My Life as a Quant (2 page)

Coincidentally, some of the same forces that compelled physicists to move out of academia made Wall Street begin to embrace them. The Arab oil embargo of 1973 caused fuel prices to soar and interest rates to climb; soon the fear of inflation propelled gold prices above $800 an ounce. Suddenly, financial markets seemed to become more volatile. Bonds, a traditionally conservative investment, were suddenly seen as much riskier than anyone had imagined. The old rules of thumb no longer applied. Understanding the motion of interest rates and stock prices became more important than ever for financial institutions. Risk management and hedging were the new imperative and, in the face of so much freshly perceived risk, complex new financial products that provided protection from change proliferated.

How could one describe and understand the movement of prices? Physics has always been concerned with dynamics, the way things change with time. It was the tried-and-true exemplar of successful theories and models. And physicists and engineers were jacks-of-all-trades, simultaneously skilled mathematicians, modelers, and computer programmers who prided themselves on their ability to adapt to new fields and put their knowledge into practice. Wall Street began to beckon to them. In the 1980s, so many physicists flocked to investment banks that one head-hunter I know referred to them as “POWs”—physicists on Wall Street.

What is it that physicists do on Wall Street? Mostly, they build models to determine the value of securities. Buried in investment banks, at hedge funds, or at financial software companies such as Bloomberg or SunGard, they tinker with old models and develop new ones. And by far the most famous and ubiquitous model in the entire financial world is the Black-Scholes options pricing model. Steve Ross, a famous financial economist, options theorist, and now a chaired professor at MIT, wrote in the
Palgrave Dictionary of Economics
that “. . . options pricing theory is the most successful theory not only in finance, but in all of economics.”

The Black-Scholes model allows us to determine the fair value of a stock option. Stocks are commonplace securities, bought and sold daily, but a call option on a stock is much more arcane. If you own a one-year call option on IBM, for example, you have the right to buy one share of IBM one year from today at a predetermined price: say, $100. The value of the option on that future date when it expires will depend on the prevailing value of a share of IBM. If, for example, a share sells for $105 on that day, the option will be worth exactly $5; if a share sells for less than $100, the option will be worth nothing. In a sense, the option is a bet that the stock price will rise.

An option is a special case of a more general
derivative security
, a contract whose value is
derived from
the value of some other simpler
underlying
security on which it “rests.” A derivative security's payoff at expiration is specified in a contract via a mathematical formula that relates the payoff to the future value of the underlying security. The formula can be simple, as is the case with the stock option just described, whose payoff is the amount by which the final stock price exceeds the value of $100, or it can be extremely complicated, with a payoff that depends on the prices of several underlying securities through detailed mathematical expressions. During the past twenty years derivative securities have become widely used in the trading of currencies, commodities, bonds, stocks, mortagages, credit, and power.

Derivatives are more intricate than unvarnished stocks or bonds. Then why do they exist? Because derivatives allow clients such as investment banks, money managers, corporations, investors, and speculators to tailor and fine-tune the risk they want to assume or avoid. An investor who simply buys a share of IBM takes on all the risk of owning it; its value waxes and wanes in direct proportion to IBM's share price. In contrast, an IBM call option provides potentially unlimited gain (as the share price rises above $100) but only limited loss (you lose nothing but the cost of the option as the stock price drops below $100). This asymmetry between upside gain and downside loss is the defining characteristic of derivatives.

You can buy or sell options retail on specialized options exchanges, or you can trade them with wholesalers, that is, the dealers. Options dealers “make markets” in options; they accomodate clients by buying options from those who want to sell them and selling options to those who want to acquire them. How, then, do dealers handle the risk they are forced to assume?

Dealers are analogous to insurance companies, who are also in the business of managing risk. Just as Allstate must allow for the possibility that your house will burn down after they sell you an insurance contract, so an options dealer must take a chance of a rise in IBM's stock price when he or she sells you a call option on IBM. Neither Allstate nor the options dealer wants to go broke if the insured-against scenario comes to pass. Because neither Allstate nor the dealer can foretell the future, they both charge a premium for taking on the risks that their clients want to avoid.

Allstate's risk strategy is to charge each client a premium such that the total sum they receive exceeds the estimated claims they will be obliged to pay for future conflagrations. An option dealer's risk strategy is different. In an ideal world, he or she would simply offset the risk that IBM's price will rise by buying an IBM option similar to the one he or she sold, from someone else and at a cheaper price, thereby making a profit. Unfortunately, this is rarely possible. So instead, the dealer
manufactures
a similar option. This is where the Black-Scholes model enters the picture.

The Black-Scholes model tells us, almost miraculously, how to manufacture an option out of the underlying stock and provides an estimate of how much it costs us to do so. According to Black and Scholes, making options is a lot like making fruit salad, and stock is a little like fruit.

Suppose you want to sell a simple fruit salad of apples and oranges. What should you charge for a one-pound can? Rationally, you should look at the market price of the raw fruit and the cost of canning and distribution, and then figure out the total cost of manufacturing the hybrid mixture from its simpler ingredients.

In 1973, Black and Scholes showed that you can manufacture an IBM option by mixing together some shares of IBM stock and cash, much as you can create the fruit salad by mixing together apples and oranges. Of course, options synthesis is somewhat more complex than making fruit salad, otherwise someone would have discovered it earlier. Whereas a fruit salad's proportions stay fixed over time (50 percent oranges and 50 percent apples, for example), an option's proportions must continually change. Options require constant adjustments to the amount of stock and cash in the mixture as the stock price changes. In fruit salad terms, you might start with 50 percent apples and 50 percent oranges, and then, as apples increase in price, move to 40 percent apples and 60 percent oranges; a similar decrease in the price of apples might dictate a move to 70 percent apples and 30 percent oranges. In a sense, you are always trying to keep the price of the mixture constant as the ingredients' prices change and time passes. The exact recipe you need to follow is generated by the Black-Scholes equation. Its solution, the Black-Scholes formula, tells you the cost of following the recipe. Before Black and Scholes, no one even guessed that you could manufacture an option out of simpler ingredients, and so there was no way to figure out its fair price.

This discovery revolutionized modern finance. With their insight, Black and Scholes made formerly gourmet options into standard fare. Dealers could now manufacture and sell options on all sorts of underlying securities, creating the precise riskiness clients wanted without taking on the risk themselves. It was as though, in a thirsty world filled with hydrogen and oxygen, someone had finally figured out how to synthesize H
2
O.

Dealers use the Black-Scholes model to manufacture (or synthesize, or financially engineer) the options they sell to their clients. They construct the option from shares of raw stock they buy in the market. Conversely, they can deconstruct an option someone sells to them by converting it back into shares of raw stock that they then sell to the market. In this way, dealers mitigate their risk. (Since the Black-Scholes model is only a model, and since no model in finance is 100 percent correct, it is impossible for them to entirely cancel their risk.) Dealers charge a fee (the option premium) for this construction and deconstruction, just as chefs at fancy restaurants charge you not only for the raw ingredients but also for the recipes and skills they use, or as couturiers bill you for the materials and talents they employ in creating
haute couture
dresses.

The history of quants on Wall Street is the history of the ways in which practitioners and academics have refined and extended the Black-Scholes model. The last thirty years have seen it applied not just to stock options but to options on just about anything you can think of, from Treasury bonds and foreign exchange to the weather. Behind all these extensions is the same original insight: It is possible to tailor securities with the precise risk desired out of a mix of simpler ingredients using a recipe that specifies how to continually readjust their proportions. The readjustment depends on the exact way in which the ingredients' prices move.

Because bond prices don't move exactly like stock prices, the recipe for a bond option must differ from that of the classic Black-Scholes model. But this is a subtlety—when a new product is first created, a crude Black-Scholes-like model often suffices. Then, an arms race begins. As competitive pressures increase and spreads tighten, quants at different firms refine and extend their first pass at the model, adding new and more accurate descriptions of the motion of the ingredients and obtaining better recipes for the salad. Extending the model demands a grasp of financial theory, mathematics, and computing, and quants work at the intersection of these three disciplines.

The life of a practitioner quant in a trading business is quite different from that of a physicist. When, after years of physics research, I first came to work on Wall Street at the end of 1985, my new boss asked me to take a second pass at a problematic Black-Scholes-like model for bond options that he had built a year earlier. I started out slowly and carefully, working like a physicist; I read the relevant papers, learned the theory, diagnosed the problem, and began to rewrite the computer program that made the model work. After several weeks he became impatient with my lack of progress. “You know,” he said a little sharply as he took me aside, “in this job you really need to know only four things: addition, subtraction, multiplication, and division—and most of the time you can get by without division!”

I took his point. Of course, the model used more advanced mathematics than arithmetic. Yet his insight was correct. The majority of options dealers make their living by manufacturing the products their clients need as efficiently as they can—that is, by providing service for a fee. For them, a simple, easy-to-understand model is more useful than a better, complicated one. Too much preoccupation with details that you cannot get right can be a hindrance when you have a large profit margin and you want to complete as many deals as possible. And often, it's hard to define exactly what constitutes a “better” model—controlled experiments in markets are rare. Though I did ultimately improve the model, the traders benefited most from the friendly user interface I programmed into it. This simple ergonomic change had a far greater impact on their business than the removal of minor inconsistencies; now they could handle many more client requests for business.

Although options theory originated in the world of stocks, it is exploited more widely in the fixed-income universe. Stocks (at least at first glance) lack mathematical detail—if you own a share of stock you are guaranteed nothing; all you really know is that its price may go up or down. In contrast, fixed-income securities such as bonds are ornate mechanisms that promise to spin off future periodic payments of interest and a final return of principal. This specification of detail makes fixed income a much more numerate business than equities, and one much more amenable to mathematical analysis. Every fixed-income security—bonds, mortgages, convertible bonds, and swaps, to name only a few—has a value that it depends on, and is therefore conveniently viewed as a derivative of the market's underlying interest rates. Interest-rate derivatives are naturally attractive products for corporations who, as part of their normal business, must borrow money by issuing bonds whose value changes when interest or exchange rates fluctuate. It is much more challenging to create realistic models of the movement of interest rates, which change in more complex ways than stock prices; interest-rate modeling has thus been the mother of invention in the theory of derivatives for the past twenty years. It is an area in which quants are ubiquitous.

In contrast, quants have been a rarer presence in the equity world. There, most investors are concerned with which stock to buy, a problem on which the advanced mathematics of derivatives can shed little light. Fixed income and equities have fundamentally different foci. When you walk around a frenetic fixed-income trading floor, you hear people shouting out numbers—yields and spreads—over the hoot-and-holler; on a busy equities floor, you mostly hear people shouting company names. Fixed-income trading requires a better grasp of technology and quantitative methods than equities trading. A trader friend of mine summed it up succinctly when, after I commented to him that the fixed-income traders I knew seemed smarter than the equity traders, he replied that “that's because there's no competitive edge to being smart in the equities business.”

I don't mean to suggest that all quants work on the Black-Scholes model. Increasingly, some of them work on statistical arbitrage, the attempt to seek order and predictability in the patterns of past stock price movements and then exploit them—that is, to divine the future from the past. Hedge funds, private pools of capital that seek out subtle price discrepancies in odd and unexplored corners of markets, have become major employers of quants during the past five years, and continue to hire them to do “stat-arb.”