My Life as a Quant (42 page)

Every Tuesday morning I held a global call at 10 Hanover Square with all the senior people in Derivatives Analysis. At 8:00 A.M. New York time they called in from London and Tokyo. One Tuesday, as we sat around the speakerphone discussing deals we were vetting, I glanced at the window and saw sheets of paper cascading out of the sky. I thought it looked like an archaic ticker-tape parade for returning astronauts or victorious Yankee teams, but it was too early for a parade. Then someone came running in to say an airplane had struck the World Trade Center. We switched on the television perched high in the corner of my office, and saw the flaming tower, listened to the reports of an accidental collision. Then, a few moments later, we heard a thunderous bang through my window as we simultaneously saw the other tower on TV burst into flame. It was instantly clear we were under attack.

Outside the building we regrouped, watching the horrific flames and smoke pour from the towers. I had visions of waves of subsequent airplanes careening in to strike more buildings. Crowds of us set off for the long walk north, careful to walk neither too close to the unprotected FDR Drive nor too close to attractive targets such as the Pan Am building. By the time we reached Chinatown we heard of the towers' collapse and the strike on the Pentagon. By 3 P.M.I reached Sonya's school on the Upper East Side, where they were releasing students only into the care of their parents.

Lower Manhattan was like a war zone for the next few months—burnt air and blockaded streets patrolled by New York City policemen and scared-looking and out-of-shape members of the National Guard. I took a cab daily from the West Side to Gracie Mansion, itself surrounded by sand-filled dump trucks, and a ferry from there down the East River to the South Street Seaport. Working and living in Manhattan was oppressive; you had no respite from the expectation of the next assault. Helicopters patrolled the night sky. People woke at 3 A.M. like clockwork to watch CNN. I noticed the palpable relief when I spent a weekend in the country or the suburbs—one felt briefly safe there. The first day I noticed a lightening of spirits in Manhattan was more than two months after September 11, on the Wednesday before Thanksgiving, when suddenly the city seemed just slightly festive.

Normally it takes me years to make up my mind about a transition. Now it took only two months of vacillation before I decided that I was ready to leave Goldman Sachs. The best times I had had there were when I worked in small groups of traders and quants with a strong joint purpose—with Peter Freund's desk when we developed BDT, and with Iraj and Dan O'Rourke when we built equity risk systems and developed our implied tree model. I decided to take a year off, write a book, and then return to work, either in academia or at a job in a smaller investment firm. On June 7, after my farewell party, more than 17 years after I started at Goldman, I went home for good. The next morning I went for a run in Central Park at 11 A.M., the best time for running. I hadn't done this in several years.

A week later I received an email at home from someone in my old Quantitative Strategies group who hadn't been able to attend my party. He and I had had occasional fierce battles over software standardization. Like most quants, he was foreign born. “In retrospect,” he wrote, “Working in your QS has been [
sic
] my happiest years in Goldman. Very often, I deeply regret not having recognized fully what a privilege it was to work next to (sometimes with) you and your colleagues. As time goes by, I realize how lucky I was to be able to work in the atmosphere of the high intellectual standards that you set, with extraordinary talented people that gathered around you. I missed the times, and the opportunities that I did not take a full advantage of.”

The snows of yesteryear inevitably melt, and there's nothing sad about it. I was ready for something new.

Full circle, back to Columbia

Physics and finance redux

Different endeavors require different degrees of precision

Financial models as
gedanken
experiments

A year later, in the fall of 2003, I had come full circle, time present and time past present in time future. I was back at Columbia, a professor and director of the program in financial engineering in the Mudd building on 120th Street and Amsterdam Avenue, a mere 100 yards east of Pupin where I spent so many years getting my PhD. I was also working part-time with a fund of funds, a firm that invests clients' money in a portfolio of hedge funds.

As I teach, I am struck again by the difference between what can be taught in school and what can be learned on the job. When I started on Wall Street, I simply assumed it made good sense to apply the techniques of physics to financial modeling. In particle physics people dreamed of GUTs (Grand Unified Theories) and strings and TOEs (Theories of Everything). The tools they used—differential calculus, partial differential equations, Fourier series, Monte Carlo simulations, even Hilbert spaces—at first seemed as appropriate for describing the movements of stocks and yield curves as they did for particles and fields.

Looking at the motion of yield curves in the mid-1980s, I saw no reason why financial theorists shouldn't shoot for their theory of everything, too. Why shouldn't one set of equations describe the motions of all interest rates, producing one rational set of fair prices for all interestrate-sensitive securities? If you had asked me where quantitative finance was headed, I would have hoped for the discovery of that theory.

Seventeen years on, I say without regret that things aren't the way I expected. There is no unified theory. Models must necessarily be pragmatic, and traders typically use a variety of similar but slightly inconsistent models—one for Treasury bonds, another for corporates, a third for caps, a fourth for swaptions—even though all these securities depend on the same underlying interest rates. Though we aspire to it, we don't expect comprehensiveness. The best quants know that it is unattainable.

Newcomers to the field find it hard to swallow. One French student in my course recently wrote in his evaluation that, although the course gave him a good feel for the way quantitative finance is practiced, he is “still not convinced that an
ab initio
model in finance (like the sophisticated ones in other fields) to explain almost everything does not exist.” Physicists new to finance, as I did, imagine a grand unified theory can be found. Many finance academics who should know better also seem to imagine it can be done, but they don't live in the real world. It isn't really possible. And it's not a question of computational power—even infinitely fast computers won't do the trick. The problem is deeper.

The techniques of physics hardly ever produce more than the most approximate truth in finance, because “true” financial value is itself a suspect notion. In physics, a model is right when it correctly predicts the future trajectories of planets or the existence and properties of new particles, such as Gell-Mann's Omega Minus. In finance, you cannot easily prove a model right by such observations. Data are scarce and, more importantly, markets are arenas of action and reaction, dialectics of thesis, antithesis, and synthesis. People learn from past mistakes and go on to make new ones. What's right in one regime is wrong in the next.

As a result, physicists turned quants don't expect too much from their theories, though many economists naively do. Perhaps this is because physicists, raised on theories capable of superb divination, know the difference between a fundamental theory and a phenomenological toy, useful though the latter may be. Trained economists have never seen a really first-class model. It's not that physics is “better,” but rather that finance is harder. In physics you're playing against God, and He doesn't change his laws very often. When you've checkmated Him, He'll concede. In finance, you're playing against God's creatures, agents who value assets based on their ephemeral opinions. They don't know when they've lost, so they keep trying.

In his textbook
Derivatives
, Paul Wilmott, an applied mathematician turned quant, writes that “every financial axiom I've ever seen is demonstrably wrong. . . . The real question is
how
wrong is the theory, and how useful is it regardless of its validity. Everything you read in any theoretical finance book, including this one, you must take with a generous pinch of salt.” I couldn't agree more. In fact, the very title Wilmott chose for his later book,
Wilmott on Derivatives
, aptly illustrates his understanding of the point. The “Wilmott” in the title implies that a difficult subject is being explained by an authority, but it also suggests that the subject matter itself lacks the coherence of true science. True science does not need this kind of authority—one cannot imagine a 1918 textbook called
Einstein on Gravitation
! Unlike finance, the theory of gravitation gets its weight from the ineluctability of its arguments and its ability to account for previously inexplicable anomalies. Gravitation needs no Einstein to lend it gravitas. Personality plays a larger part in economic writing because truth's part is smaller.

So, why is it that the methods of physics work less well in finance?

As a physicist, when you propose a model of Nature, you're pretending you can guess the structure created by God. It sounds eminently plausible. Every physicist believes he has a small chance of doing so, or else he wouldn't be in the field. Perhaps it's possible because God Himself doesn't pretend. But as a quant, when you propose a new model of value, you're pretending you can guess the structure created by other people. When you try out a new yield curve model, you're implicitly saying something like “Let's pretend people in markets care only about the level of future short-term interest rates, and that they expect them to be distributed normally.”As you say that to yourself, if you're honest, your heart sinks. You're just a poor pretender and you know immediately there is no chance at all that you are truly right. When you take on other people, you're pretending you can comprehend other pretenders, a much more difficult task.

But doesn't God make people, too? Is there really a conflict between individuals and Nature? These are ancient questions. Schrödinger, the unconventional father of the probability wave equation in quantum mechanics, wrote a short summary of his personal views on determinism and free will in the epilogue to
What is Life?
, a compilation of his influential lectures on the physico-chemical basis of living matter. “My body functions as a pure mechanism according to the Laws of Nature,” he wrote. “Yet I know, by incontrovertible direct experience, that I am directing its motions, of which I foresee the effects, that may be fateful and all-important, in which case I feel and take full responsibility for them.” The only way he could reconcile these two apparently contradictory experiences—his deep belief in the susceptibility of Nature to human theorizing and his equally firm sense of the individual autonomy that must lie beneath any attempt to theorize—was to infer that “I—I in the widest meaning of the word, that is to say, every conscious mind that has ever said or felt ‘I'—am the person, if any, who controls the ‘motion of the atoms' according to the Laws of Nature.”

Schrödinger was following in the steps of the long line of earlier German philosophers who thought that all the various worldly voices referring to themselves in conversation as “I” were not really referring to independent I's, but to the same universal I—God or Nature.

Nevertheless, it's the unpredictable I's—people like you and me—who determine financial value. Fischer Black once wrote of financial theories that:

In the end, a theory is accepted not because it is confirmed by conventional empirical tests, but because researchers persuade one another that the theory is correct and relevant.

I would go even further than this. From the viewpoint of someone who works with traders, I like to think of financial models as analogues of the way quantum and relativity physicists in the early part of the last century used
gedanken
experiments.
Gedanken
experiments—German for thought experiments—were imaginary investigations, a sort of mental stress-testing of the physical world, conducted in your head because they were too difficult to do in practice. Their aim was to force your conceptual picture of the world into a contradiction. Einstein imagined what he would see sitting on the edge of a moving light beam in order to get insight into the contradiction between a Newtonian observer and Maxwell's description of light. Would the light wave still seem to undulate from peak to trough when you sat on one of its peaks? Similarly Schrödinger, in order to highlight the radical, counterintuitive nature of quantum mechanics, imagined an unobserved cat sealed in a box containing a radioactive atom that, on decaying, would trigger a Geiger counter to release a poison. Would the cat, like an unobserved electron oscillating continuously between different quantum states, swing from alive to dead and back again?

I think this is the right way to use mathematical models in finance. Models are only models, not the thing in itself. We cannot, therefore, expect them to be truly right. Models are better regarded as a collection of parallel thought universes you can explore. Each universe should be consistent, but the actual financial and human world, unlike the world of matter, is going to be infinitely more complex than any model we make of it. We are always trying to shoehorn the real world into one of the models to see how useful an approximation it is.

You must always ask: Does the model give you a set of plausible variables to describe the world, and a set of relationships between them that permits its analysis and investigation? You're always trying to make a limited approximation of reality, using variables that people can comprehend, so that you can say to yourself or your boss, for example, “I was short emerging-market volatility, so we lost money when the crisis came.” Good theories, like Black-Scholes, provide a laboratory of ideas in which you can work out the likely consequences of possible causes. They give you a common language with which to quantify and communicate your feelings about value.