One Price To Rule Them All

Models. Behaving. Badly: Why Confusing Illusion With Reality Can Lead to Disaster, On Wall Street, And In Life by Emanuel Derman

"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."

The idea that the theories of physics are qualitatively different from the models of finance has been one of the longest running themes on the Psy-Fi Blog – all the way back to this post on Newton’s Financial Crisis. Now the polymathic ex-theoretical physicist, ex-quant for Goldman Sachs, Emanuel Derman, has written a book on this very subject; and very unusual it is too.

Being Derman this is no ordinary description of the problem, but one that roams widely across the realms of science, philosophy, autobiography and finance. At the heart of the discussion is a key idea, that the Law of One Price is a basis for most securities valuations and works not because it’s a deep law of nature but because it’s a simple rule of thumb that can’t be misused in any meaningful way.

Metaphors, Models and Theories

Models. Behaving. Badly. is a fuller exposition of an earlier paper, Metaphors, Models and Theories: if you enjoy or are simply intrigued by the essay then you’ll find much more in the book, at greater length and in greater depth. However, the structure of the argument is already visible in the earlier work and is simply stated in the summary:

“Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.”

Physics deals with theories, finance with models and failing to understand the difference has led to a lot of money being lost, along with a great deal of human misery. As Derman points out, a weather model is an attempt to model something which is abstract – the “weather” – by focusing on a few relatively important features, which will inevitably lead to errors in the long run due to simplifications of the model. An economic model is similar, but the abstractions with which it deals with – “markets” and “economies” – are even less real than “weather”. These are artefacts of the human mind, not attributes of the real world.

Dirac's Models and Newton's Intuition

Theories in physics aren’t metaphors or models, they’re the real thing. When we describe the physics of the atom using Dirac’s equations this is not an abstraction, but an actual description of the world as it is. The best theories minimize the gap between the idea and the real thing. Derman dwells on Dirac’s equations because they symbolises how this works – they explained the known physics of the electron by synthesising quantum mechanics and special relativity but also predicted the existence of an unknown particle – the positively charged electron, the positron, which was eventually discovered by accident by Carl Anderson, much to the surprise of Dirac's sceptical contemporaries.

The example of Dirac also exemplifies another idea that Derman strives to get across: that the creation of a theory requires intuition, which lies beyond mere thought and cleverness. To get this across he quotes John Maynard Keynes' speech on the tercentenary of Isaac Newton:

“I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary - 'so happy in his conjectures', said De Morgan, 'as to seem to know more than he could possibly have any means of proving'.”

Newton figured out his theories by intuition, and then figured out how to describe them afterwards, and the occult figured largely in his thinking.  As this paper points out, there aren't really seven colors in the rainbow, Newton made this up to fit his mystical beliefs: intuition comes from many sources, and theory is the final, dressed version.  Yet while theories in physics require intuition to derive them and, when correct, are indistinguishable from reality, models in finance are derived from metaphors and often only bear a tenuous connection to the real world. Theories are deep and can be relied on, models are shallow and need to be used with caution.

One Price To Rule Them All

In the later part of the book Derman moves into a description of how to use the Law of One Price to figure out the value of an asset. The Law states that in an efficient market all identical goods must have the same price – this should be a natural extension of the effect of competition. Unfortunately sellers often go to great lengths to make direct comparison very difficult, as we saw in Finance: Where the Law of One Price Doesn’t Apply. 

However, Derman shows that you can use the Law to estimate the value of an asset from similar assets and then proceeds to develop the ideas of the Black-Scholes option pricing model, the Efficient Market Model (née Hypothesis) and the Capital Asset Pricing Model (CAPM) from this core intuition. It’s fascinating to see this derivation, from a basic intuition about the way pricing models should work.  Underlying this is the key point is that using the Law of One Price means that you can dispense with the evil ghost in the machine that dogs economic models:

“The wonderful thing about this law – it’s valuation by analogy – when compared with almost everything else in economics, is that it dispenses with utility functions, the unobservable hidden variable whose ghostly presence permeates most of faux-quantitative economic theory.”

Rules and Risk

The critical thing about financial models is to use them in a sensible way, and certainly not as the equivalent of the detailed theories of electromagnetism or Spinoza’s self-contained Theory of the Affects, both of which Derman spends time describing in the book. He lays out a few useful rules for financial model users to bear in mind: keep models simple, don’t hide your assumptions, use them as thought experiments to investigate possible alternative courses of action and don’t confuse models with theories – there are no models in finance that can relieve of us of the burden of thinking for ourselves.

Derman ends the book with a criticism of the failures of the markets and models:

"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.  We were told not to expect reward without risk, gain without the possibility of loss.  Now we have been forced to accept crony capitalism, private profits and socialized losses, and corporate welfare ... When models in the social sciences fail, they fail bluntly, with no hint as to what went wrong and no clue as to what to do next.  With no way forward, people try to restore the status quo at any cost."

If you want an easy read then this ain’t for you, but if you want something that’s thought provoking and intellectually stimulating, that offers an insight into how science has developed and where the most important financial modelling tools were created then you’ll find plenty to interest you. Perhaps, most importantly, this is a book that tells us why financial modellers will always be wrong and why we’ll inevitably be put at risk by idiot financiers who don’t understand the tools they’re using.

Related articles:

• Newton’s Financial Crisis 
• Finance: Where the Law of One Price Doesn’t Apply
• Holes in Black Scholes
• Alpha and Beta: Beware Gift Bearing Greeks
• Utility, The Deus Ex Machina of Economics