My Life as a Quant (40 page)

Years ago, when I first became aware of the smile and hoped to find the “right” model, I used to ask colleagues at other firms which model they thought was correct. But now there is such a profusion of models that I ask more practical questions—not “What do you believe?” but rather “When you hedge a standard S&P 500 option, do you use the Black-Scholes hedge ratio, something larger, or something smaller?” Local volatility models produce smaller hedge ratios, while stochastic volatility models tend to produce larger ones. The differences between the models are even more dramatic for exotic options.

In 2003, at a derivatives meeting in Barcelona, I led a small roundtable discussion group on the smile. There were fifteen of us, traders and quants from derivatives desks all over the world. I asked everyone my simple question: When you hedge an S&P 500 option, would you use the Black-Scholes hedge ratio, something larger, or something smaller? I was surprised that ten years after the first smile models appeared, with the smile a fact of life in almost every derivatives market, after thousands of published papers, there was still no consensus on how to respond to it.

There still isn't. Though we know much more about the
theories
of the smile, we are still on a darkling plain regarding what's correct. A decade of speaking with traders and theorists has made me wonder what “correct” means. If you are a theorist you must never forget that you are traveling through lawless roads where the local inhabitants don't respect your principles. The more I look at the conflict between markets and theories, the more that limitations of models in the financial and human world become apparent to me.

1
A mathematically complex average, to be honest, but an average nonetheless.

Wall Street consolidates

Clothing goes casual

Moving from equity derivatives to firmwide risk

The bursting of the Internet bubble

Taking my leave

Life in the first half of 1990s was a bit too good to last. The atmosphere in Quantitative Strategies was rousing—we were an eclectic bunch of ex-physicists, ex-mathematicians, and computer programmers, with our own individual interests but all of us were passionate about finance. Most of the time we were one happy family—the quants taught financial theory to programmers who in turn taught programming style to the quants. Best of all, we worked closely with traders such as Dan O'Rourke to bridge the gap between academic theory and trading practice. Our body was in the business world but our head was inspired by academia. It was a rich existence.

To top it off, we had ample resources because we worked for traders who understood that spending money on research and development is not a zero-sum game. We believed that our models and systems were the best on Wall Street. But business is cyclical. After the punishing rise in interest rates of late 1994, power shifted from our traders to our sales-people, who had difficulty imagining that investment in new models and trading systems could lead to more business. Instead, they regarded research as an expense. Lacking the skill to distinguish indulgence from necessity, they demanded that each investment, no matter how small, be
authorized
by someone “on the business side” who could determine its merit and need. But authorization requires authority, and few salespeople had the time and interest to acquire it. Instead, they held meetings.

In the short run, it was merely time that was wasted; over the longer haul, opportunities were lost. While the business grew our infrastructure stagnated. Now traders began to stay late into the evening to handle ever larger numbers of transactions with antiquated systems. Eventually, our models suffered, too. Then, as our models and software failed to stay state-of-the-art, our self-respect declined. Soon I found myself spending more and more of my time consoling the discontented in our group. Money could no longer keep them happy when daily life ceased to be rewarding. Slowly but steadily I could feel the need for change growing within me, too.

There was one elementary fact that many of our bosses were unable to grasp: We were building these models and systems not just because
somebody
authorized it, but rather because
we
thought they were the right thing to do, because these questions fascinated us. We saw a problem, discerned a need, became absorbed, and tackled it. It was all-engrossing. Struggling to resolve the paradoxes of convertible bond models that had to combine credit and equity risk, or trying to figure out how to model the smile, I would find myself thinking about the problems in mental pictures while I showered or took a run in the park. Sometimes I lay in bed unable to put the picture out of my mind. We worked hard out of passion, pride, and the pleasure of being thanked, recognized, and appreciated; of course, we also worked for money, but money alone wasn't enough.

The investment banking universe had changed, too. In 1985 you could look for a quantitative research job at Goldman, Salomon, First Boston, Prudential, Drexel, Shearson, Lehman, E. F. Hutton, DLJ, Smith Barney, Paine Webber, Bankers Trust, Chase, Chemical, Citibank, and Mocatta Metals, to name just a few among the large and reasonably respectable banks and trading firms. Almost none of these firms exists as an independent entity anymore. By 2000 the bigger fish had swallowed up the smaller ones, and Citigroup, Morgan Stanley, Merrill, and Goldman faced off in a competition for business and capital around the globe.

To compete, the firms had grown unavoidably larger. When I began working at Goldman in 1985, the firm employed fewer than 5,000 souls; when I ate my daily lunch in the cafeteria of the 85 Broad Street building that housed all our New York employees, I could recognize many of them. After the layoffs of 1994 there were about 10,000 employees throughout the firm. By late 1999, as the millennium drew to a close, we had become a publicly listed company with a workforce of over 20,000 people. At every quarterly managing directors meeting I heard company leaders recite the mantras that more than half the people in the firm had been there less than two years, that growth was necessary to stay competitive, and that we had to figure out new ways to maintain our culture.

And there really was a culture. Goldman was a little more gentle, a touch more thoughtful, a jot more tolerant of intellectual diversity. You could talk to anyone if you needed to—there was little standing on ceremony. If you were good at something, you could be different. Even programmers and quants were paid a modicum of respect for their skill and contribution. People seemed to understand that all of these activities, in their different ways, benefited the firm, helped attract employees and customers, and helped make money.

After the IPO, quotidian life changed. The aristocratic old guard with whom I was familiar, Bob Rubin, Jon Corzine, and Roy Zuckerberg among them, had left to make their imprint on politics or enjoy their personal lives. With its newly minted shares of stock to disperse, Goldman began to raid other firms' talent and buy other firms' businesses. As we grew into a large public company, the flow of information inside the firm became more constricted and the hierarchy more stratified. None of this was necessarily bad; it simply went with the territory. I still liked Goldman better than any other place I considered.

Appearances were changing, too. In late 1999 the Nasdaq was heading towards its precipitous peak, and each day there were new cracks in the Berlin wall of Wall Street's formal business attire. Each new day another firm announced that casual clothing was henceforth
de rigueur
. Each new morning saw formerly navy-suited partners come to work in manifestly casual trousers and sports jackets over open-necked shirts. At Goldman, the first to crumble was the historically more plebeian currency and commodities division. Fixed income fell rapidly thereafter. Equities, the last bastion, at first gave in only to casual Fridays. One principled person in my group continued to wear a suit each Friday; when someone asked him why he wasn't going casual, he replied that it was bad enough to wear a uniform every day, but that wearing different uniforms on different days was too much. After a few weeks of casual Fridays, Equities fell, too, and the Velvet Revolution was over. From then on it was all casual, all the time.

The intent, of course, was to continue attracting the best young graduates to staid old investment banking in the face of competition from hipper dot-coms. On recruiting trips for Goldman we discovered that many MBA students were leaving their studies in mid-course to join new get-rich ventures. Even the undergraduates we interviewed weren't as sharp as they had been in previous years. Striking back, Goldman distributed free fruit and soft drinks each day, and, in case that didn't suffice, they further provided concierge services to junior employees working too hard to afford the time to attend to their own needs.

Finally, the hot thing in equities in the late 1990s was going after retail customer flow and electronic distribution. Investment banks, traditionally wholesalers, had to catch up fast. For the next few years, I could see, the valuation side of the business was going to take a back seat to issues of technology. So, by late 1999, a little weary of intermediating between discontented quants and resource-starved traders, I thought about change.

But how to move? On the day when I left Goldman for Salomon Brothers in 1988, Scott Pinkus had offered me the chance to move to another position within the firm. When I asked him why he hadn't broached it earlier, he explained that it would have been poaching. It was bad form to try to recruit someone from another department.

The inverse held, too. If you wanted to move to another area, you weren't supposed to set about it openly—that was putting your needs before those of the business, a bad character trait. Condoning this would have opened the floodgates. To be culturally correct, you were supposed to sit down with your boss and then, after politely explaining your need for different horizons, ask him: Is it okay with you if I explore other opportunities?

But this meant showing your hand—it was difficult to tell someone you didn't want to work for him or her anymore. Instead, in practice, you approached the person you did want to work for and asked discreetly if a position was available for you in his or her area. Then, if there was interest, you met several times to discuss possibilities. Finally, if you both wanted to proceed with the transfer, you went to your current boss and asked: Is it okay with you if I explore other opportunities?

In late 1999 I spoke to several senior people I knew around the firm and asked about possibilities. One of them was Bob Litzenberger, the head of Firmwide Risk Management at Goldman Sachs and a former well-known Wharton professor. His group's job was to monitor and report the risk of the entire firm and all of its subdivisions; Bob was well suited to lead it. He was immensely broad and knowledgeable, the author of well-known papers who had also worked in several derivatives trading firms. He also had the will for it; to control the risk carried by the well-paid heads of powerful trading desks you had to be tough. Concealed behind Bob's deceptively mild facade lay a necessarily stubborn will.

It took only a few meetings to establish that Bob was keen to have me join Firmwide Risk; for my part, I was eager to move. He needed someone who was a derivatives expert because many of the more subtle risks to the firm lay in the complex, exotic, high-margin, over-the-counter options traded by Goldman. We quickly agreed to move forward. Then, other opportunities having been explored, we rolled back the odometer. The next day I went to ask my current boss: Is it OK with you if I explore other opportunities?

In early January 2000 I departed Equity Derivatives for Firmwide Risk.

The Firmwide Risk group that I joined was located in the division of Operations, Finance, and Resources (OF&R). It was a service division and it wasn't glamorous—Resources meant Personnel, Controllers, and Legal, all essential but nevertheless auxiliary to the firm's main business activities. OF&R was a strange locus for quants, a home so foreign to mathematics and modeling that it was difficult to tempt experienced strategists to come and work there.

Despite its dull location, Firmwide Risk tackled important problems. Like insurance companies, trading desks at investment banks make money by taking calculated risks for a fee. Our major task was to measure the magnitude of the current risk of every desk, each division, and the entire firm in a systematic and uniform way, helping to decide which risks were inappropriate. Each desk ran its own risk management system, but we were responsible for coordinating the bigger picture.

Most days, a desk was likely to gain or lose small amounts, but there was always some chance of a potentially large loss. To quantify the notion of risk, we and almost everyone else on the Street used the so-called daily VaR, or Value at Risk, the dollar loss threshold above which greater losses would occur with a probability no larger than 0.4 percent, or 1 chance in 250. This corresponded to about one trading day in a year. VaR is therefore the 99.6 percentile loss. So, for example, a VaR of $50MM for the Equities Division meant that there was only a one-in-two-fifty chance that more money than this would be lost on any given day in the year.

Invented in 1994 by the J. P. Morgan bank, VaR is an unsatisfactory risk metric that has somehow become an industry standard. We estimated our daily VaR by running nightly simulations of the changes in the prices of the portfolio held by each trading desk. These simulations were huge computer programs that used the past statistics of each desk's assets to estimate the distribution of possible values the portfolio might take in the future. With those estimates we could predict the distribution of each desk's portfolio value a day later. We produced VaRs for each desk, then for each group of desks in a common trading area, then for each division, and finally for the entire firm, generating a hierarchy of potential one-day losses that gave a view of the firm's riskiness from top to bottom.