What Makes Good Models and How to Use Them: Metaphors, Models & Theories

Executive Summary

Emanuel Derman is a fascinating character. He is currently a professor at Columbia University and he is one of the first high-energy particle physicists (PhD in theoretical physics) to migrate to Wall Street. Previously, he was a Partner at Goldman Sachs and Head of Risk at Prisma Capital Partners. He has authored two books: My Life as a Quant: Reflections on Physics and Finance and Models.Behaving.Badly: Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life.

In this paper, Derman explains the differences between metaphors, models & theories while explaining what makes good models and how to use them. The concepts of this paper are applied to finance and investing, however, contemporary management scholars like Henry Mintzberg have criticized the overuse and misuse of models and theories in business. As Derman ends the paper: “In physics there may one day be a Theory of Everything; in finance and the social sciences [sic. think business, management, economics, etc.], you have to work hard to have a usable Theory of Anything.”

Defining Theories, Models and Metaphors

Theories: Tell us what something is. According to Derman, theories “deal with the world on its own terms, absolutely.”
Models: Tell us what something is partially like. According to Derman, models are “reductions in dimensionality that always simplify and sweep dirt under the rug.”
Metaphors: Models can be compared to Metaphors. Metaphors are relative descriptions that compare it to something similar, but better understood through theories or real life applications.

Models & Metaphors

A model is a metaphor, not the thing itself. Good metaphors compare something we don’t understand, to something we think we do. Based on this, a model is simple and of limited applicability when compared to the real thing as it focuses on some parts rather than the whole. It is a caricature which overemphasizes some features at the expense of others.

Theory

Models are analogies, and always describe something relative to something else. Theories don’t compare and describe the essence. Theories are the real thing, the ultimate non-metaphor. Theories are difficult to find, they require intuition which results from intimate knowledge acquired by careful observation and thorough effort.

Most social science models are metaphors. It is difficult to find the scientific laws or regularities behind these models. Human beings and societies learn, so we can’t do the repeated experiments that building theories require.

What Makes Good Models and How to Use Them

Given that some our best tools are shaky models, the best strategy is to use models as little as possible, and to make as little assumptions as we can.

“Beware of established rules and principles”
Every social sciences rules and principles are pretty much wrong; the practical question to ask is: how wrong, and can we still make use of it?

“Good Models are Vulgar in a Sophisticated Way”
According to Derman, it’s better to use models that have a direct path between observation of similarity and its consequences.

“Sweep Dirt Under The Rug, But Let Users Know About It”
According to Derman, “models inevitably mask as well as expose risk. You must start with models and then overlay them with common sense and experience.”

“Think of Theories as Gedanken Experiments”
It’s good to remember that models are only models, not the thing in itself. We can’t expect them to be truly right. Models are better regarded as a collection of parallel thought universes to explore like the Gedanken experiments that Einstein did when he pictured himself surfing a light wave.

“Beware of Idolatry”
Social sciences modellers must compromise, must firmly decide what small part of the world is of greatest current interest, decide on its key features, and make a mock-up of only those. According to Derman, “a model cannot include everything. If you are interested in everything, you are interested in too much.”

Conclusion

Theories tell us what something is, they are right when they are right. Models require explanation, they tell us only what something is more or less like. When unconsciously used models result in paradoxes or conflicts, it becomes necessary to expose and then examine unconscious assumptions. Unless we constantly remember that therein lies their danger.

A successful social science model must have limited scope and we must work with simple analogies. One should be wary of ambitious theories in social sciences, because we are adaptive species and we can’t model human behaviour like we can do with mathematical rules. We also need to beware of calibration. Fitting a wrong model to the only world we know, and then using it to extrapolate or interpolate is dangerous. The closer the model to the behaviour of the world, the less dangerous the extrapolation.

Read more: Metaphors, Models & Theories by Derman E. (2010) — Social Science Research Network (SSRN)