Models Are Useful, but . . . There’s No Holy Grail

The first myth we must dispose of is that any model of future price distribution is consistently accurate. Even though this statement may sound contradictory given our discussion previously, it is not. In the first place, no model can predict the unpredictable, and the unpredictable event occurs with disturbingly higher frequency than any model indicates.

Even aside from obvious examples such as weather calamities and wars, the number of possible unpredictable or imponderable events is enormous, and some of these will—not might, but will—intrude on our trades from time to time. No model can warn us that such events impend, and the trader who believes otherwise is headed for an appointment with a bankruptcy judge.

Looking at the matter objectively, all we traders can really do is to keep our likelihood of success, our expectation, in the plus column. Models are useful because they provide a means of calculating our approximate expectation in a trading position.Sometimes the calculated figure is rather rough,sometimes it’s very close, but it is always only an approximation. This approximation can be dead wrong at times, too.

When our trading model indicates one thing but our own eyes perceive something else entirely, we must resolutely junk the model, at least temporarily, and not bother with a visit to the optometrist. Part of Long-Term Capital Management’s downfall was due to their outright refusal to discard certain of their risk and pricing models that were being proven more and more inaccurate with each passing day by the markets’ movements.

This is an error we must avoid: falling in love with a model is just deadly to our profitability (no disrespect to Elle MacPherson or Cindy Crawford, of course).Aside from the plainly egomaniacal notion that we can somehow model future price movements with near precision, there are other reasons we must use models cautiously. Many famous models, Black-Scholes-Merton and Rubenstein-Leland (better known as “portfolio insurance”) to name two, include one or more highly dubious assumptions.

Please understand here that I’m not in any way criticizing any of these wonderfully talented theoreticians.I’d pay hard cash, any time at their convenience, to sit down with Robert Merton or Mark Rubenstein or Myron Scholes over a long lunch and discuss modeling and trading with any of them, or with numerous others. I admire these gents enormously, but notwithstanding that, some of the assumptions included in pricing models are quite suspect.The primary suspicious assumption is that markets are continuous.

Models many times (please keep in mind that I’m not familiar with all the models now in use) assume the mathematical continuity of markets, that is, that prices in markets move in small amounts, 0.01 or 0.05 or 1⁄8 or something similar. It would be delightful if this were the case, but it isn’t at all,and you and I and anyone who has traded for longer than a month know this to be a fact.

Markets frequently have ticks with large jumps, or gaps—the interjection “Duh!” must come in here someplace—and this awkward fact damages the usefulness of any model that assumes mathematically continuous markets.These gaps are by definition discontinuities, and the effects they may have on our trading results are simply not included in any model of which I’m aware. If I were feeling bold, I’d say that they can’t be included. How could anyone model the likelihood of occurrence of a 10-cent gap in soybeans, say, next Thursday? Or a 30-cent gap?

The frequency of such occurrences we can easily calculate by looking at historical price movements, but there is no way to model when the next such gap will occur.Can we compensate for the risk this and other dubious assumptions embedded in models pose to our capital? Indeed we can, and we can do so in at least two distinct ways. We’ve touched on both of them before, but we can now appreciate another reason to apply these tactics.

Diversification of our trading positions is desirable from the standpoint of limiting capacity risk, and it becomes even more so as a means of dodging the risk that our trading model will be spectacularly wrong at some point. Certainly it must pose much less risk to us to have our model become radically inaccurate regarding one of our positions if we hold 10 or 12 positions than if we hold only 2 or 3.We can also compensate in another manner.

In addition to our firm commitment to avoiding the use of more than a fraction of the total leverage available to us, we can take another bite out of the potential risk when a model becomes erratic by keeping the size of each of our positions small. Old advice, you say, nothing new here? Not really, for there’s a very practical twist to this second tactic within the context of models.