The words “complex” and “complicated” are often used as synonyms without much confusion.  This is especially prevalent when, rather than using these words as adjectives, we are using them to identify a difficult concept: “complexity” has a better ring to it than “complicatedness.”  However, having a subtle distinction between the two can be very useful when we are discussing quantitative models for the markets.

We can establish this difference by treating complicated as the opposite of simple and complex as the opposite of intuitive, at least roughly.  Complicated/simple can be applied to the description of the model or phenomenon while complex/intuitive can be applied to the behavior of the model or phenomenon.  With this framework, we can now classify models on the following spectrum:

1. Simple Intuitive – This is the most appealing area of the graphic because this is the realm of our understanding, where we see the most “satisfying” results.  A ball falling in a vacuum, an equation like f(x) = ex, directions for turning on a light, and supply and demand all could be classified in this category.  This is where risk management is relatively straightforward and outcomes are predictable.

2. Simple Complex – This title denotes models that are easy to understand but may exhibit complex behavior.  It sounds like an oxymoron until we consider some examples.  An interesting one is the logistic map given by the recurrence relation:

xn+1 = rxn(1-xn)

where x0 is a number between 0 and 1.  For different values of r and initial conditions, x0, this equation can approach a limit, oscillate between a set of fixed values, diverge, or exhibit chaotic behavior.  Other examples include Geometric Brownian Motion, disease transmission models, and systems of differential equations (e.g. predator-prey modeling).  All of these are somewhat simple to explain but have very interesting outputs.

3. Complicated Intuitive – These models often arise from being stuck in the woods without a full view of the forest.  An example is using a large multiple regression when there are only one or two explanatory variables.  Many times, the complicated model will agree with intuition for the most part but will likely demonstrate unintended behavior in other cases (i.e. the model is overfit).  Just because a 29th degree polynomial will exactly fit a 30 data points does not mean it will produce meaningful results over the entire domain of the data.

We can put many real-world phenomena in this category, as well.  A space shuttle has a variety of highly technical systems that are all required for it to function properly.  Given enough time and instruction, someone can be brought to the point of understanding all of these parts and how they come together to allow for successful takeoffs, orbits, reentries, and landings.  The complications can be mastered to the point where the outcomes make sense to the one who has put in the time and effort.

4. Complicated Complex – Finally, we have reached the domain of most of our natural world.  The workings of the human mind, the weather, water flowing over rapids, earthquakes, and the markets all fall under this classification.  Not only are there many interconnected parts, but there is also no certainty in the future based on the current observations.  Many generalities can be observed about these topics, but ultimately, much of what can be said rests on a limited set of assumptions that are not (and possibly cannot be) fully tested.  Probability reigns supreme, and observing past frequencies of events does not always accurately represent what the future holds.

Nevertheless, new research focuses on this sphere.  This is where many problems begin, and it is the goal of modeling to reduce these complicated, complex problems into the other quadrants, with the typical flow indicated by the orange arrows.

Simple by designTM is Newfound’s way of saying that we should strive to build models in the top-left corner of the graphic shown previously.  A simple method requires a parsimonious model that balances the number of variables with the description of the features in the observed data.  An intuitive method requires that the model’s behavior is as deterministic as possible; for similar inputs, you get similar outputs.

This is not always possible, especially when some models rely on simulations (e.g. Monte Carlo), but keeping that goal in sight can help reduce counterintuitive outputs from a model, while ensuring robustness through market cycles and significant future events that have little historical basis.

### Nathan Faber

Nathan is a Portfolio Manager at Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Nathan is responsible for investment research, strategy development, and supporting the portfolio management team. Prior to joining Newfound, he was a chemical engineer at URS, a global engineering firm in the oil, natural gas, and biofuels industry where he was responsible for process simulation development, project economic analysis, and the creation of in-house software. Nathan holds a Master of Science in Computational Finance from Carnegie Mellon University and graduated summa cum laude from Case Western Reserve University with a Bachelor of Science in Chemical Engineering and a minor in Mathematics.