Radical Uncertainty in Finance: The Origins of Probability Theory


Radical Uncertainty is the title of a new and remarkable book by economist and former Financial Times columnist John Kay and former Bank of England (BOE) governor Mervyn King. Kay and King describe how modern society has succumbed to the illusion that uncertainty can be transformed into calculable risks. In doing so, they build on a theme that occupied the late German sociologist Ulrich Beck. Beck concluded:

“Die Welt des berechenbaren und beherrschbaren Risikos setzt (und vielleicht sogar mit dem Siegeszug seines Berechenbarkeitsanspruchs) das Moment der Überraschung frei.”

(“The world of calculable and controllable risk liberates — perhaps even helped by its triumphal claim of calculability — the moment of surprise.”)

In this three-part series, I will explore how we came to forget how to live with real uncertainty, the profound consequences this has had on finance, and what the right way to deal with true radical uncertainty might look like.

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The ancient Greeks were gifted mathematicians. Some of us may still remember Pythagoras’s theorem for calculating the side lengths of right triangles — a2 + b2 = c2 — from our school days. Euclid of Alexandria wrote his mathematics treatise Elements in the 3rd century BCE. The text was still used in geometry classes well until the 20th century.

But one thing is strange at first glance: The ancient Greeks never studied probability theory. Why? Because they had no place in their thinking for chance and probability. To their minds, the course of events was determined by the gods. Those who wanted to reduce uncertainty about the future had to better understand the will of the gods. And mathematics was no help there.

It is therefore no coincidence that mathematicians did not begin to deal with probability theory until the Enlightenment.

“Risk enters the world stage when God takes leave of it,” Beck wrote. “For in the absence of God, risk unfolds its promising and frightening, almost incomprehensible, ambiguity”

Probability theory’s foundation was laid in a question posed by a passionate gambler, Antoine Gombaud, Chevalier de Méré, to the renowned French mathematician Blaise Pascal. Pascal then enlisted the help of an even more illustrious French mathematician, Pierre de Fermat, to devise an answer. From the correspondence between Pascal and Fermat in the 1650s, the calculus of probability emerged. While the science has developed in the centuries since, its contours today are still determined by its birthplace at the gaming tables of the 17th century.

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The next truly transformative advance in probability theory came in 1921. In Risk, Uncertainty and Profit, the University of Chicago economist Frank Knight concluded that measurable uncertainty, or what we commonly refer to as “risk,” is so far removed from real uncertainty that it cannot really be called “uncertainty.” He also introduced the concept of “radical uncertainty” to describe this phenomenon. Knight observed that the metrics developed to weigh the odds in games of chance, or those that could measure knowable risk, were not applicable to radical uncertainty.

John Maynard Keynes reached a similar conclusion in The General Theory of Employment, Interest, and Money.” Keynes showed how methods to calculate possible results at, say, the roulette table, were of little use in determining the prospects of another European war or the future price of copper. Nor could they anticipate the odds of a disruptive new invention upending an old technology or discount for the social status of property owners decades later. These possibilities were simply not calculable.

In contrast, the British mathematician Frank Ramsey and the Italian mathematician Bruno de Finetti put forward the concept of “subjective probabilities.” They concluded that probabilities could be calculated for scenarios like those outlined by Keynes based on subjective assessments. In this way, they thought that uncertainty outside the gaming table could be made calculable.

But Kay and King explain that implicit in this assumption is that all potential future scenarios are knowable. That is the only way a series of subjective probabilities could add up to one and therefore be consistent. Of course, for most future developments, this is impossible. Thus subjective probabilities are nothing more than opinions expressed in numbers.

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According to Friedrich Hayek, we make economic decisions about the future based on our subjective knowledge of facts and relationships that we do not have an objective or mathematical grasp of. This is the environment in which Joseph Schumpeter’s “dynamic entrepreneur” acts, creating something completely new for which no probabilities can be calculated in advance.

Nevertheless, in economic discourse, the scholarship of Ramsey and de Finetti prevailed over that of Knight and Keynes, and the concept of radical uncertainty retreated to the margins.

How this led to the impasse in modern finance is the subject of the next installment in this series.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

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Thomas Mayer, PhD, CFA

Thomas Mayer, PhD, CFA, is founding director of the Flossbach von Storch Research Institute. Before this, he was chief economist of Deutsche Bank Group and head of DB Research. Mayer held positions at Goldman Sachs, Salomon Brothers, and before entering the private sector, at the International Monetary Fund (IMF) and the Kiel Institute. He received a doctorate in economics from Kiel University in 1982. Since 2003 and 2015, he is a CFA charterholder and honorary professor at University of Witten-Herdecke, respectively.

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