 So I'm Emmanuel Nuneau, I'm the director of IHES and France Institute de Hauts-Études scientifiques and Before introducing our speaker, I would like to thank AXA for welcoming us tonight And I'm really a note that CEO Mark Pearson was able to join us in person and thanks a lot So I would also like to warmly thank the American friends of IHES and For organizing this event tonight special thanks to Raphael and For those of you who are attending an IHES even for the first time allow me to say a few words about our institutions So IHES is a research institute dedicated mainly to mathematics and theory of physics and from the beginning The institute has been devoted to the international community of scholars with a small permanent faculty of outstanding talent, so of One figure gives a good idea of IHES position in the academic landscape out of 10 mathematicians recruited as permanent professors Seven have been awarded the few's medal So each year we welcome an average of 200 visitors From all around the world for research visits They come to the institution for the unique Atmosphere of scientific emulation, curiosity, vision, discussion and freedom of research So genius belonging to no nation and IHES Forms together with all the institutes of basic research in mathematics and theory of physics a worldwide chain of Knowledge dedicated to the development of human understanding at its most complex IHES has very strong links with the US in fact the founding director Leon Mocchan modelled the institute after the Institute for Advanced Study and Develops strong scientific connection with its academic community For example, Oppenheimer was a member of the scientific institute of IHES at the beginning for several years and for over 50 years IHES has remained close to its American friends and enjoyed many exchange of scientists All extremely fruitful fruitful for the development of scientific research in France and in the United States Today American remains from far the number one nationality host at IHES for research visits now Allow me to introduce a great American scientist Dr. Robert Frey and so after 25 years and As an applied mathematicians in industry Maybe after 15 years spent in quantitative finance as managing director and some well-known H1 Yeah, you decide to retire in 204 and embarking on an academic career at Stony Brook So his work focused on risk management modeling the process of Managing complex and dynamic portfolios and tonight he will present his analysis of 175 years of market go down and Then maybe Michael Douglas chairman of friends of IHES and a great physicist who also works in finance will moderate some questions and answer a small debate before we invite you to join us for refreshment of the reception. I would be happy to meet you and tell you more about IHES and Mike and Robert Again, my warmest thanks for joining us tonight Thank you Well, you know, I want to thank IHES for for inviting me and saying some you know who and for widely exaggerating my capabilities, but I appreciate it I also want to thank AXA for hosting the event tonight What I want to talk about is Actually, I originally said 175 years, but I actually it ended up being 180 years of market drawdowns and You know, I think the process of drawdowns I think there's really several points. I want to make tonight one is that You know When we look at financial markets, we have a tendency to be very myopic in our focus We you know, we calibrate our models over, you know short periods of time We estimate risk based on you know, what's happened over the last five or ten years and we think that's a long-term You know view of things but in fact, you know Financial markets evolve and change over time scales that are probably won't much longer than a human lifetime So you have to look over as long a period as possible to really gain insight now again The argument often is is that well, that's you know, that's sort of irrelevant that you know We're dealing with if you're looking at the you know the 1800s. You didn't have a central bank Really, you didn't really have a central bank. You had the that was pre in the early, you know When I start here, it's really pre industrial revolution Now we're looking at the modern age. It's a you know, we have high-frequency trading. We have central bank We have all sorts of interventions in the market But I'm going to show here that at least in one important measure the market hasn't changed much in those 180 years And it's a measure that's I think very relevant from or from a risk-point of view It's it's looking at you know a maximum drawdown And so just I don't know just a quick bio I worked as a where I started as a scientist in the defense industry I worked as a systems engineer and a program manager Got my PhD in applied mathematics at Stony Brook University and I was recruited into Morgan Stanley's Automated their past trading group in the mid 80s When that was that looked like it was a little shaky I started my own firm in 1989 and I was recruited that that was acquired by Kepler By renaissance that that firm Kepler was acquired by renaissance in 1992 because I had started Kepler and as I was a partner with Jim Simons and and and then Jim Suggested that we merged the firms in 1992 was one of the best things I ever did I was a manager directed with renaissance I developed the Nova and ecometric funds which were basically Nova was essentially a stat off on the necrometrics was a longer-term analysis And then you know I retired from from from that from renaissance in 2004 It was the advisory board chair of the University of Chicago's program on financial financial mathematics and I'm founder and and well founder and originally director but now now co-director because We just hired Raphael today that he's gonna be my boss now So I'm very happy about that because I can get a little rest and he can take over and and I think bring the Department to new heights. I'm really fortunate. We were very fortunate to have him And I also I also run a fund of hedge funds FQS capital investment, which is really an outgrowth of my family office and as a lot of these things go I was managing money and other people asked me to manage money for them and suddenly we had a company Well, I'm talking a little bit sort of myopia and you know too often in finance and in life in general day-to-day details Overwhelmed overwhelm us narrowing our focus and what I what I have here is a sort of a little little graph And what this was from a blog post I had put up and what I what it was was it was a regime It was a looking at a regime shifting model of the S&P 500 and I chose the period 1985 to a 2000 this was at the time 2013 because that was sort of the extent of my of my career at the time You know, I started in about the mid-80s and went to you know This was done in 2013 and what you can see is leading up to the 2008 crash You can see that there was a period of of of unusually low volatility Now what happens, you know during periods such as this obviously people think things are you know Very steady and calm. We also are dealing with you know, perhaps Environment where returns tend to be sort of moderate and that sort of thing But since things are so steady and calm and all the risks alone, what do we do? We leverage up like crazy in order to get higher levels of return. So just as you know, Ivan minsky predicted, you know, it's a sort of standard minsky and sort of Condition what you know the market becomes so levered and so You know unstable that it doesn't that any little thing then becomes it becomes a disaster and the whole market collapses And you see in 2008, you know, we saw this you see these more increases in volatility But you know now the trouble is is that for many people their whole career existed in that little valley that we that we see You know sort of you sort of see I wish I had a laser point Is there a laser pointer? So you see here That's almost a seven or eight year period. There were a lot of people their whole careers were spent in this low low volatility regime and you know You know, you know And if you had taken the time to go back and look in markets over a longer period of time and again I mean, I just chose this period This isn't this isn't even enough time because it excludes things like the Great depression and many other things, but you know, you can see here that you know this This this sort of low volatility period here, you know, obviously was followed by you know much more erratic conditions here But preceding it where was a much higher level of sustained volatility plus these sort of Volatility jumps here and then there was another period of low volatility and again, you know, there was this there was a peak here So, you know on the one hand people people are calibrating garch models and doing all kinds of crazy things It's ridiculous. I mean, you know, they're saying that, you know, we're back to a new normal and everything's nothing's going to change again We're even a moderate historical perspective would have shown that this was a ridiculous idea We don't do it. We tend to look at these very short time periods We tend not to be we tend to be inadequate historians. We get too hung up with the mathematics and and we should be better historians And you know, that's sort of the less common you don't design a house based on the weather report And and that's what a many people do with their portfolios They they look at them they they look at tomorrow's weather forecast and build the house based on what they're going to see And that's not and that that's not a very sound way to do anything in life Okay, so let's talk about market drawdowns You know an investment drawdown is the drawdown behavior of a particular investment is an important element in In its behavior What we're going to focus on is a single market the S&P 500 total return and total return meaning any any dividends Reinvested in the index and we're going to look at the period from 1835 to 2015 and the source for this is global financial data and they have a sort of a pseudo S&P 500 for early periods. Okay, so, you know, there's some important questions, you know How can drawdowns be modeled and analyzed? You know, how do we sort of look at these drawdowns? You know, how stable is this aspect of performance over time? And then really what insights can we develop examining the drawdowns in an important market over an extended period of time? And those are really the three issues I want to I want to address here and you know what I've tried to do I know we have a sort of a mixed audience So I tried to be I tried not to avoid technical issues But I really wanted to focus on mainly the insights that you can gain from from looking at this looking at the world So let's talk about cumulative log returns. So, you know, we're going to you know if I look at the The log of the of the ratio of wealth from one period to the next, right? That's that's going to be that's my log return So my cumulative log return is this is the cumulative sum going out over time. So that's That's my basic measure. I'm going to look at the cumulative log returns. Now I want to then define my drawdown state now what a drawdown state is what I'm simply going to do is I'm going to just as I have a cumulative return I'm going to have a running maximum. So at any point in time as I go along the cumulative returns I'm going to I'm going to record the the maximum value and Obviously if the if I go through a losing period that maximum value doesn't change it just flies out, right? And so what I do is I I get it. I Get that maximum value now the difference between that running maximum and the current cumulative return is the drawdown That's fairly simple So now what I have is I have okay So now what I can do is what I have is I have these I have these these separate epochs these separate periods and What what I have is I can I can when I look at the this drawdown number because I'm I Don't care when I'm doing better than then then as I continue to hit new highs I I don't care about that. That's that's just going to be zero is from the drawdown perspective So in a drawdown state the way of sort of defined it I'm going to I'm going to I'm going to have either a period where I'm in this drawdown state So I'm going to have a continuous period of drawdown of observations that are non that are non zero and that's going to be interspersed with periods where all of the observations are going to be zero which represent periods where the market is rising, right? So That's I'm going to use that fact at partition that my drawdown the drawdown states across time and into partitions And then and then the drawdown process I'm going to study is I'm going to simply take each each subpartition and I'm going to look at the maximum drawdown that occurs in each Partition and I'm going to look at the duration of time over which that drawdown occurred And so I have a sequence of observations now which characterized that what I call the drawdown process for the For the particular investment, right? So it's fairly simple idea. So this is The partition is arbitrary. No, it's not arbitrary. It's based on the actual behavior So it yeah, so if it's a contiguous If they're the partition is contiguous segments where you're either in a drawdown state or not in a drawdown state So it's the partitions arise naturally from the data that I'm So let's look at the full data set from 1835 to 2015 and that's sort of a so what we have here is the log log index and this is the S&P total return index from global financial data and you can see in here, you know, these little red periods those are drawdowns And you can see for example, you know the great depression, right? That's a that's kind of a really big one But you know in general this You know as an investment this looks pretty good over, you know, if you're really looking very long-term There's a steady increase over time and you know, it looks wonderful and you know, it's easy to forget that those little Dips where where that are filled in with red where you're in drawdown Sometimes are, you know, five six years of pain and suffering And in the case of the great depression much much longer, so But you know, this this is the process now if I what I do now is I simply look at those drawdown processes And this is this is what I end up with when I when I look at that and so again, this is again 180 years of drawdowns now What's this kind of something surprising here? I mean if what when I look at this, you know I see a fairly steady increase over time, but when I actually pull out and look at the drawdowns The drawdowns are everywhere. I mean there and they're all different sizes There's a little tiny drawdowns and little big drawdowns and in fact, you know, what we'll see is that you know What's interesting about this process and what's maybe relevant from the point of view of an investor is that you're Usually in a drawdown state even even in a very good and positive investment, you know Now this is also something this is a what I did is I looked at the drawdown period which I identified as how so That's the length of the period versus the the size of the period Okay, and I did I actually just I just did a linear regression and you know, this these are these are highly significant and it basically says that the length of the period is proportional to the To the size of the drawdown and I did I just just for the sake of sensitivity testing What I did is I I looked at all of the data, but obviously I have a couple of high leverage points out there So if I look at if I exclude the top six outliers, I get I get the dashed line Which is really pretty much pretty close So you can you know There's a pretty pretty much at least from we can see here a pretty linear Relationship between the length of the drawdown period and the size of the maximum drawdown and again expressed as a lot Also, I should mention that these this was weighted least squares because it's also pretty obvious that the the variability is proportional to the size of the drawdown period So what I did is the weight is I the weight is basically was one over the length of the period so I'm assuming that the the variability of the drawdown is is Proportional to the length of the period Not a reasonable not an unreasonable thing. So I just so so what we get here and now again, you know I have a much fuller analysis here where I do Develop analysis of the joint distribution of these two things But what I'm going to do is I'm going to I'm just going to concentrate for now on the on the drawdowns themselves rather than the length that how deep that the max the size of the maximum drawdowns and not talk a lot about their lengths Although there's some interesting work there because I'm trying to get I'm trying to make this as accessible as possible now One of the things that's that's interesting is that you know, you have this you have the sort of the s&p And again stepping back and looking at the cumulative plot of the s&p we see You know kind of a fairly steady upward slope, you know Yeah, sure there are drawdowns in there, but you know on the scale on the scale of The increases over this period, you know First of all that the the the slope is reasonably constant and the drawdowns again Don't you know again with the perspective of 200 year of almost 200 years don't seem very large But if you look at things in the small right, what happens is that's you know, you say, okay You know, what if I pick a random point in time here? What's the probability of a random month being in a drawdown state now again? You get what does this mean? Well, you know You know it means that if you're you're an investor who's been invested in this Market for any period of time. What's the likelihood that at any random time you're looking back at a high high water mark that you're under You're on from your point of view. You're underwater. It turns out. That's true 75 percent of the time So 70 I think that surprises most people most people if you asked You know about the market you would say well, how often am I you know? okay, how often am I sort of in a state of regret and The answer is even with something fairly well fairly attractive like the stock market and again This is there's a certainly survivor bias here because it's the US stock market and it's you know, obviously this is a implicit survivor bias You know, even in the US stock market, which is probably one of the most successful You you're you're in this drawdown state the state of regret 75 percent of the time Then I just chose sort of an odd not entirely over here, but a 20 20 percent throwdown again It's a lot of 20 percent 20 percent throwdown as being a Like an excessive a large throwdown and of that 75 percent of the 75 percent about 60 percent of the time You're in you're in an extreme for them something over that 20 percent Right, so so what did what did what that implies is that you're somewhere around? 60 I say you know you're you know about 40 40 percent of the time you're in 45 percent of that you're in a really bad situation You're you're in a state of significant throwdown now again I think that this this is kind of an underappreciated fact I think when people look at investor behavior and look at the psychology of investing in markets We tend we tend not to focus on the fact that for the app for a typical investor Even one, you know who has you know as long as their their horizon is over more than a few years Most of the time they're going to be underwater even though in the long run They do tend to make money and this is kind of a I think something that's kind of interesting You know and I don't think it's something and I think it's sort of one motivation for focusing on drawdown as As a very important measure because I think it drives a lot of what people do in markets You know because that insight of that's that you know because where does regret to come from because you know We naturally anchor our viewpoint to our last highest You know what high watermark and what we're saying is most of the time when we're in we're investing in anything risky We're in a state of regret and that puts tremendous stress on an investor The second thing is is that from just from a simple mathematical view We know that you know when you do get a drawdown and your capital base shrinks You have to you know It's just a fact of life that you have to do much better when you know if you if you've lost 50% You have to make 100% to get out of that right that's right the losses and gates aren't symmetrical So being in a drawdown state also creates that stress of having you know your capital base is shrunk And the amount of performance you need to get back to even now is is much higher So you know this this whole notion of drawdowns I think is we tend to underestimate the stress on on on investors and we tend when we think about Investor behavior we don't we you know we tend not to talk enough about drawdowns. I would say So let's just look at that. So this is sort of the standard kind of plot and it's a log log plot and what I have is the the survival function along the abscissa and the the x-axis is the max drawdowns and You know here, you know this is where you would sort of you know, you know Typically if you have a power over a tail you'd see you see sort of a straight line and I have sort of this gradual curve and you know again based on looking at other other financial indices and another another And doing looking at various looking at various subsets, you know this this thing never really settles down You get this sort of curve, but it never really settles down to zero. So You know after looking at this, you know, I was sort of trying to develop You know and also by the way out and I'll show shortly that if you had if if the if the returns were normally distributed the the the Distribution of drawdowns is exponentially distributed But what we have here is we have actually some quite fat tails So what I did is that you know, I was trying to develop a max drawdown and I and I sort of again based on fitting various Looking at the looking at these log log plots, which is the typical plot that you know Mandelbrot first introduced to show, you know tails and in these distribution I Came up with just basically a gamma exponential mixture, right? So this I Realized after I went to the trouble of solving this that this is just a variant of the Pareto distribution It's typically called a Lomax distribution The only difference is that beta is usually a scale parameter sigma that's divided into the into the variable But I just kept it in this form. So so what I'm saying is that the PDF of the of when I look at when I sort of fit this The PDF of the max drawdown and again that red and so looking at each epoch the maximum drawdown I experience in each epoch the PDF follows this Pareto this this is a Pareto type for distribution basically All right, so that's it's that's it's so what I have here is you know This is the this is how this is how it's derived, right from from from the This is a beta distribution and I'm integrating over an exponential distribution and I have this PDF and that and that the CDF So when I do that So when I so now when I'm going to look at the max drawdown distribution again over this period I get I get I get a This Pareto distribution I get an alpha of 1.8 and I get a beta of 13.7 And that's a very good fit that's an excellent fit I mean the fit is I mean I use the Kramer von Mises generally that's my preferred test, but this this is This is a very this is very close. I mean, it's it's pretty it's pretty clear You know that this is this is an excellent fit to the data and you can see here What I have is the red is the theoretical and the blue is the empirical So then I said well, let me let me just sort of look at a Gaussian simulation to see see see what I get with that So this is just now again, obviously looked at a lot of simulations, but this is just one of them I just wanted to look at one of them So there's there's the the same sort of graph showing, you know, and I see you know, I see the drawdowns I see a lot of you see a lot of the drawdowns and Notice they're a lot smaller and but I still get it doesn't look dramatically different Here's the drawdowns now notice here notice in contrast, you know The drawdowns here are much then that is widely just widely distributed They look more similar to one another right then then in the in the real market case So now when I when I sort of look at this case of again I'm going to look through the same sort of division of you know What percent of time are you in a drawdown state versus what time percentage of time are you in an extreme drawdown state? And what's interesting here is that you know for the Gaussian this Gaussian This is a typical result is that it's you're in fact slightly you're 80% of the time You're in a drawdown state and of that and of that 80% about 67% of the time you're in a sick more than 20% So again, you know even with Gaussian well-behaved Gaussian Distributions you're you know, you're you're dealing with a thing where you're in a state of regret most of the time right you're you're you're going to bed with you know Upset stomach because you know, you've lost money in the market. You're not sure what's going to happen and that sort of thing Okay, so all right now the now the but this is the real difference here is that rather than a rather than a Pareto distribution the distribution of the distribution of Of max drawdowns follows an exponential distribution and here's you have the theoretical and the and the observed right and it was actually that Doing that which led me and some theoretical arguments about you know, the sort of the native relationship between stable and distributions and Well, normal is a stable distribution normal distributions and alpha stable distributions which led me to the idea of looking at mixtures of exponentials and so You can see here that you know, we have an exponential distribution and again This is this is a very close fit obviously. This is the seat CDF's the CDF's match each other extremely closely and you know and now So what's nice about this is that we're not characterizing now on one hand you could say, you know We're looking at in some sense the tails We're not characterizing the tails of the drawdown distribution We're characterizing the entire drawdown distribution looking at the whole thing and the whole thing follows Let's say this low max distribution and again for normal these things are universally exponentially distributed Which is something much much less a try tail Now so then I said I said, well, let me fit an alpha stable fit a type 1 alpha stable distribution to the data And again, I ran many simulations there, but this is I'm going to give you a sort of a characteristic one so and You can see right away. It doesn't look anything like the the real data right, there's only anything like the real day and again, this is You know, you you do get it you do get a you do get a You do get a an alpha similar I think it's 1.6. I have that plotted, but Look, you see that, you know, you know and part of the problem is is that the alpha states What's interesting is the this the when I fit in a single alpha stable distribution to the to the data I get too many large excursions and That's what causes a lot of the drawdowns and also sometimes ends the drawdowns. Yeah, so right so Again, when I look at the drawdowns, you can see here And also the size of the drawdowns are much much higher over this over again I had this simulated same period of time and where whereas the Great Depression hit hit about again a log drawdown of 1.8 or so You you see here you're hitting much higher distribution, you know much higher much higher levels with with alice stable So stable distribution at least not a single stable distribution doesn't Doesn't really hack it and I will tell you that, you know, I'm in the process of firming this up But you know, it's obviously that the market has some state memory and and that you know You're dealing with a mixture of such alpha stable processes that are you know So but there there is also some state memory that gets in here to change this But so we're saying this just a stable distribution doesn't do very well. However one One thing that's interesting is that you know, again, you see the same pattern 83% of the time you're in a drawdown distribution 84% you're in a drawdown distribution and 69% of that time you're in a significant drawdown and again This is everything having the same, you know, you in this case the alpha stable was fit using the same using the same data and again That's that's the fit and It turns out though that the alpha stable distribution does fit the Pareto type for distribution It gets a two parameter version and it has an alpha of 1.6 and Beta and this the beta and actually that again the normal the normal form would be the reciprocal Say a little more what you mean by stable What and I will have a stable stable distributions of distributions that when you add them together you get another stable distribution So there's a there's a class of distributions developed by Libby that That have this property now You know the kosher distributions an example of normal distributions an example, you know So when you combine these you actually puts on distribution when you combine that you get another person But there's a class of distributions where there's generally no closed form for the PDF But where and you have generally infinite variants and that's that's generally Right right, but it's changing in a consistent way across time because I don't what I break this up into pieces I get the same Changing Yes, exactly. That's I think it is that I say and I and the sing which seems to in the same thing It doesn't seems to have persistence. So I'm really what I'm really trying is a Libby stable thing You know essentially hidden Markov model with alpha stable emissions basically Well, I'm gonna I'm gonna do I'm gonna cover that bit of that's good question Right and what I tried to do is I tried to make the break breakouts sort of meaningful in this in the sense I'm really trying to sort of again think of it from a as much from a point of view of the history that I'm looking at is anything else But so so I but again what's what's clear is that if I have with the alpha stable distribution Does have these the drawdown state which does resemble this parade of distribution as is the other case, however It's also clear that it's a single distribution doesn't capture You know actual stock marble returns with any real fidelity It's natural No, I did monthly because because I wanted to get as long a period as possible and daily returns when you go back 200 years Well, you don't mean much really so yeah, yeah Right now I get temperate stable. Yeah, I didn't I have looked at that and that's not here But yeah, that you can I mean that doesn't change things that much. Yeah. Yeah, yeah, right All right, so let me look at what I want to do is I'm going to first look at the Pre-grade pre-grade depression because remember when I let me go back up here When you look at the original data, you know, you have the great depression in there So, you know everybody, you know the maximum hitting or hitting about point seven and the other one Then you have the great pressure depression that goes up to about 1.8 So let's see if we sort of take that period out and look at the period before and that's a 93 year period so that's the that's a period prior to the Great Depression and You know qualitatively, you know, it doesn't really look different that you know When once you scale it down, it doesn't really look different than you know the whole data set Again when I when I when I when I look at it from the point of view of fitting the Distribution I get again a very excellent fit. I get it. I get an alpha of 1.8 as opposed to 1.65 I guess was was was the No, it was about 1.8 for the whole thing I forget but you know it doesn't look very different. So so the point is that yes It's clear that there is that that you know single alpha stable distribution doesn't handle it It's clear that it's changing over time But it's also clear that when I look at this when I look at this pre Pre-grade depression period It's changing at time levels that are Less than than than that and and and you know, it's it's changing in the same way I mean it looks the same, right? The underlying process looks the same and again I have the same thing I have again by 78 75 78 percent of the time You're in a drawdown and about 60 percent of the time and what you might consider as a highly significant So so now so that was 93 years and again, you know Let's look at a post World War two and I wanted that sort of you know, we had the obviously World War two ended What 46 I guess so I Wanted to give you a few years for recovery. So I started 1950 to 2015 so that's 65 years That's a little bit shorter than they first did the other period and again Here's here's the most more recent period and again. This kind of looks You know sort of very similar doesn't really things are really Again now Alpha is a 2.3 And again, if you you know, I did some bootstrap estimates, you know, these these these alpha coefficients are Virtually really quite indistinguishable But you know, I now again the significance of an alpha point to being over two is There's some significance there, but yeah, I had an alpha of 2.3 and again beta the What you might think of as a scale parameter is 11. So again, it looks very similar in this period as well So when when I'm looking at these three periods, I'm so I'm looking at the whole period and I find okay. I have a certain You know certain behavior and I find So then I but I have in the middle of this this tremendous distortion perhaps caused by the the Great Depression And so, you know what I do is I said let me let me take that out And and let me look at the before and after periods Separately and see if things look at look any different and the answer is at least from the point of view a drawdown They they don't look different at all. You know, they don't they don't they haven't really changed changed at all and again Just I mean think about that. Yeah, we're talking about, you know Sort of a basic element of market stability. How much does it drop before it comes back again? Right that's a very important, you know Consideration for any investor for anybody planning investments and there's no evidence that you know It was different in 1840 that it is in 1940 that it is in 2015 not not not dramatically so Now again, you know, what's different? I mean, you know, I mean in 1907, you know Who is a JP Morgan had to organize all of the bankers to? Put money into the into the market because there was no central bank, right? Then we had, you know the Great Depression which probably because we had a central bank that didn't know what it was doing We got it. We got a Great Depression Then we have 2008 which is again, you know, but you know What's interesting is that if you look at all of these interventions and all of the changes in time At least this basic this aspect of the market this basic kind of an interesting Characteristic of the market hasn't really changed in 200 years Right now think about all this other stuff that's changed. We have high frequency trading We have all sorts of regulations. We have we have, you know, a central bank, which although it's not its official mission Really does consider the stock market stability as part of its mission, although it's not supposed to But there's no evidence that Any of that has any effect whatsoever in the behavior of the market, right? The draw the size of the drawdowns the distribution of the drawdowns, you know Aren't say, you know, when you look at something like the Great Depression If I exclude the Great Depression and then I say how likely is something like the Great Depression to happen? Yes, it's a rare event, but it's not a terribly rare event It's you know, it's an event that might happen every couple of lifetimes or something. It's not you know So so again, I think you know There is a there is a consistent behavior in the in these drawdowns over time I think that it's it says something about you know markets in terms of how they've driven perhaps by human nature And you know and so despite everything that's changed over the last 180 years This aspect of the market hasn't changed much at all. Okay, so let's look at some comparisons again Here's the again. Here's the PDFs of the Drought max drawdowns again. So again, so for each drawdown epic, you know, obviously I took out the pieces that weren't drawdowns So if you draw that every I took the maximum drawdown And looked at the distribution and here's the three PDFs One is for the whole period then then for the pre pre pre pre-Great Depression and post then the third post war. They're virtually the same is the here are the CDFs and again, you can see that the the post war looks a little bit better But I'm going to argue that I mean sometimes they'd argue well that isn't that some evidence that things have changed but you know, you got to remember to the The the pre-war the pre-war I had 97 years of data post-war I had 65 Frankly, my experience is the more data you have the smaller the exponent tends to grow, right? So that the the fact that the 1950 to 2015 I think is more likely due to the fact that I had a smaller period of time that the exponent was slightly higher I don't really you know and certainly from a any kind of you know, I did when I did some bootstrapping I There's really no difference here. So what we have here is a very you know We have an again a critical element of stock market behavior. That's that's constant over a very very long period of time All right, so let's let's compare the drawdowns. So again I think the key here is that the basic character of the max drawdown Is reasonably similar across time and roughly just shy of two centuries, right? There's a recent period does show a slightly lower incidence of larger drawdowns, but again I think that might be an artifact of the like say the lengths of the intervals I was comparing, you know When I look at the probability of a larger max drawdown So I'm looking at the tail of the distribution when I look at these three periods I'm looking at a 20% or 40% and 80% and I mean, but this is a log drawdown So it goes out to it goes out. So well one point one log drawdown at 1.6 You know the probabilities don't dramatically change, you know, I mean I I mean I see you know You know, you're going to see significant drawdowns in all cases and and again I again obviously when you when you look at those those extreme events that those are very noisy I don't you know None of this stuff suggests to me that we're dealing with a process that has changed in any fundamental way And again, so I think that that kind of does does surprise me because I did expect to see some effect of the interventions from You know from from government and everything else, and I just don't see it I mean say I mean the market the market in 1890 and the market in 2015 don't look at all different. I mean it just doesn't look just doesn't look all right So so what are my conclusions? I want to talk about this that you know market as a driver of regret may play a greater role than we realize You know, I don't think we think in terms of we think in terms of drawdowns and we understand how oh, yes We're going to control max drawdown I don't think we think about the fact that most of the time an investor is facing a Drawdown when when they're when they're investing and that scares the hell out of it, right? Right, so you have that psychological factor me is something that you should be considering right and whether you're doing theoretical work or Practically you're in the practice of advising an investor, right? The character of the market over the past 180 years Again doesn't seem to have changed greatly and again you can look at any number of other related things I think I like I like drawdown because it was such a Kind of to me was an important measure and and by the way it was being driven by some research I was interested in frankly managing my own investments Yes, sir True now that I control for them. No, but I mean I think the the Those might be explanatory variables that may explain some of that stuff But it's pretty clear that to the extent that they affected the behavior of the market It didn't change from one period to the next. Yeah, so at this point I'm not trying to diagnose anything or trying to go any deeper Faturi what one is that I do have much more analysis, but I wasn't sure at the level of the audience I know there's people at all different levels and I wanted to Talk about something everybody could sort of appreciate so but but the answer here is that yeah sure I'm sure you know obviously flows in and out of the market I'm gonna have a dramatic effect on on the volatility and what happens to the market But there's no evidence that it's different now Is the size of the distribution of financial Again Okay, well, let's let's I mean let's examine but you know if you know we just We just saw that you know if I look at the recent period and I look at sort of the map that maximum throw down in those periods, right? I Don't I don't see any difference now today So some of what you're saying is that in some important way things have not changed. That's that's that's what I'm saying I mean from from the point of view of someone you say, you know, should the risk premium be different But I don't why why should it be different No, no, I mean that's but that was true in the past as well. I mean, you know, I was true It doesn't change for what it's Right, you always think hey, you know, it's only think it's something different now and stuff like that. It's not Changed Right Right, it's the same and also you talk about sort of things that financial markets being, you know The world, you know, one of the reasons the Great Depression was the Great Depression was because we had become integrated Globally, you know trade wise right now that we didn't get back to the same level of global integration in terms of cross cross Border trading until I think I think it was like the mid of late 50s after the Great Depression. So, you know, there's this You know, I you know, there's plenty of you know, I don't know I mean when you're saying that it has increased maybe it's increased from, you know, 10 years ago But I don't think but again when I stand back and look at this 200 year period. I'm saying that No, it hasn't increased. It's it's maybe it may be in a high state or a low state But it's been in those states before that's that's what I'm saying, okay Yes So if you were to take Yes And even if you look at say Well, that I haven't that I know I have access to that we do have tagged that I didn't look at many But I assume I wouldn't be surprised I wouldn't be surprised to find You know Absolutely This and in fact if you look at my last point there is any study such as this suffers from survivor bias That's my last point and and the fact that we are likely to have probably underestimated our alphas because we don't have a lot of data here, frankly, so Yes, I mean, yeah, I mean, that's I mean, I fully admit that I mean this is I'm trying to describe certain thing and observe certain things But yeah, there's some real limitations here And I think but I think it's important. It's okay to use this stuff as long as you understand those Extremely brisk trading between the beginning of the war and 44 The answer is I did if you look at and I actually if you look at the Again, this isn't here But if and I we can talk about this later if you look at these stocks because one one advantage of global financial data Is that I can get this data if you look at the losers in World War two Yes, they look a lot worse than the winners of World War two So I've looked I've done the same thing for example with the with the English stock market And even though England was subject to great stress during the war, you know at bombings in London stuff like that You did not you you see pretty much the same pattern as you do in the United States and and you know So so you don't really see that doesn't change but if you do look at someplace like you know say pre-World War two Germany languages, you know the fall of the regime You know, you you know, obviously you had immense hyperinflation and that sort of thing and If you look at Japan post-World War two, you see the same thing and what you see is just Bigger drawdowns. I mean, yeah, but they're I mean, you know, you see that I mean, yes, but there is a survivor bias here in the sense that you know There's no lost war in you that that the United States has experienced during this period Not really, you know, and and if you had one, you would see a much bigger You know Yeah Listen these guys think that you should invest in stock market based on my oh, yeah Well, that wasn't my Music, but I'm asking more if people have tried to construct experiments where people form an artificial market For what I've seen in it. I mean, obviously, you know, you read the behavioral literature this notion of Anchoring is a big is a big deal. So obviously people I think, you know, if you ask the guy well, you know What would a person feel in a drawdown state they'd feel regret But no in terms of actually looking at the distribution process that that process that drawdown process and saying how it's actually going to influence Investor no, I haven't Well, actually my argument there is that somebody should that's that's not my area of interest But somebody should really look at that because I think that you know market drawdowns first of all are more pervasive than we think and That I mean for most investors it's going to it's going to present a tremendous stressor on an investor You know, and I don't think people appreciate that, you know when you look at It's just I'm saying just let me make just go down and make a few more points, you know I just want to say really realistic statistical model awaits in terms of understanding financial markets You know, we're unable to adequately model returns to reproduce With this, you know, so again, like I said, you know, if I put in an alpha stable now again as the seed said Yeah, you put in a you put in a mixture of alpha stables You do get something that looks a lot a lot more and and but again There seems to be some memory in there So something like a hit mark or a process or some some state memory that comes in that that, you know It's important, you know, but yeah, but I right now I don't I don't know I haven't done it yet. I'm trying to Somebody else wants to do it. They're welcome to do it But one thing I think it's really important to say it would be a mistake to view the Great Depression as an outline Because if one more person tells me that the Great Depression can't happen again, I'm gonna kill I'm gonna have to kill him Well, yeah, but the point is that you know even even without the observation of the Great Depression Such a such a sought thing is not even an outlier. I mean we got to stop, you know, we have to you know Look at the real reality here So yeah, you know when somebody says, oh, you know, because we've learned so much I Again, you know when I was doing this I did I wasn't I wasn't at this stage looking at any Cross-correlation and that sort of thing what I what I have thought about doing is looking at a Regime switching model where again you have these alpha stable emissions and the probability distribution You're in any one emission state is controlled by some other exogenous variables like Afflation and so on like that. So that would give you some that would give some of the effect to look that and as a matter of fact The the the the first dissertation we produced that are stony work out of the QF program was just on that topic on modeling the behavior of hedge funds where we had basically a Hierarchy of model we had we had a sort of a bunch of sub models and which which model this strategy sort of Behave like was controlled by certain macro macro variables Well, that is a regime shift Another is that that is I'm not saying I don't know what controls the regime shift Is it doesn't is it controlled by some exogenous collection of variables and some model that would allow you to you know Generate that or is it something like a hidden Markov model? I don't know what the rich I don't know what the meta model is that controls regime shows But I think it's kind of obvious that there is regime shifts here and and they probably are alpha stable or something This is the most affordable finance people tend to Trust people on the contrary cross section of the We would look at the population and when I was looking at that, you know, I was saying if you're trying to go back very long To make a statistics, right? But in fact, when you look at financial series and you have dozens of Right Oh Chinese market today looks like what was So so first of all, I mean the suggestion We are missing an If we can have some measure of temperature Here we are the property of the Prediction Absolutely, and I think that's You know You know what I think that's one advantage of having that's again, let's talk about that meta model that selects what state is It's much better if you have something that's driven by some other exogenous process that you can examine and Use the forecast and predict even if you just even if you just can observe it in situ and say, okay This is where we're at. This is the environment We're in and and obviously if you if you look I mean the results here if you looked at the Because they're highly correlated the this and the British won't and you'd find us Everything's pretty much the same Oh, no, no, but I'm sorry. Yeah, right, right. Yes. Yeah. Oh, yeah Well, you know the thing is though that you know, what's interesting here though is that these these drawdown behaviors Which include the effect of financial bubbles remember I wasn't just modeling the big financial drawdowns. I was modeling all of them Right and and the whole the whole distribution fit very well Right because most of it when you when you when you're you know, in fact if you use something even if you use like a Fairly tough one like a comagora smirnoff when you're looking at the maximum deviation in the in the CDFs These things these things are all the same Well, well, yeah, well, maybe well, maybe you know, maybe then you end you have to sort of frack the light from process right, so I don't know but but the point here is that you know, it's There's there's a very Definite easily sort of identifiable behavior to these drawdowns and it's been fairly stable over nearly 200 years and When you and I will tell you if you look at other markets, you will find exactly the same thing And if you look at other types of markets, not just equity markets, you will find exactly Okay, there's one more question. I don't want to Yeah Problem Well drawdown not the pressure Seems that you are the normal you can explain Oh, no, no, yeah, no normal doesn't slide No, no, no, actually, I think actually that the difference was that with a normal distribution the distributions of these drawdowns is exponential which is Not fact. I mean, it's just, you know, like very well behaved, you know nice furry Distribution, you know, it's very good, you know, but yes, memoryless, right, right? It's memoryless, right? Exactly, so whereas whereas the whereas the if you look at the real the real markets, they have Pareto distribution and They have quite fat tails. I mean those exponents were one more between 1.6 and 2.3 And those are relatively low exponents and that means you have some fairly fat tails Right, but but I guess I guess what I'm saying is other things that we have to be you know, when we talk about we talk about what's what may happen We have to be prepared for what? You know where I mean, there's pretty good solid evidence that what may happen is pretty big I mean, you know, it's it's you know, and I think I think we we tend to you know First of all, again, I think there's really two points here. One is that in order to gain some insight You have to look back over Long as long a period of time as possible to it is surprising that many many many things you look at You can go back 200 years and find the data is relevant completely relevant, you know It's very important to understand that and and and the third thing is when you do that and you are successful Isn't always true that you can go back all the stuff, but when you can do that you find you find some very surprising Things about the world, you know and and and in finance It's it's usually that we live in a fat-tailed world Okay, so well, let's thank dr. Fray for a great