You’ll find it hard to build a wheel that’s both completely uniform and completely unpredictable. In fact, no one has ever managed to do it, with roulette or anything else. If no one can build one under controlled conditions, there’s no reason to expect events that are both completely uniform and completely unpredictable to occur naturally.
What Thorp (and many others who have attacked this problem) discovered is that the roulette spin has two phases:
✔ In the first phase, the ball spins around the outer lip of the bowl. This action is highly predictable, you can easily compute when the ball will start spiralling down from the lip and what number will be underneath it when it does.
✔ The second phase starts when the ball begins spiralling downward. The path of the ball becomes hard to predict, due to deflectors built into the wheel and the violent bounces possible when the ball first makes contact with the wheel. But that unpredictability isn’t uniform and you can determine the segment of the wheel where the ball is most likely to end up.
Thus you have a period of predictability in which the result can be calculated, followed by a period of chaos, in which statistical patterns can be found. As you get deeper into this problem, you find phases within phases, but at each level you can segregate the phases into predictable elements to be computed and chaotic elements for which you compile statistics.
For almost any risk of practical importance, a line risk taker, such as a portfolio manager, actuary and credit officer hired to choose which risks to take, automatically handles all the obviously predictable aspects and is well aware of the statistics about the range of outcomes. In order to add value, risk managers have to drill down to a deeper level to find the randomness within the predictability and the predictability within the randomness. It’s always there; you can always find deeper levels than those line risk managers use. Going one level deeper in your analysis is the trademark of a good risk manager.
Most quantitative modelers model situations, including predictable aspects and random ones. But unless they have long experience managing real risk, they never have the obsessive drive to go deep enough in their risk analysis. Moreover, they’re constrained by needing to produce results that are explainable and statistically significant, and that can be achieved at reasonable cost through accepted methods. These handicaps usually make the results worthless for risk management.
But risk management isn’t about making slightly better choices than the front-line risk taker. It’s about drilling down to a deeper level where the real uncertainty resides. The front-line risk taker already manages the risk at the level she understands, and all the preceding levels as well (or if she doesn’t, it’s easy to fix – you don’t need a risk manager to do it – fire her).
This is the big gulf between risk management and most conventional quantitative modelling. If you see people casually assuming something is random and compiling statistics or casually assuming something is predictable and making calculations, you’re not looking at risk managers. Risk managers are sure that they can exploit the wisps of pattern in other people’s randomness and the wisps of noise in other people’s signals. You see them obsessively cleaning data that everyone else thinks are both irrelevant and already clean enough for all practical purposes. At the same time, the risk managers are ignoring what everyone else thinks are the important data.
Getting Scientific with Risk
It’s a little embarrassing philosophically that neither of the two main concepts of randomness actually exists. Dice rolls are determined by physics, not chance. We just pretend they’re random. And, although experts know less about the human mind than about simple physics, you can be confident that people do not have a consistent set of subjective beliefs about any possible eventuality. So Bayesian probabilities don’t really exist either. (See “Betting with Bayes” earlier in this chapter for an explanation of Baynesianism.)
However, in the 350 years since mathematical investigation of probability began, science has uncovered some important kinds of randomness that actually exist in nature. These models have been much more important to the development of risk management than traditional probability and statistics.
Darwinian evolution is defined as random variation and natural selection. It was the random part that was revolutionary when Darwin published On the Origin of Species in 1859. The idea of random selection is what distinguished Darwin’s ideas from earlier theories of evolution and is what upset many religious people at the time.
The main difference between the randomness exploited by evolution and the randomness manufactured in a casino or used to model the uncertainty of an individual is that the mechanism of randomness is created and regulated by evolution. I’m not going to go into the complex theoretical and mathematical meaning of that, but I can illustrate it with three examples.
Stealing from a tiger
Consider the question of what the stock market will do tomorrow. A frequentist pretends that the result will be the draw from some probability distribution, and tries to guess the characteristics of that distribution. She knows that the actual outcome will be the result of a complex interaction of economic news and traders’ reactions, but she considered that too complicated to model in detail. To a Bayesian, the question is, ‘What do I think are the possible moves the market might make and what probability do I assign them?’ The frequentist treats the market like a roulette wheel and tries to guess what numbers will come up with what frequency. The Bayesian treats it as something she’s uncertain about and tries to quantify that uncertainty.
Both attitudes are unwise for someone managing risk. They fail to give the market the respect it deserves. Suppose instead that you think about the stock market as a highly evolved entity. In order to survive, it evolves defences against people guessing what it would do. If people make accurate guesses they can extract money, which comes from other participants who eventually leave the market. The market’s defences don’t have to be perfect – they can allow some people to make some money – but the defences have to be extremely good given the number of smart people devoting great resources to beating the market.
✔ Encourage people to bring information to it
✔ Attract both issuers of securities and investors in securities
✔ Direct economic activity in reasonable ways
If the market fails in any of these tasks, it won’t survive. Of course, many financial markets have failed over the years.
If you think of the market as a roulette wheel, you think that all you have to do is predict its next number with a bit better than random accuracy. If you think that the market is a highly evolved entity threatened by any profits you extract, you think you have to snatch a piece of meat from a tiger. One of the formative events in the career of a risk manager is getting mauled by the market. I don’t mean