The Einsteins of Wall Street Jeremy Bernstein

The Einsteins of Wall Street Jeremy Bernstein If you decide you don’t have to get A’s, you can learn by his rather recently acquired wife Vila, a very at- an enormous amount in college. tractive and voluble Yugoslavian. —I.I. Rabi The three of us spent a good deal of time to- n the spring of 1969, I got the somewhat gether—Stone, an inveterate traveler, had also I lunatic idea of going to the Northwest Fron- come to Pakistan to visit the frontier—and in the tier of Pakistan to see the high mountains—K-2, course of it Vila mentioned that she had a daugh- Nanga Parbat, and the like. As it happened, I had ter in New York whom I might like to meet. When a Pakistani colleague in physics with a connection I returned to the States, I called this young woman. to both the University of Islamabad and the Ford She was seeing someone at the time, but she Foundation. He arranged for me to become a thought that her beau and I might have things to Ford Foundation visiting professor at the universi- talk about. He was, she said, studying “derivatives,” ty, and before taking up my teaching duties I man- which in calculus refers to the rate of change along aged to explore all sorts of places on the frontier a curve. Since this is one of the first things one that are now presumably inaccessible to travelers. learns in calculus, I assumed that he was a begin- In Islamabad I led a pleasant but somewhat lone- ner, which did not seem to promise much by way ly existence—until, after about a month, I heard a of conversation. In the event, he turned out to be pair of English-speaking voices that turned out to an amiable chap by the name of Myron. belong to another Ford Foundation professor and I forget what we talked about. But I do dimly re- his wife. This was not any old professor. It was member that at one point his girlfriend whispered in Marshall Stone, one of the world’s best mathemati- my ear that Myron was going to win the Nobel Prize cians. In addition to creating, at the University of someday. She turned out to be right about that, al- Chicago, the leading school of mathematics in the though it took a while: in 1997, Myron Scholes and country, Stone had also been the teacher of my Robert Merton shared the Nobel Prize in econom- teacher at Harvard, George Mackey, who had in- ics. Together with Fischer Black, who had died two terested me in the mathematical foundations of years earlier (and who will come into this story later quantum theory. Now here he was, accompanied on), Scholes had created what is known as the Black- Jeremy Bernstein is the author most recently of Oppen- Scholes equation, published in 1973. Merton invent- heimer: Portrait of an Enigma (Ivan Dee). His books in- ed another approach to the same problem. clude Cranks, Quarks, and the Cosmos, Albert Einstein, The Black-Scholes equation does indeed deal and Quantum Profiles. with derivatives, but in another sense: that is, in- [64] The Einsteins of Wall Street vestment instruments, like options on stocks or wife, until finally taking a position in the business- bonds, whose present value is “derived” from the systems center at Bell Labs in New Jersey, to which projected future values of the financial commodi- he could commute from New York. Although he ties that underlie them. The Black-Scholes equation, seems to have hated Bell—his chapter on it is called with its many adumbrations, is used to assess the “In the Penal Colony”—in those years the place market value of such options at any given point in was full of people at the top of their fields, includ- time. It is the Newton’s Law, or the Schrödinger ing Arno Penzias, Robert Wilson, and other past equation, of the whole field of financial engineer- and future Nobelists.† ing that makes these markets operate. At Bell, Derman wanted to join the research group working on the UNIX operating system— had more or less forgotten about all this until the multi-user, multi-task system that now runs I reading a new book by Emanuel Derman called computer complexes around the world. But all his My Life As A Quant: Reflections on Physics and Fi- requests were denied, and by the early 1980’s he nance.* A “quant” is the rubric used on Wall had had enough. By coincidence, this happened to Street and elsewhere to denote people who practice be the time when the major brokerage firms were quantitative financial analysis—financial engineer- building up their financial-engineering depart- ing—for which the Black-Scholes equation is a ments and were headhunting at places like Bell. prototype. Physics comes into Derman’s memoir because he has a Ph.D. in physics from Columbia II and was one of the early pows (Physicists on Wall Street), having joined the financial firm of Gold- he brokerage business had changed: from man Sachs in 1985. T merely selling stocks and bonds, it was now The first part of Derman’s book traces the dealing in all sorts of derivatives, which play an im- somewhat unlikely steps that took him from his na- portant role in the marketplace in diversifying risk tive Cape Town, South Africa, first to Columbia and maintaining price stability. For example, the and then via the AT&T Bell Labs and elsewhere to firm of Salomon Brothers had put together a pow- Wall Street. As he notes in his book, our paths erful group of analysts under John Meriwether; one crossed at various times. I do not have specific of its consultants was Robert Merton, the Harvard memories of our meetings, but both of us are theo- professor who would later share the Nobel Prize retical elementary-particle physicists, and our with Scholes (and whose father, also Robert but with a different middle initial, was a noted sociol- world is not large. ogist of science at Columbia). Similarly deep into Derman arrived in New York in 1966. The derivatives was Goldman Sachs; it was there, in physics department at Columbia was then still December 1985, that Derman took a job in the fi- under the aegis of I.I. Rabi, whose standards were nancial-strategies group and had his first encounter extremely high. Apart from Rabi himself, there with Black-Scholes. were other present and future Nobel Prize win- If you put “Black-Scholes” into Google, you will ners. You had to be very good, and very deter- come up with something like 128,000 entries. Most mined, to survive in that department. of them are technical; some, clearly by ex-physi- Derman, who remarks wryly that about 10 per- cists, offer to tutor you for a considerable fee. cent of his projected life span was spent getting While wandering through this jungle I came across a Ph.D. at Columbia, wrote his thesis on what we the perfect site for my purposes. It is called “Black- refer to as “phenomenology”—deriving some un- Scholes the Easy Way,” and can be found at derlying theory to make a model that either predicts http://homepage.mac.com/j.norstad. The person or explains an experimental result. From the sound who put it up, John Norstad, is a computer scien- of it, Derman’s was a very respectable piece of tist whose notes, representing his own learning work, one that incidentally required him to learn process, are very unassuming and clear. In what fol- to use the rather primitive computer facilities that lows I will use Norstad’s examples. were then available. The thesis was good enough In the early 80’s, as I mentioned, financial insti- to get him a post-doctoral position at the Universi- tutions were doing a substantial business in the sale ty of Pennsylvania. of derivatives. A typical example is a stock option. The next several years were difficult. Derman * Wiley, 288 pp., $29.95. moved from one temporary academic job to anoth- † I wrote a series of linked profiles of some of these physicists that er, usually in cities where he was separated from his was published as a book in 1984, Three Degrees Above Zero. [65] Commentary September 2004 This involves a contract between two parties that modify the results, look at Norstad’s website.) As- allows you, the buyer, to purchase a particular stock sume finally that I can buy fractional shares of the at a future time from the seller at a specified price $100 stock itself from a friendly broker, commis- called the “strike price”—which is often the price sion-free. By means of these assumptions, to use of the stock itself when you buy the option. another term of art, we have made the problem Until that future time, you do not own the stock “frictionless.” itself, only the option to buy it. If, when you do buy Now suppose you have calculated the expected it, the value of the stock has gone up, you will be “in outcomes according to the formula presented the money.” If it has gone down, you will be “out of above and are willing to give me $15 to buy the op- the money”—that is, out the cost of the option.* tion. I will now show how, no matter what the real The question is: what should be the price of the outcome might be, I can always come away with $5 option when you buy it? This is what the Black- for myself.

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