James Weatherall’s book, The Physics of Wall Street
is the subject of this series. It is a brilliantly arrogant book that makes all the classic errors of non-risk-taking quantitative people when first exposed to finance. This week we’ll consider the analogy between roulette wheels and the financial system.
Last week, in Part III, we saw how Ed Thorp and Claude Shannon beat roulette. They started with Ed’s insight that each aspect of roulette wheels is either uniform or unpredictable, but not both at the same time. The non-uniform aspects can be exploited through statistical analysis, the predictable aspects through calculation.
It’s easy to see how this attitude transfers to financial markets. The real economy is enormously complex, which makes assessing the future values of cash flows associated with a real security a difficult problem. This is like the chaotic parts of a roulette spin. However, if financial markets are sufficiently free, liquid, and transparent, there will be strong forces pushing security prices to equilibria where price changes are unpredictable and excess expected return is proportionate to risk, appropriately defined. This is like the precise engineering of a roulette wheel to ensure uniformity. The counterpart to uniformity of a roulette wheel—every number comes up with equal frequency—in financial markets is that every security has precisely the correct risk-adjusted expected return and so there is no way to beat the market.
While market price movements appear random at a macro level, they are really tangles of chaotic processes that are either unpredictable but nonuniform, or uniform and predictable. The former generate exploitable statistical patterns, the latter generate opportunities for taking small amounts of data—often data other people ignore as inconsequential or that require extraordinarily painstaking measurement—and creating useful predictions relying on the precision of the process that generates the uniformity. Roulette wheels are simpler; they have only three steps: chaos-uniform-chaos, which occur in known order and with no overlaps. Market prices combine many threads of each type, chaotic and uniform. Financial engineering resembles disentangling knots by alternately pushing (exploiting statistical patterns until the residual is uniform) and pulling (exploiting uniformity to predict from small measurements).
So while random walk research, the only kind Weatherall recognizes, was historically important, it cannot describe the complexity of modern finance. It’s like trying to beat roulette looking only at the sequence of historical numbers, without measurements of the spins. This can only reveal statistical patterns. It is the financial equivalent of one hand clapping.
This particular description of financial engineering is not accepted universally. There are practitioners who deny the analogy between finance and roulette, and others who analyze it differently. Quant finance is a young field evolving through intellectual natural selection, not an organized body of consensus knowledge. Quants don’t argue much; they believe in demonstration rather than authority. And all would agree that it has been convincingly demonstrated that there is more to financial markets than random walks—and I don’t mean refinements, elaborations, or second-order effects; I mean central elements that are inconsistent with random-walk thinking.
How does Weatherall account for some of these other major ideas in finance, such as the efficient market hypothesis, in which physicists played no part? Easy, he says the efficient market hypothesis is the same thing as the random walk model. Imagine the arrogance it takes to write a book explaining finance to everyone, without bothering to learn the basic principles of the field, and to assume all the research and publishing activity in finance is saying the same thing over and over.
In fact, the ideas aren’t even about the same thing. The random walk model is a statement about the statistical behavior of price changes; the efficient market hypothesis is a statement about their information content. Weatherall discusses how M. F. M. Osborne took logarithms of prices to generate better random walks. Taking a logarithm changes the statistical properties of a variable, so it affects the random walk model, but it does not change the information content, so it is irrelevant to the efficient market hypothesis. On the other hand, if someone told you prices were in euros instead of US dollars, it would change the information content, but not the statistical properties.
The random walk model and the efficient market hypothesis are related, but more as opposites than twins, more yin and yang than Tweedledum and Tweedledee. The random walk model treats prices as divorced from any economic consequence, they are studied as random variables. It’s like studying the distribution of numbers from a roulette wheel, ignoring the physical process that created the numbers. The efficient market hypothesis concerns only the economic information incorporated in prices. It is like modeling the physics of a roulette wheel for which the numbers on the slots have been erased. Neither one alone is much good for practical financial work, but together they are the hammer and anvil of financial engineering.
What about the most famous accomplishment of theoretical finance, the capital asset pricing model? The Physics of Wall Street
says it’s also synonymous with the random walk model. The capital asset pricing model is a statement about the equilibrium relation among future expected returns on securities, and thus is logically and empirically distinct from either the random walk model or the efficient market hypothesis.
This naturally calls to mind a story the great physicist Stephen Hawking tells in A Brief History of Time:
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the Earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!"