The Model as Metaphor
Building financial models is challenging and worthwhile: you need to combine the qualitative and the quantitative, imagination and observation, art and science, all in the service of finding approximate patterns in the behavior of markets and securities.
— The Financial Modelers’ Manifesto
Finance and economics like to present models as scientific, but they are far from science. Economics and finance are not physics, and their use of models is very different from the hard sciences.
In economics and finance, models are efforts to better understand reality. They are not descriptions of reality. Model risk is a very real problem with serious consequences. Much of the sub-prime crisis was the result of model risk. Models are not to be trusted implicitly.
That said, models have real power and tremendous use if you think of them as thought experiments, as ways of putting ideas to paper to see how they hold up under different assumptions and scenarios. A good model helps us understand reality without replicating it in detail. It doesn’t say what reality is; it says what reality is like.
So it is essential to understand any model’s limits and flaws. Here are some rules to guide the use of models in economics and finance:
- The Model is not an Oracle. Models do not reveal deep truths.
- Financial models use math as a means, not an end. If the model is all about the math, it is likely wrong.
- Simple models are best. It isn’t necessary to account for each and every variable. As daVinci said, simplicity is the height of sophistication.
- The model need not capture the complexity of a situation. It is better for the model to be a useful approximation. The perfect is the enemy of the good.
- Variables should be understandable. Outputs should be expressed as ranges and not pinpoint values.
- Models should make it clear what the underlying assumptions are and what has been excluded.
- Models need to be well documented and user friendly.
As Emanuel Derman, who teaches financial engineering at Columbia University, says in his paper, Metaphors, Models, and Theories, “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.”
Yet another metaphor — Art imitating Life:
… In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.
Suárez Miranda, Viajes de varones prudentes, Libro IV, Cap. XLV, Lérida, 1658
Borges, J. L. 1998. On exactitude in science. P. 325, In, Jorge Luis Borges, Collected Fictions (Trans. Hurley, H.) Penguin Books.