Occasional reflections on Life, the World, and Mathematics

Where the money is…


Mathematical finance as an accessory to crime

Not long after I finished my PhD in probability theory, a significant fraction of the field was devoured by the financial mathematics moloch. Particularly in Europe, probability theory positions disappeared, to be replaced by openings in financial mathematics, which either went unfilled or cycled among a very few senior researchers and a few quick-change opportunists (and, gradually, their fledgeling academic progeny).

Everyone felt they had to get in on the action, and of course there was a certain amount of positive feedback. When many jobs chase few graduates, it generates huge demand among students for training in such a demonstrably burgeoning field. Obviously, the academic feedback was limited by the fact that most of the eager young ‘uns were seeking employment in banks, not in academia — but the banks were hiring as well. Anyway, just about 10 years ago, a Dutch colleague asked me if I might be interested in joining his own institute’s planned financial mathematics group, for which they were proposing to create TEN new positions. My reply was that finance did not interest me as a topic of research, but I added that there was something unseemly — bordering on unethical — in mathematicians’ headlong chase after banking lucre. The current generation of mathematicians is the trustee of a vast and powerful system of analysis, whose creators were supported, honoured, and financed by public institutions. What is it but a crime, when we abscond with the fruits of this scholarship, and sell it off (cheaply) to banks, who will use it to extract billions of dollars from financial markets?

The usual sort of collaboration between universities and industry bears significant ethical dangers, but financial mathematics goes a level beyond. After all, if a scientist collaborates with a drug company (let us say) to produce a new medicine, the company takes much of the profit — likely too much, since the public is never reimbursed for the decades of pure research that made the discovery possible, but only for the last patentable step — but at least the public gets the new medicine, which is presumably better to have than not. When a scientist develops a new technology for arbitraging more complicated financial instruments, the banks he or she works with take all the profit, and it must be coming from someone else’s account, since the markets are zero-sum. The only benefit that the public might get is in an overall increase in the efficiency of the markets, and that is a fairly abstract benefit. The market fundamentalists believe it is inevitable, but now we see where it leads… but I get ahead of my story. The fact that our democratically elected political masters were encouraging us to throw ourselves at the feet of the stock traders did not absolve us of our individual responsibility.

Looking back, I am not ashamed to admit that my judgement then was basically wrong. My mistake was in believing the propaganda that the elaborate mathematical models — often lacking any empirical grounding in actual science of market behaviour — were actually making money for anyone. I knew enough to be skeptical of them, but I assumed that if the banks were clamouring to hire these people, and investing money in the research, they must be getting something useful out of it. Indeed they were, but it wasn’t the something that they claimed to be getting. I thought that the mathematicians were like post-Soviet nuclear scientists, selling out their dangerous skills to the highest bidder, who may be a rogue state eager to arm terrorists or blackmail its neighbours. It turns out that they were actually like the Tintoretto painting in the mafia chief’s foyer: Not a practical contribution, but a decoration and a distraction, intended to inveigle the public and imply respectability. At best, they were like the mafioso’s accountant or lawyer, who uses his specialised skill to contrive a convoluted subterranean way of doing what would be straightforward — and straightforwardly illegal — if done out in the open. The clearest example of this are the now-infamous credit default swaps, which are simply insurance by another name, without the requirements of capital reserves and intricate regulations imposed on the insurance industry; as a lagniappe, credit default swaps could turn into just another speculative instrument, as people insured not just the actual risks they had, but invented risks. (This harks back to the early days of life insurance, when people would buy policies on the lives of unconnected third parties, effectively betting that that person would die soon.) Another example is auction-rate securities, that essentially duplicate banking functions, but seem to produce miraculously higher returns than the stodgy old banks. The bonus (as many, including Paul Krugman in this book, have pointed out) came not from added efficiency — as they suggested — but from evading the expensive regulation that was supposed to ensure the stability of real banks. There’s real technical skill involved in this evasion, similar in kind but far more intricate in detail, to the skill that the mob bookkeeper needs to keep the public set of books pristine while laundering extortion money through the business.

The financial pirates of each generation have one central challenge: How to induce the marks to abandon the lessons in prudence learned and passed on from the last economic crash. By coincidence, perhaps, another lesson in the social implications of finance came to me around the same time (1997) from another Dutch mathematician. At lunch one day, after I’d given a seminar talk in Utrecht, this illustrious probabilist had a good chuckle over the riots that were tearing Albania apart just then, following on half the population losing what little savings they had to post-communist government-backed pyramid schemes. It’s hard to conceive of the training that leaves people so naïve, he remarked. “In the west, no one could fall for a scheme like that. Everyone knows that if someone’s promising 50 percent returns a year, it must be fake.”

Well, no, but we do demand better marketing. Pyramidist Madoff had the simplest and most audacious approach: Apparently he may not have made any financial transactions at all, but counted on fellow Jews to believe that there would be a Jewish genius who could beat all the goyim, and would only invest for his friends and friends of friends, and you’re lucky he’s willing to accept you, so don’t ask too many questions. (In technical jargon, this is an “affinity scheme”, in which a scammer preys upon his own ethnic group.) The banks demanded, not more security and verification, but better camouflage. The insiders, of course, were getting enormously rich on the flow of money, whichever way it went — the most recent rounds of billion-dollar bonuses, paid directly out of funds that the taxpayers put up to rescue the banks, are only the last bite at the apple (this particular apple at any rate), laying bare the mechanisms of cronyism and self-dealing, of indifference to broader consequences, that have been pervasive all along — so they had no concern about whether they might be dragging down the world financial system to long-term ruin. But the money had to come from somewhere. To get the investments flowing they needed a convincing theory for why the implausibly high returns could be genuine and sustainable, without the risk that usually is the exchange for high returns.

As with Madoff, the con works by flattery: You’re special. You understand, unlike the others. The risk has been purged from the system, and what’s left has been calculated to the last decimal place by our in-house mathematicians. The others, alas, don’t understand the Itô equation, but that’s just more opportunity for you. In all the lectures I heard over the years where someone made clever calculations of the fair price for (say) a put option, allowing them to sell stocks at a fixed price at a future date, I never heard anyone deduct for the possibility that the counterparty would not buy the stocks at that price because he is bankrupt, or because he disputes the contract and threatens expensive litigation.

The Newspeak for this young field is “Financial engineering”. So called is a new department at Princeton, and numerous less-illustrious but equally half-baked programs of study. “Engineering”, with its long tradition and professional strictures for grappling with the exigencies of unforgiving matter and its cold equations, redolent of cantilevered bridges and steam engines, bespeaks solidity, exactly what this field lacks. “Financial engineering” is like developing a theoretical model for the design of bridges (in weightless conditions, since gravity introduces unnecessary complications), so that vast structures were being constructed, and explained away when towers and bridges collapsed as merely confirming the model, because we discovered that the builders skimped on the materials, and anyway, there must have been a misunderstanding, since we never really meant the structure to be built on Earth. The financial mathematicians have been doing this two-step for a long time: They scoop up funds from education ministries with hymns to the enormous practical importance of their work — after all, governments never tire of finding new ways to transfer public funds into the pockets of bankers and bank shareholders. But then when you ask what they really know about economics and finance — or if you accuse them of “selling out” — they say, don’t be silly, we’re just doing beautiful mathematics. (In their minds’ eye they are but oysters, creating beautiful pearls out of their theoretical irritation, indifferent and even oblivious to the practical value that others may see in the product. And then, periodically — to extend the metaphor — there comes a red tide and they poison thousands.)

The real scam is the claim that we can make risk disappear by waving our mathemagical wand. Probability theory is good at one thing only: Balancing a large number of small risks against one big risk. It’s good to have an exact calculus for that, because we our intuition can easily go astray on this sort of judgement. The problem is (and mathematicians are peculiarly susceptible to this thought crime) once you have a mathematical calculus for something, everything that comes out of it sparkles with mathematical precision, so it’s easy to assume it must be accurate. My high school physics teacher tried to beat this out of us: Don’t keep too many significant figures, he’d say. Just because your calculator keeps eight places after the decimal point, doesn’t mean that you get to keep all those digits. Precision is not the same as accuracy. There’s indeed something beautiful about exploring an intricate mathematical model, and determining how to describe and predict its behaviour with perfect clarity. This is not, however, the same as describing the real world with perfect clarity. It is rather as though I were planning a mountain expedition in the Alps, starting from a large-scale map of Europe, and decided to collect information about our route, not by collecting new information from satellite photos and smaller-scale topographic maps, but by photographically enlargeing my continental map, perhaps employing an expert cartographer to analyse the projection of the continent.

This is never more true than when the subject under consideration is risk itself. Yes, within the model you may compute the risk of the bank defaulting, or of all parts of a complicated hedged trade all happening to move in the same direction, to one part in 1000. But the inaccuracies of the model are many orders of magnitude higher than the problems of computing within the model. Engineers understand this, which is why they do their model-based calculations, then do experiments, and then build in a several-fold margin of tolerance.

One thing has become clear since I moved here : No one loves banks like the British establishment. The current government thinks the world would be much better if only everything were run like a bank. For instance, they’ve been wageing a campaign to force Oxford and Cambridge to abandon democratic government and move to a CEO-type system. The universities are supposed to have more external members on their governing councils — and when they say “external”, they don’t mean more environmental activists, artists, and school teachers. They mean people who know about the real world, i.e., businesspeople. Apparently, the British financial honchos are underemployed in just bankrupting — I mean, extracting value from — the companies that pay their princely salaries. In their spare time, they apply their expertise to wrecking higher education and the health services. You might think that the cold slap of experience, in the form of the exquisitely managed and MBAed crash of the world economy might at least soften this confidence that it’s the biznesmeni who know how to get things done, but the much-self-admired British pragmatism only goes so far. You can’t smash all the household gods… More than likely, with unemployment running high in the banking sector, we’ll be seeing even more business types with time on their hands marauding across the landscape of higher education.

In the end, though, you wonder whether the UK might be compared to the latter-volume Don Quijote, having no realistic way of supporting itself, but still being humoured and even pampered by a world happy to enjoy its delusions. Since we’ve arrived in this country we’ve had to replace all of the British-made appliances in our house with German ones, since the British ones either stopped working, or made horrible burning smells while approximately doing their jobs. The only thing the UK has been good at making and selling in recent years are financial products. Personal debt levels are (I believe) the highest in the world. Presumably, now that the “sophisticated” modern financial instruments have been revealed as mere cover for old-fashioned fraud, there will be not much left of the UK economy actually running. The UK government will never acknowledge the fact that their banker friends are a pack of criminals, but the rest of the world will pat them on the head gently — this is, after all, still a nuclear-armed state — and leave them in the economic equivalent of a padded cell.

And one final word: I asked an economist colleague in early January, whether he thought the world economy was just suffering a slowdown, or whether popular economists like Krugman were right who suggest that we’ve run off a cliff, and are just waiting like the proverbial cartoon coyote for gravity to assert itself. He said that talk of a looming depression was absurd, since we now know what to do to stop it — fiscal stimulus I presume he meant. As the punchline goes, what do you mean “we”, paleface? Maybe the economists know that, or think they do, but, hard as it may be to acknowledge, they do not run the world. And the politicians who do run the world, or at least pretend to, may not believe them. Or, if they do, they still may not be sufficiently motivated (or powerful) to do what the economists “know” needs to be done. It seems to be a déformation professionelle of economists to a) think they know how to solve real problems in the world, even when different economists have diametrically opposite “sure prescriptions”; and b) to assume that the decision-makers are paying attention to them. Add to this recently c) an academic imperialist belief that they can solve all the world’s noneconomic problems as well, as evidenced by Mssrs Summers — whose insistence on telling everyone else at Harvard how they ought to be doing their jobs eventually cost him his own job — and Levitt, who seems to feel a kind of academic white man’s burden, to lift up the struggling academic lower races, since economists have been blessed by a gracious God with the secret of fire steam power multiple regression. In that, they’re a lot like British businesspeople, actually…

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