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BREAKING THE CYCLE

[EMANUEL DERMAN:] One of the things I've been thinking about a lot, both in relation to the financial crisis and in relation to the way people understand the world in general, is the role of models in the world. There are a variety of different approaches to trying to understand the world, in all its facets, from the physical sciences to the social sciences and even one's personal life. I've categorized them in two ways: I like to distinguish what are called "theories" from "models". Theories, in my view, really try to capture the essence of the world, as in physics in one short equation, or in other fields, in one short schema.

It seems to me you can't really act in the world without having some kind of model or theory of how the world is going to behave in the future.

Models are simpler to describe in that they are similar to metaphors or analogies: you try to understand something that is difficult to comprehend in terms of something else you already comprehend. You try to understand the brain, for example, and you say, well, the brain is a lot like a computer. Or you try to understand a computer, and you assume people understand the brain and then say a computer is a lot like a brain.

In the same way in finance one says stock prices behave a lot like smoke diffusing off the tip of a cigarette . These are models or metaphorical ways of describing the world that add insight but you can't really rely on them very substantially in the long run. I'll give some examples in a little while.

The other extreme is to use theories, which are really ways of directly apprehending the way the world or the universe works: examples are Freud, Einstein and Newton. Of course, theories can be right or wrong, but theories are different from models.

Take the Dirac equation, for example, the most famous and most successful equation in physics. Dirac started out with a theory, produced a metaphor, and then turned it into a theory again, as I said, the most successful one. He began by trying to combine quantum mechanics, which was already a well established theory in late 1925, and relativity, special relativity, which had been around since 1905. The two theories weren't really compatible.

The Schrodinger equation which explains the hydrogen atom and all of chemistry is not relativistically invariant. Dirac, who was a big proponent of beauty, struggled very hard to elegantly unify the two and eventually wrote down one simple, literally one-inch-long equation. When he started to solve it, he discovered that it does miraculously explain the fact that the electron has spin, which was something that was only discovered experimentally after 1925 or 1926. The Dirac equation has four solutions. Two of the solutions described pretty well the electron and the hydrogen atom that everybody knew at that point. But there were two more solutions that have negative energy. Weird.

Nobody could make sense of this for several years after Dirac wrote it down in 1928. Nobody could quite understand what these negative energy electrons really meant. Dirac eventually came up with a pretty metaphorical explanation. He was reluctant to give up on the beauty of the equation and concluded after some struggles that the only way to understand it is to imagine that the entire universe and the whole world and what he calls the vacuum is actually filled up with negative energy electrons that you can't see and you don't sense. Sort of in the way when you're born you don't smell the air even though there is air around you, because it's the familiar background in which you live.

In the same way all the negative energy electrons that you are born into form part of the vacuum and nobody ever detects them under normal conditions. But then he realized that if you were to shoot photons or light into "empty "space, empty space isn't really empty. It's full of these negative energy electrons that you don't normally perceive. You can do a photoelectric effect on the vacuum, on empty space: shoot one photon in and hit an invisible negative energy electron, give it enough energy to make it positive and it becomes visible. 

You will kick out what was formerly a negative energy electron and convert it into one with positive energy which everybody will observe as a normal electron, and what it will leave behind is a hole in the sea of negative energy electrons. This sea is called the Dirac sea. It is a metaphorical description of the way the vacuum works.

Dirac realized that a hole in this negative energy sea is an absence of negative charge and will behave like a positive charge and have exactly the mass of the electron but the opposite charge.

Except for Maxwell's completion of Maxwell's equations for electromagnetic fields, this is the first case where somebody literally plucked an equation out of their head and ended up predicting the existence of a new particle or a new phenomenon, which has been the style template for theoretical physics ever since.

Sure enough in 1931 or 1932, though nobody really believed Dirac, Andersen at UCLA or Caltech discovered the existence of positrons, which are positively charged electrons. All of this is described by Dirac's equation with incredible accuracy, nowadays to about ten significant figures. That to me is a good example of a theory.

Maxwell's equations, which describe electricity and magnetism are another example. What they illustrate about a theory is that nobody thinks light is "like" Maxwell's equations. There is an absolute identity between the way we think about light and the equations that describe it. Nobody says Maxwell's equations are a "model" for light. Maxwell's equations and light are the same thing. The same way with the electron: the Dirac equation and the electron are literally inseparable. That for me is a good example of a theory. I'll give some more soon when I talk about the social sciences.

Let me step aside and talk about the difference between theory and model. I was brought up reading the Torah and going to Hebrew school, and there is the story of Moses and the burning bush. God tells Moses to go to Pharaoh to Let My People Go. Moses doesn't like being sent to do this and he doesn't speak very well and so he runs away into the desert of Midian to evade his responsibility. Eventually he comes across a burning bush and a voice speaks to him from the burning bush and tells him to go to Pharaoh and tell him to free his people.

Moses tries to wriggle out of it and says, who shall I say sent me? The voice from the burning bush says, I am that which I am, which is a sort of pun on the Hebrew word Jehovah for God. I like to think of that as being the example of a theory: God in the story isn't saying "I'm a lot like this" or "I'm a lot like that." I'm absolutely exactly what I am and not like anything else, he says, and that is kind of true of the quality of theories. You're not comparing yourself to anything. You're saying this is the way I behave.

If I can give an example that I have been interested in from a different, more qualitative aspect: I have been reading Spinoza's "Ethics". It's a lot like Freud. He's trying to explain the behavior of human emotions and eventually derives a theory of ethics out of all of this. It's also very astoundingly similar to the theory of derivatives in finance in that he says there are three underliers, which are desire, pain and pleasure. Spinoza's avowedly trying to do a version of Euclid, who defines points and lines and then derive theorems about triangles. So analogously Spinoza defines the primitives, which are pleasure, pain and desire, plus a few others like wonder and contempt, which I'll mention later perhaps, but the three I mentioned are the ones that, even though he defines them, you don't really need him to. Everybody who has lived and who speaks English understands what points and lines are, and so do they understand what pleasure, pain and desire are.

Then he starts to define in a self consistent way all the emotions that people experience as derivatives of pleasure, pain and desire. I actually made a table of them which I could show. I drew a dependency chart. So, for example, he says love is pleasure associated with an external object. Hate is pain associated with an external object. Then he gets to more complex derivatives, which are like convertible bonds: envy is pain at somebody else's pleasure. He doesn't talk about Schadenfreude but clearly Schadenfreude is pleasure at somebody's pain and envy is the other way around. Cruelty, for example, is a triple derivative, a desire to inflict pain, on someone that you love.

In this way he builds up a categorical description of almost every single emotion you can name in the way they relate to the primitives, desire, pleasure and pain.

I like it because : A) it leads to a theory of ethics and B) there is no reference to anything outside of itself. He doesn't say the brain is like a computer. It's totally self contained. In a sense it's a theory of the way things are, not a model of saying this is a lot like something else.

To give the opposite example, let me distinguish everything I've just said about theories from models. Models really depend on analogies. So, for example, in physics, look at the liquid drop model of the nucleus for which Bohr and Mottelson got the Nobel Prize. Bohr is the son, Aage Bohr, of Niels Bohr. The nucleus which really consists of protons and neutrons, say, in uranium, all jammed together very tightly, you can instead approximately think of as a liquid drop, and if you think of all these things jammed tightly together as liquid drop, then the drop can oscillate and can vibrate and can rotate. If you know its mass and you figure out roughly what its elasticity is, you can figure out what the normal modes of vibration are when it oscillates. Bohr and Mottelson end up predicting other excited states of uranium or of heavy nuclei based on this analogy of the drop.

But it really is an analogy, and a limited one. It's not saying the nucleus is a liquid drop. It's saying, in a range of energies if it doesn't break apart, it's a convenient way to think about it. That's very different from something like the Dirac equation where you're writing down an equation and saying, this is the way the world is, this is not an approximate version of the way the world is.

I've been thinking about this a lot in relation to finance because it seems to me true of financial models. The ethics in Spinoza is a theory of psychology and maybe Freud is too, in a self consistent way, but most financial models are metaphors and are based on saying you can picture stock prices as smoke diffusing or as smoke diffusing and jumping. It's not a holistic description. It's just saying that I can understand this if I think about it as much like something else I already understand in another context.

I've become a bit of a Platonist. What I like about Spinoza is that he's unlike most people I know who are monists and like to explain the world mostly in terms of matter. So, they like to say the brain is a computer or love is equivalent to a set of neural currents in your brain.

Spinoza won't give primary power to mind or matter. He believes, even if I say it somewhat clumsily, that there is a mind side to everything and there is a physical side to everything. Neither the physical side causes the mental side nor the mental side causes the physical side but they live in parallel to each other. I like that approach; it seems to agree with my experience of the world.

It doesn't explain much about the things that matter to you as a human being to say they happen because of circuits in your brain. I'm not saying that circuits don't fire in your brain, but it doesn't give you a way of dealing with it other than a very mechanical and uninsightful sort of way.

What I like about Spinoza's theory of emotions is that he tries to deal with everything in human terms, in a self-contained sort of way. That's not to say that there isn't an electronic and chemical correlate to love or envy or that there isn't something pounding in your heart when you're anxious. But that's not the part that matters when you're trying to deal with it as a human being.

My background plays a role in my interest in these ideas. I'm originally from South Africa and when I was in high school I liked literature and writing as well as science. Then, as I was good at science and I liked it, I eventually gravitated into that and I gave up writing, but in my heart I liked philosophy and literature.

I started out in physics and graduated from Columbia in 1973. Then I was a post-doc and assistant professor doing theoretical particle physics for seven years. Then at some point the difficulty of getting jobs in cities I wanted to be in got to be too much for me and I took a job at Bell Labs, which in 1980 was the canonical way out of academic life for physicists. What Wall Street is to physicists today, Bell Labs and the Solar Energy Research Institute and places like that were for physicists - telecommunications or energy research as a result of the energy crisis of the late Seventies.

I took a job at Bell Labs not in basic research but in a Business Analysis Systems Center, which literally was a bunch of ex-rocket scientists who had worked for Bell Labs on some of the moon shots. They were running a business analysis center to try and retrain themselves. I spent five years there in the sort of middle ground between academic life and real industry. I didn't like it very much, to tell the truth, because it was never quite clear what your aim was. They wanted you to write papers but you couldn't publish them and they were always secret in some sense. Whether something was a success or failure often just depended on whether your boss said he liked it or he didn't. A lot of it didn't see the outside world. I spent five years there learning a lot, nevertheless.

What I really learned, which was most useful for me coming to Wall Street in 1985, was computer science, computer science from a point of view of doing symbolic programming and building programs that people could actually use, little languages to model their own needs. I built a language there which we called HEQS, which stood for hierarchical equation solver. This was before the days of spreadsheets and analysts had to solve big financial models, but the people who created the models couldn't actually do the math to solve them, and my language gave them a way of them describing the model and then letting the computer provide the solution. I spent five years doing this kind of stuff. I learned a little bit about option theory but not much. I didn't like the management culture. I still wanted to be a person who worked with his hands, and everybody there, except in the research area, was aspiring to get into management.

Eventually Wall Street came knocking at the door, as a result I believe of rising interest rates in the late '70s. Wall Street suddenly started having a lot more trouble managing their inventory when interest rates became a risky business. They were hiring more and more computer people and applied mathematicians, physicists. I took a job at Goldman Sachs in late 1985. I wasn't quite the first of the people who went from physics to finance or the first of the quants, but I was among the early group. It was very exciting because Goldman was small in those days, maybe 5,000 people. A few years earlier it had probably only been 2,000 people. So you got to know everybody and see them in the cafeteria and it was intimate in a good way.

There was a very close linkage between people who were doing technical work and people who were trading or doing sales. There weren't a lot of barriers to dealing with different people. It was a place that valued you if you had a skill, no matter what it was, if you were a good lawyer or if you were a good computer programmer. They might treat you as a geek if you were more of a scientist than a businessman or an MBA or a lawyer. Nevertheless they needed what you had and they respected it. So I really enjoyed working there. For me it was a shot in the arm after being at Bell Labs and having felt like I had quit physics. I suddenly got excited again about doing something new.

In terms of how physics figured into Wall Street at that point, I was among the first physicists there. I don't know if I was literally the first, but I was certainly among the first few, although there had been three of four engineering people in the group I was in who had been there a few years longer.

It was kind of a natural match for physicists because first of all options and interest rates were becoming big in terms of sales and marketing and hence valuation and hedging were necessary. Most of the models that had been developed in the financial world for treating the risk of bonds or the risk of options or valuing options were all essentially diffusion models, related to diffusion of heat in classical physics. Physicists spend their life doing this kind of stuff, so even if they didn't know much finance, it was very easy. In fact, when I came, the guy I worked for said to me, read this paper by Cox, Ross and Rubinstein over the weekend and then start trying to fix this program that I wrote for valuing options which seems to have some problem for bond options rather than stock options. I literally spent the week reading this paper and learned economics out of it.

Now Wall Street is much more sophisticated. The hurdle is higher. You really have to know something before you start. But in those days it was enough just to be a reasonably smart person who was willing to learn. So I leapt into it. There weren't a lot of textbooks. It was very exciting to be in a field where there wasn't much traditional stuff to learn and to study.

Although it was economics, the mathematics was very similar to that of physics, and physicists are kind of jack of all trades in that they can do modeling, they can do mathematics, they can do numerical analysis and they had to do their own programming pretty much. They were not like business people who needed somebody they could give the programming to.

To build a model of options — there are a lot of little things that can go wrong. If there is a gap between the person who understands the model and the person who does the implementation, then a lot of little things can go wrong which you have an incredibly hard time rooting out because the person who understands the theory can't implement it and the person who understands the implementation can't understand what might be wrong when you get some mistake.

So I liked being the person who spans both sides of their bridge. In the culture I worked in, everybody did their own programming. When I ran groups for the next 15 years at Goldman, it was pretty much like that too. The physicists or the computer scientists– it was mostly the physicists — knew enough programming to do their own dirty work. In my case I actually built interactive screen interfaces for traders. I had learned how to do this at Bell Labs. It was a good way to work. It was good for a physicist in that you got to span many different areas. If you were the person who actually built the model as well, it gave you a great deal of close contact with the traders. They used it and you were the guy who controlled their access to it. It was really a perfect job.

It was a very interesting non-management, non-managerial culture, unlike Bell Labs. It was in many ways much like a university research department where I worked, except it was a business. I would say the fixed income bond options group that I worked for when I started was more like a hedge fund in terms of culture. There were a few smart traders, some smart sales people, and then our group that supported them. We all spoke every day and worked pretty closely. You didn't need a lot of managerial permission to start some project. Everything was a little bit fly by the seat of your pants. You would talk to somebody and then go off and do something. That was what I liked about the culture, and what I didn't like towards the end of my time on Wall Street was that you could spend more time asking for permission to do something than it actually took to do it, when it became more managerially oriented.

In terms of what physicists brought to Wall Street — really good pragmatic modeling skills. The difference between being an economist and being a physicist is that most economists have never really seen a successful model. So they don't know what constitutes a good model and a bad model. They either denigrate models too much or they respect them too much and think they are much better than they are.

Physicists, going back to what I said earlier, know the difference between a really accurate theory and between a more or less pragmatic model and they understand where to make approximations and what not to take too seriously. It's that sort of understanding of how much theory is useful, but not too much, is one of the skills that physicists bring. The second is really a hands-on approach to doing things yourself.

Later on I helped run risk management. There are two levels of risk management in a trading firm. One level is desk by desk, where you're working, say, as I did, on an equity trading desk between 1990-2000. You have thousands of positions and they move around every minute as the market changes, and you want to understand how exposed you are to volatility to the S&P, to various market factors, to interest rates. You want to know that on a daily basis. You care what's going to happen to you every minute because you want to hedge your potential losses.

That's very engaging and very hands-on. What happened in the late '90s, maybe mid-'90s, is people started to tackle what is now called firm-wide risk, which is looking at the risk of the whole enterprise, where you want to understand not so much what will happen to you at any instant, but where the big market risks lie for the firm as a whole. It's a global approach. This is where the whole of the Value-at-Risk culture comes in. That's a much fuzzier business. The difference between "local" and "global" is one of the interesting things in life, in physics and in financial models.

It's interesting in this regard that the three biggest banks recently announced their quarterly results and not only day in the last quarter did they lose money. That is totally astonishing. It's really a reflection of what the administration has done. They've made interest rates very low so it's cheap for the banks to borrow money. They have eliminated a lot of the players, so there is much less competition for taking on risky trades and you can do them at a price that is much more preferable to the person who is in control. This is a risk profile that is a result of regulation and administrative policies rather than of genuine market conditions.

In terms of styles of regulation, I'm very disillusioned by what's happened in terms of the bailout. I don't know what is the right thing to do but one of the worst things for society's ethical sense is to see other people having the upside of risky positions and not suffering the downside. It makes me feel very uncomfortable.

What I also dislike is that firms that have made a lot of money out of this won't acknowledge that they made this money by being saved by the taxpayers and the administration.

There's a lot of talk about the role of algorithms and the change in markets. The financial world has changed a lot since I worked in it and the biggest change is more people are playing with more of other people's money. When most of the banks were partnerships, they had to be in it for the long run because people who were partners were playing with their own capital and taking risk with their own assets. Their money was tied up for 10 or 15 years. Even if somebody retired, they still couldn't take their money out of there. They just got paid interest while it was being used and drawn down. So there was a certain culture of not taking extreme risks because you didn't really have limited liability. Ultimately you could be broken completely by your company going bankrupt. With trading houses going public, they're playing with other people's money. They're immediately liquid in terms of stock and cash payment. The culture in all of these places has changed in that it's make money liquid and fast. The way this crisis has been treated exacerbates that attitude in that if you do badly, the government bails you out and if you do well, you keep the profits. 

I used to hear 10 years ago at Goldman from colleagues that there was going to be doom one day at Fannie Mae and Freddie Mac because they were hedge funds in disguise. To some extent the government and regulators have encouraged this and they still haven't tackled the problems at Fannie Mae and Freddie Mac and are doing with them what they accuse Wall Street banks of doing, which is treating them as off-balance sheet and not counting the money they are spending on them as real money.

In terms of algorithmic trading, that's a big change too. I'm not against it — it's inevitable from a technology point of view. You trade airline tickets with computers. You buy things off the internet. There is no way people are going to trade stocks in vast amounts by making verbal or written orders. Stocks are going to be traded electronically and eventually bonds, currencies and everything else will be traded electronically too.

It's unfair, though, to allow high-frequency traders to get what essentially amounts to insider trading, to getting an early look at trades and deciding what to do because they are allowed to put powerful computers closer to the stock exchange. That doesn't make it a flat playing field.

Also, people who benefit from it tend to over-accentuate the need for efficiency. Everybody who makes money out of something to do with trading tends to say, oh, we're got to do this because it makes the market more efficient. But a lot of the people who provide this so-called liquidity and efficiency are not there when you really need it. It's only liquidity when the world is running smoothly. When the world is running roughly, they can withdraw their liquidity. There is no terrible need to be allowed to trade large amounts in fractions of a second. It's kind of a self-serving argument. Maybe a tax on trading to insert some friction isn't a bad idea, just as long term capital gains are taxed lower than short term gains.

Economics is a strange field. One of the things I noticed on Wall Street was that firms use the economists to talk to clients but their trading desks don't necessarily pay attention to what the economists are saying. Unexpected things happen unexpectedly and damage positions and net worths. I don't think there is a good quantitative solution to all of this. I sometimes get letters from mathematicians in Europe saying that they have come up with a better formula for capturing risk or for valuing risk or for trying to control or measure risk. You can do better than VaR but there isn't one formula, one number, that is going to save you in the end.

More important is incentives and disincentives and making sure that people understand they are going to pay the penalties for their own mistakes and somebody isn't going to bail them out. Jim Grant, who writes a newsletter called "Grant's Interest Rate Observer" that I like, had a column recently pointing out that in Brazil they haven't had a big banking crisis and that there, anybody who runs a trading firm is personally responsible for losses. It's not company risk. It comes down to their own assets. So they are much more cautious about this. Those kinds of incentives are going to make a much bigger difference than finding a better mathematical formula for handing risk.

And the scale at which people get paid has become quite astonishing. There is an increasing gap in America in general between what people make at the bottom and what people make at the top.

When I decided to work on Wall Street, I interviewed in '83. The guy who interviewed me said, this is one of the few jobs where you won't have to be an accountant or a lawyer and you can make $150,000 a year eventually. Now a trader might make $20 million. If they can't make it at an investment bank, they go to a hedge fund, if they have a really good track record.

I have less of a pay problem with hedge funds — I'm not sure if I'm right — from an ethical point of view than I do with very big, too-big-to-fail companies because hedge funds are by and large putting their own money or their clients' money at risk, and it's a clearly articulated compact between them. While there is a possibility of systemic contagion, it's a cleaner business in terms of potential conflicts. They are just doing proprietary trading for their own account or their clients' account.

Whereas, what is confusing about the big investment banks, if you watched the Senate hearings, is that there is a very unclear overlap between being a producer and being a market maker. So Goldman, for example, always used to be pretty much a service provider in the old days. Now they and all the other big banks want to be both a producer and the marketplace on which product trades. There are a many conflicts of interest. To make an analogy, I've read articles about how Amazon wants to be not just a place that sells books but one that also publishes books. That becomes dangerous — if you're a dominant player in both the conduit and the content. There is too much concentrated power. It used to be you were either a market maker or a producer.