How strongly should investors believe in models of financial markets and asset prices? In his contemplative November 2010 paper entitled “Metaphors, Models & Theories”, Emanuel Derman reflects on the tractability of finance in general and the degree to which financial models are useful. Largely by comparison to theorizing and modeling in physics, he observes that:
“Financial models are always models of comparison, of relative value. They are metaphors. …there are no genuine theories in finance because finance is concerned with [highly subjective] value…”
“Calibration is dangerous; it’s always the fitting a wrong model to the only world we know, and then using it to extrapolate or interpolate…a means of translating acquired intuition into dollar values.”
“The one law you can rely on in finance is the law of one price, which roughly put, dictates: ‘If you want to know the value of a financial security, use the known price of another security that’s as similar to it as possible.’ The wonderful thing about this law…is that it dispenses with utility functions…”
“…markets always eventually outwit us. Even if markets are not strictly random, their vagaries are too rich to capture in a few sentences or equations. So die the dreams of financial theories. Only imperfect models remain. …Given that finance’s best tools are shaky models, the best strategy is to use models as little as possible, and to replicate making as little assumptions as you can. …Every financial axiom is pretty much wrong; the practical question is: how wrong, and can you still make use of it?”
“In financial valuation, which lacks deep scientific principles, it’s better to stay shallow and use models that have as direct as possible a path between observation of similarity and its consequences. …the most useful models are…vulgar…, using variables that the crowd uses… Build vulgar models in a sophisticated way. Of course, over time crowds and markets get smarter and the definition of vulgarity changes to encompass increasingly sophisticated concepts.”
“The world of markets doesn’t exactly match the ideal circumstances a model assumes, but a robust model allows a savvy user to qualitatively adjust for those mismatches. A user should know what has been assumed when he uses the model, and he should know exactly what has been swept out of view.”
“The greatest conceptual danger is idolatry, imagining that someone can write down a theory that encapsulates human behavior and relieves you of the difficulty of constant thinking.”
“Financial modelers must therefore compromise, must firmly decide what small part of the financial world is of greatest current interest, decide on its key features, and make a mock-up of only those. …A successful financial model must have limited scope; you must work with simple analogies…”
In summary: “In physics there may one day be a Theory of Everything; in finance and the social sciences, you have to work hard to have a usable Theory of Anything.” Alternatively, scientific enterprise takes every field to the limit of tractability. That’s a short trip for finance (and the other social sciences).
The message for investors is that any edges available are probably small, not highly reliable, linked to common sense (but not obviously) and eventually (soon?) lost to market adaptation.
