Musings on Models

Since the dawn of time, humanity has been finding ways to make sense of the reality we exist in. The fundamental nature of science is that it discards old models and replaces it with new ones, sometimes in a manner that is incremental and sometimes turning our understanding of reality on its head. Some ideas like Alchemy, Geo-centrism, Humorism were completely demolished, while others such as Newtonian mechanics were recognized as flawed beyond a point (Newtonian mechanics breaks down when dealing with relativistic velocities)

When the statistician George Box observed –  “All models are wrong but some are useful”, he was no doubt referring to the fact that every model we make will always be a best case approximation of reality, since we do not have the resources to mimic the universe itself exactly, that would be too complex a task with an incomprehensible number of variables. To use a computing analogy, when we draw the polygons necessary to create a wire-mesh 3D model, more number of vertices will lead to a more accurate model, but will also take increasingly more computing power to render.


This is a trade-off that will always be necessary, though as our knowledge and capabilities improve we will continue to push the boundaries of how well we capture the nature of the universe, perhaps doing so with greater efficiency.

Much like a computer program is only as good as the logic built into the code by the programmer, a financial or economic model is only as good as the inputs and assumptions built into it by the analyst. It is human nature to seek certainty, however the pursuit of this at any cost is to forget that the world operates on rules that are more probabilistic than deterministic, and that much of what will matter cannot be quantified on a spreadsheet. As Charlie Munger puts it:

“You’ve got a complex system, and it spews out a lot of wonderful numbers that enable you
to measure some factors. But there are other factors that are terribly important and there’s no precise numbering you can put to these factors. You know they’re important but you don’t have the numbers. Well, practically everybody over-weighs the stuff that can be numbered, because it yields to the statistical techniques they’re taught in academia, and doesn’t mix in the hard-to-measure stuff that may be more important” 

Not only are we prone to psychological biases such as the availability heuristic (over-weighting information that comes to mind first), we fail to realize that in a complex adaptive system, a small change in one variable can lead to drastic differences in outcomes (the popular example of this would be the butterfly effect). This is what makes the idea that a stock market level can be fore-casted with any degree of accuracy so absurd a fiction, it’s hard enough to figure out the value of any one stock; adding dozens or hundreds raises complexity exponentially. There are just too many moving parts and unknown unknowns: add human emotion and irrationality to the mix and it makes things even more unpredictable.

This craziness also leads to some misconceptions about intrinsic value and how determinable it is.

Intrinsic Value is a nebulous concept.

“We must recognize, however, that intrinsic value is an elusive concept. In general terms it is understood to be that value which is justified by the facts, e.g., the assets, earnings, dividends, definite prospects, as distinct, let us say, from market quotations established by artificial
manipulation or distorted by psychological excesses. But it is a great mistake to imagine that intrinsic value is as definite and as determinable as is the market price” – Benjamin Graham

“Intrinsic value is terribly important but very fuzzy. We try to work with businesses where we have fairly high probability of knowing what the future will hold. If you own a gas pipeline, not much is going to go wrong. Maybe a competitor enters forcing you to cut prices, but intrinsic value hasn’t gone down if you already factored this in. We looked at a pipeline recently that we think will come under pressure from other ways of delivering gas [to the area the pipeline serves]. We look at this differently from another pipeline that has the lowest costs [and does not face threats from alternative pipelines]. If you calculate intrinsic value properly, you factor in things like declining prices. When we buy a business, we try to look out and estimate the cash it will generate and compare it to the purchase price. We have to feel pretty good about our projections and then have a purchase price that makes sense”  – Warren Buffett

When Graham came out with the idea of intrinsic value i.e recognizing that an asset had a certain value based on it’s fundamentals, he did not mean for this value to be calculated to the last decimal place, recognizing that this was fundamentally impossible.

Using a simple model, a company’s value can be expressed as

Value = (Assets – Liabilities) + Discounted value of future cash flows to the owner

The first component of value is derived from the balance sheet – things like cash, working capital or real estate are some key aspects. However, asset value is rather static in nature, with most of its components only realizable in the event of liquidation (barring excess cash on the balance sheet, which can be returned to owners via dividends or used for share-buybacks.

The second component of value is the cash that the firm will produce for it’s owner, discounted back to the present to account for the time value of money. It depends on many things – growth rates, interest rates, competitive advantage period, input prices and so on. This is the real driver of intrinsic value for most businesses.

Since the future is uncertain,  multiple scenarios are possible, each having a certain probability. Thus the intrinsic value of a company’s cash flows will always be more of a distribution than a fixed number. The very nature of this is fuzzy, which is why analyst talk of “target prices” is silly. I mean, I’ve seen cases where analysts revise their target price by Rs 1 (probably changed the some 3rd decimal value in their model somewhere)

A common example of probabilistic, scenario based planning would be a commodity based business – wherein fluctuations in the price of oil would cause the intrinsic value of the business to change greatly.


Source: Professor Ashwath Damodaran

The same issue that any model faces apply in estimations of intrinsic value: the model could be made increasingly detailed ad-infinitum, but that would involve a trade-off in terms of time and resources. Moreover, if the inputs don’t hold, then it becomes a case of garbage in-garbage out.

As with most things in life, the Pareto Principle applies: 20% of the factors influence 80% of the outcome, and the value of fundamental research follows the principle of diminishing returns. More information beyond a point will not enhance the quality of the decision or remove the inherent uncertainty in the outcome. Great investors like Warren Buffett recognize and embrace this uncertainty, as well as know how to reduce a business problem to its key drivers and effectively “handicap” the odds behind each outcome, a skill that no amount of Microsoft Excel wizardry can substitute for.


Additional Reading:

(1) Worldly Wisdom in an Equation by Professor Sanjay Bakshi on the topic of Bayes theorem and probabilistic thinking.

(2) The Signal and the Noise by Nate Silver

(3) Superforecasting by  Phillip Tetlock







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