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March 05, 2005

Theory and Practice

Yesterday, I made a mistake. A fairly annoying one, too, because I should know better.

I wore my "practice" hat to a "theory" discussion, and then took forever (in discussion terms) to recognize this and (as best I could) change hats.

This is, of course, an issue I deal with all the time, not in my hobbies (where yesterday's mistake was, thankfully) but in my occupation. As an actuary, in particular as a product development actuary, I'm frequently challenged to take academic economic theory and re-cast it into a practical, executable plan, and in doing so I've had to recognize the limitations of both perspectives. My friend Grant often says (with no claim to have originated it) "In Theory, there is no difference between Theory and Practice. In Practice, there is no relationship between Theory and Practice." It's taken a bit too far, but it's essentially a correct observation.

The Theory world is ruled by the unforgiving taskmaster of logic. If Theory A is used as part of the justification/derivation/proof of Theory B, then if Theory A is proven wrong even just a little, then Theory B is immediately and totally discredited as well. That's why, in the Theory world, one must be very careful with words and what they mean, and why having a fundamental assumption questioned even in the slightest can cause an intense and forceful uproar, often resulting in statements that, on their face, seem totally out of proportion to the issue at hand (to a layman).

The Practice world is ruled by practicality. In the Practice world, Practice A may be used to justify Practice B, but it is recognized that a change to Practice A only might affect Practice B. One must review the implications on an individual basis. Changes are expected and the norm, review of assumptions and practices is continuous. Anything else is assured to fail.

So, in Mathematical Theory, 2+2=4. This is a hard, cold fact. But in Mathematical Practice, 2+2 can equal anything from just above 3 to just below 5, because 2 can be recognized as "anything from 1.5 to 2.5". There it is in simple terms... Theory and Practice are two different things.

This gets even hairier when you get to the advanced stuff. For example, the Black-Scholes Option Valuation Pricing Model (the basis of vast arrays of modern high-finance, usually in one of its successor forms) is proposed as a mathematical proof, fairly straightforwardly derived from a set of assumptions. The problem is that, in practice, each and every one of those assumptions is almost always false. Despite this, Black-Scholes works. This is because (as demonstrated in an excellent follow-up paper by one of the original creators of the theory, I believe Black) the sensitivity of the model to the inherent error in each of its assumptions is, in fact, quite small. It will fail now and then (there is one particularly large international hedge fund collapse that can be blamed on just such a failure at heart), but the vast majority of the time it will be as accurate as any of the other calculations used in financial work.

So, in Theory, Black-Scholes is wrong (based on several false assumptions) and cannot be used as a basis for further work (unless you carry forward all its questionable assumptions). In fact, it's right far, far more often than it's wrong, and when wrong it's usually wrong by a very small amount. It is flawed in that it's hard to see when it is very wrong until after the fact... In Practice, that means it can be used with appropriate care and understanding even if, in Theory, it must be thrown out.

One must recognize which realm the discussion is in and, thus, which set of reactions questioning a base assumption will create. In a Theory discussion, the reaction is sudden and forceful. In a Practice discussion, it's usually a quiet "hmm". From the exact same question.

Yesterday, I forgot to do this. As such, I wasted several good people's time and likely frayed a temper or two (temporarily, I hope). And that was completely and totally my mistake, not theirs.

Posted by ghoul at March 5, 2005 08:11 AM

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