When I started this blog I took pains to explain that what some of the blurbs called the author’s “erudition” was in fact a kind of optical illusion facilitated by the Internet. (See the answer to question 5.) Just yesterday I found this in an article about translation:
Any translator of [German author W.G.] Sebald can spend days skipping from one website to another and feel very erudite, but with scant practical results.
In my case the practical results were considerable: 69 pages of endnotes and a 25-page bibliography. But erudition is much more than that. In the process leading up to the writing of MWA, I had the privilege of meeting genuinely erudite people. They know things before they look them up. Big difference. It means, specifically, that their writing is not marred by gaps and glaring omissions.
I can illustrate this by pointing to a particularly glaring omission in MWA
. Early in Chapter 4 MWA
quotes a Le Monde interview
in which former French Prime Minister Michel Rocard accuses mathematics professors of “crimes against humanity
” for teaching their students how to make “a killing on the stock market” [coups boursiers
]. The interview was published in early November 2008, six weeks after Lehman Brothers filed for bankruptcy, setting off a recession from which Europe, at least, has yet to recover. Rocard said at the time that
ce qui frappe, c’est le silence de la science [what’s striking is the silence of science].
A few days later, science responded in the persons of Jean-Pierre Kahane, Denis Talay and Marc Yor, but Le Monde “n’a pas jugé bon
” to print their response; it was finally made public the following May in Images des mathématiques
. Every word in their answer to Rocard is worth reading. It was quoted briefly in Chapter 4 and I won’t repeat what I wrote there. It suffices to mention that they distinguished between the responsibility of mathematicians, which is to develop quantitative models that are “indispensable to deal with risks of an increasingly complex world”; that of the quants, who apply the models they learn from the mathematicians; that of the traders and bankers who used these models to create the dangerous derivatives that brought global finance to the brink of collapse; and that of the politicians, whose task it is to make such abuses impossible, but who failed in that task and thus “are much more guilty than the mathematicians…”
Au fait, le pouvoir politique n’a-t-il pas été bien plus coupable que les mathématiciens en n’imposant pas aux institutions financières de réelles contraintes sur leurs risques ?
And one more quotation in the same vein:
Exprimés sous forme de modèles mathématiques et d’équations, les risques deviennent, au moins en partie, objectifs et quantifiables. Le pouvoir politique dispose alors d’informations utiles pour que la minimisation des risques, plutôt que la maximisation des profits, soit un objectif prioritaire.
At the time I was convinced that concerns must have been expressed in print before the crash, but I had no idea where to look. I confess I didn’t try very hard. Just this week, though, I found a pair of articles in MIT’s Technology Review, dating from November-December 2007, that a truly knowledgeable author would not have failed to cite.
The first article, entitled The Blow-Up
, by Bryant Urstadt, was a Featured Story
that reported on the implications of the collapse of the subprime market during the summer of 2007. “Is Subprime the Canary in the Mine?” was the title of a conference attended by “200 of the smartest people on Wall Street” that August. We learned the answer to that question just over a year later, but at the time only “the most pessimistic” quants
imagined that the collapse of the subprime market could lead to a shortage of credit as banks dealt with defaults. That would chill the economy, causing worldwide job losses, still more defaults, decreased spending, and withdrawals from the stock market, culminating in a global recession, or worse.
The most pessimistic of the quants were far from pessimistic enough, it turns out. The second article
, by the eminent MIT probabilist Daniel W. Stroock, did not address that question, however. Instead, Stroock, who identified himself as a teacher of quants, reacted to one passage in the Blow-Up
The events of August were outliers, and they were of the quants’ own making.…To begin with, quants were indirectly responsible for the boom in housing loans offered to shaky candidates.
Stroock disagreed; he considered the role of quants “closer to that of the sweepers who used to clear the ticker tape off the floor of the stock exchange than to that of a traditional investment banker.”
The role that so-called quants play in the financial world is analogous to the role batfish play in keeping coral reefs tidy. Just as batfish do not construct the reef but are essential to its health, quants do not create the structure financial markets depend on but do preserve the conditions that make markets function. So it would be misleading to suggest that quants were responsible for this summer’s meltdown in the subprime-mortgage market or for the broader troubles that followed….
Readers of MWA will recognize Stroock’s batfish as the genteel cousins of the flesh-eating Wall Street piranhas that make an appearance on p. 101; as Stroock goes on to explain:
By scrutinizing financial data, quants spot arbitrage opportunities and alert their employers to act before others have a chance to do the same.
Stroock concludes that quants are not responsible
for the mess in which the financial world finds itself. Quants may have greased the rails, but others were supposed to man the brakes.
Who, one is entitled to wonder, are these “others?” When Kahane, Talay, and Yor wrote their response to Rocard, the crash had happened and it was too late to pass the buck:
Les scientifiques ont un devoir d’alerte quand ils peuvent mettre en évidence un danger collectif. A cet égard, les mathématiciens ont une responsabilité particulière. [Scientists have a duty to sound the alarm when they can make a collective danger visible. In this respect (with regard to finance, that is) mathematicians have a special responsibility.]
Have mathematicians been exercising this responsibility in the drafting of regulations to prevent future abuses like those that caused the crash of 2008 — or at least to make sure there is someone to “man [sic] the brakes?” Have the teachers of quants been sounding the alarm? Are they making sure their students receive the ethical training to sound the alarm when their employers are unable or unwilling to do so? Have codes of professional responsibility been drafted so that quants can recognize an ethical problem when they see one?
These are sincere questions (even though I’m pretty sure I know the answers). My knowledge of the relevant literature is severely deficient, whatever may be claimed regarding my supposed erudition. Worse, although the Black-Scholes equation is displayed in all its enigmatic majesty on p. 85, and although I did more or less manage to follow its derivation
on Terry Tao’s blog, my command of the underlying concepts has always been shaky at best. It’s not that I’m incapable of learning the basics of stochastic differential equations. It’s because the theorems of financial mathematics are about money
, which, frankly, is something whose appeal I have never understood.
At this point, many of you are probably asking why I am presuming to talk about these matters, since I obviously lack the necessary professional qualifications. I will answer with an autobiographical digression. The incidents described in the first of the excerpts (the one that starts “Now you’re in for it”) really took place. At the European Congress of Mathematicians in Barcelona I really did experience a sense of dread and foreboding when a speaker said something on the order of “Thank God for Finance Mathematics” because it “providentially brought so many undergraduate and masters’ students to our departments’ lonely corridors” (as you can read in the excerpt). At that moment, in 2000, I had a premonition that the whole scheme would collapse; that no one would “man [sic] the brakes” and governments would be forced to bail out the too-big-to-fail banks, as in the Savings and Loan crisis of the 1980s; and that mathematicians would be blamed. Naturally, out of a minimal sense of professional responsibility, I resolved then and there that, together with like-minded mathematicians, I would teach myself what those providential students were learning, and explain the dangers to anyone who would listen.
I didn’t find any like-minded mathematicians at the time. I actually bought a few texts on financial mathematics and tried to read them, but all that talk of money and investments, from the very first pages, clouded my understanding. And so, because I failed in my mission to make myself an expert, I decided I had no standing to speak out. What I learned from the crisis that started in 2008, with no end in sight, is that one can’t wait for the experts to speak out. Chapter 4 is my penance. What have the experts learned?