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The Limits of Financial Models: Why the Map is Not the Territory

October 14, 2020 / by Ben Cohen, FSA, MAAA

On election days worldwide, as voters leave the voting booth, reporters and interested parties ask people how they voted. We use exit polls to report on developing voting patterns on an election day to predict winners. Elections usually require time to count all the votes, but news stations use exit polls as an early indicator of the result. 

Exit polls, however, can create misinterpretations or falsehood altogether. This comes at no surprise because exit polls are a snapshot of the full picture. Pollsters don’t ask every individual and some lie to pollsters. Exit polls are accurate most of the time, but they do not create a perfect one to one image of the voting patterns.

If we wanted to gain a 100% perfect understanding of the voting patterns, we would need to ask every person voting, and they would need to be honest with us. We would have perfect clarity, but we would also have conducted the same election again, wasting time and resources. 

This is one example of a map not being the same thing as the territory it is attempting to represent. This mental model applies to elections, physical maps, and even financial models. 

History of Maps and Territories

In his mathematics essay on general semantics, “A Non-Aristotelian System and its Necessity for Rigour in Mathematics and Physics,” Alfred Korzybski accidentally laid out the foundation for the concept. While presenting his essay at a meeting of the American Association for the Advancement of Science in New Orleans, he gave the following conditions of defining a map concerning a territory.

  1. A map may have a structure similar or dissimilar to the structure of the territory.
  2. Two similar structures have similar ‘logical’ characteristics. Thus, if in a correct map, Dresden is given as between Paris and Warsaw, a similar relation is found in the actual territory.
  3. A map is not the actual territory.
  4. An ideal map would contain the map of the map, the map of the map of the map, etc., endlessly…We may call this characteristic self-reflexiveness.

Korzybski was not the only person to speak on the Map is not the Territory. There are two examples in the liberal arts that illustrate the concept. 

René Magritte, a Belgian surrealist, illustrates this concept in his painting The Treachery of Images. The picture appears satirical at first. Magritte creates an image of a pipe and captions the image with the phrase, “Ceci n'est pas une pipe” (this is not a pipe). The idea he is communicating is that a representation of reality is not reality itself. 

Lewis Carroll also discusses the idea in “Sylvie and Bruno.” A professor recalls a story of map-makers in Germany experimenting with larger maps until they produced a map of a 1:1 ratio, thus recreating the land and making the map extraneous. It was a perfectly accurate map, but it was useless as a map altogether. 

Maps and Territories for Decision-Making in Business

We use maps to describe physical locations, or they can be used to illustrate points in time. Financial and actuarial models are examples of these maps depicting time. We take account of certain factors to create an understanding of how a company is performing. 

For many, the model becomes its own reality, and they misinterpret the reduction of information as high-fidelity. Financial models are extremely useful tools, but mistaking them as reality or believing they can always describe the picture with complete clarity can be costly.

What We've Seen in Our Business

In our financial modeling work as actuaries, we very often create detailed models of how a company’s business is going to perform. Typically, these models encompass using seriatim records that are intended to account for ALL policyholders. To support our assumptions, we perform experience studies that are intended to reflect the company’s ACTUAL experience. The framework of the model and the process to set assumptions is often repeated from year to year once established. 

Just like an exit poll, a territory map, or even a painting, the “model” will never achieve the reality of the real world result. As consultants, we are often asked to step back and evaluate why our models did not reflect reality (because they often won’t). In some cases, this could be due to unforeseen circumstances, like a pandemic. But, in other cases, the framework needs to be refined. 

For example, each year we do budget and cash flow testing models for our client companies. As a first step to that process, rather than repeating the process with new data, we REDO the prior year’s model with updated assumptions to evaluate how well last year predicted the current year. In an ideal world, you would evaluate the behavior and outcome of EVERY policyholder individually. Practically speaking this approach isn’t possible. So, the modeler must be able to evaluate the overall picture in order to produce a final work of “art” or a model that is best representative of the true image. 

In our work, this approach may include using simplified methods for segments of business with very stable results, but more complex methods (and time/cost investment) into expanding those areas with more volatility. It may also include evaluating the materiality of business before significant time and resources are invested. For specific lines of business, a company might consider outsourcing that part of their modeling if they do not have the expertise. It can be possible for an outside expert to prepare financial projections at very little cost given their volume of work in this area. In any case, it becomes important to evaluate those key segments to effectively utilize resources.

Although it sounds unusual, an actuary’s ability to apply their “artistic interpretation” (rather than mathematical ability), can be invaluable in finding the right balance when mapping your company’s reality. 

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Topics: Insider, Insights

Ben Cohen, FSA, MAAA

Written by Ben Cohen, FSA, MAAA

Ben serves as Wakely Actuarial’s President & Consulting Actuary. He joined Wakely in 2002 and enjoys the variety in the day-to-day of his current role.

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