We are in a period analogous to the early 1970s, when developments like the Capital Asset Pricing Model and the Black-Scholes equation transformed finance, changing it from an art to a science, and opening enormous new markets in the process. Now, new equations describing “crowd dynamics” are about to change our lives. And not always for the better. This is one of the most significant technology trends I have seen in years; it may also be one of the most pernicious.Particularly if the models don't work.
In more words:
In order to make a mathematical model like Black-Scholes work, you need to make simplifying assumptions. And once you've accepted the models as real and useful, the assumptions, or the fact that they were assumptions, can be forgotten. Witness this clinker in Charles Morris's generally excellent (and highly critical) book on what the self-described "science of finance" has wrought, "The Trillion Dollar Meltdown":
Such arbitrage strategies are usually quite safe. It makes no difference if [relative] bond prices rise or fall, so long as the relative prices of [certain short term bonds] move closer together. Occasionally, they don't, but Black-Scholes tells you those are rare occurrences.In fact, it's an assumption of the Black-Scholes model that there are no arbitrage opportunities. Maybe it's true, maybe it isn't, but either way, Black-Scholes itself has nothing to say about the matter, or the viability of arbitrage in general. (If anything, the "no arbitrage opportunities" assumption may appear true in the real world only because when arbitrage opportunities do arise --- and they do --- a real arb generally comes along to wipe them out.)
And, as I've already mentioned, a similar mistake is at the heart of the mortgage-backed security mess. These securities were rated on the assumption that even in a pool of risky mortgages, you wouldn't see all the loans defaulting, all at once. Mass defaults happened to be the predictable response to a predictable situation --- a rise in interest rates --- but since it wasn't in their model, the raters had an excuse for pretending it just wouldn't happen.
Turn now to Steve Steinberg's blog post on psychohistory, which presents the white hope:
It shows up, for example, in Isaac Asimov’s Foundation Trilogy, the best-selling albeit thinly-plotted space opera, in which protagonist Hari Seldon develops the science of “psychohistory”. According to Seldon, just as physics can predict the mass motion of a gas, even though any individual molecule is unpredictable, psychohistory allows us to predict the future of large groups of people.Reading about it like that, you could almost forget Seldon was fictional. But again, the models are only as good as their assumptions.
Sometimes, those assumptions may be pretty safe. One of Steinberg's sample models concerns the behavior of a crowd trying to get through a narrow doorway. The crowd's motivations are simple, the constraints are largely physical, and the results are probably pretty good.
But in messier situations, things are a lot more tenuous.
Steinberg's very worried about what the largely military sponsors of this research will do with it if it works.
Me, I'm more worried with what happens if it doesn't.
"Yeah, Iraq was a mess. But this situation is different. Our models say so. We have mathematical proof!"