“Give them a turn and they make new”

“There is no such thing as a new idea. It is impossible. We simply take a lot of old ideas and put them into a sort of mental kaleidoscope.” Mark Twain

The precepts and practice of modern finance and economy have delivered the highest standard of living to the greatest portion of mankind in history. Those involved could be justly proud of the benefits that have been bestowed. True, not all those benefits are equally distributed, though trickle-down has occurred. More-or-less everyone in Asia, Europe or America can afford a computer and access to the internet, which is a fair measure of the distribution of real value. Yet, finance and economics suffer from a solipsism which appears mystifying, and clearly hinders adoption of advances in ideas that have appeared in other disciplines. Where there are advances, there is often resistance properly to credit ideas from other disciplines. Where outside sources are credited, there is often a ‘creation myth’ attached to suggest that the ‘moderns’ (invariably American) identified and rescued some important and otherwise forgotten foreign genius from a benighted earlier or foreign environment, unfamiliar with the blessings of modern America. We may call this tendency the ‘exorbitant privilege’ of the American academy’. Why does this resistance persist?

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Source: creator.nightcafe.studio

The insular self-regard of financial economics can be traced to two related developments: the rise of dollar dominance post-WWII and the simultaneous emergence of digital communication. The success of one was dependent on the other, as is strikingly obvious to anyone connected to the global economy today. Both are crucial to modern financial theory. Their combined effect encouraged a particular socio-political quantification. That is not to diminish the advantages of ‘advances’ in financial and economic ideas. It does suggest, however, they may be understood primarily as political arrangements, subject to constraints and incentives.

This becomes clear by tracing the ‘moulding’ of historic ideas that make up the canon. For economics and finance did not begin with Bretton Woods in 1945. And many of the seminal ideas that go to make up Modern Portfolio Theory and its sibling ideas did not originate in MIT or Chicago in the 1950s and 1960s, but much earlier, often in the physical or mathematical sciences. Moreover, some of the more radical ideas of financial economics which were novel, such as Efficient Market Hypothesis (EMH), seem to perform a convenient political function supported by the trappings of scientific measurement; to reduce agency of ‘outsiders’ and to enhance agency of ‘insiders’.

The EMH discussion will have to wait for another post. In this post I’ll look at a) an important example of academic repurposing and b) an important example of ‘myth creation’ by modern American financial theorists.

2023 marked the 50th anniversary of the publication of: “The Pricing of Options and Corporate Liabilities” by Fischer Black and Myron Scholes. With refinements, notably from Robert C. Merton, the Black Scholes model can lay claim to being a key foundation of modern finance, contributing not only to the development of the global derivatives market but also to new understanding of corporate structure, equity prices and, importantly, the estimation of financial risk. Without the Black Scholes formula, a lot of rich bankers wouldn’t be rich, and probably wouldn’t be bankers. The formula is a beautiful thing, as partial differential equations go. But it was not original.

Fourier’s Law of Heat Transfer can be rearranged to match the original Black Scholes formula. Fourier published the heat equation in 1822 in Théorie analytique de la chaleur. Fourier himself based his own work on Isaac Newton’s 1701 work, “Scala graduum Caloris“. It is worth a detour to illustrate the connection between Black Scholes and the heat equation. I omit the full transformation while, hopefully, illustrating the major similarities.

Jean-Baptiste Joseph Fourier

The heat equation is a partial differential equation that models temperature flow through a medium over time.

Fourier’s Heat Equation

A solution to the equation reveals the temperature of an identified point in a medium given time and space of the medium. Assume a perfectly insulated metal rod with open ends; the heat equation tells us how long it will take for heat applied at one end of the rod to travel to the opposite end.

Fourier’s heat equation states that change in energy with respect to time is proportional to the change in temperature with respect to space. An identical relationship holds in the Black Scholes formula, which states that option value with respect to time is proportional to change in asset price.

A key part of the heat equation is the assumption of uncertainty in the medium transmitting the heat. The characteristics of the medium determine the way Brownian motion behaves, principally through speed of molecular vibration. The volatility of the molecules in a medium define how heat propagates along its length. This echoes the property of implied volatility in the Black Scholes formula.

Given the canonical authority afforded the Black Scholes model it feels embarrassing to point out the salient features of the model were published 151 years before the appearance of the 1973 paper. What took finance so long?

The second example illustrates a form of categorisation by American financial theorists used to enhance their own authority by adopting ideas of others. In this case, the invocation by numerous American financial theorists of the French mathematician Louis Bachelier.

Louis Bachelier, in academic robes

Today, Bachelier is credited by many financial economists as the previously unsung identifier of stochastic processes in financial markets. The consequence of a stochastic process is that current values contain no memory, meaning future evolution of values can never be known. This idea led, in the later 20th century, to many of the central concepts of securities analysis.

The ‘creation myth’ propagated by many in financial circles is that Bachelier was largely ignored in his own country and lifetime, suffering academic rejection by his peers and obscurity. According to financial economists, his reputation was rescued by Americans; notably Jimmie Savage, Paul Samuelson, and others. These modern authorities cultivated a proper regard for this mistreated French genius from half a century earlier. Focus largely fixated on Bachelier’s PhD thesis of 1900, ‘Théorie de la Spéculation’ from which emerged the view that this lost French academic provided the ‘origin of modern (American) finance’.

In fact, Bachelier was known throughout European and American mathematical circles during and after his lifetime. His work was cited in a number of journals in the early 20th century, especially his more detailed later publications, notably the 1912 work ‘Calcul des probabilités’, which influenced a number of important mathematicians and statisticians, long before his ‘discovery’ by Samuelson and co.

It is worth illustrating the widespread influence of Bachelier in his own era. The economic giant, Maynard Keynes, was familiar with Bachelier’s work in the 1920s. Montessus de Ballore, a French professor of mathematics, wrote in 1908 that speculation may be subject to “Bachelier’s Theorem”. Marcel Boll, another French professor, this time of physics wrote in 1912 that Bachelier had exposed the “fair game theory of speculation.”

Nor was his renown limited to Europe. Henry Lewis Rietz was president of the Mathematical Association of America in 1924 and cited Bachelier’s work. Another American mathematician, Arne Fisher published an important work on ‘The Mathematical Theory of Probabilities and Its Application to Frequency Curves and Statistical Methods’ in 1915, including reference to Bachelier. At the seventh annual meeting of the Mathematical Association of America in December 1922, Fisher referenced Bachelier’s work in relation to securities prices: “The Bachelier and Gram methods might, for instance, be used to solve the following problem: What is the probability that a certain stock or bond will be quoted at a price X at time T on the stock exchange?”

Paul Samuelson himself reported he came across Bachelier in the 1930s. Immediately after WWII, Americans Doob and Feller both cited Bachelier’s work. Doob wrote he ‘started studying probability in 1934 and found references to Bachelier in French texts’.

However, it is only in the 1950s and 1960s that American financial economists, such as Samuelson, confidently awarded Bachelier the mantle of ‘important contributor to current thinking in American financial theory’. The stamp of Samuelson certainly made a big difference to the spread of Bachelier’s ideas within economics. Later, Black and Scholes referred to the importance of Bachelier’s insights in their original paper on option prices. And so, the myth arose of a foreign genius rescued by modern American economic academia. This myth is obviously incorrect.

So why were these, and other, attributions so misconstrued? A plausible explanation is that only in the 1950s did the global importance of the dollar, and the American consumer confirm the United States as the unassailable economic hegemon. This dominance encouraged a set of ideas promoting, and justifying, their exceptionalism to Americans. This was particularly important in finance, as dollar centrality was one of the most important metrics of global dominance. American finance needed a formal construct, and it wasn’t going to waste time on self-reflection or antecedents. History needed to be made to match the current reality.

Bachelier was ‘adopted’ and promoted because his ideas converged with emerging American strands of thought and acted as a kind of ‘appeal to ancient authority’, in much the same way the Renaissance thinkers acquired authority by citing, and ‘rediscovering’ ancient knowledge. The ‘rescue myth’ bestowed a role of benefaction on American school of financial economics. The fact that the ideas had long been present and influenced many predecessors in other disciplines was conveniently omitted. The ‘exorbitant privilege’ of the dollar led to the ‘exorbitant privilege’ of Chicago (and MIT) researchers to construct their own ‘origin myth’. The following plot of the citations of Bachelier, as well as all of the examples used above, is taken from Franck Jovanovic 2012 detailed paper ‘Bachelier: Not the forgotten forerunner he has been depicted as.’ It shows how his influence spread in line with the emergence of America’s financial dominance post-Cold War and especially with the rise of the internet and global ‘financialisation’.

Source: Bachelier: Not the forgotten forerunner he has been depicted as.

These two examples raise another, wider, observation. It is striking how financial economics (and economics in general) is slow to absorb innovative views about the world from other disciplines. Science has pushed back the boundaries of understanding of natural processes for several hundred years. Financial economics appears to need to rediscover the same processes only when it suits those running the financial system. That is one possible lesson from the examples given here. This is curious, because finance must operate under the same physical laws as every other action in the universe. Yet the physical laws of thermo-dynamics, energy conservation, entropy and uncertainty still appear as distractions in much of financial economics. More time is spent by financial economists, practitioners, and regulatory authorities on trying to find tricks to circumvent the stochastic processes (VaR?) than is spent on learning to live with randomness. In that sense, financial economics continues to be driven by post-hoc explanation of past mishaps than by scientific enquiry.

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