In The Problem of China,1 Lord Russell quotes a certain Mr Chi Li,2 on the influence of hieroglyphic writing upon education and ways of thinking:
…The accumulative effect of language-symbols upon one’s mental formulation is still an unexploited field. Dividing the world culture of the living races on this basis, one perceives a fundamental difference of its types between the alphabetical users and the hieroglyphic users, each of which has its own virtues and vices...
The above analysis leaves us with an interesting conclusion: Our ways of thinking or “mental formulations” are affected by the tools we use to express our ideas. And I would suggest to the reader that the way we look at financial and investing issues is affected by the tools we use. Since the 1870s, six innovations have developed that shaped what we know today as Theory of Finance. They underlie the way we approach investing, but in my view, they also constitute fundamental fallacies. In no particular order, these are (1) the use of differential analysis, (2) the use of general equilibrium theory (dealt with in the Appendix section), (3) the use of probability theory, (4) the (corruption of the) concept of liquidity, (5) the misunderstanding of sovereign risk and, by transitivity, (6) the risk of contagion, also known as systemic risk or correlation.
Differential Analysis
Every paper in the Theory of Finance and most algorithmic trading strategies today are based on differential analysis. However, the assumption that human action (of any kind, not just limited to investing) takes place in continuous form is erroneous. It is an assumption that cannot pass the slightest test of reality. The “taste” for continuity dates back to the origin of infinitesimal calculus,3 to Gottfried Leibniz (1646–1716).
This mathematical concept, as useful as it is in other fields, is misleading when applied to human action and, therefore, to investing. Infinitesimal or minimal changes in the context in which we unfold entrepreneurial behaviour do not produce infinitesimal results. I may have a business, and if the government increases my capital gains tax rate from 15% to 16% during one year, I will probably not change a single process or decision in my daily operations. It can happen again two years later, taking the rate from 16% to 18%, and still although I will get concerned and think twice before making capital expenditures, most likely, nothing will have changed with the way in which my business operates. But if five years after the first increase, another hike takes the tax rate on capital gains from 18% to 21%, it is likely that a whole new front of opportunities will open, with tax advisers cold-calling me to discuss how to reorganize the legal structure of my company. And a significant wave of mergers, acquisitions, asset sales, spin-offs, capital outflows or conversions may ensue, taking policy makers by surprise, as they end up collecting less revenue from this tax at a 21% marginal rate, than previously, when they charged only 15%.
Why did I not react before the 21% tax rate was imposed? Probably because the cost of seeking advice or reorganizing the legal structure of the company was too high to justify change at a 15% or 18% rate. And probably too, other entrepreneurs in the tax-advisory sector saw that as well. However, at a 21% rate, perhaps suddenly these entrepreneurs came up with a cost-effective marketing strategy, and once they began discovering the new market opportunity, reorganizations became a no-brainer.
This is simply one of the infinite examples that illustrate how we react to small changes. Inertia does not just belong to the world of physics. It is also omnipresent in human action. We only change the status quo after we realize that the cost of maintaining it is higher than that of changing it. In the meantime, we do not react. We put up with discomfort as long as our appreciation of the cost of getting rid of it is higher than its benefit.
One can legitimately ask why we use infinitesimal calculus in Finance and Economics. When a paradigm is incorrect, two consequences follow: First, a wrong paradigm leads to wrong conclusions. And second and most important, when we are comfortably using a wrong paradigm, we refrain ourselves from discovering the correct one.
In Finance (and in Economics too), the assumption of continuity gives a false sense of reality.4 What underlies and is vitally connected to this assumption is the misunderstanding of the concept of liquidity, which I deal with later in this lesson.
Human action unfolds in leaps; it is discreet, not continuous. It has to be so, because we face eternal uncertainty, not risk. Risk is bounded, like Cauchy5 put it, “between the given limits”. Uncertainty knows no a priori limits. And it is the recognition of this that drove humans to develop institutions, to coordinate behaviour and thus, over time, to come up with the “given limits”. The proof that our actions cannot be described in continuous time, with continuous functions, using infinitesimal analysis is in the fact that we use money. If life was ruled by continuities, bounded by limits, we would have developed institutions to barter. But we do not barter. We trade indirectly, through an institution that we call “money”.
Probability Theory
The ability to use probability in Finance is the least challenged axiom that I have encountered. The theory of probability itself is also relatively recent, more recent than the study of Finance. Like most breakthrough innovations, the study of probability began as an applied discipline. Nobody knows exactly when it did, but there is a consensus that the first attempts were initiated by Girolamo Cardano (1501–1576), who among other things was a gambler. Later on, Pierre de Fermat (1601–1665, lawyer), Blaise Pascal (1623–1662), Jacob Bernoulli (1654–1705), Pierre Simon Marquis de Laplace (1749–1827) and Siméon Denis Poisson (1781–1840) established the basis for the comprehensive work that blossomed at the end of the nineteenth century, led by Andrey Markov (1856–1922).
But it was only very recently, less than a century ago, that the foundations of probability theory were laid definitively and with singular clarity by the most inconvenient of mathematicians: Someone actively involved in World War I (for the Central Powers and against the Allies) and in unmasking what would be called the subjective theory of probability. He was unfortunate, because the subjective theory had been championed by no other than John Maynard Keynes, who at the time was the most influential (and charismatic) economist. These two stain spots on his otherwise immaculate career (he would become the Gordon-McKay Professor of Aerodynamics and Applied Mathematics at Harvard University in 1944) were enough to earn him a cruel indifference towards his work on the foundations of probability theory, titled “Probability, Statistics and Truth”, first published in 1928.
If this author had published his work before the times of the French Revolution, or if Andrey Markov had survived long enough to comment on Keynes’ essay, his ideas on probability would have likely outlasted him. But history is flushed with tragic coincidences. Notwithstanding them, by 1928, he had impeccably demonstrated that:
…It is possible to speak about probabilities only in reference to a properly defined collective . A collective is a mass phenomenon or an unlimited sequence of observations fulfilling the following two conditions: (i) the relative frequencies of particular attributes within the collective tend to fixed limits (ii) these fixed limits are not affected by any place selection . That is to say, if we calculate the relative frequency of some attribute not in the original sequence, but in a partial set, selected according to some fixed rule, then we require that the relative frequency so calculated should tend to the same limit as it does in the original set. The fulfillment of the condition (ii) will be described as the Principle of Randomness or the Principle of the Impossibility of a Gambling System … 6
The first quoted sentence above, in my view, should be clear enough to conclude that in Finance, the only proper collectives we can speak of are asset classes. To demand more granularity would be inappropriate. We can think of stocks or convertible notes or credit default swaps as collectives. And only as such, can w...