By Emanuel Derman

The views expressed are his own.

The great financial crisis has been marked by the failure of models both qualitative and quantitative. During the past two decades the United States has suffered the decline of manufacturing; the ballooning of the financial sector; that sector’s capture of the regulatory system; ceaseless stimulus whenever the economy has wavered; taxpayer-funded bailouts of large capitalist corporations; crony capitalism; private profits and public losses; the redemption of the rich and powerful by the poor and weak; companies that shorted stock for a living being legally protected from the shorting of their own stock; compromised yet unpunished ratings agencies; government policies that tried to cure insolvency by branding it as illiquidity; and, on the quantitative side, the widespread use of obviously poor quantitative security valuation models for the purpose of marketing.

People and models and theories have been behaving badly, and there has been a frantic attempt to prevent loss, to restore the status quo ante at all cost.

For better or worse, humans worry about what’s ahead. Deep inside, everyone recognizes that the purpose of building models and creating theories is divination: foretelling the future, and controlling it.

What makes a model or theory good or bad? In physics it’s fairly easy to tell the crackpots from the experts by the content of their writings, without having to know their academic pedigrees. In finance it’s not easy at all. Sometimes it looks as though anything goes. Anyone who intends to rely on theories or models must first understand how they work and what their limits are. Yet few people have the practical experience to understand those limits or whence they originate. In the wake of the financial crisis naïve extremists want to do away with financial models completely, imagining that humans can proceed on purely empirical grounds. Conversely, naïve idealists pin their faith on the belief that somewhere just offstage there is a model that will capture the nuances of markets, a model that will do away with the need for common sense. The truth is somewhere in between.

Widespread shock at the failure of quantitative models in the mortgage crisis of 2007 results from a misunderstanding of the difference between models and theories. Though their syntax is often similar, their semantics are very different.

Theories are attempts to discover the principles that drive the world; they need confirmation, but no justification for their existence. Theories describe and deal with the world on its own terms and must stand on their own two feet. Models stand on someone else’s feet. They are metaphors that compare the object of their attention to something else that it resembles. Resemblance is always partial, and so models necessarily simplify things and reduce the dimensions of the world. In a nutshell, theories tell you what something is; models tell you merely what something is like.

Intuition is more comprehensive. It unifies the subject with the object, the understander with the understood, the archer with the bow. Intuition isn’t easy to come by, but is the result of arduous struggle.

I wasn’t surprised by the failure of economic models to make accurate forecasts. Any assurance economists pretend to with regard to cause and effect is merely a pose. They whistle in the dark while they write their regressions that ignore the humans behind the equations. I was similarly unsurprised by the failure of financial models. Sensible people don’t forecast with financial models; they use a model to transform one’s forecasts of future parameters into present value. Everyone should understand the difference between a model and reality and no one should be astonished at the inability of one- or two-inch equations to represent the convolutions of people and markets.

What did shock and disturb me was the abandonment of the principle that everyone had paid lip service to: the link between democracy and capitalism.

Capitalism’s problems will not be solved by models. But in the meanwhile, financial models are not going to disappear. Data alone doesn’t tell you anything, it carries no message. Theorizing and modeling are what humans do and will continue to do. So how do we use models wisely and well?

First, one must recognize that there are no genuine theories in finance. In physics, Newton’s laws and Maxwell’s equations are facts of nature, entirely equivalent and identical to the phenomena of mechanics and electromagnetism that they describe. In finance, the Efficient Market Model’s assumption that stock prices behave like smoke diffusing through a room is not even remotely a fact. It is a metaphor, entirely approximate and limited, as are all financial models.

Wise practitioners know that the point of a model in finance is not the same as the point of a model in physics. In physics one wants to predict or control the future. In finance one wants to determine present value and goes about it by forming opinions about the future, about the interest rates or defaults or volatilities or housing prices or prices per square foot that will come to pass. Models are used to interpolate or extrapolate from the current known prices of liquid securities to the estimated values of illiquid securities—relating the unknown value of a Park Avenue penthouse to the known prices of smaller apartments in Battery Park City, for instance, using one’s opinion about the price per square foot.

The Right Way to Use Models

Given the inevitable unreliability of models and the limited truth or likely falseness of the assumptions they’re based on, the best strategy is to use them sparingly and to make as few assumptions as possible when you do. Here are some other observations I’ve found useful in modeling:

Avoid Axiomatization

Axioms and theorems are suitable for mathematics, but finance is concerned with the real world. Every financial axiom is pretty much wrong; the most relevant questions in creating a model are how wrong, and in what way?

Sweep Dirt Under the Rug, but Let Users Know About It

Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister’s foot into Cinderella’s pretty glass slipper. It doesn’t fit without cutting off some essential parts. Financial models, because of their incompleteness, inevitably mask risk. You must start with models, but then overlay them with common sense and experience.

The world of markets never matches the ideal circumstances a model assumes. Whenever one uses a model, one should know exactly what has been assumed in its creation and, equally important, exactly what has been swept out of view. A robust model allows a user to qualitatively adjust for those omissions.

Use Imagination

The perfect axiom or model doesn’t exist, so we have to use imperfect ones intelligently. When someone shows you an economic or financial model that involves mathematics, you should understand that, despite the confident appearance of the equations, what lies beneath is a substrate of great simplification and—only sometimes—great imagination, perhaps even intuition. But you should never forget that even the best financial model can never be truly valid because, despite the fancy mathematics, a model is a toy. No wonder it often breaks down and causes havoc.

Beware of Idolatry

The greatest conceptual danger is idolatry: believing that someone can write down a theory that encapsulates human behavior and thereby free you of the obligation to think for yourself. A model may be entrancing, but no matter how hard you try, you will not be able to breathe life into it. To confuse a model with a theory is to believe that humans obey mathematical rules, and so to invite future disaster. Financial modelers must therefore compromise. They must decide what small part of the financial world is of greatest current interest to them, describe its key features, and then mock up only those features. A successful financial model must have limited scope and must work with simple analogies. In the end you are trying to rank complex objects by projecting them onto a scale with only a few dimensions.

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 model of anything.

Excerpted from Models.Behaving.Badly by Emanuel Derman. Copyright 2011 by Emanuel Derman. Excerpted by permission of Free Press, a division of Simon & Schuster. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.”