My Life as a Quant (27 page)

It takes only a good idea and a few people to develop a model, but it takes many more people to turn the model into a usable tool. For that you need a graphical user interface, a database that contains the details of traded products you own, and current market data for calibration.

But even collecting data isn't as simple as it seems—models are everywhere. What one thinks of as “market data” are often prices filtered through another model or calculation. Yields are extracted from collections of bond prices. Volatility is calculated from historical returns. Each year, as markets mature, products become more liquid and traders calibrate their quotes to greater numbers of related securities, sometimes so many that their prices must be obtained via electronic price feeds. All of this involves software. Sooner or later everyone who creates a useful model gets exposed to the truth that building a trading and risk management system around the model is a huge and often overwhelming software project that requires many more programmers than quants. Models, critical though they are, are only a small part of the story.

Back in 1986 when we developed our yield curve model, traders were quite willing to enter a yield curve into the system manually, and I was perfectly capable of building most of the system and user interface around the model myself. I delivered it to the traders on the bond options desk and they began testing it immediately.

As they began to use our model I ran into my first taste of battle with “middlemen,” the people appointed to intermediate between the producers and users of models. Middlemen—usually one per desk—sat with the traders and got to know their business well.

Middlemen serve a useful task. It's not easy for a quant to understand the finance, build the model, do the math, write the program, and still have the time to work closely with the trading desk. Traders, always rushed, need a middleman to coordinate their requirements, to make them agree on their most urgent needs. Since traders and quants speak slightly different languages, it's good to have someone who can understand both sides' dialects and serve as the designated mediator.

Unfortunately, the middlemen on the corporate and Treasury desks at that time preferred that the model creators remain invisible; one of them who used our model to generate prices for traders wouldn't even admit to doing so. Since you are paid in proportion to the perception of your benefit to the business, this was not good.

There wasn't much I could do about being front-run, but I decided to at least confirm my suspicions. A few days later I went back to the source code of my program and temporarily added a few lines that ensured that, when you tried to use it, you got a pop-up window saying “Model Under Repair.” Within a few hours I started to get calls from the middlemen asking what had happened to the model they had not admitted that they were using.

Ever since, I have been wary of people who stand between model creators and end users. Quants everywhere have firsthand experience of being bypassed by more technically challenged people who extract information from you and then pass it on to other people at meetings you're not invited to. For a long time afterwards, whenever I wrote programs for traders, I used to include a swatch of code that kept a log of who used my program, and when. I encouraged people in my group to do the same. That way I had documented proof of our utility, even though I couldn't put a dollar value on it. In 1994, when the investment banking industry was forced to lay off people and Goldman went through difficult times, I sent a copy of the log to my bosses, showing how many tens of thousands of times some of our Quantitative Strategies group's programs had been used. No one in our group was laid off that year, and that bit of information may have helped a little.

I met with Fischer regularly over the next eight years, though we never again worked as closely as we did when we developed BDT. He was the most remarkable person I met at Goldman.

His most noticeable quality was his stubborn and meticulous devotion to clarity and simplicity. In writing and speaking, he put weight on both content and style. When we wrote the first draft of our paper on a one-factor model of interest rates, Fischer wanted no equations in it, and I had to struggle long and hard to satisfy his standards: He wanted accuracy and honesty without the technical details, which meant that you had to understand the model viscerally, and then explain that understanding. I think it was the clarity of the mechanics of our model that made it so popular and widely used.

Because he liked clarity, and perhaps because his training was not in economics, Fischer avoided excessive formalization. His papers were the antithesis of the unnecessarily rigorous lemma-filled research papers of financial economics journals. He tried to write as he spoke, in a terse but good-natured conversational style, using clear but casual, unadorned English. There was a touch of jerkiness to his prose because it lacked the technically superfluous conjunctions—and, but, thus, and therefore—that people commonly use to link the flow of sentences in scientific articles.

Fischer expected clarity and directness from others, too. Though he was generous with his time and didn't care about rank, you had to prepare for an audience with him. If it was evident that you hadn't thought carefully about your question, you quickly discovered that he wasn't going to do the thinking for you. And, if you didn't grasp his answer and repeated your question, he would simply repeat his answer.

A very direct man, he was uncomfortable with small talk. When he had nothing to say, he said nothing; this could be disconcerting on the telephone, where he often simply kept silent for a minute or two without terminating the conversation. Sometimes, this led you to babble in an attempt to fill the silence, until Fischer simply said an abrupt goodbye and hung up.

He once told me that one of the things that limited his influence was the fact that he always told people the truth, even if they didn't want to hear it, a characteristic I can vouch for myself. When he grew skeptical of some of the information technology managers in his division at Goldman in the early 1990s, he purposefully met with them all and then made a frank list of who was good and who was bad, and handed it over to his bosses. He laughed sheepishly but half-proudly when he conceded that he had been naive to think that he would gain anything from this.

Among Goldman partners he struck me as always a bit of an outsider. In the era before the firm went public, a “class” of partners was appointed once every two years, and each of them then advanced by being allowed to buy progressively larger shares of the company. Fischer once said to me that he was proud of possessing fewer shares than anyone else in his class of 1986.

This directness and informality characterized his research, too. His approach seemed to me to consist of unafraid hard thinking, intuition, and no great reliance on advanced mathematics. This was inspiring to lesser mortals. He attacked problems directly, with whatever skills he had at his command, and often they worked. He gave you the sense (perhaps misguided) that you could discover deep truths with whatever skills you had, too, if you were willing to think hard. He was guided by his great economic intuition; though his mathematical skills were unexceptional, his instinct was strong, and he was tenacious in trying to attain insight before resorting to mathematics.

In modeling he had a taste for the concrete: He liked to describe the financial world with variables that represented observable phenomena rather than hidden statistical or econometric factors. He thought practical usefulness and accuracy were more important than elegance, despite the unquestionable elegance that lends so much appeal to the Black-Scholes-Merton framework he founded. He had a strong pragmatic streak; he was at least as much a practitioner as an academic, willing to devote time and attention to software, trading systems, and user interfaces. He thought that these were just as important as the models themselves.

Fischer preferred reality to elegance in modeling. In one of his last published papers,
Equilibrium Exchanges
, he succinctly stated his attitude in the last part of his introduction. “In the end,” he wrote, “this entire article amounts to a series of conjectures about the nature of equilibrium, if one exists. I have been unable to provide an exhaustive and precise analysis of the implications of my assumptions, but I would rather guess about what follows from more-relevant assumptions than derive precise conclusions from less-relevant assumptions.”

Clearly, though style was important to him, content was paramount. Between 1990 and 1995, when he worked first in Goldman Sachs Asset Management and then in Fixed Income Research, I invited him to come and listen to the occasional seminar speaker we had visit the Quantitative Strategies group I ran. I noticed that he didn't attend if the seminars were on new or improved numerical solutions to problems that were already soluble; it's not that he was uninterested in numerical solutions, but rather that he was more interested in financial economics. Similarly, he didn't get carried away by the need to find analytical solutions to equations; he was just as happy to use numerical methods when fast computers were available.

Fischer also had a good grasp of the overwhelming importance of computing in making effective use of models. People have often asked why we publicized our research on the BDT model in 1990, given that we worked at a profit-making investment bank. In fact, when we published it, traders at Goldman had already been using it for several years. But more importantly, Fischer distinguished between releasing models (which he thought legitimate) and releasing a computer implementation or trading system that incorporates the model, which he thought should be sold.

The truth is that models are rarely an unambiguous source of profits. What counts as much or more is the trading system and the discipline it imposes, the operational errors it disallows and the intuition that traders gain from being able to experiment with a model.

Fischer had his own way of thinking about markets. He was deeply inspired by the so-called “general equilibrium” approach of the capital asset pricing model, the idea that prices and markets equilibrate when the expected return per unit of risk is the same for all securities. This belief was the source of much of his intuition, and was the method he first used to derive the Black-Scholes differential equation. In late July of 1995, shortly before his death, in response to a question I sent him about these matters, he emailed me: “I view all our work on fixed-income models as resulting from the application of the capital asset pricing model to fixed-income markets.”

I had a touching glimpse of his love for this approach a few years before he died when, together with a few of my colleagues, I tried to assess the effect of transactions costs and hedging frequency on our trading desk's options prices. We built a Monte Carlo simulation program that dynamically replicated each option as the stock price changed, adding the assumed transactions costs as each rebalancing of the hedging portfolio took place. In the long run we intended to use the program to see how much this caused options prices to deviate from the Platonic Black-Scholes value; in this way we could estimate the actual cost of our hedging strategy rather than accept the value of the idealized value embodied in the Black-Scholes model.

Whenever you write a program to do something new, you should first make sure that it does the old things correctly. In testing the program written by one of my colleagues, we first ran it assuming that there were no transactions costs and that you could hedge continuously, in order to ensure that we obtained the exact Black-Scholes replication price. Of course, you cannot really hedge continuously in a computer simulation, so we rehedged very often, several times a day. To our amazement, we discovered that even for 10,000 rehedgings on a one-year option—that is, for more than thirty rebalancings in a day—we still couldn't obtain the exact Black-Scholes value. There was always a residual discrepancy. This seemed wrong, so I wrote my own version of the program and found the same small but significant discrepancy. This was very puzzling; it suggested that the Black-Scholes formula was less applicable to the conditions of actual markets than we had expected.

I was perturbed enough to want to speak to Fischer about this, and went over to his office in another building on Goldman's growing campus. When I explain what I had found, he briefly became quite excited at the apparent inability of Merton's replication method to produce the exact Black-Scholes value, and said something like, “You know, I always thought there was something wrong with the replication method.”

Sad to say, I discovered a little later that both my simulation program and my colleague's contained small but different errors, which, once corrected, confirmed that the replication method rapidly converged to the exact Black-Scholes value! In his heart, though, Fischer mistrusted the Merton derivation and preferred his original proof.

Fischer's independent thinking led him to unorthodox but well-thought-out ideas, many of which sounded obvious once he articulated them. He voiced some of them in speeches, and others in a collection of brief, pointed notes that he circulated informally at Goldman in the early 1990s.

In one short essay he struck at the foundation of financial economics, writing that “certain economic quantities are so hard to estimate that I call them ‘unobservables.' ” One unobservable, he pointed out, is
expected return
, the amount by which people expect to profit when buying a security. So much of finance, from Markowitz on, deals with this quantity unquestioningly. Yet, wrote Fischer, “Our estimates of expected return are so poor they are almost laughable.”

In another essay entitled
Managing Traders
, he argued that a trader should be judged on the rationale behind his or her methods and rewarded only if it is sound, irrespective of whether or not he or she profited in the most recent period. “It's crucial to judge the stories they trade on,” he wrote about traders. “Stories can be wrong, but I'm uncomfortable trading without one . . . Looking only or primarily at their profit and loss statements is a recipe for disaster.” He wanted to reward intelligence and long-term thinking rather than the short-term vagaries of markets.