Model-dependent realism and the markets

I just finished reading The Grand Design by Stephen Hawking and Leonard Mlodinow (Bantam Books, 2010). The authors advocate model-dependent realism “based on the idea that our brains interpret the input from our sensory organs by making a model of the world. When such a model is successful at explaining events, we tend to attribute to it, and to the elements and concepts that constitute it, the quality of reality or absolute truth. But there may be different ways in which one could model the same physical situation, with each employing different fundamental elements and concepts. If two such physical theories or models accurately predict the same events, one cannot be said to be more real than the other; rather, we are free to use whichever model is most convenient.”

Is there an ultimate theory or model of the universe? Although Hawking and Mlodinow don’t have a definitive answer, they offer M-theory as a candidate for “the ultimate theory of everything, if indeed one exists.” M-theory is actually “a whole family of different theories, each of which is a good description of observations only in some range of physical situations. It is a bit like a map. … To faithfully map the entire earth, one has to use a collection of maps, each of which covers a limited region. The maps overlap each other, and where they do, they show the same landscape. M-theory is similar. The different theories in the M-theory family may look very different, but they can all be regarded as aspects of the same underlying theory. They are versions of the theory that are applicable only in limited ranges—for example, when certain quantities such as energy are small. … [J]ust as there is no flat map that is a good representation of the earth’s entire surface, there is no single theory that is a good representation of observations in all situations.”

The authors propose four qualities of a good scientific model. It is elegant, it contains few arbitrary or adjustable elements, it agrees with and explains all existing observations, and it makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out.

In a brief post I can’t possibly do justice to these hypotheses. Perhaps somewhere down the pike I’ll analyze, criticize, tinker around the edges. For now suffice it to say that they should provide a lot of grist for the mill of trading system designers. Let me throw out a few very quick, somewhat telegraphic thoughts.

One of my personal bête noirs is the claim that a single system should be applicable across a range of time frames because markets are presumably fractal in nature. This strikes me as an example of intellectual laziness. Do we really think that the programs of successful high-frequency traders are the same as or analogous to those of successful traders who hold equities for a couple of days or weeks? Do we think that those who hedge a portfolio on a daily basis can use the same formulas as those who rejigger their hedges once a month and merely adjust by a factor of 20 or 21?

Another question: In testing a system, how long a period should the designer choose and what data set should he use? Which page of the atlas is he focused on? If I want to know how to get from one town in Connecticut to another I’m certainly not going to find the answer on the map displaying all the continents or even on the map of the U.S. A map showing elevations is irrelevant to my needs, a geological map even more so; I don’t even care about rivers and lakes. I need a map (or its digital equivalent) that clearly delineates the highways and byways of Connecticut, preferably with a distance scale.

Similarly, if I believe that market action changed when fast money stepped in and the retail investor exited, why would I do a ten-year backtest on an equity trading system? Or if I have devised a system that takes advantage of elevated volatility, why in the world would I test it out in low-volatility environments?

Those who have been searching for a monolithic unified theory of trading akin to a unified theory of science should rethink their endeavor. If Hawking and Mlodinow are correct, there is no such animal. Instead, designing systems should be a boutique business.