mathbabe

This morning I want to talk about Emanuel Derman’s beautifully written and wise new book “Models. Behaving. Badly.”, available in some book stores now and on Amazon starting tomorrow.

It is in some sense an expanded version of this essay he wrote in January 2009 with Paul Wilmott. I particularly like the end of the essay where they present the “Modeler’s Hippocratic Oath”:

• I will remember that I didn’t make the world, and it doesn’t satisfy my equations.
• Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.
• I will never sacrifice reality for elegance without explaining why I have done so.
• Nor will I give the people who use my model false comfort about its accuracy. Instead, I will make explicit its assumptions and oversights.
• I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension.

This was written in direct reaction to the financial crisis of 2008, clearly, but I think data scientists should all be asked to sign at the bottom of the page. As I’ve said before, financial modelers are just data scientists working in the most sophisticated (under some metrics) subfield of data science; just as they have ridiculous powers of profit using their methods, data scientists in other fields have ridiculous powers as well, sometimes in ways that affect people even more directly than money. Modelers absolutely need to be aware of and wary of these powers. This oath is an excellent step towards that.

In the book, Derman sets up a dichotomy between models and theories. For him, theories are stand-alone descriptions of how things are, whereas models are relative descriptions of how things work, by analogy. He also differentiates between the models (and theories) and the way that humans ascribe truth to them, which is to me the most profound and important message of his book. I’ll discuss below.

His examples of theories come mostly from physics: he has a really beautiful explanation of the evolution of the theory of electro-magnetism, for example, which actually explains how people can sometimes develop theories using temporary models. One idea that emerges is that, sometimes, models work out so well that they eventually become part of the theory. The obvious love that Derman has for physics (which he trained in as a young man) shines through this entire part of the book, and it’s beautiful and intimate reading.

Another example Derman gives of a theory was Spinoza’s theory of human emotion, wherein the basic objects were pleasure and pain, and everything was a derivative of those. For example, love is defined as “pleasure associated with an external object,” pity as “pain arising from another’s hurt.” My favorite: to Spinoza, cruelty is “the desire to inflict pain on someone you love.”

To Derman, Spinoza’s theory is a theory, even though it’s not mathematical, and even though it may not be even “true” in the sense that you could just as well have an alternative theory (although it may not be as beautiful). It is a theory, then, because it describes a mini universe of existence without depending on an assumed external frame of reference. It describes emotions themselves rather than comparing them to something else.

What then is a model? It is something that tried to explain (and predict) the behavior of something through analogy or proxy; its accuracy depends on external conditions. He talks about the Black-Scholes option pricing model as a good model in that, in its purest form, it is actually a model for the price of something depending on the abstract concept of “risk”. Then the fact that it can be misused is due more to the fact that people incorrectly proxy risk itself as described by some brownian motion somewhere. With a better model of risk, then, we’d be happy to use Black-Scholes.

Of course Black-Scholes, or rather its use, is not what caused the financial crisis. It was rather the Efficient Market Model and its corollary the Capital Asset Pricing Model that he considers much more dangerous (I agree). He describes these models very clearly, for the uninitiated, and talk about their ubiquitous use in the vocabulary of finance (and how money mangers describe their Sharpe ratios, which is a ratio of their (past) return and their perceived risk, as if they are meaningful statistics).

The basic mistake people make in ascribing power to their financial models, he says, is that they depend on human beings and their actions to be as predictable as physics. Electrons, it turns out, are much more predictable than people with money on the line.

He also goes into a beautiful riff on how there is, but shouldn’t be, a “Fundamental Theorem of Finance.” Not only is it not fundamental (and not even understandable), but there shouldn’t even be such a thing, because it depends on a model which isn’t true, and cannot deserve the name “theorem”, and moreover can only serve as a false sense of security. This kind of mathematical idolatry, he believes, is at the very root of the problem which led us into the financial crisis. Agreed.

Another aspect of the book I want to bring up, because I find it fascinating, is the way we model things in our lives. As Derman correctly points out, we each model our futures; he describes growing up in South Africa during Apartheid and his involvement with a youth Zionist movement, and how he felt pressure to model his life in a very precise way from the youth leaders there, to move to Israel and work as a laborer (examples among many of how sometimes people blithely model other peoples’ lives as well as their own). He then went on to talk about studying physics, moving to finance and his early desire to find a “theory of everything” in finance.

It may be reasonable to say that, until we die, we are on an endless quest for the perfect model for ourselves. In other words, it’s not only that we use models for our internal lives, but we intensely desire models as well – they give us pleasure, they alleviate our worries and stress. We have trouble letting go of our internal models, even when they don’t work (or we even ignore their failure completely; this was described in a recent New York Times article on confidence). When we model the person we love loving us back, it gives us enormous strength and hope. We model our future success: getting tenure, a promotion, or a child. We model our gods.

But our models are not always realistic, and they don’t always account for bad conditions; just look at the Eurozone for one huge example of this. Sometimes our beloved doesn’t care, and sometimes we don’t get tenure.

The most essential question for me then is: how do we react in that moment when we realize our model is bad? Otherwise put, how do we disagree with ourselves? It’s an excruciating moment that we can learn from – do we take away from a moment like that only the pain? Or do we grab hold of it as an opportunity for growth? Can I train myself to be the kind of person who learns from her broken models?

A related question, which I will take up in another post, is whether the people in finance (or mathematics, or data science) are people who react well to their models failing.