Letter from France - All well again on the finance front?

In another letter inspired by the recent crisis, Alan Kirman takes a look at the French origins of the efficient market hypothesis that has been one of its principal victims.

There were many things which would have made good subjects for this letter this year. There was the ‘grand emprunt’ the great public loan which was originally to have been a call to the French public to buy bonds to finance the projects which were to be specified before the bonds were issued. The government finally got cold feet and decided to raise the money, conventionally on the financial markets. The only difference in the end being that the funds raised in this way were to be attached to specific targets and ever since the government announced that some 11 billion of the 35 to be raised were to go to higher education there has been little criticism from academic economists. Another fascinating topic is provided by the rate of unemployment and the satisfaction in some quarters on seeing the US unemployment rate rise above that in France. More than one commentator has put this down to the rigidity of the French labour market which has suddenly become a source of self-satisfaction. However it is the financial crisis that will be the centre piece for this letter. This, not least because the financial sector seems to have decided that all is now well again and that we can go back to business as usual. You might well ask, what happened to the soul searching that was to take place in the financial sector and the demise of the Efficient Markets Hypothesis? Recall that in September 2008 Alan Greenspan,when talking about the hypothesis in question, declared to the finance committee of the House of Representatives that ‘in the summer of 2008 the whole intellectual edifice collapsed’. In France the banks are back in fine form, not lending to many clients but certainly again paying large bonuses to their traders. Nicolas Sarkozy like Gordon Brown felt the heat of public opinion and decided to levy a substantial tax on all such payments. Nevertheless, the way in which the tax is to be imposed and the way in which the proceeds are to be used means that this is no more than a gesture to popular opinion.

But what is interesting here is the peculiarly French story which underlies the origins of the Efficient Markets Hypothesis whose demise has been perhaps prematurely announced by Greenspan. The standard legend is that Bachelier developed the basis of the theory in his thesis and in so doing preceded the work of Einstein on Brownian motion. The legend continues saying that Bachelier made this step on his own, the originality of his work went unrecognised and unnoticed until the development of modern finance from the 50s onwards, first with optimal portfolio theory and then with option pricing. All of this happened after Bachelier’s death in 1946 and so he went to his grave and never lived to see the glory which should have been his right. He was poorly treated by his contemporaries and died a bitter man. This legend like many others is a considerable distortion of the truth. What is true is that Bachelier who was definitely paranoid, was, to use Groucho Marx’s notion, rationally paranoid, just because he believed that everybody was against him did not mean that this was not the case in reality. Not only did he have terrible luck in his life, losing both his parents early and having to earn to keep the family together but he was treated with condescension or disdain by those who controlled the mathematical profession in France at the time. Because of his personal hardship he could not afford to go through the ‘Classes Préparatoires’ and enter a Grande Ecole. To this day the chances of getting an academic job in mathematics if you did not follow this royal route are negligible. This meant that he had not had the two or three years of intensive training which gave students the necessary equipment to develop their arguments rigorously. Indeed one of the main criticisms of Bachelier was that both his reasoning and his subject were outside the realm of what was normally considered as mathematics. For this reason he was given the mark ‘honorable’ rather than the ‘très honorable’ necessary to get a university job. Again, this is still true to this day. As a result he lived with part time or temporary jobs till the age of 55 when he finally got a chair in Besançon when the holder moved to Aix en Provence! He was prevented from getting a job in Dijon because of Paul Levy’s negative report, based on an erroneous interpretation of Bachelier’s thesis. Levy claimed to have found a fundamental error in the thesis but this was not the case and he later apologised to Bachelier for his mistake. But now to the other parts of the legend. Was Bachelier as original as is claimed in his anticipation of the efficient markets hypothesis? Not really, because he was preceded by Regnault who wrote in 1863

It is useless for the actor in a market to claim that it is only by forecasting what will happen in the distant future that he can predict whether the market will rise or fall, we know that these future events, if they exist at all, are already incorporated in the current price ; so if one thinks about the meaning of the word  'value' one can see that the value of an asset can only be given by the asset’s current price. (Regnault, 1863)

What is more Bachelier, was aware of Regnault’s work and some of his notes on the latter’s work can still be found. Regnault was actually employed in financial markets, had little or no mathematical training, and therefore did not develop his arguments formally. However, much of the intuition was there. Bachelier also used some of the graphs from Lefebvre (Lefebvre, 1870) who had worked on the movement of stock prices. Again, while it is true that Bachelier developed the notion of Brownian motion in 1900 it is not true that it was ignored either by mathematicians or by economists. What is true is that his argument that stock prices should follow this sort of stochastic process, was only acclaimed and welcomed by economists much later, both for analytic and ideological reasons. The idea that he was ignored for a long time is false. A number of people examined and dismissed his work more or less lightly. Bachelier’s way of thinking and of expressing himself did not help his cause. For example, whilst working on his thesis he tried to find an expression for the price of a call option. In effect he arrived at Fourier’s heat equation by inventing a concept which he called the ‘radiation of probability’. Again, he was anticipating Black-Scholes but his geometric analysis did not help in communicating his result to the academic community but his arguments did not convince those that understood them. For example, shortly after having written his report on Bachelier’s thesis, the great French mathematician Henri Poincaré (1905), observed that it would not be sensible to take this model as a basis for analysing what happens on financial markets. As he said, individuals who are close to each other, as they are in a market, do not take independent decisions, they watch each other and if there is any consistency in human behaviour, it is always herd behaviour that persists. Thus Poincaré clearly envisaged one of the most prevalent features of financial markets long before modern economists took this theme up to explain ‘excess volatility’. Again, the claim that economists ignored Bachelier’s work is not really founded. Keynes wrote a review in 1912 of Bachelier’s book (Bachelier, 1912) on probability theory, (which the author considered somewhat immodestly to be the first real advance on Laplace), and said the following,


M. Bachelier’s book is large and makes large claims…the author is evidently of much ability and perseverance and of great mathematical ingenuity, and a good many of his results are undoubtedly novel. Yet, on the whole, I am inclined to doubt their value, and, in some important cases their validity. His artificial hypotheses certainly make these results out of touch to a quite extraordinary degree with most important problems and they can be capable of few applications. (Keynes, 1912).

However he did add., ‘I do not make this judgement with complete confidence, for the book shows qualities of no negligible order’.

What is interesting is that despite the initial reticence of both mathematicians and economists, once the theoretical train was under way in the 50s, all opposition was simply pushed to one side. The two major steps which firmly established the Gaussian random walk in the financial landscape ignored both the empirical evidence and theoretical criticisms. The first of these was the development of optimal portfolio theory by Markowitz whose theory used the assumption that the changes in asset prices had a Gaussian distribution. Despite the pleas of Benoit Mandelbrot, also a Frenchman by naturalisation, and others and the empirical evidence, this assumption was maintained. This was for reasons of analytical convenience since then the central limit theorem could be applied while if other distributions, favoured by Mandelbrot, from the family of Levy stable distributions (the same Levy who blackballed Bachelier in Dijon), had been chosen this could not have been done. The same thing applies to the development of Black-Scholes (1973) option pricing. This again relies on the refutable and often refuted assumption that the price of an asset follows a lognormal process. Theory ploughed ahead ignoring its own weaknesses despite the criticisms of many mathematicians and economists.

Fama, himself in 1965 (Fama, 1965), wrote an article in which he indicated that changing the distributional assumption of the theory undermined the notion that diversification necessarily diminished risk. This was of little interest to those who wished to use the theory to develop financial instruments and was quietly swept under the rug. This might seem irrelevant but it should be remembered that the whole of the justification for CDOs and other derivatives was based on the normality assumption. Yet there were those who were well aware of the shortcomings of these instruments and as Warren Buffet remarked in 2003, 'In our view,however, derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal'.

This story has a particularly French flavour since many of the principal actors were French, and the barriers that Bachelier faced 90 years ago are still firmly in place in France.

As a footnote, Poincaré did not confine his criticism of economics to Bachelier’s theory. With regard to general equilibriium models, which Walras was pioneering at the time, he wrote to Walras and chided him for his assumptions of infinite farsightedness and infinite selfishness. The latter he could believe at a pinch, but the former he found dubious to say the least. Yet, we are still faced today with macro models, in which these two assumptions are central.

Perhaps the small comfort that we can take from this last observation is that the enormous inertia in our systems is not confined to France.

References:

Bachelier Louis (1912), Calcul des Probabilités, Paris: Gauthier-Villars

Fama E, (1965) ‘Portfolio Analysis in a Stable Paretian Market’, Management Science, Vol. 11, pp. 404-419

Keynes J. M.(1912) ‘Review of L. Bachelier, Calcul des Probabilités’ Journal of the Royal Statistical Society

Lefebvre H, (1870) Traité Théorique et Pratique des Valeurs Mobilières et des Opérations de Bourse, Paris, Lachaud.

Regnault J, (1863) Calcul des Chances et Philosophie, Paris: Mallet, Bachelier et Castel.

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