My Life as a Quant (23 page)

Jonathan traveled from business to academia. Others at Goldman took the reverse route. Another South African colleague in FSG was Ron Dembo, an academic and expert at optimization whom Mutt and Jeff had brought in as a consultant to help structure bond portfolios. Ron flew down from Toronto to New York for three days a week, staying in an apartment provided for him by Goldman, and in turn hired several other academics. For many of us it was our first glimpse of the perquisites of life with an expense account, and we marveled at it. Ron had an entrepreneurial streak and understood the value of systems and software for managing portfolio risk. He left Goldman in 1987, and shortly thereafter founded Algorithmics, a now prominent company that produces risk-management software.

I also began a long association with Bill Toy, who was already working for Fischer Black in the Equities Division when I arrived. Bill and I had both come to Goldman from physics by way of Bell Labs, and we had the same mutual scorn for the Bell environment and its bureaucracy. Fischer, whom I met only briefly in my first few weeks at Goldman, was in charge of the small Quantitative Strategies group in the Equities Division that built models and trading software for the equities business.

Another immensely talented programmer in FSG was Dave Griswold, who had been hired into Financial Strategies from Grumman Aircraft on Long Island only a few months before me. In his late twenties and armed with a BS in Computer Science from Rensselaer Polytechnic, Dave loved software in general and object-oriented programming, a methodology then beginning to penetrate the commercial world, in particular. Perhaps because there are several famous Griswolds in academic computer science, as well as the character Chevy Chase plays in “National Lampoon's Vacation” series, Dave liked to refer to himself as “Griswlod.” It was sophomoric, but it grew on you.

Dave was less a Wall Streeter and more a genuine computer science aficionado at heart. In classic UNIX style, he liked to first build the tools he needed for any new job. He always thought big. Asked to write a new program, he would ambitiously decide that it should be capable of running on any hardware and under any operating system. In order to achieve that, he had to shield his program from the details of a particular machine by creating his own version of all the infrastructure his program needed. Dave therefore created his own portable version of most of the facilities (windows, menus, files, databases, and so on) that DOS or UNIX provided.

I have seen many smart programmers indulge themselves by attempting to create everything
ab initio
; most of them who try fall into bottomless pits from which they never emerge, ceaselessly spiraling inwards in their effort to recreate portable versions of everything you could normally take for granted and get for free. What distinguished Dave from the ordinary stubborn people who wanted to build their own hammers, saws, and levels before starting to build the house was that he knew where to stop; he would finish building just the tools he needed and then use them to create the system itself.

David was a great fan of elegant and consistent computer languages. He loved Lisp and adored Smalltalk, one of the many Xerox PARC inventions that inspired the Macintosh environment. He was a devotee of Objective C, a Smalltalk-flavored C dialect that was an integral part of the operating system for Steve Jobs's Next computer before he returned to Apple. A few years later Dave wrote his own object-oriented language, which he called GoldC, for internal use at Goldman. In the long run, his interests would take him back to the software world.

Only three months after I arrived, Ravi departed to run Prudential-Bache's fixed income strategies group a few blocks away on Water Street. Several of Diller's senior strategists in FSG had already left, and now more of them continued out the door. Dennis Adler left for Dillon Reed and eventually ended up at Salomon Brothers, both firms that no longer exist as independent entities as a result of the enormous consolidation in financial services over the past fifteen years. Diller called me once to invite me to join him at Bear Stearns, but, disturbed though I was by Ravi's abrupt departure, it was much too soon for me to leave a place where I had just arrived. Instead, I put my head down and concentrated on work.

The bond options traders who were using
Bosco
began asking for many enhancements, and so, sometime in mid-1986, they authorized Dave Griswold and me to build them a more advanced trading system. I would provide the analytical and computational subroutines which Dave would embed in his infrastructure. For several months we all fiercely debated which computing platform to use. I was vehemently in favor of UNIX, the richest development environment, and the one I knew best. Bill Toy, who claimed great experience with the UNIX file system from the Labs, thought it was unreliable. Dave, predictably idiosyncratic and uncorporate, wanted to use Symbolics Lisp machines, then the cutting-edge computers for artificial intelligence. He envisaged that their massive amount of RAM would store the entire trading system in memory rather than on disk. (Massive is highly relative. The 64 Mb RAM of yesteryear's shared Symbolics machine is puny compared with the now modest 640 Mb on the personal Apple laptop that I use today.) Eventually we built the system on Sun workstations running UNIX.

Thus passed my first few happy months in the financial industry. At Bell Labs, from the day I had arrived, I had felt like someone past his prime. Now, at Goldman, despite the forty years behind me, I felt renewed. In the evenings I rode the subway home along Broadway to the Upper West Side and pored over textbooks by Cox and Rubinstein or Jarrow and Rudd, excited to be learning stochastic calculus and using my head again. One evening, someone from my old vanpool to the Labs got into the same subway car as me on Fourteenth Street. Seeing me engrossed in symbols, scribbling proofs on my lap on the shaky train, he laughed good-naturedly but incredulously at me for sitting there and doing mathematics on the subway—that was what you were meant to leave behind when you joined the business world!

But I remember thinking quite the opposite: What an enormous relief it was to be in a place where people actually wanted you to spend your time on what you liked! I told my vanpool friend that I could easily imagine doing this sort of work for another ten or fifteen years.

The history of options theory

Meeting and working with Fischer Black

The Black-Derman-Toy model

Wall Street had never been a place for academics. Yet, from the day I got to Goldman in late 1985, I kept hearing people talk with awe about Fischer Black, codiscoverer of the Black-Scholes equation for options pricing and the head of Goldman's Quantitative Strategies group. I saw him once at a meeting in the first few months after I arrived, but never spoke to him until the traders on the bond options desk arranged for us to meet.

Some traders are scornful of models; others will rely on them blindly. Our bond options traders knew that you need to layer visceral trading smarts over and above a consistent options pricing model. They understood they needed something beyond Ravi's original model, and so they approached Fischer about taking the next step. Since I had earned some credit for having diagnosed and then eliminated one small but glaring inconsistency in Ravi's model soon after I arrived, they therefore suggested that I join Fischer in an effort to build a better model.

Before I went up to his office on the twenty-ninth floor to meet him, to show him what I had done so far, and, implicitly, to see if he would have me work with him, I read a little more on the history of options theory.

Until the early 1970s, no one knew how to estimate the value of options in a convincing way. A call option that paid off when the stock price rose seemed much like a bet on a horse: The more optimistic you were about the stock's future prospects, the more you should be willing to pay for it. Each person set his own fair price.

Then, in 1973, Fischer Black and Myron Scholes published their eponymous Black-Scholes equation for the value of an option. That same year, Robert Merton provided a more rigorous and insightful way of understanding the argument behind their equation. Eventually, his formalism came to supplant theirs, and became the standard. Merton and Scholes won the 1997 Nobel Prize in Economics for their work, but Fischer, who was certainly their equal, died in 1995. Had he been fortunate enough to have lived a couple of years longer, he would surely have been a corecipient of the Prize.

I used to find it almost impossible to understand why the Nobel committee didn't award the Prize for options theory before Fischer died. Everyone in the finance community knew that it was only a matter of time before Black, Scholes, and Merton would receive the award, and it had also been common knowledge for several years that Black was mortally ill with throat cancer. I've heard speculations that the Nobel committee was reluctant to give the award to someone who worked in the business world, especially in the profitable and untheoretical business of investment banking.

Fischer, who had a PhD in Applied Mathematics from Harvard, had been a management consultant at Arthur D. Little and Co. when he developed the Black-Scholes model. One did not think of management consulting as the locus of groundbreaking theorists, but Fischer was always proud of his practical and unorthodox background. Once his contributions were recognized, he became a professor of finance at Chicago and then at MIT, finally leaving academia for Goldman Sachs in 1984. Though Merton and Scholes had each kept at least one foot in the academic world, both of them had worked as consultants or employees of Salomon Brothers at various times, and in 1994, became partners and attractors of capital at Long Term Capital Management, the leveraged hedge fund run by John Meriwether and his ex-Salomon “arb group.” I noticed that the 1997 Nobel Prize citation referred only to the university affiliations of Merton and Scholes, and not to their corporate connection—perhaps the Nobel committee really did have an aversion to the business world. Though the Nobel Prize sounds as though it is awarded by the gods, committees are merely groups of people with their own preferences.

Throughout his life, Fischer was genuinely in love with the idea of equilibrium, and he invented the Black-Scholes equation in the late 1960s by applying the condition of equilibrium to markets themselves. Equilibrium is a common and very powerful concept in physics; in equilibrium, the numerical values we observe for quantities of interest in a stable system are the values that cause two opposing forces to cancel exactly. For example, the temperature of a body stops rising at that equilibrium temperature at which the heat flowing into the body is canceled by the heat flowing out. Fischer believed that market prices were determined by similar cancelations.

Fischer first obtained the Black-Scholes equation by demanding that an option on stock and the stock itself be in equilibrium with each other, in the sense that their respective prices should each provide investors with the same expected return per unit of risk they carried. An investor would then be impartial between buying the stock and buying the option. This condition, written down mathematically, was the Black-Scholes equation; it determined the value of the option. It took several years more before Black and Scholes provided the eventual solution to the equation.

Merton, working in parallel, went deeper. He showed that there was a recipe for synthesizing a stock option out of a mixture of shares of stock and cash, a mixture whose proportions must be readjusted continuously by exchanging some shares of stock for cash, or vice versa. An investor who bought the initial mixture and then carried out the readjustment recipe would end up with precisely the same payout as the stock option, and so the option's value should be exactly the cost of purchasing the initial mixture.

The recipe for synthesizing an option was called
dynamic replication
—replication because you were reproducing the option, dynamic because you had to keep changing the mixture in order to do it. Replicating an option was like riding a toboggan with your eyes closed down its serpentine track—you needed a recipe for which way to bank at each point in time. Black-Scholes gave you that recipe. Merton justified it.

That you could dynamically replicate an option was an almost confounding result. Until Black, Scholes, and Merton, came along, no one imagined that you could create an option out of simpler securities. Now an option was seen to be merely a subtle mixture of simpler securities, stock and cash, in constantly changing but known proportions.

Merton relied on a mathematical formalism called
stochastic calculus
, the study of the rate of change of randomly varying quantities such as the price of a stock or the position of a dust particle in a room. At graduate school in the 1960s, 1970s, and throughout my subsequent life as a postdoc, I had never heard of stochastic calculus. Nowadays, its methods are commonplace to all quants and graduate students in finance; every ex-physicist looking for a job on Wall Street begins by studying the subject. Black and Scholes's 1973 paper, in which they presented both their own and Merton's derivation of the equation, was sufficiently arcane that it took several years to get it published. Indeed, it was repeatedly rejected until Merton Miller at the University of Chicago interceded on their behalf.

The two simultaneous but complementary derivations of the theory of options pricing in the early 1970s, Black and Scholes's and Merton's, reminded me of the complementary derivations of renormalizable quantum electrodynamics by Feynman and Schwinger in the late 1940s. Feynman and Schwinger each used drastically different approaches to reach similar results, their respective formalisms so dissimilar that no one understood their equivalence until it was demonstrated by Freeman Dyson. Thereafter, Feynman's more intuitive approach became the standard. Black and Scholes and Merton also utilized different approaches; over the long run Merton's more formal and powerful methods became the standard, and were eventually used by Fischer himself.