Linear perception, exponential change, and the new value

Dan Ramsden
7 min readMay 18, 2021


From a recent interview around the release of his new book, the following remark by Daniel Kahneman stands out: “The technology is developing very rapidly, possibly exponentially. But people are linear. When linear people are faced with exponential change, they’re not going to be able to adapt to that very easily.” The observation is broader, I believe, than strictly about technology and its societal effects, even if those things are now central. More broadly, the multitude of inputs in a complicating world, which burst out in a multitude of outcomes and effects that circle back to shape new inputs in an ever growing cycle of complexity, is like a compounding effect. Our linearly focused vision, like simple interest — as most of us can only see the whole in pieces and through slits — brings to our attention ever smaller sections of the whole as it deepens and expands. This is a notion that would lend itself to almost any subject. What follows is a commentary on the market (which perhaps contains them all), seen through the lens of valuation. It is an incomplete perspective, distorted by exponential changes all around.

Related samples

It is a noticed aspect of financial analysis that recent patterns of business performance (e.g., growth, profit margins, product mix, etc.) tend to be extended in a line, or something more or less resembling that, when forecasts are created. This can’t be helped, even though the gaps are known, as the further subjectivity of adding fractal elements to an exercise as inherently imprecise as a forecast would make the outcome doubly unreliable.

The same intrinsic flaw is prevalent at the macro-economic level. Most currently, market analysts and commentators have been in conflict over the nature of inflation that may lie ahead — a convoluted and multivariate exercise — where the core of the debate lies in the linear extension of recent history. One faction would extrapolate the latest results out in a line that leads to higher interest rates and, thus, collapsing asset values (more on this below), while the other would dismiss the current data as noise and rather draw the line from the pattern that preceded.

So it goes. The distorting quality of recency bias may or may not be at play in these examples, but Kahneman’s observation about linear thought (which may contain recency bias as an element) versus exponential change (suggesting turbulence and even randomness, or at least unexpected, unintended consequences) is, I believe, more critical to consider. Because, unlike recency bias, which once exposed can well be factored into sensitivities and modified scenarios, the distorting effect of narrow vision is a vaster challenge, as it provides no clue as to the missing parts that lie outside the filter.

There is a market inefficiency combining both referenced examples. Economic outlook shapes business planning, while both shape market value, which reflexively or not turns back around to impact the economy. Perhaps there is a long-term opportunity in this, as inefficiencies eventually favor those who notice, while the markets take their time to self-correct.

The largesse of future value

In the conventional approach, rising interest rates (such as in the present case caused by rising-inflation expectations) lead to a higher discount rate applied to cash flow forecast for a business. The discounted cash flow (DCF) methodology of asset valuation, which is sensitive to rates and to which all other methods (e.g., value multiples, sum of parts) relate, contains two cash flow elements — the operating forecast, as touched upon, and the “terminal” or “future” value of the asset. This represents a hypothetical price that a future hypothetical buyer would pay for the very actual asset in question.

While this so-called future value is discounted back to the present like the interim cash flows anticipated for the business, it has been noted and stands to reason that the former constitutes the majority (by far, in many instances) of the resulting present value estimation. This is particularly true for companies that plan to generate most of their expected earnings in the outer years of the financial forecast, but really it’s a matter of degree: Almost all businesses plan for growth, even the staid utility, and so the outer years exceed the early ones by nature. Only in some cases more so than in others.

The distorting impact of that on terminal value and its disproportionate effect on present valuation, stems from two main drivers:

  1. As business profits and cash flows are projected to grow with time, this is a valuation risk that is compensated for through the discounting mechanism. The early periods are discounted least, correctly, since the early periods contain the highest certainty. But as these are also the less profitable ones, their impact in the multi-year continuum is limited. The later years are stronger but are also discounted the most. And thus, business cash flows, no matter when, typically combine to form a small proportion of the present value total.
  2. Terminal value, which is also deeply discounted from a late year in the outlook, compensates for that discount (and then some) as it formed by a multiple — often not insubstantial — of the late-year profit that’s predicted, which, as noted, is a profit that is based on growth — often also not insubstantial. In other words, this future value constitutes a potentially two-fold exaggeration: the application of a multiple to significant forecasted profits.

Additionally, the excessive weight of the terminal value in the total DCF calculus comes with yet another challenge when considering what this future value signifies: It is the future price that a supposed future buyer will at some point pay (in future currency), which is itself a present-value amount in the future, which at that time will be the discounted future value that another and more distant buyer still will hypothetically agree to, who in turn will pay that price because another even further removed next buyer in line will in theory have paid… and so on, so on, so on…


The question of perpetuity

Now, forever is quite a while. It is now generally believed that the universe itself has not existed for as long as that. Let alone Kodak, or GE, or Google Finance. Some companies, if they should be so lucky, have transformed, evolved, been integrated and are now unrecognizable from what they used to be. We can all think of historical examples, even if the majority by far is no longer in existence. In practice, which is far removed from theory much of the time, this is how “terminal” value manifests itself.

Despite all that, when the theorists created the DCF construct they were correct or at the very least excusable. Firstly, the succeeding links in the increasingly distant future value chain, as described, are diminished by an increasing discount over time, to where each distant mathematical result might turn into a tiny little rounding error in the total (never-ending) present value calculation.

Secondly, and more central to the subject of this essay, when the model was invented the nature of business was more stable than it has become. A bookstore was reasonably expected to be a bookstore for a long, long time, certainly in the investor’s life, and not become, say, a healthcare provider, a cloud infrastructure host, a supermarket chain, a living-room robot companion, or all these things and many more combined. That such changes are now as often the rule as the exception, and that these take place in years rather than decades (let alone, never), this is what breaks the underlying perpetuity motif of the valuation exercise.

It isn’t now a question of how big or small a company will be some years from now — this is linear thinking in an exponential world — but rather, what will it be and, will it be at all?

It resolves in optionality

The basic imperfection in the valuation math (a flaw that can’t be helped, for there is no better mathematical approach to a solution) is a manifestation of exponentially changing circumstances exposed to a linear review, to Kahneman’s point, and the slowness of the adaptation.

If one is so inclined, it’s possible to research certain companies, like the most visible examples — Amazon or Apple, say — and draw points on their historic arc at which new products, capabilities, extensions, or more generally changes in direction had been introduced. So doing, one will likely find the frequency of these points accelerating while the resulting interconnected layers multiply. And it is not far-fetched, based on experience, to presuppose that the expansionary patterns will be mirrored in value over time.

With hindsight, we call this sustained growth; with foresight, we call it option value. It is the unknown and maybe unknowable possibilities that exist, which, I believe, tend to exist more for the enterprise that is a network platform than for that which isn’t. The big [5] techs, as they are now referred to (although technology isn’t a distinction anymore), also known as the FAA[M]G contingent (an arbitrary acronym that gets tweaked from time to time), are big and getting bigger for a reason, while still just a lonesome 5 that, depending on the day, seems to be getting lonelier. The optionality created by this group and certain others — from their network effects in a network-architected system — has no match in mere technology, which is there to be disrupted.

The question that an analyst might ask when studying resultant valuations is, does optionality support the current market price? This is not a DCF exercise, nor a Black-Scholes calculation — a business is not a liquid trading asset — but its value is similarly influenced by the economy, and interest rates, and volatility, and all the other forecasts referenced herein, like any option.

Does optionality support the perceived value? It is a subjective question, true enough, but it comes closer, I believe, to exponential thought than would a formula, on many levels. One such is that it is a question — rather than a linear conclusion, which these days would almost certainly provide a narrow sliver of an answer.

Other related reading:

The end of cycles (Part 1 & Part 2) (2022)

Fractals of the market voice (2021)

Reinterpreting the networks (2020)

Finance notes from underground (2020)

Interpreting the networks (2017)

Networks 3.0: Defined by digital dimensions (2016)