James Owen Weatherall's Reading List

"Let me begin by touching on Mandelbrot’s role in the history of financial thinking. As I have said, it was in the 1950s and 1960s that Bachelier’s work was rediscovered, that Osborne began introducing new ideas from physics and that Thorp began to get interested in the whole field. There was a flurry of interest in the use of statistics, particularly the idea of randomness in stock markets. The important thing to note here is that you might think that randomness in markets makes markets unpredictable. In fact, it’s the opposite. If markets are random that means that certain kinds of statistical tools are going to be extraordinarily useful. There isn’t extra information on top of the statistics that one could use to gain advantage, if in fact markets are random. So, if you want to price something like an option, where what you care about is the probability of certain events happening, random markets actually make things much more convenient for making the sorts of predictions that you’d like. What Mandelbrot realised early on, at the start of the 1960s, was that the kind of assumptions about statistics that everyone was making were wrong. They just weren’t borne out by the data. He argued there was a much broader class of ways in which a system could be random, including ways of being random in which extreme events, such as market crashes, are much more common. Mandelbrot developed a theory of these sorts of extreme events, and how to do statistics in the presence of the dominance of these events. He showed that the kind of models being constructed were systematically missing the fact that market crashes and huge market gains were going to happen much more often. No-one paid attention to him at the time. His papers were published and anthologised, but the field progressed without him. The Misbehaviour of Markets, which was published in 2004, is, in some sense, his vindication. After being ignored, he left the field and developed lots of fabulous new ideas related to fractal geometry. It was only in the early 1990s, after the 1987 financial crash, that people in mainstream finance began to think there was something wrong with the Black-Scholes model and related ideas. Many saw that the problem was precisely the one Mandelbrot had first identified 30 years earlier. This really points to the way in which the problem isn’t with mathematical modelling and the use of mathematical methodology to understand finance, but with the inattentiveness to certain kinds of assumptions. Mandelbrot was able to figure out the way in which these assumptions were faulty. In this book he very concretely lays out proposals for how we ought to think about the mathematics in light of these sorts of issues and questions. It’s not a very technical book. It’s written for a general audience."

"Samuelson is rightly called the father of modern mathematical economics and this book is its foundations. It was Samuelson’s doctoral dissertation that was turned into a monograph. Samuelson was a student of Edwin Bidwell Wilson, who, when Samuelson met him, was a polymath at the School of Public Health at Harvard, but had previously been a very successful mathematician and engineer. Wilson himself had been a student of J Willard Gibbs, probably the first great American mathematical physicist. He developed much of the modern theory of thermodynamics and was one of the first Americans able to genuinely compete with the greatest European scientists in the nineteenth century. So Samuelson had this direct academic lineage back to Gibbs and what is striking about this book is the extent to which this new economic science that Samuelson was introducing was so strongly in the Gibbsian tradition – it was doing economics the way that Gibbs did thermodynamics and statistical physics. Get the weekly Five Books newsletter The basic idea here is that one can relate certain postulates about how individual atoms – or in Samuelson’s case individual investors and consumers – behave with higher level statistical treatments and even general macroscopic observables. The idea is that one can treat a box of gas in terms of things like its temperature, pressure and volume and derive formulas relating them to one another while ignoring the details of what each individual particle is doing. That one can develop a whole theory of gases, heat and of engines, using those kinds of macroscopic variables was part of Gibbs’ big contribution. These are the ideas that you’ll find in Samuelson’s book – that we can use mathematics in the same way to develop statistical accounts of individual level phenomenon and also develop macroscopic, large scale treatments of things like inflation, GDP and economy wide variables. He saw very clearly that you could treat economies as a whole mathematically and that there was a statistical relationship between economy wide variables and the behaviours of people who make up an economy. What makes it relevant today is that basically it’s where everything in mathematical economics comes from. What’s striking from the point of view of science and markets is that we tend to think that sometime in the 1980s and 1990s, physicists started coming to Wall Street and the City of London introducing new ideas that changed economics and finance. Samuelson’s book makes clear how important statistical physics was at the very beginning of mathematical economics."

"Sornette is another hugely impressive and wide ranging intellect who has contributed to many different areas of physics and economics. The ideas in this book can be traced back to his work on Ariane 4 rockets for the European Space Agency. There was a problem with these rockets when certain pressure tanks would randomly explode and no one could predict when this was going to happen. He developed a theory for how to predict when the explosions would happen. His theory relied on this basic insight: that the explosions were occurring not because of some particularly large effect – it wasn’t that the tanks were being hit by something or gas inside them was applying a large force – rather they were exploding because the tanks themselves were evolving into a state that would make them particularly susceptible to small kinds of effects. This was an idea that Sornette developed in many different contexts. One of the areas it was most productive was, as you say, in trying to predict earthquakes. He suggested that the largest earthquakes weren’t caused by a single large outside effect, such as a large change in the centre of the earth; it was that in certain circumstances the rocks at the surface of the earth were much like the rocket pressure tanks, and evolved into a state where relatively small fractures would get amplified. Sornette then looked to see if the same ideas could be applied to stock markets. Under what circumstances, he asked, do the small ups and downs in stock markets get amplified into major crashes? He argued that the same sorts of considerations were at play in markets as in rocket pressure tanks and earthquakes. The basic idea is a kind of co-ordination – that small effects are going to be amplified when there are correlations between different kinds of investor behaviour. One thing we hear about in connection with finance is ‘group think’ – that it seems at times that entire markets will take certain sorts of assumptions, behave as if they are true and stop questioning them even though the evidence is questionable; there is this co-ordination of investor behaviour based on a belief that something is true. Sornette argues that it’s the analogue of that sort of co-ordination in pressure tanks, earthquakes and financial markets that leads to this amplification process. He develops a whole mathematical theory of how to identify when that sort of condition develops in a market and to using that to predict when an ordinary intraday change is going to potentially get amplified into a market crash or bubble. I think of it as the gold standard of what ideas from mathematics and physics can in principle do. He takes an incredibly difficult problem and applies an entirely novel way of thinking about it and offers concrete mathematical tools coming out of physics to bring that problem under control. I think what Sornette has shown is just how wide ranging methods can be and just how hard the problems that can be tackled are."

"Ed Thorp is a really fascinating guy. He started as a physics graduate student before switching to maths at UCLA, where he developed an interest in gambling and in particular roulette. He thought that basic physics was pretty good at telling you how balls behave on rotating wheels and tried to use it to predict where the balls were going to land. That sounds a bit outlandish, but he believed that you could build a computer to do this and sure enough he did ultimately manage to do that. His interest in roulette took him to Las Vegas, where he also became interested in Blackjack. He realised that there was a source of information that was not being taken into account in the standard Blackjack strategy books, namely card counting. If you pay attention to the cards that have already appeared, he concluded, you can develop a strategy that allows you to reliably beat casinos at Blackjack. He wrote a book called Beat the Dealer, and in some ways Beat the Market is its sequel. After writing about Blackjack, Thorp began looking for other betting scenarios in which the methods he had developed to beat casinos could be used. Financial markets were natural candidates. So, he read as much as he could about statistics and stock markets – including Mandelbrot, Osborne Samuelson and Bachelier – and developed a version of Bachelier’s option pricing formula that he thought would give reliable predictions about the value of an option. Beat the Market really does draw on many of the ideas in his Blackjack book. One of the keys in Beat the Dealer is figuring out how to manage your money. In Blackjack you have to sit there playing at the table, watching how the cards come out; you know when conditions are bad for you and you know when the conditions are good. The question is how much you should bet under those different circumstances, because even if the conditions are good for you there’s a chance you could lose, so you don’t want to bet everything. At the same time, you also want to maximise your profits when things are in your favour. So, he developed a set of tools for thinking about how much to bet under certain circumstances. These tools also play a central role in his stock market strategy. “In 2007/2008 we continued using models that were designed for market conditions that disappeared in 2005.” What’s shocking about this book is how little attention it got when it was first published. Subsequently it has become something all quantitative hedge fund managers have read and Thorp has become something of an idol. These days people are so secretive about their trading strategies and the models they develop. In 1967, Thorp wrote book on how to do it, and almost no-one did anything with it. There was, however, a New York broker dealer called Jay Regan who recognised its importance and suggested to Thorp that they start a hedge fund together, which they did. They consistently made almost 20% a year over a 20-year period which is pretty outstanding. The methods they started with had been in the public domain through Thorp’s book, but no one else recognised their value."

"That is about right. Smolin is a leader in an area of physics called loop quantum gravity, which is an attempt to put together Einstein’s theory of general relativity and quantum mechanics to develop a quantum theory of gravity. Physicists have been working on this for more than 100 years, and they haven’t yet done it. Smolin has his approach to this problem but his is essentially the runner up when it comes to funding and position in the physics community. The more dominant approach is string theory, which has had a lot of attention over the last 30 years. Smolin’s argument in The Trouble with Physics is that string theory is both puzzling and hugely problematic. It’s supposed to be a theory of everything – that’s its aspiration. Smolin’s contention, which is widely agreed upon, is that it hasn’t yet accomplished that goal. There is significant disagreement about how far along that path it has gotten and how successful it’s likely to be, but people have been working on it for 30 years and it hasn’t had the kind of experimental and theoretical successes that one might have hoped for and were promised by the theory’s advocates. Smolin’s point is that given that it hasn’t lived up to its promise, we should be very cautious about it and should be keen to look for alternatives. He argues that the physics community hasn’t done this and that this one approach has continued to dominate despite criticisms. Get the weekly Five Books newsletter The reason I put this book on the list is that Smolin’s basic point is that sociological factors can be an impediment to success in science. His diagnosis about what’s happened in physics is that the string theory community became powerful when there was a lot of initial excitement about the programme, but then became entrenched and self-reinforcing. He argues that people who work on string theory are extraordinarily influential and hold powerful positions in the best universities and are able to dictate what kind of work is most important and interesting, and, in some sense, discourage criticism of that work. I think the same kind of sociological factors that Smolin says have derailed physics, play an even stronger role in economics. Economics is in many ways a political discipline. There are strong vested interests in business and politics that are concerned about how certain problems in economics are solved, and what views get developed. For individual economists, there’s often a lot of money on the line in consulting contracts and this means there’s often more resistance in economics to outside ideas from fields like physics or even heterodox ideas coming from economics itself. If we learnt anything since the 2007/2008 crisis, it’s that the old ways of doing things have gaping holes. But we still aren’t looking to new ideas, or looking beyond the well-worn contours of classical debates in economics, and I think that we should."