kritzman: My recurring answer. So well, just warning you, I.

Speaker4: Have multiple questions.

Cayla Seder: On here. So that's okay.

Speaker4: We have to know the answer.

Mark Kritzman: To one of them. I should point out I was mainly the spiritual advisor of this project. You know, I didn't get into a lot of the detail, but carry on Cayla okay.

Cayla Seder: So and we have do you want to sit? We do have a couple minutes.

Mark Kritzman: You think I'm old and frail, don't you? Actually. Okay.

Speaker4: I'll say all righty. All right.

Cayla Seder: Let's get situated. We have eight minutes. Okay. Are there any. Do you see any other applications of this outside of equities or since this was very or US centric, you know, do you have a sense that bubbles react similarly in other regions?

Mark Kritzman: I, I, I think they do. And so I think this could be applied globally lots of different markets and, and my guess not having done it is that we would get very similar results. And I think it could also be applied to perhaps other asset classes, maybe currencies, for example. So you know, I think the technology is new. And you know, to be fair to pharma, right? When, you know, when he made the claims he made about, you know, price bubbles don't exist or they, you know, certainly they can't be foreseen. you know, he was using standard tools. Right? So this is something new. Yeah. And maybe he would change his tune if he, if he were aware of this. But, anyway, I think this new technology can be used very broadly and I would expect to get similar results.

Cayla Seder: Well, I hope that means it's inspiration, maybe for future, future research retreat topics.

Mark Kritzman: It could be, it could be. And I, you know, I pity the people who live in Hoboken, though.

Cayla Seder: So actually taking this a bit more macro, as you know, you were spiritually advising the topic and the research. did you happen to notice anything about overall market liquidity helping to perhaps, you know, does that lead to more bubbles if liquidity is excessive?

Mark Kritzman: I didn't notice that. I don't recall I don't think we have any liquidity measures, do we, Dave? No. So I think if we did include liquidity measures that might even improve the results. But we didn't we didn't look at liquidity measures.

Cayla Seder: Okay. Is there sorry. These lights are a little bright okay. Is there a trading rule for the sell off path before the overreaction rule. And how does the performance look look.

Mark Kritzman: Yeah, we didn't find, very useful information to do that. In other words, to say we're at the peak or or, you know, just a little bit after the peak, we found that, That this, that the patterns were very unstable around the peak. So we did not, we did not come up with a good rule for the sell off phase other than, you know, noting that there's this overreaction to take advantage of.

Cayla Seder: Okay. And actually so going back closer to this or I guess a quarter of the way through the presentation, we talked a little bit about, or you talked a little bit about the definition of what a bubble actually is. You know, how does that jive with with your thinking? Do you think there should be a a do you agree with that definition? And also should there be a hard definition?

Mark Kritzman: No. I think it's silly to say that there should be. I was just I was making fun of Robin, you know, since he wasn't here. But I think, you know, I think that's silly. I think, you know, if you have some kind of run up and sell off that is disconnected from fundamentals, and if you can profit by knowing where you are in that process, that to me is a, you know, a sufficient definition of a bubble.

Cayla Seder: So actually tying this to some of Robin's presentation, do you think the way a retail investor would use this, would that be differently than maybe an institutional investor?

Mark Kritzman: Okay. So. You cannot do this at home. Right. Because it's so computationally intensive. You think of like, you know, six, almost 7 million bubble pairs. And then with cross-validation ten times, we're talking 60 to 70. In your calculating covariance matrices, every single time this is not there'd be blackouts everywhere. Yes. So and moreover, it's reliant on proprietary State Street data right now. It could be the case that others can come up with their own sentiment and behavior characteristics, or they can just ignore them and just use publicly available price and fundamental, information. But, yeah, I don't see some retail investor programming this at home on their laptop. And I and even for an institutional investor. So there's sort of an analogy here with ChatGPT. Chatgpt was built. Right. It doesn't have to get rebuilt for, you know, who knows, maybe another century, right. We have this massive, massive database which is going to be relevant for a very long period of time. Now, you know, we can update it periodically, maybe yearly or every couple of years, but we don't really have to because it's such a huge database that covers a whole host of, stock market events. Right. So I think the question is, you know, how do State Street clients access this information that's contained in that database? And for that, I would ask encourage people out here to talk to their State Street representatives, because I think this is really, really valuable information. Yeah, but I don't yeah. Like when I, when Robin was giving his talk, I thought he was he's a very tough act to follow because he's so smooth. But when he said, oh we did this so that you can replicate it yourself. And I'm thinking, oh, this is yet another contrast between what we've done and what Robin, you cannot replicate this yourself.

Cayla Seder: Heard? Okay. So I've actually gotten questions similar to the one I'm about to ask multiple times on here. do you see any bubbles in the S&P right now?

Mark Kritzman: Ah, I, you know, this goes through May 23rd. Oh no. May 16th 2023 I think we'll see you updated it recently I don't know I guess again I think my you know, my standard answer should be address that to Huili. You know at lunchtime.

Speaker4: She.

Mark Kritzman: May know she may know stocks that are in early, you know, in a phase of a bubble, okay. That one could profit from. So yeah, I would really cozy up to Willie to get that information.

Cayla Seder: She's going to be the most popular person in the room.

Mark Kritzman: She should be.

Cayla Seder: Okay. And then when it comes to different sectors that you all looked at, you know, are there certain qualities of sectors that make them, you know, more prone to bubbles?

Mark Kritzman: . Not that I know of. Again, Willie would know that. One thing I should point out is that, you know, when we did the analysis of individual stock bubbles, right. It could be that those stocks were in bubbles, not for stock specific reasons, because they were a tech company during the.com bubble or, you know, whatever. Right. There could be these more macro influences. And we and so we didn't. And then the other thing is we didn't adjust for we didn't look at prices or returns net of what's going on in the overall market. Right. Because we thought if we're talking about a bubble and you're saying something's in a bubble because it's going down less than the S&P is going down, most people that wouldn't resonate with very many people. So that was sort of a non-answer and getting ready for election season. I hear.

Speaker4: You.

Cayla Seder: All right. So we are out of time.

Speaker4: Oh, thankfully.

Cayla Seder: Thank you so much. You've been great. Thank you for answering all of the questions. This is wonderful.