 Thank you very much I'm very pleased to be here I originally studied in South Africa and it was always my dream to come to England and in those days everybody wanted to get a PhD you wanted to come and study in somewhere in England and eventually I was a postdoc over here and I studied in the United States and I was a postdoc over here and I'm happy to be back again now. So I'm gonna launch into my talk it is a little bit about what I was introduced as about the precarious state of models in finance and my the book that I wrote was called models behaving badly the periods between the models and behaving in badly because there were actually three subsections to the book the first part was about models the second part about was about models behaving and the third part was about models behaving badly so it wasn't all about models behaving badly. So I'm gonna start by trying to give a summary of where I'm trying to go and it's a bit of an epistemological talk about theories models and intuition and I thought I'd just have a summary slide first so yeah put that over there models models behaving and models behaving badly and this is sort of a summary of what I want to try to get across from my point of view. So theories I'm going to argue that theories are ways of describing the world and they stand on their own feet and don't rely on analogies models I'm going to argue stand on somebody else's feet their metaphors that explain the world we don't understand in terms of worlds that we think we understand better models tell you what something is more or less like whereas theories try to tell you what something is it sounds like I'm putting down models and I'm not I'm going to explain this but but the application of models is often much less successful especially in finance than in theories and then one of the points I want to make and which try to make in my book is that the equations of physics and the equations of finance really do resemble each other very closely especially especially classical classical physics they resemble each other very closely from an equational point of view syntactically but that their semantics is actually very different which I think people get confused that when they first come into the field physicists who make the transition and I want to argue that financial models are actually almost never theories unlike in physics which has both models and theories and they're always analogies they're always idealizations that sweep dirt under the rug and good models and good modelers really have an obligation to explain to the people that use them and to the world in general what the dirt is and where it will be found and and when you might run into it so that's a short precy of what I want to talk about and I will launch into them I'm happy to take questions along the way if I say something that isn't clear or at the end so I want to talk a little bit about ways of knowing in terms of trying to understand the inanimate world and the and the animate world and how do you approach understanding the world I know a lot of people here are physicists I've thought normally talk to physicists I'm going to actually maybe tell you stuff you know but but I need to do it in order to to describe the way I like to think about things so I'm gonna talk about what everybody in elementary physics learns or maybe in this country even learns in high school the great triumph at the dawn of modern science the understanding of gravitation and motion and as everybody knows especially in this audience for millennia after the Greeks scientists and everybody else described the planetary movements in terms of circles about a stationary earth and when they didn't work very well they had epicycles which in a sense are a kind of furry analysis of circles within circles within circles and and that was the way they like to think about things but as everybody also knows the the word planet comes from the latin planeo for wanderer for for to wonder and I've seen from the orbiting earth itself if you look at planets moving in the sky they do retrograde motion they don't move smoothly against the fixed stars they go forward and come back for a while depending on where they are relative to the earth and so you need more than one circle to describe their motion unlike the stars that that seem to rotate about the earth and eventually Galileo pointed out that the earth wasn't stationary and that the earth and planets actually orbited the Sun and that all these weird retrograde motions were actually one's mind boggles at how he figured it out actually and that they were not intrinsically theirs but but rather a consequence of being observed from a moving rather than a stationary platform and so when the earth speeded up relative to one of the planets they seemed to go backwards when they were when they were both on the same side of the Sun after Galileo came Kepler and Kepler Peck Kepler it's hot and said how he did this without computers but Kepler was able to take the the tick of bright observations of the of the planets and and formulate these three laws of planetary motion which he had to unfold out and the motion of the earth so he could figure out how these planets moved relative to the Sun and he came up with these three rather astonishing laws of planetary motion the first one is that planets move in ellipses about the Sun and with the Sun at one of the foci secondly and to me even more astonishing which I'm going to talk about on the next slide the line between the Sun and a planet sweeps out equal areas in equal times which ends up being equivalent to the law of conservation of angular momentum and and so sorry the first the second law tells you the relation between the speed of a planet when it's close to the Sun and when it's far from the Sun for a single planet then the third law tells you the relation between the orbits of different planets and says that the square of the orbital period the time taken to travel around the Sun is proportional to the cube of the radius so relates different planetary orbits to each other the second one relates motion within the same within the same planetary orbit Kepler's second law to me is kind of astonishing because here's a diagram of a schematic diagram of the Sun at one of the foci of the ellipse and you see when those two green triangles or arcs are meant to have equal area approximately and you can see that when you're far away you have to move more slowly to sweep out the same area compared to when you're close on the left you have to move faster in the same unit time to sweep out the same area and if you look at how Kepler phrases this he says the line between the Sun and the planet sweeps out equal areas in equal times and as I said later on that becomes equivalent to Newton's law or follows from Newton's laws and the law of conservation of angular momentum but I said this the closer the planet is to the Sun the more rapidly it moves the astonishing thing for me is that there actually is no line between the planet and the Sun and so how does Kepler get to formulate if he looks at the data how does he get to say I'm going to describe the motion of the planet in terms of a line that is actually invisible and doesn't exist between the planet and the Sun at all and there was no line therefore Kepler to observe he really only had planetary positions in the in the sky and I don't know how he did this there's a there's a there's a very interesting book by Arthur Kistler about 50 years old whose title I suddenly forget but all about the going from the Greek discoveries all the way through to how Kepler came up successively with the three laws and then Newton the title suddenly slips me maybe somebody remembers it okay anyway nobody knows exactly but if you read his book you see it involved long immersion in data lots of struggle lots of associative thinking and then a ha's at the end some intuition followed by checking the data first for the fact that these orbits are are actually ellipses and not circles and secondly that he gets equal equal areas swept out in equal times Kepler's laws are only really description of planets and actually if you come from a financial background you should be kind of surprised because he says the square of the planet the square of the of the of the orbital period is proportional to the cube of the of the of the radius he doesn't say the square is 2.1 plus or minus 0.3 and the cube is 3.05 plus or minus 0.15 so he says it's very very very dogmatically it's not it's not data science and and they're only descriptions of patterns so although one calls them laws they're not laws in the same sense that Newton then comes along with his laws and Kepler described planets describe the pattern of the planets but he doesn't actually say anything about their causes he's just describing them and describing the the arc that they that they the relation between between different things but not what causes them and what's Newton then comes along and actually finds the cause he shows that Kepler's laws were a mathematical consequence of Newton's own theories and in fact Newton's embraced immediately because he's able to explain Kepler's laws from from from much more fundamental statements so again I'm gonna get beyond telling you things you know but I want to go through them so first of all he writes down the theory of gravitation in the mid 1600s the inverse square law of attraction which says that any two masses attract each other and proportional to the product of the masses and inversely proportional to the radius squared and so that tells him the force between the planets the planet and the Sun the earth and an apple etc the earth and the moon and then he writes down how you calculate the motion from the force and he says force equals mass times acceleration so two laws which are shortly want to call theories and so different from Kepler's laws they the laws of causality or statements of causality rather than statements about patterns and how did Newton discover his theories again I want to argue against data science the orbiting planets and the falling apples don't stand there and announce F equals ma or g equals m1 m2 over r squared or even the equation for an ellipse or equal areas in equal times it's sort of astonishing that somebody can look at the world and come up with the state come up with the description of a statement like that I'm gonna say later that this doesn't really happen in finance I'm getting a little bit ahead of myself and so Newton does this by some kind of intuition and I want to talk about four modes of understanding and the first one which nobody understands that well is intuition and I think it takes intuition to attempt to discover and to actually discover the nature of the world be it animate or inanimate if you look at Kepler or Newton or ampere or Maxwell or Einstein at Iraq many of whose pictures are saw in the in the in the entrance hall over here with descriptions of what they achieved and they all actually if you read the history they all recursively refer to each other as making these discoveries that nobody can understand I want to quote a few of them and by intuition I don't mean I sort of don't mean something casual but if you read about how they did this it takes intimate knowledge and long struggle and and lots of mathematical work and data analysis acquired by careful observation and painstaking effort it's not just a flash in the pan it's a flash in the pan after a lot of struggle and and a rare flash in the pan but nevertheless some intuitive insight that isn't there in the data and the famous Keynes who's who's who's all in the news for the last four or five years over here as well as in the United States and with all the quantitative easing and there's a talk that he gave in he actually wrote it in 16 excuse me in 1942 John Maynard Keynes on the tercentenary of Newton's birth and then didn't actually deliver it until 1945 because of the war in Cambridge at which point he was actually dead but his brother delivered the talk and and it's very interesting you can find it I actually quoted in my book but I had to pay somebody in the Keynes estate $500 in order to quote it but actually you can find it anywhere you like on the internet for free but you can't actually put it in a book without paying for it but the thousands of copies I always think there's a job opportunity here business opportunity for somebody to intermediate people who want to who want to quote somebody and people who want to be paid but don't really want to go to the trouble of being paid I tried to quote Philip Larkin at some point and they didn't want to take my money honestly and it was too much trouble for them so and and publishers won't let you quote more than two lines without without written permission so I recommend looking up this article if you just Google Keynes on Newton so this is what he wrote he wrote this is a short quote he wrote about Newton I fancy his preeminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection his peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it and Keynes actually found a lot of a box of Newton's old papers somewhere in a college in in in Cambridge that nobody had read before and somewhere in the rest of the speech he says Keynes actually wasn't the last the first of the rationality was the last of the great magicians sorry says Newton was the last of the great magicians and gives lots of examples and quotes and De Morgan saying that occasionally when when somebody asked Newton how he knew something he sort of said I know it if you give me a couple of days I'll prove it so very very interesting speech that Keynes gave and so that's one thing about intuition the second thing is just to give a couple of examples is Maxwell on Ampere if you if for those of you remember or don't just as Newton Newton and Coulomb wrote down the inverse square law of attraction between two charges or two particles Ampere wrote down the law of force between two current elements which is more complicated because they're victorial and you have to write down the the direction that the current elements are pointing in the angle that it makes with the line between them and Ampere wrote down the law and he entitled his paper a derivation of the law of force between current elements based on experiment and Maxwell and Poincare later point out that it can't be based on experiment because nobody can get too isolated current elements they're always part of a circuit and so he's his description of how he got it isn't isn't him isn't totally honest or not that he's trying to mislead people but Maxwell actually says we can scarcely believe that Ampere really discovered the law of action by means of the experiments which he describes we are led to suspect what indeed he tells us himself that he discovered the law by some process which he has not shown us and that when he had afterwards built up a perfect demonstration he removed all traces of the scaffolding which he had which had built which he had used to build it so again what I'm trying to accentuate is some kind of insight or intuition that these people can't really describe and is not coming from the data itself and Maxwell calls Ampere the Newton of electricity and later on other people make similar remarks Einstein about Maxwell's discovery of the extra term that he adds to Maxwell's equations that lead to deciding discovering that light and light waves are really just electromagnetic waves so I want to sort of say that intuition sort of a little bit metaphorically is when the observer becomes so close to the either the object or the person that he's observing that he or she begins to experience their existence almost in a quantum mechanical way from both inside and outside simultaneously and it's a kind of a merging of the observer with the observed and what what isn't obvious becomes perceived in some way. Now I want to talk about theories like Maxwell's and like Newton's that I think get their inspiration from some kind of intuition and I couldn't make this pop up later but so it's there before because it's an image but you can see Maxwell's equations and the Dirac equation but I'm going to get to them so I want to argue that after intuition theories are really deep descriptions of the laws of the world or some or sometimes not correct and just an attempt to make deep descriptions of the laws of the world and I want to explain why but I want to argue that theories are a qualitative way of understanding things in the sense that they can be right they could be partially right or theory could actually be wrong but it can still be a theory and not be a model which I'm going to get to shortly so I like to argue this because occasionally people will say to me that Newton's laws aren't quite correct and special relativity or quantum mechanics supersedes them and therefore they're only a model but I want to for various reasons which I'll get to shortly argue that they still a theory they just not 100% right but in in essence they're a theory oh sorry wrong button okay so if I can give an example I'm when I was smaller I read a lot of I read a lot of the Bible and there's a story about Moses in the desert when God tells Moses to to go to Pharaoh and tell Pharaoh to let his people go and Moses somewhat like Jonah who's told to to go and tell the people of Nineveh to stop to stop sinning they both run away from their obligation and Moses Jonah gets swallowed by a whale and Moses actually goes into the desert and tends his father in little sheep and doesn't really want to do what he's supposed to do and at some point when he's wandering in the desert and he comes across a burning bush which keeps burning but he's never actually consumed and you sort of understand that God is inside the bush and the voice says to him go to Pharaoh and tell him to let your people go and Moses says who shall he's playing for time really and he says who shall I say sent me since he doesn't really want to go and and the voice comes out and says to him and tell them I am what I am and what God is saying actually in Hebrew it's it's yeah share a head means I am what I am why I will be what I will be and the root of the word I am in Hebrew is actually the same as the root of the word Jehovah so he's kind of making a bit of a pun on his name and it's a root of the word being but he's saying I am what I am and in a sense I think what he's saying is you can't compare me to anything else you can't make graven images of me because there's nothing you can compare me to I am simply I am simply what I am it's a little bit like Popeye as well but but um but um he's saying you can't compare me to other things that you know about and I think that's kind of for me the the quality of theories in that theories are an absolute form of knowledge not a relative form of knowledge or an absolute form of attempted knowledge not a relative form theories say this is the way the world behaves or this is the way I think the way the world behaves without referencing some analogy to something else so um I would argue that yes I know Newton's laws have been supplanted by Einstein's in the sense that they're more accurate but to me Newton is still a theory he's not an understand the results or Einstein ends up giving a results to which Newton is just an approximation or an approximation to Einstein is Newton's and Newton's gravitational force but I would argue they still both theories um if I can make an analogy if if I can do handwriting and write with the with the fountain pen and write cursive or if I can do typing they're both ways of transmitting information but they're independent ways the one isn't an approximation to the other typing isn't an approximation to handwriting handwriting isn't an approximation to typing one might be more accurate but they're different ways similarly navigating by the stars or navigating via global positioning satellite or independent ways of navigation but the one isn't an approximation to the other the one may be more accurate than the other so I want to argue both of those are still theories and I said there's a two different approaches reach the same end by different means of different accuracies but both still have a both still an absolute attempt to describe the facts I wrote down here Maxwell's theory for light which describes everything I'm using right now together with with the Dirac equation and um Maxwell also added this this extra term for the displacement current which wasn't there before and he somehow came up with by pulling it out of his head or out of the vacuum um um the Dirac equation describes electrons in conmolectro dynamics um together these describe all the laser pointers and quantum optics more or less with quantum mechanics um I think these are I think these are absolute descriptions rather than relative if you look at Maxwell he actually started out trying to describe light by comparing it to hydrodynamics then he actually says he's building a model because he doesn't understand things well enough to create a theory and then when he writes his subsequent paper and he says he's sort of doing a warm-up exercise then when he writes his final paper on he calls it a theory of electromagnetic phenomena and he eventually writes down these equations and theory in the sense being absolute not a comparison with with water flow um similarly the Dirac equation which I don't really have time to go into a lot but it starts out with an attempt to um unify um unify quantum mechanics and special relativity and becomes metaphorical for a while with the description of the Dirac C but um but ends up really being an absolute description of the electron and I'm not sure but from my experience in physics I would argue that most physicists who look at light um don't think Maxwell's equations are a model for light but think Maxwell's equations are the mental or or or verbal or symbolic description of the behavior of light with quantum mechanics that the two are sides of the same coin rather than one of them being an approximate model of what happens I think it must be very my perception of having been in physics a long time ago but for a long time is that when he crates Maxwell's equations with light one doesn't think of Maxwell's equations as being a model for light but thinks that there's some feels there's some identity similarly with the with the Dirac equation quantum electrodynamics um there's a line by Goethe in one of his books where he says one day we will realize that every fact is really a theory and it sounds a little um a little obtuse but I think what he's saying is is that to my understanding that um if you take for example Maxwell's equation that light is the fact and the obvious side of the coin is that the equations of the theory and and what he means by it being a fact is that if you know that light satisfies Maxwell's equations you can't ask why that's just the bottom of the chain you can't recurse any further or if you know the electron satisfies the Dirac equation you can't ask why because that's just a fact maybe maybe it'll come from a deeper theory but that will be a fact um okay I want to move on oh I gave a lot of examples which are all um mathematical so I want to give an example of something that's a theory which is not mathematical and more easily accessible to people who don't come from a physics background so there's a famous book by Spinoza written also around the time of Newton a little bit earlier um called um the ethics which is all about um people's misery in life and how to overcome it and he starts out by discussing people's emotions or the passions as he called them that as he calls them that sweep everybody in their power and ends up talking about how to liberate oneself from them but to start with he does a sort of phenomenological analysis of what he calls the passions and um he does this actually avowedly by trying to adopt a scientific approach and he actually says he wants to treat people's behavior um or people's emotions the way Euclid treats geometry and he actually says that in words um it was only published posthumously and so um in the same way as Euclid starts out with points and lines and planes and everybody intuitively knows what a point on a line and a plane is from having lived but nevertheless Euclid defines him in a fairly abstract sort of way um Spinoza says he's going to do the same thing for emotions so he starts out with three primitives too which are desire and I've got them in colors for various reasons in the diagram coming up he starts out with desire and pleasure and pain and he actually defines desire and pleasure and pain very very abstractly but you wouldn't know what they were if you didn't actually know what their meaning was like points lines and planes from from everyday life and experience and then he starts to build up what I would call a theory of how all the other emotions or passions um his ultimate aim is going to be how to overcome them um but he first wants to describe them and so he relates them all to desire pleasure and pain so rather utilitarianly he says good is everything that brings pleasure and evil is everything that brings pain and then he says love is pleasure associated with an external object this is sort of a very modern derivative theory in the sense he's saying just like an option is related to its underlying stock um love is simply related to um at the bottom at bottom to pleasure and rather obviously hate pain hate is pain associated with an external object and then he says gets a little more sophisticated he says envy is pain at somebody else's pleasure so for those of you come from a financial background this is a bit like a convertible bond in the sense that it's got an equity and a and a and a fixed income underlier and he's actually very clever this is written more than 400 350 years ago he says um they're going to be all kinds of emotions that he can define some of which actually don't have names and he presumably doesn't know about Schadenfreude which is actually pleasure at somebody else's pain and so he actually he's actually open to all of this and then he says hope is expectation of future pleasure tins with doubt um fear is expectation of future pain and he says cruelty is what you call somebody's desire to inflict pain on someone that you love and that's like a convertible bond with credit risk as well as the underlying and so it actually is really a derivative theory and very modern he's actually got want to make sure I have enough time he's actually got three more primitives in their desire and pleasure and pain lie at the bottom and then he has three more things which are vacillation and wonder and contempt and they're not and they're not at the bottom substrate the way pleasure, plain and desire are there more like vacillation is the oscillation between two different emotions so for example he says jealousy is an oscillation between lots of our members act of oscillation between love and envy and and wonder is sort of what Moses experiences the at the burning bush wonder is what you experience when you confronted by something that doesn't fit any of your categories and contempt or scorn yes conceptually is what you feel when you confronted by something who's um who's who's um who's most pertinent features of the absence of what it has rather than the qualities that it has and I made a diagram which I kind of like um which I put in my book but they wouldn't let me print it in color unfortunately um but I actually but it's actually it's all Spinoza's definitions but um I put them cruelty and pain and pleasure over there and this is wonder and vacillation and um and and contempt over there and actually if you look at it it's too small to see I have it on my website but he actually has almost it he has melancholy compassion benevolence hate shame derision humility disappointment confidence joy honor disdain self approval all of them ultimately go down through several levels to the three bottom ones which are pleasure pain and desire somebody wrote me an email which which pointed out that there's actually no anxiety there apparently that's either a 19th or 20th century emotion or some people argue it's not an emotion at all it's something different but he never has anxiety so the reason I'm showing you all this is a it's kind of related or be it's kind of related to to a modern theory of derivatives in finance and a I think it may it may it may be true it may not be true but I think it's got the qualities of a theory in that it's an attempt to describe an emotional framework based on introspection and an absolute description of the relation between various things not by saying the brain is like a computer or the heart is like a hydraulic pump or all sorts of things which are which are half true but but faulty this may not be true but it's but it's it's an attempt to find an absolute like Freud or like the theory of evolution and attempt to find an absolute description rather than a relative one which for me is what makes it a theory and now I want to talk about models and this is from Schopenhauer just to to have a financial metaphor he says sleep is the interest that we have to pay on the capital which is called in a death and the higher the rate of interest in the more regularly it is paid the further the date of redemption is postponed so very pretty metaphor comparing sleep to um to paying interest on a loan but if you think about it um um there's actually only one overlap between sleep and between interest on a loan and that is the periodicity you sleep at regular intervals and um and you pay interest on a loan at regular intervals and based on that he's then building this quite elaborate metaphor based on really only a partial overlap between the two things that says since they both periodic um but since in the case of the bond you once borrowed money and you have to repay it at the end in the case of sleep you must have once borrowed your light from the void and you have to give it back at the end and your incremental sleep is simply paying paying the interest on the darkness so to speak um so I think metaphors like that are an insight that there's a similarity between something you're interested in and something else you think you understand better um I want to argue that all models from a from a qualitative or or an epistemological point of view are really metaphors and that they compare something you don't understand too well to something you think you do um so I spoke about Maxwell's equations and Newton's laws and the wrack equation and I think those are theories being absolute descriptions um there's a famous liquid drop model of the atomic nucleus which people several people got the Nobel Prize for about 40 or 50 years ago and they describe the nucleus which is 10 to the minus 12 centimeters large but very dense as and really made up say in the case of uranium of 238 protons and neutrons but they describe it as a liquid drop that can vibrate and rotate and oscillate and they calibrate it to what they know about the nucleus and then from its excited states from its vibrational and rotational excited states predict the existence of higher order excited um nuclear levels and um and um that's useful and it's picturesque and it works very well but it's not true in the same sense that Maxwell's equations or Newton's laws or um or the Dirac equation are true it's qualitatively an attempt to compare something that isn't like something else but has some similarity to it and to and to use it and push push that notion as far as you can um so their models in physics and their theories and I think physicists I think partly that's one of the advantages have um somebody asked me earlier before I came here one of the advantages that physicists maybe have when they come to do economics despite their lack of economic backgrounds that they understand the difference between a model and a theory in between a good model and a bad model because they've seen them whereas most economists have never really seen a good model so it becomes very hard to to to know when you've seen a bad one I don't mean to put down economics totally I think it's just a much more difficult field because you're dealing with social and human phenomena so in the same way the black shoals financial option model which um I and probably a lot of people in this room have spent a lot of time working on it compares by analogy the uncertain up and down movements of stock prices or stock returns to the diffusion of smoke from a cigarette and that's useful too because cigarette smoke does move in a diffusive uncertain way and stock prices move in an uncertain way too but they don't really diffuse they do much more dramatic things and so it's it's a useful way of thinking about the possible behavior of stock prices but unlike the Dirac equation it's nothing remotely like a fact um it's it's quite inaccurate but nevertheless a useful way of thinking about things much more like the liquid drop model um so I said theories tell you what something is models merely attempt to tell you what something's more or less like and models are really metaphors and I think that's one of the semantic differences that people forget about even if financial models use the same symbols they really images of reality um but not reality itself and um we're all in danger of forgetting that and if you forget that you I would argue in some sense you'll be coming an idolater and thinking that something that you wrote down out of out of with a pen and paper or out of clay um um you're you're making an image of something that's really living like markets and people and um it's not going to be correct and and you suffer all the dangers of of worshiping idols um I want to before I go on to finance I want to talk a little bit about um data and statistics because for the last couple of years you read a lot in the paper about big data and big data being a possible way of um of uh of of getting into truth too um there was an article in Wired Magazine maybe in the British version a few years ago about Chris Anderson saying that in the future people won't have to worry about them theories anymore because they'll just find out everything they need to from doing regressions on data and I don't think that's really true um there's statistical analysis that lies behind big data um statistics I'm really saying obvious stuff here but I like to repeat it because I think people forget it statistics is really just an attempt to find past tendencies and correlations in data that one's already collected um often people like to assume that they will persist and people aren't stupid they often have some dynamical or causal model in the back of their heads when they write down a regression or when they when they get the results of a regression but um but there's no causality involved in any really quantitative or even very qualitative way and correlation doesn't really doesn't really imply causation at all and is subject to all the mistakes of assuming that um so I I like to think that big data is definitely useful especially in the advertising world of course um but it's not really a replacement for the classic ways of understanding the world which are still um well I'm getting ahead of myself I think data as I said at the beginning I don't think data really has a voice Kepler's Kepler's look at ticker brahese data didn't announce um I'm moving in the ellipse or um or I'm moving sweeping out equal areas in equal time there's no such thing as raw data it's choosing what data to collect take some insight and deciding what way to look at it and what way to make sense of it and still requires some classic some one of the classic methods which are either intuition or a model or a theory and the data's useful for that but doesn't announce doesn't announce the truth in any way at all um in the medical field or or I believe in any other field but especially not in physics um there's a line um in Wittgenstein's book that says philosophy is a battle against the bewitchment of our intelligence by means of language which I take to mean that um if you take language too seriously it can deceive your natural intuition but if you take the the meaning of the words more literally than than than maybe you should and you need philosophy to reclaim your intuition and um in the same way I want to sort of paraphrase him and say science is a battle against the smothering of your intelligence by big data and um and it takes models of theories or or um or intuition often at the beginning to try to make sense out of them um I want to talk a little bit about financial models since um I spent I spent the whole second part of my career working on financial models and often using using physics techniques um ah this is this is a little bit polemical but but everybody knows what this is it's a picture of a hedge probably somewhere in England um it comes out of Wikipedia um here's my polemic a hedge is a line of closely spaced shrubs and tree species planted and trained to form a barrier to mark the boundary of an area um what JP Morgan with the with the London Whale recently called a hedge is a collection of securities that aim to protect another collection of securities against changes in value and hedge it's a metaphor what I'm really trying to say is it's a metaphorical use of the word in a different context for something that really does form a boundary to something that you hope will form a boundary but but you shouldn't be misled um value really isn't the same as price um values always determined pretty much by a model different people have different models for value um a financial hedge as I just said is a metaphor and really a very imperfect analogy and although people use the word all the time um a security is kind of a metaphor too when you think about it um it's not really that secure so I want to argue sort of getting ahead of myself don't be fooled by equations in finance they there's nothing wrong with them they look very precise I'm going to talk a little bit later about what's the right attitude to have to them but they don't really describe in an accurate factual way what they aim to describe and you always have to be aware or not not forget that um so okay let me let me talk about models in finance um whoa okay um I said this before I think physics really has in a useful way theories and models and I think there are few people that would disagree with me but but I would argue that finance finance pretty much only has models there's nothing there that's really a description of financial facts except maybe you can't fool all of the people all of the time or something like that but no mathematical statement the Dirac equation really can write down a one-inch equation that really describes to immense accuracy um the behavior of something even if not to infinite accuracy to 12 decimal places um finance has nothing like that um and I believe never will and nevertheless the equations tend to look as though they're usable with that kind of accurate not even that accuracy with even one or two decimal places it's really not true at all um people who come from physics or sometimes that use people who came for nance but never worked with markets tend to think that the point of a model is divination or trying to tell you what's going to happen into the future and that really doesn't work very well in finance as as um as we've seen for the last four years but I think if you work for a few years in markets you sort of get to realize that um and I want to try to explain at least from my point of view the way people seriously use models in finance um so I want to give an example um I come from New York so um there's probably an analogy in London but supposing you um you want to buy a very fancy 12 room penthouse on Park Avenue I don't on a high floor I don't know what the analogy is here maybe somewhere I don't know Belgravia or or Mayfair or somewhere um and and you don't know what to pay for it because there's been a crisis and it hasn't traded very often and so you can't really find a price um and instead all you can do is look say in Battery Park City where Wall Street is hiring and firing employees all the time and so there's a high turnover and you can see what the price of an apartment is every day or every second day so how would you figure out the price of this fancy apartment based on the sale or price of a one-bedroom or studio apartment on Battery Park City um my argument is if I were being rational I would say okay let me try to replicate a 12 bedroom or 12 room apartment on Park Avenue out of more fungible liquid Battery Park City apartments and I could say assuming that price per square foot is a constant which I understand it isn't but as a first approximation it takes me seven and a half Battery Park City apartments to replicate one big penthouse on Park Avenue and so backing out the price per square foot for a Battery Park City apartment I can estimate what the fair price of a of a of a grand apartment is and that's the zeroth order attempt at a model and then I can start to make higher order corrections by taking account of the number of staff that you have in the building the school location the views etc etc the appliances and then you become aware um then you become aware that actually price per square foot it's sort of a model it's not really the price per square foot because there are many other things in the apartment that have value from location to appliances to school district but if you insist on quoting everything in terms of price per square foot then it gives you a zeroth order way to try to extrapolate to something from something liquid to something illiquid and then you have to make higher order corrections um and I think that's what most models that that's a corny example but that's what most models do in finance um they take something you can intuitively think about in a linear sense like the price per square foot you pay for something and that you transform that into the value via model of something that's um that you would have a harder time estimating the amount of dollars or pounds or euros you should pay for it so models are really used to move from liquid fungible things to estimate the value the value but not the price of things that don't have values or whose values you can't easily tell from from the market because I don't trade too often so for example price per square foot to go to apartment price um with bonds um you can look at a lot of different bonds and they have different maturities and different issuers and different coupons and you don't know where value lies but if somebody tells you the yield to maturity of the bond that becomes something like price per square foot that tells you what value you're getting if you hold it to maturity similarly with options I mean the black souls model you can take something fairly sophisticated which was very sophisticated in 1973 but now is is everyday knowledge as people get get more numerate and smarter you can take an estimate of future volatility of stock prices and use that to calculate an option price by comparing the option in the black souls model to making to to to replicating it out of a liquid stock and a liquid bond and you know the price of a stock you know the price of a bond black souls tells you via equations how to create it gives you a recipe for creating an option out of a stock and a bond and the one unknown is the volatility and if you have an estimate for volatility which you can think about as you get smart and watch markets and get some experience for volatility under different circumstances you can come up with an estimate of the option price but it is a model it's based on diffusion um so the point I want to make about models is mostly people don't use them to predict the future they use them to interpolate from liquid prices to illiquid ones from it's always a relative thing rather than an absolute thing um maybe I will say there's some in in in physics some if you shoot a rocket to the moon you start now and and um Newton's laws or general relativity if you if you more careful tells you um how the rocket is going to move and how to make it link up with something else in space um so in in physics you really start now and work your way into the future in finance you mostly don't you're always working in the present you start with a bunch of liquid things today and you say if the model is right what must the future be like to make this thing have the price that the model says so for example you say um here's the price of a bond what must yields be like what must interest rates be in the future to make this bond fairly priced and then you calibrate the future you don't predict the future you calibrate it to something that you know and then you say okay now if that's a fair price for the bond then that's what the world expects interest rates to be and now I can use those future interest rates to price something more complicated that I don't have a price for so um you're not really predicting the future you're calibrating the future to the present and then using it to to calculate the value of something else in the present if you want to calculate the value of that thing in the future so it's like what I did with the apartment you say if if battery park city apartments are fairly priced then the fair price per square foot must be a thousand dollars a square foot now let me figure out what something I don't know is based on that um and then models are very powerful sales tools although they're based on mathematics they used to tell you this option has a higher volatility than that one this bond has a higher yield to maturity this credit default swap has a has a higher implied default rate than that one and they let you rank order um complicated things on a linear scale and give people who are dying for information or for or for an opinion some kind of idea of what the model tells you is rich or cheap and what to buy or what to sell and um and they're not really predicting the future but they're telling you what the fair price is and hoping that in the future things will evolve towards their fair price not by dynamics but by not by detailed dynamics but by market forces um have I still got like 10 minutes okay so um I want to talk a little about laws of financial modeling there's a very nice let me go back there's a very nice statement um which I don't agree with but it's very funny by Andy Lowe who's a professor at um at um at MIT um who said in physics there three laws that explain 99 percent of the phenomenon in finance and 99 laws that explain 3 percent of the phenomena and it's kind of a good line and I always laugh but I actually I've decided it's not really true I think in finance there's really only one law that works um and that is this one if you want to know the value of more or less alluded to this if you want to know the value of some target financial security whose price you don't know use the known price of another replicating portfolio of securities that's as similar to it as possible so in the case of the park avenue apartment you replicated out of simpler things like battery park city apartments that was the target battery park city ones or the replicating ones um this has a more precise precise statement in finance it's called the law of one price that says any two securities with identical future payoffs and this is the key part really no matter how the future turns out should have identical current prices so um that's that's the one law that doesn't always work but but the one law that people use most of the time and you have to use that to build models and the way people build most financial models is by using that by using the the top the top bullet point there so first of all you have to do two things you have to first of all specify what you mean by saying no matter how the future turns out you have to write down all the possible scenarios the stochastic differential equation or the Monte Carlo scenarios that you mean by the future and that's kind of the science part of all of the model building can you describe accurately what the not what the future is going to be but what the range of futures are going to be stochastically can you even do that and then once you've done that you then have to show that under all of those scenarios the thing you're interested in has the same payoff meaning dollars or pounds in every scenario in the future as the replicating thing that you put together so with the rents on all the battery park city apartments collectively be the same under all circumstances as the rent on the on the park avenue apartment in the future and that's the constructive engineering part the trouble is if you do this in mechanical engineering you have newton underlying the engineering the science part if you do it in electrical engineering you have maxill underlying your electrical engineering and quantum mechanics i'm not quite sure what you have underneath the financial engineering part you do have brownie in motion and more advanced theories but none of them really have anything like the accuracy even to zero decimal places of the theories that you use in other kinds of engineering so i think financial engineering is a good term but you can build electrical and mechanical devices that behave in predictable ways you can't really build financial devices that behave in predictable ways it's a little bit actually i once 30 or 40 years ago saw this movie called bedazzled with them with peter cook and dudley moore which i'm sure people in america don't know but everybody knows here and i sort of when i was taking my qualifying exams the night before in physics and it's a story of fast um said in a one piece in london where where um where dudley moore um dudley moore is a short order cook who's in love with the waitress who doesn't have one or anything to do with him and peter cook is the devil and asks him and he agrees dudley the short order cook agrees to sell his soul to the devil in exchange for seven chances to seduce the waitress and he does it quite willingly and then he gets to pick his scenarios and he picks the first one he says i want to be her to be in love with me and both of us to be somewhere in the castle and wealthy and and both of us be in love with each other and the devil snaps his fingers and they're in a castle in oxford chair somewhere and they're in love with each other but they married to different people and and and she has great scruples and so it goes for all seven the last one he actually says um he frustrating he says he just wants to be um he just wants to be in a quiet place when everyone disturbed them and they both end up being nuns in a trappist monastery so um and that's kind of the trouble with with trying to write down the financial science is that things always happen that you can't write down in one stochastic differential equation that will describe all the things that will happen because they're people reacting if somebody does come up with a correct theory which people lately have um physics like models of them of earthquake like models which sound quite interesting about the way markets behave but presumably if people start using them and people start introspecting the planets don't really care what you say about them but but markets actually do and if you start announcing that there's a forthcoming crisis people's behavior will change so very difficult um yeah i said brandy and motion is a theory for dust particles it's really only a model for stock prices so if i've got five minutes i'm going to say a little bit about the right way to use valuation models i think you have to use replication um i don't want to get too technical but the the various kinds of replication the simplest is static where you don't do anything at all you replicate it's like the apartments you make a a big apartment out of small apartments there's dynamic replication where you have to do something every day to rebalance your portfolio to replicate something complicated and that's what happens with black and shoulders and that's much riskier and much more model dependent um there's been a tendency for the last 20 years in my lifetime in in finance to to make um to make finance more and more axiomatic and there's something called the fundamental theorem of finance um which i'm not quite sure what it is actually but um but um it's roughly related to one of those to the law that i sat down but there's been a tendency i remember when i was in physics somebody once wrote a textbook on trying to teach electrodynamics by writing down for those of you in physics d mu f mu nu equals j nu and just writing down maxles equations and deriving all the consequences and that's a great way to maybe teach a second or third course but it seems to me a really lousy way to teach the first course for you want to talk about currents and and things that people can actually have a visceral feel for and unfortunately finance has gotten a lot more axiomatic where people try to write down axioms and derive the theorems but the truth is the world doesn't really satisfy any of them so it's it's a very unfortunate way to to teach without intuition um there's also another difference in physics it really does somehow pay and work to drop down deep and write down the principle of least action or hamilton's equations or newton's laws or the dirac equation um use very fundamental variables that don't seem to be related to anything you can observe in the world at all and formulate a principle and then come back up again and discover that you can write down the dirac equation here and and discover a positron over there and who would have believed it that doesn't really work very well in finance i think deep it's tempting to be deep and there's no harm in being deep but shallow often works much better and um it's kind of a lot of people in markets actually use fairly vulgar variables vulgar meaning using parameters that aren't deep ones but are ones that everybody uses every day that aren't quite accurate but describe the market and find that the shortest path to get a good price is to go from here to there rather than to go down to something very deep and come up again the deep stuff is interesting but but you're unlikely to write down the right equation for the way the world behaves um so i said sweep dirt under the rug when you build a model but make sure that people understand that you're sweeping dirt under the rug and what you're ignoring um i'll actually like to think a lot of models as gedunkin experiments in physics where you making a lot of imaginary experiments in imaginary worlds and um they're interesting as possible rational behaviors but the real world isn't going to correspond for a long time to any one of them and whenever you do one of these things you have to remember to look over your shoulder because it's going to be violated sooner or later um okay um yeah i'm gonna jump through this but paul walmott and i once tried to ape the communist revolution the communist manifesto about five years ago um he's a british applied mathematician finance guy um because a lot of people blame financial financial engineers for the for the crash and um a little bit unfairly i think and they backed off at the beginning they said it's all models that caused the problem later on when they got smarter including paul valker who shamed his grandson financial engineer in public um by saying um he had an interesting article in which he's he's grandson said i'm not responsible i was just doing what i was told and paul valker said i will not accept the the nuremberg excuse um which i thought was a little extreme um but never so i honestly think the financial crisis came more from from macro issues like keeping interest rates low whenever there was a crisis and stimulating the economy ceaselessly um plus a bunch of other things too many to too too many for anybody to eat well hard to even describe but but i wouldn't say financial modelers were were um were blameless either but i think they were more a tool for people trying to build securities that would give high yield in a low yield environment and using models to sell things as i described before then an actual cause of the situation as paul krugman later pointed out spain had a big financial crisis too and there were no models involved there was just an immense immense bubble in the mortgage market and the islandic banks collapsed for no reasons other than over leveraging themselves nothing to do with nothing to do with anything mathematical so um i wouldn't belabor this but we were trying to say that if you build models you you have to remember that you're um that you're um that you're using mathematics but that the mathematics isn't going to work at some point and um you should remember that they may have great consequences that um that you can't even apprehend when you build them and you want to give people a very accurate idea about their about their limitations so i'm going to finish up i don't think the solution to our financial crisis still ongoing is going to lie in mathematics i'm not saying one shouldn't try to build better models but the problem isn't really there isn't some mathematical solution or equation or risk measure that's going to capture all the immensely complicated things that people can do once they know about it um there's a line by william blake that's if a fool would persist in his folly he would become wise and i think that's kind of a good way to use models in finance in that um you take a model um you take a model like the black shoal's model you know it's not quite right um you'd be a little bit foolish in trying to push it as far as you can and seeing like a liquid drop model you push it as far as you can to see what you can get out of it that's useful but you've always got to look over your shoulder and remember that at some point it's going to break down because it's only an analogy it's not a fact so be foolish but but be careful um so a little hubris in using models in finance is kind of good but um catastrophes strike when your hubris goes one step too far into idolatry and you start to think that what you've written down is actually a really accurate description of markets and people and behavior and you've always got to be somewhere between these two extremes a little bit north of hubris but be careful to stay south of idolatry i'm i'm happy to end there thank you is there any way of assessing the uncertainty associated with things like the psychology of people involved uh the temperature of the day things which are uh that's virtually random elements but at least can you assess how much that would affect any mathematical description or are they simply too large i'm sorry caution this on on using mathematical description and believing into it but do you have any assessment of of the of the factors which are outside the mathematics but which affect the real world yeah um that's a good question i'm not quite sure there are always i mean smart people who use these models like smart traders who use these models like black souls for example which really only has one parameter going into it and that's you have to guess what the volatility in the future will be and everything else is known in the model interest rates stock prices um so there's obviously more things that affect option prices than that and what smart people do is try to um the model is kind of robust in the sense that if you think that transaction costs for example which the model ignores you can try to say okay my estimate of transaction cost is that you should raise the volatility by one point effectively or about two points or we're about to enter an illiquid period because people are scared so you should have a bit as spread that's three vol points instead of one vol point so yes people i mean good models allow you to to take account of um things you can understand qualitatively and embed them in one parameter am i am i answering you more or less no okay about temperature um if you look there are a lot of articles in behavioral finance which is which is a big craze for the last few years sort of um not really a discipline but more picking a part of all the of all the assumptions that um i would argue not really a discipline but a picking a part of all the mistakes that people make by assuming that people behave rationally but but um they go in for a lot of data mining and i actually like to look at it you occasionally see articles that claim yes um countries that um lost in the world cup their stock markets do worse the next day and um and um people do worse in winter than in summer and temperature i have no idea whether those things are true they sound kind of implausible to me but but people look at those things models that are um sort of complex non-linear models non-linear systems like climate modeling or biological modeling yeah that's a great question and i should have said something about that there are a bunch of people actually um i think they still models they're not theories but there are a bunch of people who actually call themselves iconophysicists um and then they joke that icono doesn't mean cheap um um and one of them is there's there's a man called Eugene Stanley who's a solid state physicist in Boston University and there's another man called Don Farmer who's actually i think at Cambridge now used to be at Santa Fe and that's just a number of them there are a lot and they all build sort of more like statistical mechanics solid state models you know with um maybe i'm i'm i'm stretchable with the possibility of phase transitions and collective behavior um and those are very interesting i think they're still models they they sort of you know they they simplify the world but they they try numerically to look at the effect of collective effects and contagion like phase transitions and those are really interesting and and related more to like macro effects you know where where um where crises spill over from one market to another or across markets and they the people looking at um sort of network analyses um of the links between all the people that borrow money you know all the institutions that borrow money in the world and how they will affect each other if one of them defaults and how it will propagate oh oh just come on you have to shout or get away for the mic i've often been struck about um the lack of data in finance and i sometimes think that if all the big data buried in the archives of different institutions could be unearthed that we might learn a lot from it um do you think that there is merit in that that we might actually be able to go a little deeper with some validity if we if we knew more yeah i do i'm i'm she's asking whether there's merit in collecting data i i think there isn't the people i was just mentioning in econophysics and they look very carefully at lots of data on a very small timescale to do with um the impact of trading on a market like if you if you sell a hundred shares how much will the market move in response and and on a small timescale they collect you know terabytes of data for for this and try to try to build them market impact models i think it's good i think it's good for that i'm a little skeptical about things like black souls are looking at models that that whose testing requires um you know two or three or four years of data because the world just changes a lot over several years and and financial well financial markets seem to go into different regimes where once upon a time you know the price of gold was important for interest rates then oil became important so things things change too fast to get to to test the model people people actually test models very very little in finance it's sort of shocking but people use them if they give them a good way of thinking a good way of estimating more than testing them against data and the and the future implied data usually turns out not to be true in any case say it again the implied data the future data tends not to be true in actuality yes yes she's saying what what most people do is i said this a little bit it's like um what what what people actually mostly do with models is look at a liquid price in the market of something complicated say if the model is right it has to fit it and then they say therefore the model implies that in the future volatility will be 20 per cent per year and so the model if you believe all that matters is volatility the price is telling you that in the future volatility it better be 20 if that price is fair and usually that doesn't turn out to be the case so every day people recalibrate their model and everybody in finance longs for a model that's stationary and time invariant the way newtons laws are and they criticize everybody who doesn't have one but actually nobody has one it's a fair aspiration but but but not possible yet ever thank you um it all seems to be a bit one way at the moment that is that concepts and techniques developed in physics are being taken into the financial world have you seen anything that could possibly go in the other direction from the financial world to the to the to the scientific world where is the speaker sorry oh okay from the financial world to the yes um well that's sleep metaphor something we might actually use going from going from finance to um you know it's a good question i'm not sure i mean for psychology yes because because financial markets are one of the few places where you can see honest answers to to questions because people in the input their money where their thoughts are no matter what they say and so i think there's a lot of interesting um behavioral finance related to what people actually do as opposed to what they say they what they say they do so i think it's a good field for for looking at um looking at for for looking at psychology and behavioral psychology um what there's been a tendency for people the other way to start saying physics is no good let's look at biology as a as a model for for for markets it's sort of a sorry okay um but i think it's more wishful thinking nobody's really done that done that convincingly but you see people say they have you know sort of evolutionary models or or biological i quite like the little hubris is good i think sometimes i like i quite like a little hubris is good sometimes we're a little bit too cautious i think yeah i i believe it if you if you otherwise you would just throw up your hands at the beginning and do nothing um what's your view of the difference between using data and doing experiments which seems to me one of the crucial differences between modelers and physicists between big data and doing experiments big data doesn't work no no it doesn't you say what's the difference what's your view of the difference um i think you put your finger i mean big data you you can't control in most cases you can't control the experimental conditions all you can do is is look at what happened and and it's a bit like doing cosmology in a way um you know you you've only got one history to look through although although i know people maybe not so much for finance but i know people who work on websites most most of it's advertising related unfortunately um but people who who who put up websites and change websites a little bit and immediately try to test i mean really in an experimental way what effect that has on people clicking on it and then experimentally see which you know which one works best um so but but yeah for the most part um it's looking at the past rather than trying to change conditions better go on it's a bit different but i just wanted to ask which did you find in your career more satisfying doing physics or doing finance you know no um i was very sad when i left physics i left physics for sort of i don't want to call force of circumstance in that i i i was a postdoc for seven years i was a phd student for seven years which was really bad um and um and i really i felt like i felt like i committed treason when i left physics it was like awful and and and some people treated me like i committed treason too um and so i was very sad to leave um but i'm not sorry in retrospect it was kind of a lonely life in physics you feel like if um if you're not fine when you're nobody a little bit and and um and in finance um if you're not a genius it's kind of a in some sense i don't know maybe this is just the generation i grew up in where everybody sort of uh i sort of once joked in a book that i wrote i said i thought about like wanting to be einstein and then i wanted to be boar and then i wanted to be um tidily and finally i was just jealous when the guy in the office next door to me got invited to give a seminar somewhere where i didn't um so my my aspirations came down came down slowly and fast slowly and painfully um but um but but maybe that was just me but but what was nice about finance and working on wall street for a long time was that it was a very nice mix of applied and and and pure so you were actually building models but at the same time you were in some sense helping people there were people who were interested in your results you were doing computer programming you were talking to clients you were talking to traders it was kind of it was kind of a fairly rich rich life from a social point of view and um it was a bit of a relief after sitting in an office and sort of struggling and getting depressed sometimes and if you got a good idea early in the day you would say i'm going to go home because i don't want to find out whether it fails today i'll leave that till tomorrow and on that note i think we'll draw things for a temporary conclusion that that's the minute for a really stimulating and wonderful thought thank you very much thank you very much thank you so do join this time that's