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.”

However there are correct theories within the social sciences, economics being the best developed theory so far in the social sciences.

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.

Without a doubt, the physical sciences are different from the social science of finance. Duh. So let’s see what this PhD chappie has to offer.

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.

The physical sciences gain knowledge via empiricism, the social sciences via a priori. The so called ‘law of one price’ is neither: as already referred to by the author, it is a rule of thumb, which means that it is a heuristic, and prone to failure, likely when you need it most.

“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.”

I can live with that. Models allow you to isolate variables in a mental construct, that in reality could never be isolated, and allow you to examine specific facets. They have their uses, but should never be confused with reality.

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.

Physics deals with empirical data, gathered via the scientific method. Finance is a sub-category of economics: economics has valid theory, generated via a priori reasoning. Finance largely ignores the theory, unfortunately, largely because finance is controlled by government via the banking system, in which both are morally corrupt.

As Derman points out, a weather model is an attempt to model something which is abstract – the “weather”

The ‘weather’ is not an abstract, the weather is not an idea, the weather exists, and we experience weather on this planet at all times and places. The weather is generated by physical forces. Thus the ‘weather’ is not a great example when we talk about models.

– by focusing on a few relatively important features, which will inevitably lead to errors in the long run due to simplifications of the model.

Which adds to the failure of the original statement: if your model limits to the inputs, arbitrary variables, as a best guess, then in all probability it will fail periodically, as it simply cannot produce real results, especially when the realities incorporate variables that are not included in your models.

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.

Economies are not physical manifestations of the real world as is weather. Economies are interactions between billions of individuals that create the ‘economy’. Billions of individuals that act. That act in ways that are sometimes deemed irrational, hence the failure of Samuelson’s ‘economic man’, who was a model, based on a faulty hypothesis, generated via empirical data. Economies and society are the manifestation of co-operation between individuals. If the co-operation ends, so does society and the various economies.

Dirac’s Models and Newton’s Intuition

Theories in physics aren’t metaphors or models, they’re the real thing.

Well actually they are a hypothesis, that is constantly open to falsification through continued experimentation and the scientific method. Physics operates on the the empirical methodology, where the outcomes, or historical data are known, but the ’causes’ are unknown. This is the very opposite of the social sciences, where the causes are already known, viz. ourselves, human action.

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.

The ‘physical’ world, where chemical, electrical, energy properties are constant. Not in the social world, where there are no ‘constants’.

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.

All well and good. As far as ‘finance’ is concerned, a sub-category of economics, a social science, totally useless.

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:

Disagree. Rationality, or a priori, which is pure theory, relies on logic. Logic is the structure of the human brain. Certainly flashes of genius and intuition exist, but they are not a ‘necessary’ condition.

“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 dealt with ‘physical’ properties. Newton famously lost his shirt in the South Sea Bubble stock trading scam, “I can calculate the motions of the heavenly bodies, but not the madness of people.”

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.

As already stated, finance is social science, not physical science.

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.

Absolute nonsense. The ‘law of one price’ violates the ‘law of supply and demand’, whereby the supply of fungible commodities or goods command different prices. The law of supply and demand is predicated upon diminishing marginal utility, which is the ‘theory of value’. Derman is simply incorrect. Now you are starting to understand why the ‘quants’ blew-up Wall St. Essentially they equated finance with the physical sciences.

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.

CAPM and efficient markets, surely have been so thoroughly discredited by now, no-one would actually use them?

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:

At your financial peril.

“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.”

While there is a lot of dross in economics, for example the latest theory of money as envisaged in Mosler’s MMT, which is Chartalism, simply dressed up and repackaged.

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.

They shouldn’t really be used at all, certainly blindly.

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.

Well that is sensible enough.

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.

Capitalism and democracy are totally separate. Capitalism is the implementation of free markets in the allocation of scarce resources. Democracy is a form of government, which as with all forms of government involves a minority dictating to the majority: it is the curbing of individual free choice.

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 …

Crony capitalism is not capitalism, it is socialism. Socialism however is not honest. It is an ideology of lies, and of expropriation, a violation of property rights. Capitalism incorporates property rights and the recognition thereof.

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.”

Largely because they are built on an empirical foundation, which is inappropriate for the social sciences. The social sciences must be deduced a priori to create valid theory, which is true for all times and all places, viz. it fulfills the necessity of ‘universalism’.