What is Value?
Published on SSRN
What is Value?
Abstract
The work of Jules Regnault, Francis Galton, John Rae and Vilfredo Pareto covered Duration, Behavior, and Value. Regnault talked about stock market science, statistical nature of Value, duration importance and price behavior. Galton laid the foundation for the robust behavior of Reversion in natural phenomenon. Rae introduced the idea of intertemporal choices which showcased time inconsistency in human behavior and Pareto talked about another robust behavior now known to be ubiquitous in natural systems as a power law. Duration, Behavior, and Value are inseparable. Statistical behavior of natural systems ( e.g. stock markets) expresses themselves durationally. And because stock market systems exhibit uncertainty and order, this creates inconsistencies (anomalies). Instead of acknowledging the statistical behavior of stock market systems, a few generations of researchers have focussed on explaining these inconsistencies through behavioral biases, leading to a polarized debate around efficiency and inefficiency of markets.
This debate has many casualties, one of the key being the global investor and how he(she) understands Value. If stock market systems function statistically, value creation and its transformation into growth are statistical phenomena rather than driven by fundamental, psychological or economic factors. Value is misunderstood by the global investor. Despite the fact that Value stocks move from an inexpensive state to expensive state while Growth underperforms and drags in performance over the longer durations moving from an expensive state to a less expensive state, Value and Growth are interpreted as disconnected ideas which are assumed to be only defined fundamentally. This narrow definition of Value has added to the academic confusion around inconsistencies and created an investing style bias.
Investing styles are at the heart of the investment business, which brings along with it new factors like ‘Size’. These various factors overlap with each other. On occasions, it has been even seen that the factors are a proxy for each other. This raises the question regarding the theoretical foundation driving the respective factors. If Value can be explained statistically, it will also explain factors like Growth, Size, Momentum and other factors and hence bring in a needed clarity of how markets function and whether there is a universal factor that drives stock market systems.
1697-1790 Dojma to American Stock Exchange
1834-1886 Value, Behavior, Duration is Statistical
1920-1934 Value is Fundamental and Cheap
1952 Linear Assumptions
1958 Is Capital Structure Relevant or Irrelevant?
1962 The Non-Linear Model
1964 Divergence of Risk from Return
1966 Outperformance
1977 - 2001 The Size Proxy
1988-2015 Is Reversion Statistical?
2000 - Power Law Criticism and Ising Model
2006-2014 The Duration Factor
2007 Divergence Cyclicality
2010, Mean Reversion Framework
2015 Reversion and Diversion Hypothesis
2015 Is Smart Beta Dumb?
2016 Conclusion
1834-1886 Duration, Behavior, and Value
It is essential to revisit the history of research before we answer the questions about Value. The Value was defined statistically 100 years before value investing got a fundamental label. Though on one side going back in time to identify the roots of Value can help appreciate the contribution of various thinkers in refining big picture thinking, while on the other side one can also see that a piecemeal thinking creates confusion and distortion of historical facts. One can assume this misinterpretation to be unintentional as deciphering historical research required a multidisciplinary knowledge and in some cases even knowledge of various languages.The aim of this paper is to dig deeper into historical research and relook at those seminal ideas which formed the basis of the modern finance. Jules Regnault (1863), Francis Galton (1886), Vilfredo Pareto (1896) and John Rae (1834) were the first to lay down the statistical foundations for duration, behavior and value.
Duration, John Rae, 1834
Intertemporal choice is the study of how people make choices about what and how much to do at various points in time when choices at one time influence the possibilities available at other points in time. These choices are influenced by the relative value people assign to two or more payoffs at different points in time.
Behavior, Galton, 1884
Galton was the first to describe and explain the common phenomenon of regression toward the mean, which he first observed in his experiments on the size of the seeds of successive generations of sweet peas.
Jules Regnault, 1863
Jules Augustin Frédéric Regnault was a French stock broker's assistant who first suggested a modern theory of stock price changes in Calcul des Chances et Philosophie de la Bourse (1863) and used a random walk model. He is also one of the first authors who tried to create a "stock exchange science" based on a statistical and probabilistic analysis. His hypotheses were used by Louis Bachelier.
Vilfredo Pareto, 1886
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power law probability distribution that is used in the description of social, scientific, geophysical, actuarial, and many other types of observable phenomena.
Galton and Regnault
Galton though a contemporary of Regnault was more focussed on the behavior towards mean (mediocrity) in various systems different than stock markets. Regnault’s experience in markets assisted him in seeing stock market systems and the science in them. Both Regnault and Galton talked about mean and the variance around it. For Jules Value was connected to the idea of statistical reversion, duration relevance, and random walk. Markets according to Regnault were about reversion to true Value. Regnault’s work laid the basis for the random walk for Louis Bachelier. Both the ideas involving random walk and reversion to mean are an integral part of modern finance.
Regnault, Bachelier and Einstein
Bell Curve history starts from, ‘The doctrine of chances’, Abraham de Moivre in 1738. This was followed by Carl Friedrich Gauss’s, ‘Theoria motus corporum coelestium in sectionibus conicis solem ambientium’ in 1809. Although Gauss was the first to suggest the normal distribution law, Pierre - Simon Laplace made significant contributions in his ‘Mémoire sur la probabilité des causes par les événements, in 1774. And it was only in 1860 that James Clerk Maxwell, in ‘Illustrations of the dynamical theory of gases’ illustrated that normal distribution is not just a convenient mathematical tool, but may also occur in natural phenomena. It was Francis Galton, who illustrated the idea in ‘Regression towards mediocrity in hereditary stature’ in 1886. Louis Jean-Baptiste Alphonse Bachelier, The Theory of Speculation, 1900 was the first to model the stochastic process now called the brownian motion, which is normally distributed.
Does God practice a random walk? The ‘financial physics’ of a nineteenth-century forerunner, Jules Regnault, Franck Jovanovic and Philippe Le Gall, 2001
“Bachelier had anticipated many of the mathematical results developed in Albert Einstein’s 1905 paper’ (LeRoy 1989: 1587). Random processes happen to have been first considered in the context of economics, in 1900, by Louis Bachelier’ (Mandelbrot 1966: 243)…Though his contributions were ignored for sixty years, the first statement and test of the random walk model was that of Bachelier’ (Fama 1970: 389).”
Calcul des Chances et Philosophie de la Bourse (1863)
“…we suspect that such an identification of the origin of the random walk hypothesis in finance, and consequently of the modern approaches to capital markets, is historically imperfect and mistaken. In this paper, we indeed claim that in his book, Jules Regnault, laid the basis of modern stochastic models of price behavior.”
It is not the first time that acknowledgments have alluded many historical thinkers. There was 60 years delayed acknowledgment of Bachelier’s work, which was based on Regnault’s earlier thoughts on Random Walk. It was Jovanovic and Gall who analyzed the work of Jules Regnault in 2001.
Why is Regnault’s work important to understand ‘Value’? Regnault’s contribution along with Rae, Pareto and Galton form the foundation of understanding randomness, behavior, and their statistical relationship. Though Mandelbrot was the one who acknowledged Bachelier for his contributions on Random Walk, he challenged the Bell Curve as an expression in stock markets, “Bell Curve is Nonsense” in The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin, and Reward. Mandelbrot was a proponent of Pareto distributions. The exaggeration of trends and failure of trends to revert have come to be seen as the predominance of Pareto in stock markets. Because reversion phenomenon was so widely accepted, the appearance of exaggerated trends came to be seen as a failure of mean reversion as a robust law. This fueled the argument for Pareto believers who came to see the statistical distribution as a challenger to Galtonian reversion, even coming to suggest it as irrelevant for natural systems.
In, Is smart beta dumb?, Pal, 2015, the author explained how Pareto and Galton together defined the framework for natural systems. Vilfredo Pareto, father of microeconomics created the Pareto curve explaining wealth distribution in Italy. The popular rebranded 80-20 law suggests that “80% of effects come from 20% of the causes”. In stock market terms it means, “Winners and losers persist”, “Momentum is a natural continuum”. Pareto is also referred to as the Power law, the behavior observed in stock markets and also used to make a case against the normally distributed bell curve. Though the bell curve has been challenged as the natural expression for stock markets and Pareto has been stated to be the real expression, markets express both Pareto and Galton. As markets express the four states (a,b,c,d); Past winners tend to lose, past winners tend to win, past losers tend to lose, past losers tend to win. Momentum persists and fails just like reversion. Both these diametrically opposite observances may seem incomplete, but they do occur often at the same time. This durational aspect links back to John Rae and his work on behavior and inter-temporal choices.
Behavioral Finance acknowledges Reversion in many popular research papers, “Does stock market overreact?” DeBondt and Thaler (1985)
Scientific and Deterministic
According to Regnault, the scientific and deterministic were synonymous and inseparably connected. The deviation, noise, the error was an intrinsic part of the scientific determination.
Le Jardin au Noyer. Pour un Nouveau Rationalisme. Paris: Le Seuil, Jovanovic, Franck (2000)
“..great part of Bachelier’s reasoning came directly from Regnault most importantly the random walk hypothesis….Regnault undoubtedly followed Quételet’s program of social physics, designed to form the foundation for an exact science of human societies, and approached ‘scientifically’ the issue of speculation. His work tried to show that short-term speculation based on the search for immediate gains leads to ruin but that, by contrast, another kind of speculation, based on the long-term gains, was socially useful…But his approach to economics was also certainly pioneering: as early as 1863, his work took the shape of theoretical and mathematical models that were however discussed in literary terms and, at a time when the application of statistics to economic affairs was controversial in France, some of these models were combined with statistical procedures…the construction of a ‘scientific’ approach to the stock market, Regnault followed a statistical and probabilistic path…His aim was the identification of ‘new laws of the variations on the stock market’. It has to be noted that he saw his investigations as undoubtedly scientific his agenda was the construction of a ‘Science of the stock market’.”
“His aim was thus, in a scientific perspective, to separate two kinds of speculation: short-term speculation and long-term speculation…Regnault believed that the terms ‘scientific’ and ‘deterministic’ were synonymous and inseparably connected…good reasons to refer to Laplace in the early pages of his book. His fundamental postulate was that chance does not exist: ‘in nature, nothing is arbitrary’. Nature was characterized by ‘general and unchanging [immutables] laws’, society was ‘a huge machine made up of springs that are connected’.”
Bounded Knowledge
Jovanovic and Gall, explain how Regnault was much ahead of his time. Here he talks about bounded knowledge, which is imperfect and approximated. Though Regnault talks about how neither the variations nor previous prices were useful to predict future variations, he also mentions how future inexorably originates in the past, just like the effect constantly originates in the cause. The knowledge about laws is an art of approximation and uncertainty arose because of errors and deviations from these laws. Putting it differently, Jules meant that laws are an expression of human approximation of nature and to take them on face value and not embrace them with their failures and weaknesses is bounded knowledge or ignorance. Suggesting that Galtonian Reversion is redundant and Pareto is the only law points to academic ignorance.
A conceptual history of the emergence of bounded rationality, Matthias Klaes, ESHET conference, Paris, 2003.
The idea of bounded rationality has roots in limited intelligence 1840, finite intelligence in 1880, and Herbert Simon 1957.
“…‘nothing can happen without a previous cause’ and that ‘anytime, everywhere, the same causes produce the same effects’..second, the deterministic laws were only accessible to us in a state of perfect knowledge: it would then be possible to discover what the future had in store for us. However, individuals have bounded knowledge and have to content themselves with an approximate knowledge of these laws. This imperfection of knowledge has two consequences. On the one hand, individuals can only try to tame the future through the elaboration of probabilities that are, of course, of a subjective nature: ‘Chance does not exist, only our ignorance exists’. ‘Our whole calculations are only based on our personal observation’. On the other hand, he emphasized that the underlying uncertainty favored errors and deviations: ‘Ignorance, that . . . maintains our illusions and errors, is the first cause of our excesses, our passions, our misfortunes’.”
Mean Value, Statistics, and Society
Here Jovanovic and Gall explain how Regnault explained ‘Mean Value’ as equilibrium in the social world, a sign of order, a deterministic law that governed human affairs. He connected societal behavior with a statistical mean.
“On the other hand, the mean value represented a harmonious equilibrium in the social world, the ideal in morals: it was the sign for an order that he supposed to prevail beneath…The mean was seen as the manifestation of the deterministic laws that rule natural and human affairs, and statistics was seen as a means to approximate determinism. Once these exact laws were discovered by scientists, the individuals could then reach ‘a stable and quiet state’. Deviations should thus be reduced through a progress of civilization or of advancement in scientific knowledge.”
Stock Markets Variations and Universal Laws
Here Jovanovic and Gall explain how Regnault expresses societal activities in the context of a multitude of unrelated events while still looking at the society as a part of a unified conception of nature, through time and space. For Regnault the moral world ruled by the same laws as the physical world, the reason he talked about stock market science explaining the fundamental wheels of nature.
“The variations of the Stock market are ruled by constant mathematical laws! Events that are generated by the caprices of men, the most unpredictable shocks of politics, the most cleverly studied financial combinations, the result of a multitude of events that are not related, all these effects are tied up in an admirable set, and chance is now a meaningless word….A unified conception of the world: analogies and transfers at work another feature of Regnault’s deterministic framework is to be found in the idea of reductionism: the various bodies that constitute the universe were seen as ruled by the same kinds of laws. A unified conception of nature means here that some laws were constantly at work, through time and through space, and at very different levels, and that various sciences and disciplines have to share principles, methods and also laws in common. It is well known that several social scientists of the nineteenth century and of the turn-of-the- century era developed similar ideas, and were consequently led to approach economics at the light of the natural sciences…that ‘the moral world is ruled by the same laws as the physical world’. Regnault to ensure that his own work in the social field was connected to fundamental wheels of nature.”
Short Term Speculation
Here the authors explain how Regnault considered speculation as short term, as moral with perfect equal chances to make profits. Speculators had no advantage as price behavior was a random walk. It was Regnault’s work that formed the basis of a contemporary theory of informational efficiency of financial markets. Information as well as its interpretation were seen as two kinds of causes that generate the short-term variations of stock prices.
“Regnault aimed here at constructing a model of moral short-term speculation, i.e. at showing that speculation is moral because each agent has here perfectly equal chances to make profits ‘at any moment, no advantage is existing for one possibility or for the other’. In such a case, the expected profit is zero for each operation and consequently he aimed at showing that the stock market should not be condemned per se. In a very pioneering way, price behavior took the shape of a random walk model although he never used the word….This was undoubtedly an important step in the construction of financial theory as well as in its theoretical basis. Bachelier will follow this path in his 1900 dissertation in which he first offered a formalization of the Brownian motion and thus initiated the mathematical theory of stochastic processes in continuous time (Mandelbrot 1966). Models of that kind will also be used in the construction and the test of the theory of informational efficiency that was synthesized by Fama (1970). Given this relation between the theory of efficient markets and the random walk model, it is not surprising to discover in Regnault’s book the main lines of the contemporary theory of informational efficiency of financial markets: information as well as its interpretation were seen as two kinds of causes that generate the short-term variations of stock prices.”
The author believes that it was Regnault’s information hypothesis that forms the basis of Efficient Market Hypothesis. Regnault was more focussed on information irrelevance as for him information was more a factor of short-term speculation. It was Kenneth Boulding who laid a more comprehensive framework in 1966.
“Regnault’s originality lies in this association of these causes with the new information that arrives on the market. In addition, he claimed that at every moment of time, the price contains the whole information:..he deduced that the probability for the price to increase is equal to the probability for the price to decrease, i.e. a half. If such was not the case, agents could arbitrage and choose systematically the strategy that has the greatest probability…In all the games of chance that contain two opposite chances, relative equality precisely results from the possibility for the player to choose one chance or the other: moreover, these two conditions cannot be separated, because if a possibility would generate a greater advantage than the other one, it would be constantly chosen..like in a game of heads or tails, the movements of stock prices are independent: neither the variations, nor previous prices were useful to predict future variations…analysis of the price behavior in terms of a random walk. However, another particular feature of the short- term behavior is the subjective nature of the probabilities…The movement of prices and the subjective evaluation of new information. The subjective nature of the probabilities affects the evaluation of securities as well as their price, but Regnault suggested that the evaluations made by individuals were following a normal law….evaluation of the height of a building by a group of individuals, and was led to think that these evaluations were ruled by a law close to the Gaussian one…”
Value, Duration, Reversion
Regnault was the one to not only talk about Random walk model but also connect it to the law of variations through time. Though the challenge to the Random walk emerged as prices were shown to be non-normally distributed the approximation that price variance is a factor of square root of time holds well. This was the first ever proof of the co-existence of non-normal distribution in prices and normal distribution in variance; both Pareto and Galton coexisting together. The security, through its variations, was in search for true value and this it did by reverting around the mean variation.
“These assumptions thus enabled him to construct a symmetrical random walk model. We must now show the way he obtained from this model a law of variations of the price through time…The law of deviations thus showed that there was an equal probability of a half for the price to increase or decrease at each moment of time. He then investigated the way the prices were varying through time, and he discovered a relation between the mean deviation of prices and time…In the latter case, a mean deviation for a given period can be calculated, he looked for a relation between time and that deviation. He remarked that the mean deviations for a given period of time were approximately equal and that the shorter the period of time considered, the smaller the deviations…if the period of time is only half as much, the deviation is divided by a number inferior to two. …the deviation of the prices increases with the square root of time…Otherwise stated, it is not possible for an agent to anticipate in an exact way the future price of a security, but he can anticipate its mean deviation for a given period of time.”
“The security, in its variations, is constantly in search for its true price, or an absolute price, that we can represent as the center of a circle, the radius of which would represent the deviation that can equally appear in the one or the other direction, and on each point of the surface, in a period of time consequently equal to the surface, and the whole points of its circumference would represent the limits of the deviations. In its variations, the security is only moving away or getting closer to the center, and from the basic notions of geometry, we know that the radius or the deviations are proportional to the square roots of the area or of time.”
Law of Ruin
Jovanovic and Gall explain how Regnault believed that it was the frequency of trades that caused the ruin for the speculator. He referred to it as the law of ruin. This resonates with the current debate regarding passive investing versus active money management and a case for tactical passive investment management.
“However, Regnault constructed a second model of short-term speculation that incorporated the transaction costs and that enabled him to demonstrate the inexorable ruin of the short-term speculation….Other things the same, the unfavorable possibilities are largely reduced on a large market, where the business is very important, and they proportionally increase on a small and especially a sensitive market….Regnault thus had in his hands the elements that could pave the way for a ‘law of ruin’…The chances of loss are increasing the power of the inverse ratio of time…The frequency of operations is an abuse; and since the unique motivation of each exchange is and has to be usefulness, each time this usefulness disappears, there is an error or a bad use; from this, we can thus clearly separate the game from the speculation…the transaction costs represent for him twenty times more, that is 2.5%. As a consequence, since the gain and the loss equilibrates, no more that forty operations will lead to the loss of his capital.”
Non Random Long Duration
Regnault was also the one suggesting persistent trends, which he referred to as deterministic laws that rule the stock market, existed in the longer term. As the duration became larger, there was anticipation, predictability and social usefulness of statistical approach for the social world. Stock prices had a longer term expression, which differentiated itself from the short term noise game. Simply putting, Regnault talked about Random walk in the shorter term and statistical reversion in value over the longer term, a non-random behavior.
“…In the long term, deterministic laws rule the stock market. We shall first examine the way long-term speculation was defined, the way it was seen as representing a social usefulness, and explain its relations with constant causes. Then, it will be possible to shed some light on Regnault’s methodological choices: he thought that the accidental causes compensate on the long term and consequently that the underlying order that rules society could be discovered. In Quételet’s style, his approach was closely associated with the determination of mean values and this was an opportunity to claim the usefulness of a statistical approach to the social world…Some speculation about long-term causal laws…The construction of this second model originates in the belief that true deterministic laws were permanently acting although masked by the accidental causes…The knowledge of such a constant cause was indeed delineating the outlines of a moral behaviour that leads to a social usefulness. At that stage, Regnault clearly opposed the short-term game to long-term speculation.”
Reversion is statistical, Diversion is a vice
Statistics was a way for Regnault to approximate deterministic laws. The moral expression and its vices which cause deviations are brought in balance with statistical longer term regularity. Galton continued (1886), similar work, regarding variation away and back to mean generationally keeping natural systems in a balance. Regnault rather accepted divergences expressed as social vices as a necessary evil for the statistical longer term laws of reversion to work. Galton ignored the role of deviations and divergence as being essential component to the mean reversion process (Pal, 2015).
“He extensively discussed its applications to numerous issues and focused on the resulting possibility of forecasting. More precisely, statistics was for him a way to discover and to approximate deterministic laws. Statistical laws are not only the concern of material things. . . . Most importantly, they are also and as rigorously the concern of the moral facts, those which are precisely the less likely to belong to a stable or normal state. Births, marriages, diseases, suicides, crimes, etc. can fluctuate from year to year under the influence of accidental causes, but on a rather long period, they will appear as regular. . . .Most surprisingly, our mistakes, our distractions, our biases, and even our caprices are ruled by the law of probabilities. The human mind can appear as indiscernible. . . . Yet, the phenomena that produce it . . . appear as more regular than the physical phenomena when men are free, that is when they are not disturbed by private causes of personal interest….Like Quételet, the statistical approach Regnault had in mind was closely associated with the calculus of mean values, seen as signs of stability and order every kind of variation from an average was considered as an error or a vice.”
In the long duration, Past is connected to future
This role of divergence, deviation and variance was why there was a dependence between past and future. The future originated from the past, as while short-term deviations cancel each other in the longer term behavior was admitted regular around the use of averages. A history of researchers has cited the longer term cycles including Shiller’s CAPE (1988)
“The future inexorably originates in the past, just like the effect constantly originates in the cause….He thus showed that all data was including a short-term or accidental component and a long-term or constant component…The short-term components were seen as the product of causes that ‘inexorably cancel each other’. By contrast, the long-term components are ‘admirably regular’, and ‘the demonstration of this fact is given by the use of averages’…In accordance with his deterministic views, he thus believed that some averaging procedures, associated with the law of large numbers, should be useful to reveal the long-term tendencies. Although he did not construct a formal decomposition of time-series such as those devised during the early twentieth century, Regnault deserves a place in the history of time-series analysis”
Reversion stronger than Diversion
Regnault was also the first thinker to talk about the symmetry of reversion and diversion and how there was a less frequent, but more marked and stronger tendency to revert towards to mean i.e. statistical Value compared to the more frequent tendency to diverge and increase away from the mean.
“He then statistically examined the robustness of this hypothesis. Of course, he had no testing procedures available; however, he proceeded just like turn-of-the-century pioneers of econometrics did and used a graphical approach…Regnault then investigated the way these probable errors were distributed around the mean value and an analysis of the observed deviations led him to think that no symmetry was prevailing…The fluctuations in the prices of public bonds are variable, and their extraordinary deviations reveal a more marked tendency to be inferior to the mean value than to be superior to it. We can thus consider that the increasing state, more than the decreasing state, is a normal one; the decreasing state is more intense, but less durable. . . . In other words, the causes that generate the decline are less frequent than the causes that generate the increase, but their strength is superior.”
Deterministic Law
For Regnault, unlike the deviations, there was a statistical attraction mechanism that constantly moves the prices toward the mean. The attraction centers that brought balance were driving the universal law and this is why it was necessary to wait. In summary, Regnault talked about divergence, its connection with duration and the determinism brought by the universality of the longer term back to the mean.
“The final step: the law of attraction The final step was that of the deduction of a deterministic law that rules long-term speculation: a kind of attraction mechanism that constantly moves the price toward the mean…In the first part of his book, Regnault presented a law of deviations, according to which ‘The deviation of the prices increases with the square root of time’ and is also independent of the price itself. This law could not, of course, contribute to explain a possible relation between the observed price and a mean price. However, on the basis of the preceding steps, he put forward the existence of a second law that stipulates a relation between these deviations and the mean price. The normal distributions around the ‘attraction centers’ led him to think that a kind of ‘force’ was acting. This second law at work states that the price, in all its deviations, is permanently attracted to its mean price, and this attraction is increasing with the square of its distance…Apart from this example, Regnault himself dealt cautiously with this law and confessed that he ignored ‘the measure of this force, and the very moment when it will be at work’ (1863: 188). However, he had good reasons to suppose the existence of this law. The ‘attraction law’ was indeed seen as a ‘universal law’ (1863: 168)…This ‘law of attraction’ was undoubtedly the law Regnault was looking for. It crystallized the various constant causes at work and, consequently, aimed at proving that the short-term speculation was a mere illusion: in spite of its apparent randomness, the price of the French 3 per cent bond was dependent on a deterministic law. The short-term speculator was thus considered as ‘blind’, whereas the ‘true speculator’ behaves ‘in relation with the interests; he does not focus on the current circumstances, but on the future’. The end of the story was thus a moral one: the short-term speculator was favoring and took advantage of – the existing (moral) deviations of society, but ‘the extreme things always lead individuals and people to their loss’. The deterministic laws Regnault put forward had thus to induce a (moral) change in the behaviour of the economic agents: they have to learn the crucial importance of time – ‘it is necessary to WAIT’, since ‘Time will always lead the price to their true value and will correct the deviations of speculation’. The knowledge of these laws could then lead to a kind of convergence towards a state of certainty – ‘the constant feature of events invariably leads to a convergence in a more or less immediate future’.