The Illusion of Precision: When Finance Ignores the Black Swan

The irony of prediction as an industry.

“We are quick to forget that just being alive is an extraordinary piece of good luck, a remote event, a chance occurrence of monstrous proportions.”

― Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable

The rarity of the chance of our existence on this strange planet, as Taleb underlines in this quote, is already something hard for most of us to comprehend. Indeed, our brain has difficulty in digesting abstract and existential thoughts like this one. However, sometimes, you too will find yourself trapped in those small moments of derealization that occur throughout our ordinary days – you will feel the weight of this heavy truth. Still, we do not give much importance to it, in the end it is not something that actively affects our daily life, our jobs, or our families.

What We Were Taught

Numbers are the rule. This is what we have learned since we started studying. They are precise, cold, clear. They are not a subject of interpretation or opinion: they are the best way to represent, forecast, describe, and summarize things. Or this is what we are taught. We are taught that with numbers and calculations we would have been able to foresee the future, to forecast events. With the publication of “The Black Swan” Nassim Nicholas Taleb makes this steady truth waver.

“What is surprising is not the magnitude of our forecast errors, but our absence of awareness of it.”

— Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable

Wall Street, brokers, investors, traders base their life on forecasting events, numbers, possible favourable or unfavourable situations. So are we just deluding ourselves for centuries? Are we just jumping into the void while thinking that at the bottom there is a nest made of numbers while, in fact, there is absolutely nothing? And when we fall and hit the ground, we realize we were wrong altogether, we realize that outliers exist, and that we just encountered a Black Swan.

What is a Black Swan?

The term “Black Swan” as a symbol did not actually originate with Taleb. It comes from a Latin expression, created by the Roman satirist Juvenal: “rara avis in terris nigroque simillima cygno“, which translates to “a rare bird on earth, and very much like a black swan.” [1]. While Juvenal originally used it to mock the idea of finding a perfect wife, the phrase evolved over centuries to symbolize an absolute impossibility [1]. Centuries passed, and the misconception of the impossibility to have non-white swans stayed, until the late 17th century after the discovery of an actual black swan in Australia [1]. One sighting was enough to overturn a certainty built on centuries of observation, and that is the blind spot Taleb sets out to expose.

Taleb turns this philosophical concept into a lens for looking at the world. In his definition, a Black Swan is an event with three traits: it is rare, it has an extreme impact, and it can be explained only in hindsight, never predicted beforehand [2]. The sudden collapse of the Soviet bloc is one example, or the rise of Hitler, or 9/11, or the spread of the Internet [2][4]. What makes these events unsettling is what happens afterwards: we build a story in which they look obvious. Taleb calls this the narrative fallacy, the habit of seeing past events as more predictable and less random than they were [2].

One of the book’s best-known images is a turkey – Bertrand Russell’s original chicken story which Taleb adapted to a turkey. For 1,000 days the animal is fed and looked after, and it becomes convinced that this will never change; on day 1,001 the feeding stops and the turkey dies [3]. Its record was perfect, and that record was exactly what misled it. Whether an event is a Black Swan also depends on who is watching: the turkey is taken by surprise, while for the butcher nothing unexpected happened [3].

To explain why some spheres allow surprises like this and others do not, Taleb splits the world in two. In “Mediocristan”, no single observation changes the total much: human height is the classic example, since even the tallest person alive is not dramatically taller than the average one [2]. In “Extremistan”, a single observation can dominate everything – wealth, book sales, and financial markets belong here [2]. Taleb calls this the catastrophe principle: in Extremistan, ruin is more likely to come from one extreme event than from a series of bad episodes. Taleb’s thesis is that such events have a far greater effect, in financial markets, and in human affairs, than we usually suppose [2]. The problem, then, is not that we forecast badly. It is that we use tools built for Mediocristan, such as averages and bell curves, in a world that behaves like Extremistan. Finance is the clearest case, and it is where we go next.

Where Finance Meets the Swan

“The inability to predict outliers implies the inability to predict the course of history”

― Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable

Finance is built on prediction. Valuation models, risk measures, and back-tested strategies all promise to turn uncertainty into a number. Taleb’s objection is that these tools were made for Mediocristan, while financial markets belong to Extremistan [3]. Three of them show the gap.

The DCF

Take the discounted cash flow model (DCF), the workhorse of valuation. Its scope is forecasting a company’s cash flows for a few years and adding a terminal value for everything after. Aswath Damodaran, a leading valuation academic and a defender of the method, argues that a terminal value, the component that makes up most of a DCF, is not a flaw in itself, because investors earn most of their returns from price appreciation [6]. Yet his own numbers show how much rests on it. In one of his examples, with terminal growth fixed at 2%, the terminal value ranges from roughly $1.2 billion to $2.1 billion depending only on what is assumed about growth and returns in the first five years [6]. A DCF extends a smooth path into the future, while a Black Swan is precisely a break in that path: a crisis, a technology shift, a regulatory shock that no sensitivity table has a column for. Like the turkey, the model reads a good past as a promise about the future. The output is one clean figure, but behind it sits a chain of assumptions about a world nobody can observe.

Risk Management

Risk management has the same issue. Value at Risk (VaR) marks the threshold where the tail of possible losses begins; it is blind to how far the tail extends [7]. Taleb argues that a single measure such as standard deviation cannot stand for “risk”, and that the figures in fund documents rest on tools derived from the bell curve, which lets managers claim they followed standard scientific method [2]. He adds that when someone announces an n-sigma event, it is far more likely that the model is wrong than that the event happened [5]. Regulators reached a similar view: in 2012 the Basel Committee listed VaR’s inability to capture tail risk among its weaknesses and proposed replacing it with Expected Shortfall, which averages the losses inside the tail [7].

Backtesting

Backtesting, testing a model against history, faces the turkey‘s problem. Taleb points to the hedge fund Amaranth, which lost $7 billion after reassuring investors that it employed twelve risk managers. The point is that even a hundred specialists would not have changed the outcome, since no one can extract more information from the past than it contains [3]. History also misleads in a systematic way. In his Cambridge lecture, Taleb showed that in the S&P 500 a single observation accounted for about 80% of the kurtosis, a measure of fat tails, and he described banks that seem to make money outside of crises until a rare event takes it back [5]. A model calibrated on calm years looks reliable exactly until the event it never saw. The near-collapse of Long-Term Capital Management in 1998 fits this pattern. The LTCM was a highly leveraged fund, led by a team that included two Nobel laureates, and known for its sophisticated mathematical models, lost 44% of its value in a single month after Russia’s default, and had to be rescued by a consortium of banks arranged by the Federal Reserve [8].

DCFs, VaR and backtests share one habit: they present uncertainty as a number. The distance between what the number claims and what the world allows is where Black Swans live. And the problem goes beyond finance: it is a human one.

What Taleb Suggests Instead

If forecasting fails, then what remains? It is important how we interpret Taleb’s words. In fact, it would be a mistake to think that Taleb gave us a better model. We could see what he offered as a different perspective: we should stop trying to predict the swan and try to limit what it can do to us [2]. The question, then, is no longer “what will happen?” but “what can we survive?”. We have to start planning for being wrong.

A life spent in predicting the unpredictable

Life can only be understood backwards; but it must be lived forwards.

— Søren Kierkegaard, Journals (1843), commonly cited form [9]

Apart from finance and statistics, perhaps Taleb tried to tell us something more. Our desire to turn uncertainty into certainty is not only a mathematical habit: it is a human one. We cannot bear uncertainty, we struggle to move and decide without planning, and analysing. Yet no model, plan, or analysis can transform an unknowable future into a fully predictable one. The rare event, the outlier, will always remain outside the frame until it suddenly becomes the event that changes everything. In finance, as in life, wisdom may therefore consist not in believing that we can predict the future, but in recognizing how little of it we truly understand. Indeed, the past can be interpreted; the future must be faced.

Edited by Adrian Kai Fraile Itagaki.

References

[1]Grammarphobia. (2020, May 12). The origin of “black swan”. https://grammarphobia.com/blog/2020/05/black-swan-rara-avis.html

[2] Aldous, D. (2009). Review of “The Black Swan: The impact of the highly improbable” by N. N. Taleb. University of California, Berkeley. https://www.stat.berkeley.edu/~aldous/157/Books/Black_Swan-sub.pdf

[3] The Investors Podcast Network. (n.d.). The Black Swan: The impact of the highly improbable—Book summary. https://www.theinvestorspodcast.com/billionaire-book-club-executive-summary/the-black-swan/

[4]The New York Times. (2007, April 22). The Black Swan: The impact of the highly improbable. https://www.nytimes.com/2007/04/22/books/chapters/0422-1st-tale.html

[5] Taleb, Nassim Nicholas. “Extreme Events and How to Live with Them.” Darwin College Lecture Series 2017: Extremes, University of Cambridge, 20 Feb. 2017. Lecture. https://fooledbyrandomness.com/DarwinCollege.pdf.

[6] Damodaran, A. (2016, November 30). Myth 5.5: The terminal value ate my DCF! Musings on Markets. https://aswathdamodaran.blogspot.com/2016/11/myth-55-terminal-value-ate-my-dcf.html

[7] Herdegen, M., Khan, N., & Munari, C. (2024). Risk, utility and sensitivity to large losses. arXiv:2405.12154. https://arxiv.org/pdf/2405.12154 (quotes the Basel Committee’s 2012 consultative document on the Fundamental Review of the Trading Book.)

[8] Fleming, M., & Liu, W. (2013). Near failure of Long-Term Capital Management. Federal Reserve History. https://www.federalreservehistory.org/essays/ltcm-near-failure

[9] Kierkegaard, S. (1843). Journal entry JJ:167. In Søren Kierkegaards Skrifter (Vol. 18, p. 306). Søren Kierkegaard Research Center, Copenhagen. Quoted in Jorgensen, P. E. T., Kierkegaard quotes and sources, University of Iowa. https://homepage.divms.uiowa.edu/~jorgen/kierkegaardquotesource.html

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