Famously, Merton, of Black-Scholes-Merton, disagrees. And in his blockbuster "the quants" investigative journalist Scott Patterson relays interviews with leading (anonymous) Quants who seem to be suggesting that they are not at all to blame. Perhaps this is a European only dis-ease, or perhaps things change in a couple of months ?
The arguments are simple. On the one hand, the quants provided the numbers, did the modelling, created the mathematics. And the bankers, traders and risk managers, mere consumers of this information, acted on it in good faith. After all mathematics models reality right?
On the other hand, the quants were only modelling the real world, describing what they observed not stating fact, only probability. And they made a number of simplifications to make the maths easier. It wasn't their fault that the consumers of the results chose to ignore the simplification and caveats that they attached to the results.
Take for example the copula method, which is a simplification of ways in which the mathematics if default correlations can be expressed. In order to arrive at this modelling approach a number of assumptions were made: the Merton model of a risky debt; and the idea that probabilities of default remain constant over the life of an asset. Neither of these match reality accurately, but they allowed thinking that lead to an approach that gave an indicative view. The problem here is that although the quants that develop the model were clear, their assumptions (you only have to read the research paper to identify them) were forgotten as general excitement about the method and its implications for trading grew.
Lets return to the idea that mathematics models reality. The key word here is "model. This is a central issues in debates about the meaning of mathematics. Rubens and Hersch, authors of the Mathematical experience, wrote that "the typical working mathematician is a Platonist on weekdays and a formalist on Sundays". A platonists essentially believes that mathematics is an empirical science, and that there is nothing created in mathematics, the mathematician is discovering what is already there. The formalist is the other extreme, believing that mathematical signs and symbols are mere abstractions, containing no meaning of themselves yet are free from possible doubt because all mathematical ideas and theorems derive from a given set of axioms, through the process of logical proof.
Often mathematicans don't think about this, they just do mathematics, and typically, Monday to Friday, it helps them to think that they are in fact discovering, or at least modelling, the real world. In physics and engineering, this is exactly what we have to do. After all we would not be able to build bridges if we didn't make models based upon physical principles. mathematics is the tool that we use, to create and manipulate those models.
But then again, finance is not physics. There are no underlying physical laws defining how macro and micro economies behave, and no fundamental principles from which consequences can be deduced. There is no Second law of Thermodynamics, no Newton law equivalents. Finance is fundamentally a behavioural science, and the best that we can do is create models based upon probable outcomes. This is where the Platonists fall foul, and where the Formalists cause problems. For the Platonist quant, the message is that - sorry, there is nothing to discover... For the Formalist - please remember that the axioms that you are working with are little more than simplifications and assumptions. For the trader, risk manager and CEO the message is to check the assumptions, bring them to the forefront of your mind, and make fully informed decisions.
Of course, the problem is somewhat compounded by the fact that many quants, some of the greatest minds, are not mathematicians at all, but have trained as theoretical and empirical physicists, who are used to modelling the real world, (all are serial Platonists, by design, or perhaps Empiricist at a push ) looking for the Higgs boson, establishing the fundamental principles of the universe. Their very training encourages them to take observed phenomena and abstract it to fundamental laws and mathematical principles. They can't help it, but they think that they are doing science when they are modelling financial products, even when they try not to, and they are really good at it!
But then this is not the first time that physicists and mathematicians have got in to trouble by doing their job. Consider the following:
|"When you see something that is technically sweet, you go ahead and do it and you argue about what to do about it only after you have had your technical success."|
The parallels here are not difficult to see: scientists and mathematicians, follow a line of enquiry for the sake of science. The results of each were disastrous, though significantly more in the case of the A-bomb. Yet the debate still rages, was Oppenheimer to blame for the destruction, after all it was Truman who gave the order to drop the bomb, but without Oppenheimer he wouldn't have had a bomb to drop?
It is not our purpose here to discuss the ethics of following certain lines of scientific enquiry, only to point out that in a less significant way that we could ask equally, are the quants really to blame, or were they just following lines of scientific and mathematical enquiry which lead to interesting conclusions ? They didn't create the business, they didn't buy and sell the credit instruments, they merely made it possible for others to do so.
And so the question seems to be, who to blame? But the answer is very complex. Surely it would be better to learn from what has happened, agree to follow legitimate lines of enquiry, to pay much more attention to the assumptions, simplifications and models and to leave the real decision makers better informed. As we begin to move out of this recession, all Platonists, Formalists, Pragmatists and Empiricists are responsible for ensuring that we do not enter another one.