My Life as a Quant (35 page)

Within a few months, finance academics at several universities published papers on the valuation of GER options. One or two of them got it wrong the first time, because it was subtle, but several got it right. Had we published our paper, Goldman would have given up little; they might even have gained some minor kudos as a haven for analytically talented people. A few copies of our internal report did leak out over the next year, probably distributed by salesperson eager to set up a dialogue with clients. Ten years later it was finally reprinted, belatedly but verbatim, in a book on currency derivatives.

Later that summer I gave a talk on GER options at a course organized by John Hull at the University of Toronto. While listening to the other speakers, I began to realize how lucky I was to be working in equity derivatives at Goldman. GER options were merely the forerunner of many new and intriguing problems that the blossoming equity options markets were beginning to throw our way, problems of which academics were unaware.

The problems of intellectual and business interest often came to us as questions, ill-posed by traders, who knew they had a difficulty but could not always articulate it. The first battle was understanding what the problem was. The traders didn't always have the patience to listen to our solutions. Sometimes, as we discovered from the salespeople, it was the firm's clients, especially in mathophiliac France and Japan, who had a greater taste for learning about financial models and exotic products. I began to realize that there was a market for honest, simple, direct and nonpatronizing writing about complex topics.

During the next ten years in Quantitative Strategies we wrote many reports on the subtleties and complexities of equity volatility. We tried to straddle the line between academia and Wall Street, attempting to explain the theory of trading and valuation in a picturesque and pedagogic style using only a modicum of academic rigor, the latter often relegated to an appendix. We aimed to make our papers accessible to an audience of intelligent traders, salespeople and clients, all with a presumed short attention span.

In my mind's eye I retained a 1980s view of quant groups, an outlook I had absorbed by osmosis from Stan Diller and Fischer. I felt that we were advantaged by working at the intersection point between theory and the real world. I saw that it was good to have one foot in both the academic and practitioner universes; I found that publication of our models could simultaneously move financial economics forward while bringing prestige to Goldman Sachs, thereby helping to attract people of high quality to the firm. Finally, I learned that persuading the world to measure value with your model is an effective and honest endeavor.

People outside Goldman thought that we spent all of our time doing abstract research and writing it up for publication. It wasn't so. Our main activity was always building models and trading systems for use by the derivatives desks, trying to solve their practical problems with our theories. In the time we had left we wrote our reports, often for love rather than money. We were immensely lucky to be the theorists living in the experimenters' laboratory, with the opportunity to be the first to hear about new irregularities and the difficulties they posed for trading desks.

The success of Granny's structured deal made everyone hungry for more. It was clear that further deals would require more quants and better risk management systems, and the QS group began to grow.

Though no one used that term in those days, it was Piotr's “financial engineering” that showed us how to eliminate the mismatch between the risk of the warrants we owned and the GER puts we sold. Executing the hedge in practice was more complicated. The trading desk was long a diverse assortment of yen-valued Nikkei puts. They were correspondingly short a large homogeneous batch of the dollar-valued Kingdom of Denmark Nikkei puts that Goldman had issued. To hedge the mismatch, they had to continually trade varying quantities of Nikkei futures and yen currency, as well as some individual Japanese stocks. This entire “Nikkei book” had to be hedged at least once each day, and sometimes more often.

When I arrived in January 1990, all this complexity was being handled on a vintage DOS-based PC running a Lotus spreadsheet into which various Black-Scholes options formulas had been embedded. It was neither flexible nor robust enough for interactive risk management.

I was lucky to have come to QS from the fixed-income world, which has always been a few sophisticated steps ahead of equities in these matters. The rapid rise of interest rates in the late 1970s, after years of stable returns with low volatility, had forced fixed-income clients and the trading desks that serviced them to become the early pioneers of portfolio hedging systems. As a result, I knew a great deal about designing and building risk systems, and saw that this was where I could contribute.

In a month or two, Piotr and I, together with Rao Achyuthuni, one of the QS consultants, quickly designed and built a rudimentary Nikkei risk management system that we called
Samurai
. It was simple, but it did the job: We entered our trading positions in tabular fashion into a flat computer file, one security to a row. Within each row the first column indicated the number of securities we owned, the second specified the security type (stock, option, index, futures contract, currency, and so on), while the remaining columns spelled out the details (strike, expiration, and so on) necessary for valuation. Each day we edited the file to reflect new trades or expirations. Samurai read the positions in the file and then reported the model value and hedge ratio for the entire portfolio at current market levels. It also reported the impact on the portfolio of more extreme scenarios in which the Nikkei level, the yen, interest rates, and volatilities moved up or down by as much as 20 percent. This latter feature was perhaps the most useful; we could use it to discover the potential “hot zones” in the book that might take us down, and we could estimate what types of new trades could ameliorate these potential disasters.

Samurai made a giant splash; simple as it was, nobody in the division had ever seen a built-from-scratch, risk-management system for derivatives portfolios before. The desk embraced it and invited Jeff, Piotr, and me to demonstrate it to Roy Zuckerberg and David Silfen, the dauntingly patrician heads of the Equities Division.

What we had built suited the desk so well because we had collaborated so closely with Dan. Traders have their own vernacular and, though he spoke it himself, Dan was one of the few traders I met who was willing and able to bridge the language gap. He would spend hours with us on the chalkboard each day, trying to help specify and test the system; he would patiently debate with me what should be displayed on the screen and in what format. Dan was also a bit of a closet quant, who one day proudly took out of his desk drawer the senior thesis on option pricing he had written years earlier. Most of the programs we wrote in QS over the next several years worked so well in part because Dan took on the role of the trading desk's agent.

Unlike many traders, Dan also knew that success comes from incremental improvements. We weren't building the space shuttle, whose specifications had to be written down in minute detail and handed over to the engineers. When we began to build risk systems for the developing business of equity derivatives, we had entered uncharted terrain, and there was no commonly acknowledged best path through it. Every time we spoke with the traders, we faced such a flood of demands and choices that it was difficult to decide what to do first. Dan, more than anyone else I worked with from trading, understood what physicists call perturbation theory, the approach by which you get the most critical feature completed first, and then at each next step you tackle the next most important feature. In contrast, many other traders and desks were like the “old sailor my grandfather knew” in A. A. Milne's poem “who had so many things he wanted to do that whenever he thought it was time to begin, he couldn't because of the state he was in.” Dan perceived his job to be the definition and creation of a uniform and well-designed trading infrastructure for the entire desk, wherever they worked, so that traders could move from one country to another and find a consistent environment. Most traders just want to trade; Dan was willing to think about the tools you need to trade safely. When the firm moved Dan to London a few years later, no one adopted his role, and from then on giving the desk what they needed became much harder. For more than ten years afterward, the methodology we created in Samurai remained the core of our risk system, despite manyfold increases in the size of our desk and our book.

By the early 1990s, the Soviet Union had collapsed, the end of history was ostensibly upon us, and global capitalism was rampant. In equity derivatives, the era of exotic options had begun. Exotics seemed the preferred way for investors in one country to gain just the exposure they wanted to the markets in another. Suppose you were an American investor who wanted to gain if the French stock market rose. In the old days you had to buy and hold a diverse collection of French stocks and face the detailed bother of tracking their prices in francs, collecting their dividends, converting them to dollars, paying income and capital gains tax; after all that, however, you were still exposed to the risk that the French franc might deteriorate against the dollar. Now you could instead come to our equity derivatives desk and buy a call option on the CAC-30 French equity index, GER'd into dollars; you got the simplicity of looking at the daily closing level of the CAC-30 in the newspaper or on a screen and knowing what your P&L was, as traders like to refer to their profits and losses. You could leave the messy stuff to us.

Exotic options like these and others were taking off, and Goldman was determined to build a Structured Equity Products business. The success of Samurai made QS the natural support framework, and during the next five years we grew to about 30 people, with approximately three software developers in our group for every pure quant. Each day we thought about new options we could design and value, all of them providing exposure to more granular contingencies than the coarse, standard options on which we had sharpened our teeth. There were barrier options, options on the maximum of a stock price, options on the average of a stock price, lookback options, outperformance options, rate-contingent options, options on options themselves. When, during the late 1970s and early 1980s, these structures had first been invented and their value found by means of ingenious mathematical manipulations, they were merely a curiosity, a pushing of the theoretical limits. Now, ten years later, investment banks saw them as tailored instruments in the business of giving customers exactly the risk profile they desired—for a premium of course.

Behind all of these exotic structures, if they were successful in the marketplace, were two obvious principles. First, since an option is a type of bet on a future scenario that may never occur, investors want to pay as little as possible for it. Second, in order to minimize an option's cost, you must define as precisely as possible the exact scenario you are betting on. The more precise you can be about the scenario from which you want to benefit or protect yourself, the less you pay.

We had options for every attitude. The classic was a standard call option. A call on the Standard & Poor's (S&P) 500 index, for example, was a straightforward bet that the index would rise by the expiration date; when you bought it you paid for all scenarios in which the index would ultimately rise, including those in which the index first dropped and then recovered.

There were more exotic flavors. A
knock-in barrier
call option was a bet that the index would first drop below some barrier level and then regain its ground. If you thought that this dip followed by a rise were likely, you could pay only for that scenario, and it would cost you less than a standard call. There were many similar variations on this theme.

If you didn't want to worry about small fluctuations in the S&P 500 as long as its trend was upwards, you could buy an
average
(or
Asian
) call option on the index, whose payout depended only on the average level of the index over the life of the option. Since the time average of an index is a more stable quantity than the index itself, this option, too, was generally cheaper than a standard call.

Alternatively, if you thought that the stock market would rise only if the Federal Reserve kept interest rates low, you could buy a rate-contingent call option on the S&P 500 that would extinguish (or
knockout
, in options parlance) if interest rates were to rise. Again, since this call would pay out only if interest rates were to stay low
and
the index were to rise, a less likely occurrence than the index rising under all circumstances, you paid less for it.

A typical buyer of our options was a European commercial bank that, as interest rates kept falling, wanted to attract depositors by giving them a chance of earning a higher return. The bank would promise its depositors an enhanced rate of interest proportional to the rise (if it occurred) in the one-year average of the CAC-30 over the next year. To provide that payout, the bank bought options on the average of the CAC-30 index from our desk. Instead of providing its depositors with a simple fixed-income investment, it was giving them a hybrid product they couldn't get elsewhere, a bond combined with an equity “kicker.”

Conversely, many of the sellers of equity options were European pension and mutual funds or insurance companies who, unhappy with the decline in bond yields, sold options on equity indexes to enhance their return. They gambled that the indexes wouldn't rise and that the options they sold would finish out of the money.

The development of new options structures resembled an arms race. Any firm that created something popular with clients had a few months to press their advantage before another firm copied them. It took that long to reverse-engineer a product, add a few wrinkles, develop a risk management strategy, put in place the legal and technical infrastructure, and then market it.