La capacité de mise en forme des pratiques par une formule qui change le monde est clairement évoquée dans un dialogue crucial tenu entre la directrice des risques et le directeur de la banque d’investissement, que nous reproduisons ci-dessous.
- − (Sarah Robertson) La formule ne vaut rien, annonce la directrice des risques au directeur de la banque.
- − (Jared Cohen) Qu’est-ce que cela veut dire, a-t-on vérifié les calculs ? lui répond-il.
- − (Sarah Robertson) Les calculs sont justes mais la formule n’est pas adaptée.
- − (Jared Cohen) Huit milliards de dollars dans le monde reposent sur cette équation.
- − (Sarah Robertson) On s’est tous trompés.
C’est on ne peut plus clair : l’usage de cette formule a conduit aux pertes massives que la banque va à présent devoir écouler sur le marché à défaut de quoi elle se retrouvera en faillite.
It is a well-documented fact today that one of the central problems in the 2008 financial crisis lay in a specific pricing equation – a mathematical formula that priced credit default swaps (CDS), the financial products supposed to provide financial protection against default risks – the mathematical copula devised by David Li and known as “Li’s copula”. This formula was faulty, not in the sense that the risks were miscalculated, but in the sense that they were mismodelled. Now, I will elaborate on this.
There have been many debates about this equation, which a famous article by Felix Salmon called a “Recipe for Disaster: The Formula That Killed Wall Street”. The devil, it is said, is in the details. Playing with the words, I would say that, in this case, the detail was in the D-tails, D for “distribution” tails. The tails of a probability distribution describe the behaviour of a random variable in the zone that is far from its central value. Distribution tails can be “thin” (indicating a very low probability) or “fat” or “heavy” (indicating the opposite: a very high probability). Li thought that the risks of simultaneous credit default could be modelled using a mathematical coupling function called a “copula”. However, he chose to use a probability of joint default based on Gaussian distribution (a Gaussian copula formula). The cognitive framework of the Gaussian distribution underestimates the probability of rare events, and creates the illusion that the risk is under control. The Gaussian copula formula encouraged excessive risk-taking because it gave precisely that cognitive illusion.
Here I analysed in detail a movie that is crucial to grasping the epistemological issues of financial risk modelling – Jeffrey Chandor’s movie, Margin Call (2011). According to the philosopher Stanley Cavell, cinema can be, for us, a means of ethical teaching which does not use learned reasoning but only the power of images that touch us. The American philosopher Cora Diamond gave a reason for this: Images can often better convey ethical thinking than reasoned reflections. Images touch on an infra-rational level. That is what we are doing now, considering a particular scene from the movie Margin Call.
Margin Call tells the story of the fall of a merchant bank. The faulty risk modelling problem is very well presented with great epistemological accuracy in one central dialogue: a conversation between the risk management officer (Sarah Robertson) and the head of fixed income securities (Jared Cohen). This dialogue perfectly describes the epistemological and ethical issues carried by the probabilistic assumptions. The scene happens late at night, just after they have realised there is a problem with the mathematical risk assessment formula. They are beginning to assess the consequences of the wrong risk formula, in terms of potential losses for the bank. It is such an almost-perfect illustration of the difference between risk calculation and risk modelling that it should be part of every course aiming to teach financial ethics.
I will now quote the dialogue of Robertson and Cohen discussing Li’s formula:
- − (Sarah Robertson) It’s legit… the kid killed it. The formula’s worthless
- − (Jared Cohen) What does that mean?
- − (Sarah Robertson) It’s broken
- − (Jared Cohen) There are 8 trillion dollars of paper around the world relying on that equation!
- − (Sarah Robertson) Well, we were wrong.
This dialogue illustrates that a mathematical equation – here, Li’s formula – led to financial disaster because it was ill-conceived (“the formula’s worthless”). A simple, but ill-conceived, equation led to financial disaster.
In this sense, the financial crisis cannot be simplified in a “casino capitalism” approach, an expression which is a conflation of a particularly unhelpful kind, because it fails to help to understand the role of the risk modelling issue. Similarly, the financial crisis cannot be reduced to a massive misjudgement about the consequences of financial innovation because, if there was a massive misjudgement, it concerns, first, the risk modelling issue. In neoclassical finance, something has not worked, which is not only linked to the avidity or greed of financial actors, but to the mathematical structure of financial risk modelling, the practices and techniques of a given risk culture carrying financialised tools. It is therefore of primary importance to investigate what, in the neoclassical modelling of financial risk, was inherently dangerous for the sustainability of the economy; for any ecological financial theory will have to start by getting rid of these dangerous elements and replace them with models adapted to sustainable aims