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Models and their limits

Options traders tend to think mathematically. When considering selection of an underlying, risks and expected profits, the model of outcomes is a primary tool for making selections. Without a model how can anyone understand the differences between two or more options that might otherwise appear the same – similar moneyness, same strike, and same premium.

Where models become useful is in how the various attributes of an option are quantified and placed on a graph (at least mentally) to make sound judgments about whether one option is more feasible than another.

The problem arises, however, when the trader begins depending on the model so heavily that the line between model and reality is overlooked. The definition of a model explains how this potential flaw comes into play: A model is intended to provide a real-world version of likely outcomes. As a mathematical construct, the model should help an options trader to grasp the option’s risks and potential for profit or loss. However, the key is to realize that the model and the actual world of trading are not identical in every important way.

A popular assumption among traders is that an accurate model is the same as how the real world works, and this is not the case. For example, everyone is familiar with the formulas used to calculate maximum profit, maximum loss, and breakeven for any strategy. But these models of the maximum range of outcomes is not how things go in most cases. First, they represent the maximum levels only. Second, they assume that a position will remain open until the last trading day. In practice, only a small percentage of all options are kept open in this manner. Most are closed or exercised well before last trading day.

Modeling can cause misunderstandings as well. The commonly cited statistics that “75% of all options expire worthless” is highly inaccurate and untrue. The actual statement should be that 75% of all options kept open until expiration will expire worthless. This is a small number of options and does not present a true picture of how a position is likely to end up.

Modeling of expected return and bail-out points is another type of calculation most traders perform. For example, a trader might say, “I will close the position when I double my money, or when I lose half.” This statement encompasses both a profit goal and a bail-out point. But every trader has faced this situation, and most have violated their own well intended goal. For example, if profits accumulate rapidly in a position, it is all too easy to keep it open in the belief (or hope) that the positive trend will continue. If losses occur, the same trader might hope for a rebound and fail to close and take the loss. In both cases, there is a good chance that the trader will end up seeing profits evaporate, or seeing a small loss turn into a complete loss. In this situation, failure to faithfully follow a goal once set, means unacceptably high losses result. It is likely that every trader has faced this dilemma at one time or another. The lesson here is: Setting profit or bail-out goals is a worthy exercise, but only if you can adhere to those goals once reached.

Another point to keep in mind about models: Even the best model (of profitability, option premium, or outcome) is only going to be as reliable as the data used. If the data are incorrect, the outcomes produced by the model will also be incorrect.

Are models and the practice of modeling worthwhile? It depends not only on which model is used, but also on whether the conclusions are useful. If you model for maximum profit or loss in a position, will you act according to the actual movement of values once it occurs? Or to be realistic, do you struggle with self-discipline in trading? Are you likely to act according to a profit or bail-out point being reached, or will you hope that (a) profits continue or (b) losses reverse?

The observation has been made that taking a small loss is preferable to waiting for a larger loss to take over. The same logic states that taking profits when they exist is wiser than waiting for even more profit. To “model” these observations realistically, another observation should be made. As humans, options traders may be aware of their original goals, but following them is much more difficult. It is the same dilemma faced by those who profess to be contrarians. Acting on logic rather than on emotion is an easy piece of advice. But when the market has moved several hundred points, and losses are mounting by the minute, a contrarian approach to trading requires courage and self-assurance that is not always easy to apply. The real model for market behavior must be based on the analysis of goals on the one hand, and human nature on the other.

Even when a trader (contrarian or otherwise) discovers a model that appears to work, self-discipline is still needed, because risk is a constant. There is going to be a tendency among those believing that finally have stumbled upon a “sure thing,” to increase the size of their trade so that their profits will multiply as well. This is where the trouble begins.

In deciding whether to model trades and outcomes, a realistic understanding of modeling (and human) limits is essential. Models can be valuable if only to better understand how trades should be evaluated. In the final analysis of models, it does not always make sense to model expected outcomes. It could be more realistic to model trader tendencies and risks. That is where the typical model fails, but where trouble usually will be found. Either the model is not like the real world, or the trader has difficulty adhering to the planned behavior based on outcomes.

Michael C. Thomsett is a widely published author with over 80 business and investing books, including the best-selling Getting Started in Options, coming out in its 10th edition later this year. He also wrote the recently released The Mathematics of Options. Thomsett is a frequent speaker at trade shows and blogs on his website at Thomsett Publishing as well as on Seeking Alpha, LinkedIn, Twitter and Facebook.

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