Against his government's instructions, Sugihara was issuing letters of transit to Lithuania's Jewish refugees hundreds every day. One of Sugihara's visas took Melamed's family to Moscow, to Vladivostok, and to Kobe. The American embassy in Tokyo Japan and the United States were not yet at war) provided them with a visa, and in 1941 they reached Chicago, where Melamed eventually became a "runner" and then a trader at the Chicago Mercantile Exchange.

The "Mere" had been Chicago's junior exchange. The Board of Trade, with its glorious art deco skyscraper towering over LaSalle Street, dominated futures on grain, the Midwest's primary commodity. The Mere traded futures on humbler products when Melamed joined it, eggs and onions. As Melamed's influence grew, he took the exchange in a new direction. Trading futures on currencies, on Treasury bills, on "Eurodollar" interest rates, and on stock indices, it was the first modern financial derivatives exchange. By the mid 1980s, it was central to global finance.

During the day, America's financial markets had crashed. The Dow Jones industrial average had plummeted 22.6 percent. The Standard and Poor's (S&P) 500 index had lost about 20 percent. Futures on the S&P 500 were traded on the Mercantile Exchange, and they should have moved in tandem with the index. Instead, they had "disconnected," falling 29 percent Jackwerth and Rubinstein 1996, p. 1611).

Every evening, after a futures exchange such as the Merc closes, the process of clearing is undertaken. Those whose trading positions have lost money must transfer cash or collateral to the exchange's clearinghouse for deposit into the accounts of those whose positions have gained. After a normal day on the Merc in the late 1980s, $120 million would change hands. On the evening of October 19, however, those who had bought S&P futures contracts owed those who had sold such contracts twenty times that amount (Melamed and Tamarkin 1996, p. 359).

If clearing failed, the Mercantile Exchange could not open. That would fuel the spreading panic that threatened to engulf America's financial institutions in a cascade of bankruptcies. Melamed knew, that Monday night, just how important it was that clearing be completed. Frantic activity by Melamed and his colleagues throughout the night (including a 3 A.M. call to the home of the president of Morgan Stanley to tell him that his bank owed them $1 billion) achieved the transfer of $2.1 billion, but as morning approached $400 million was still owed to Continental Illinois Bank, which acted as the Merc's agent.

"Please listen, Wilma; you have to take it upon yourself to guarantee the balance because if you don't, I've got to call Alan Greenspan, and we're going to cause the next depression." … There was silence on the other end of the phone.... Suddenly, fate intervened. "Hold it a minute, Leo," she shouted into my earpiece, "Tom Theobald just walked in." Theobald was then the chairman of Continental Bank. A couple of minutes later, but what seemed to me like an eternity, Smelcer was back on the phone. "Leo, we're okay. Tom said to go ahead. You've got your money." I looked at the time, it was 7:17 A.M. We had three full minutes to spare.

The resolution of the crisis shows something of the little-understood network of personal interconnections that often underpins even the most global and apparently impersonal of markets. The Merc's salvation was, as we have seen, a verbal agreement among three people who knew and trusted each other. What eased Tuesday's panic was likewise often quite personal. Senior officials from the Federal Reserve telephoned top bankers and stockbrokers, pressuring them to keep extending credit and not to hold back from settling transactions with firms that might be about to fail. Those to whom they spoke generally did what was asked of them. Bankers telephoned their corporate clients to persuade them to announce programs to buy back stock (First Boston, for example, called some 200 clients on Tuesday morning), and enough of their clients responded to help halt the plunge in stock prices.

In 1970, the market in financial derivatives in the United States and elsewhere was very small by today's standards (there are no reliable figures for its total size), and to trade many of today's derivatives, such as the Merc's S&P 500 futures, would have been illegal. By 1987, derivatives played a central role in the U.S. financial system, which is why the fate of the Mercantile Exchange was so critical to that system. Derivatives markets were also beginning to emerge around the world.

ByJune 2004, derivatives contracts totaling $273 trillion (roughly $43,000 for every human being on earth) were outstanding worldwide.' The overall sum of such contracts exaggerates the economic significance of derivatives (for example, it is common for a derivatives contract to be entered into to "cancel out" an earlier contract, but both will appear in the overall figure), and the total must be deflated by a factor of about 100 to reach a realistic estimate of the aggregate market value of derivatives. Even after this correction, derivatives remain a major economic activity. The Bank for International Settlements estimated the total gross credit exposure8 in respect to derivatives of the sixty or so largest participants in the over-the-counter (direct, institution-to-institution) market at the end of June 2004 as $1.48 trillion, roughly equivalent to the annual output of the French economy.

This book's other story is the emergence of modern economic theories of financial markets. Finance was a mainstream subject of study in the business schools of U.S. universities, but until the 1960s it was treated largely descriptively. There was little or nothing in the way of sophisticated mathematical theory of financial markets. However, a distinctive academic specialty of "financial economics," which had begun to emerge in the 1950s, gathered pace in the 1960s and the 1970s. At its core were elegant mathematical models of markets.

Many economists did not see financial economics as central to their discipline, viewing it as specialized and relatively unimportant in almost the same way as the economics of ketchup, studied in isolation, would be trivial. ("Ketchup economics" was how the economist Lawrence Summers once memorably depicted how work on finance could appear to the discipline's mainstream.9) The academic base of financial economics was not in economics departments; it remained primarily in business schools.

The academic base of financial economics was not in economics departments; it remained primarily in business schools. This often brought higher salaries," but it also meant an institutional separation from the wider discipline and a culture that differed from it in some respects. Nevertheless, by the 1990s finance had moved from the margins of economics to become one of the discipline's central topics. Five of the finance theorists discussed in this book Harry Markowitz, Merton Miller, William Sharpe, Robert C. Merton, and Myron Scholes became Nobel laureates as a result of their work in finance theory, and other economists who won Nobel Prizes for their wider research also contributed to finance theory.

The central questions addressed by this book concern the relationship between its two stories: that of changing financial markets and that of the emergence of modern finance theory. The markets provided financial economists with their subject matter, with data against which to test their models, and with some of at least the more elementary concepts they employed. Part of the explanation of why financial economics grew in its perceived importance is the gradual recovery of the stock market's prestige badly damaged by the Great Crash of 1929 and the malpractices it brought to light and its growing centrality, along with other financial markets, to the U.S. and world economies. But how significant was the other direction of influence? What were the effects on financial markets of the emergence of an authoritative theory of those markets?

The models discussed in this book are verbal and mathematical representations of markets or of economic processes. These representations are deliberately simplified so that economic reasoning about those markets or processes can take a precise, mathematical form. (Appendix E contains a very simple example of such a model, although to keep that appendix accessible I have expressed the model numerically rather than algebraically.)

The models described in the chapters that follow are the outcomes of analytical thinking, of the manipulation of equations, and sometimes of geometric reasoning. They are underpinned by sophisticated economic thinking, and sometimes by advanced mathematics, but computationally they are not overwhelmingly complex. The Black-Scholes-Merton model of option pricing, for example, yields as its central result a differential equation (the "Black-Scholes equation" equation 1 in appendix D) that has no immediately obvious solution but is nevertheless a version of the "heat" or "diffusion" equation, which is well known to physicists.

The theoretical work discussed in this book was conducted primarily with pen or pencil and paper, with the computer in the background. The computer's presence is nevertheless important, as would be expected by readers of Philip Mirowski's (2002) account of the encounter between modern economics and the "cyborg sciences." Two major contributors to finance theory, Harry Markowitz and Jack Treynor, worked in operations research (a field whose interweaving with computing and whose influence on economics have been investigated by Mirowski), and the exigencies of computerization were important to William Sharpe's development of Markowitz's model.

Computers were needed to apply finance theory's models to trading. They also were needed to test the models against market data. As will be discussed in chapter 4, the results of those tests were by no means always positive, but as in analogous cases in the natural sciences (Harvey 1981) the very fact of finance theory's testability added to its credibility. It also helped the field to grow by creating roles in financial economics for those whose skills were primarily empirical rather than theoretical. Without computers, testing would have been very laborious if not impossible.

Economics had developed in the eighteenth and nineteenth centuries predominantly as what the historian of economics Mary Morgan calls a "verbal tradition." Even as late as 1900, "there was relatively little mathematics, statistics, or modeling contained in any economic work" (Morgan 2003, p. 277). Although the use of mathematics and statistics increased in the first half of the twentieth century, economics remained pluralistic.

The Great Depression of the interwar years had shaken faith in the capacity of markets to avoid mass unemployment. In response, economists following in the footsteps of John Maynard Keynes emphasized the possibility of far-from-optimal market outcomes and the consequent need for government action to manage overall levels of demand. Their analyses were influential both within the economics profession and among policy makers in many countries. … Gradually, however, disenchantment with Keynesian economics and with government intervention grew. The experience of the 1970s when the tools of such intervention often seemed powerless in the face of escalating inflation combined with faltering growth was a factor in the growing influence of free-market economists such as Milton Friedman of the University of Chicago, with his "monetarist" theory that the cause of inflation lay in over-expansion of the money supply.

No simple mechanical link can be drawn between the way economics as a whole was changing and the way financial markets were theorized. The unity of orthodox, neoclassical economics in the postwar United States is easy to overstate, as Mirowski and Hands (1998) have pointed out, and, as was noted above, even in the 1960s and the 1970s the financial markets did not seem to many economists to be a central topic for their discipline. The mainstream economists who did take finance seriously notably Franco Modigliani, Paul Samuelson, and James Tobin often had Keynesian sympathies, while Milton Friedman was among the economists who doubted that some of finance theory counted as proper economics (see chapter 2).

Typically, those assumptions involve matters such as the following: that stocks and other financial assets can be bought and sold at prevailing market prices without affecting those prices, that no commissions or other "transaction costs" are incurred in so doing, that stocks can be "sold short" (e.g., borrowed and sold, and later repurchased and returned) freely and without penalty, and that money can be borrowed and can be lent at the same "riskless" rate of interest.

Friedman distinguished "positive" economics (the study of "what is") from "normative" economics (the study of "what ought to be"). The goal of positive economics, he wrote, "is to provide a system of generalizations that can be used to make correct predictions about the consequences of any change in circumstances. Its performance is to be judged by the precision, scope, and conformity with experience of the predictions it yields. In short, positive economics is, or can be, an `objective' science, in precisely the same sense as any of the physical sciences."

To assess theories by whether their assumptions were empirically accurate was, Friedman argued, fundamentally mistaken: "Truly important and significant hypotheses will be found to have assumptions' that are wildly inaccurate descriptive representations of reality.... A hypothesis is important if it explains' much by little ... if it abstracts the common and crucial elements from the mass of complex and detailed circumstances ... and permits valid predictions on the basis of them alone. To be important, therefore, a hypothesis must be descriptively false in its assumptions." (p. 14) The test of a theory was not whether its assumptions were "descriptively `realistic,' for they never are, but ... whether the theory works, which means whether it yields sufficiently accurate predictions" (p. 15).

Ultimately, though, Friedman's "Methodology of Positive Economics" was oriented not to the philosophy of science but to economics," and his stance provoked sharp debate within the profession. The best-known opponent of Friedman's position was Paul Samuelson, an economist at the Massachusetts Institute of Technology. With Foundations of Economic Analysis (1947) and other works, Samuelson played a big part in the mathematicization of economics in the postwar United States. He wrote the discipline's definitive postwar textbook (Economics, which sold some 4 million copies"), and in 1970 he was the third recipient of the Prize in Economic Sciences in Memory of Alfred Nobel.

Just as there is no unitary "scientific method," faithful following of which guarantees scientific advances, there is not likely to be a productive, rule-like economic methodology. For example, Friedman noted that the "rules for using [a] model ... cannot possibly be abstract and complete." How the "entities in [a] model" are to be connected to "observable phenomena ... can be learned only by experience and exposure in the right' scientific atmosphere, not by rote" (1953a, p. 25). And on page 9 of the 1953 essay he inserted a crucial parenthetical phrase into the passage putting forward falsificationism, writing that a hypothesis should be "rejected if its predictions are contradicted (frequently' or more often than predictions from an alternative hypothesis)" a formulation that left room for the exercise of professional judgment.

By the standards of a strict falsificationism, for example, virtually all the models discussed in this book should have been discarded immediately on the grounds that some of their predictions were empirically false. Yet financial economists did not discard them, and they were right not to. For instance, the Capital Asset Pricing Model (discussed in chapter 2) led to the conclusion that all investors' portfolios of risky assets are identical in their relative composition. That was plainly not so, and it was known not to be so, but the model was still highly prized.

Friedman's methodological views were, therefore, not a precise prescription for how economics should be done. His view that economic theory was "an `engine' to analyze [the world], not a photographic reproduction of it" (1953a, p. 35) was in a sense a truism: a theory that incorporates all detail, as if photographically, is clearly as much an impossibility as a map that reproduces exactly every aspect and feature of terrain and landscape. Nevertheless, the view that economic theory was an "engine" of inquiry, not an (infeasible) camera faithfully reproducing all empirical facts, was important to the developments discussed in this book.

When, in the 1950s and the 1960s, an older generation of more descriptively oriented scholars of finance encountered the work of the new finance theorists, their reaction was, as has already been noted, often a species of "the perennial criticism of orthodox' economic theory as unrealistic"' (Friedman 1953a, p. 30) that Friedman's essay was designed to rebut. Friedman made explicit a vital aspect of what, borrowing a term from Knorr Cetina (1999), we might call the "epistemic culture" of modern orthodox economics. In so doing, he gave finance theorists a defense against the most common criticism of them, despite his doubts as to whether some parts of finance theory were genuine contributions to economics.

Around here," the prominent finance theorist Merton Miller told me, "we just sort of take [Friedman's viewpoint] for granted. Of course you don't worry about the assumptions." (Miller interview) By "here" Miller meant the University of Chicago, but he could as easily have been describing much of finance theory. Attitudes to the verisimilitude of assumptions did differ, with Samuelson and (to a lesser extent) his student Robert C. Merton distancing themselves somewhat from the more Friedmanesque attitudes of some of their colleagues. However, that a model's assumptions were "unrealistic" did not generally count, in the epistemic culture of financial economics, as a valid argument against the model.

The "machineries of knowing" (Knorr Cetina 1999, p. 5) that make up finance theory's engines of inquiry are among this book's topics. More central to the book, however, is another issue. Financial economics, I argue, did more than analyze markets; it altered them. It was an "engine" in a sense not intended by Friedman: an active force transforming its environment, not a camera passively recording it.

Callon rightly refuses to confine economic sociology to the role economists often seem to expect it to take as an effort to demonstrate irrational "social" elements intruding into market processes and sees it instead as what might be called an "anthropology of calculation" which inquires into the processes that make calculative economic action and markets possible: ...

Markets' infrastructures matter. Consider, for example, the market in "futures" on agricultural products such as grain, which is relevant to this book because it was from agricultural futures markets the Chicago Mercantile Exchange and Board of Trade that the first of today's financial derivatives exchanges emerged. A "future" is a standardized, exchange-traded contract in which one party undertakes to sell, and the other to buy, a set quantity of a given type of asset at a set price at a set future time. Futures markets did not originate in the United States. What seem to have been in effect rice futures were traded in eighteenth-century Osaka (Schaede 1989), and some European markets also predated those of the United States (Cronon 1991, p. 418). But futures trading developed in Chicago on an unprecedented scale in the second half of the nineteenth century, and it is the subject of a justly celebrated analysis by the historian William Cronon (1991).

For futures trading to be possible, the underlying asset has to be standardized, and that involves a version of Callon's "disentanglement" and "framing." The grain to which a futures contract makes reference may not even have been harvested yet, so a buyer cannot pick out a representative sack, slit it open, and judge the quality of the grain by letting it run through his or her fingers. "Five thousand bushels of Chicago No. 2 white winter wheat" has to be definable, even if it does not yet physically exist.

As Gronon shows, the processes that made Chicago's trading in grain futures possible were based on the disentanglement of grain from its grower that took place when transport in railroad cars and storage in steam-powered grain elevators replaced transport and storage in sacks. Sacks kept grain and grower tied together, the sacks remaining the latter's property, identified as such by a bill of lading in each sack, until they reached the final purchaser. In contrast, grain from different growers was mixed irreversibly in the elevators' giant bins, and the trace of ownership was now a paper receipt, redeemable for an equivalent quantity of similar grain but not for the original physical substance.

The standardization of grain was both a technical and a social process. In Chicago the bushel, originally a unit of volume, became a unit of weight in order to permit measurement on scales on top of each elevator. A team of inspectors employed first by the Chicago Board of Trade and then by the state of Illinois checked that the scales were fair and made the inevitably contestable judgments that the contents of this bin were good enough to be classed as "No. 1 white winter wheat," which had to "be plump, well cleaned and free from other grains," while that bin contained only "No. 2," which was defined as "sound, but not clean enough for No. 1" (Cronon 1991, p. 118).

With grains thus turned into "homogeneous abstractions" (Cronon 1991, p. 132), disentangled at least partially from their heterogeneous physical reality, it was possible to enter into a contract to buy or to sell 5,000 bushels (the standard contract size) of, for example, "Chicago No. 2 white winter wheat" at a set price at a given future time. Such a contract had no link to any particular physical entity, and because its terms were standardized it was not connected permanently to those who had initially entered into it.

Despite the name, pits are generally raised above the floor of an exchange, not sunk into it. Standing on the steps of a pit, rather than crowded at one level, futures traders can more easily see each other, which is critical to facilitating Chicago's "open outcry" trading, in which deals are struck by voice or (when it gets too noisy, as it often does) by an elaborate system of hand signals and by eye contact. Where one stands in a pit is important both socially and economically: one's physical position can, quite literally, be worth fighting for, even though throwing a punch can bring a $25,000 fine from an exchange.

The coiner of the term "performative" was the philosopherJ. L. Austin. He admitted that it was "rather an ugly word," but it was one that lie thought necessary to distinguish utterances that do something (performative utterances) from those that report on an already-existing state of affairs. If I say "I apologize," or "I name this ship the Queen Elizabeth," or "I bet you sixpence it will rain tomorrow," then "in saying what I do, I actually perform the action" (Austin 1970, p. 235).

At least three levels of the performativity of economics seem to me to be possible (figure 1. 1). The first, weakest level is what might be called "generic performativity." For an aspect of economics to be performative in this sense means that it is used, not just by academic economists, but in the "real world": by market participants, policy makers, regulators, and so on. Instead of being external to economic processes, the aspect of economics in question is "performed" in the generic sense of being used in those processes.

What is less straightforward conceptually, and more complicated empirically, is to determine what effect, if any, the use of economics has on the economic process in question. The presence of such an effect is what is required for a stronger meaning of "performativity": the subset of generic performativity that one might call "effective performativity." For the use of a theory, a model, a concept, a procedure, a data set, or some other aspect of economics to count as effective performativity, the use must make a dference. Perhaps it makes possible an economic process that would otherwise be impossible, or perhaps a process involving use of the aspect of economics in question differs in some significant way (has different features, different outcomes, and so on) from what would take place if economics was not used.

Except in the simplest cases, one cannot expect observation alone to reveal the effect of the use of an aspect of economics. One cannot assume, just because one can observe economics being used in an economic process, that the process is thereby altered significantly. It might be that the use of economics is epiphenomenal an empty gloss on a process that would have had essentially the same outcomes without it, as Mirowski and Nik-Khah (2004) in effect suggest was the case for the celebrated use of "game theory" from economics in the auctions of the communications spectrum in the United States.

The strong, Barnesian sense of "performativity," in which the use of a model (or some other aspect of economics) makes it "more true," raises the possibility of its converse: that the effect of the practical use of a theory or model may be to alter economic processes so that they conform less well to the theory or model. Let me call this possibility which is not explicit in Gallon's work "counterperformativity." An aspect of economics is being used in "realworld" processes, and the use is having effects, but among those effects is that economic processes are being altered in such a way that the empirical accuracy of the aspect of economics in question is undermined.

First, I want the terminology to reflect the way in which the strongest senses of "performativity" are subsets of a more general phenomenon: the incorporation of economics into the infrastructures of markets. … Second, the notion of "prophecy," whether self-fulfilling or self-negating, can suggest that we are dealing only with beliefs and world views. While beliefs about markets are clearly important, an aspect of economics that is incorporated only into beliefs "in the heads" of economic actors may have a precarious status. A form of incorporation that is in some senses deeper is incorporation into algorithms, procedures, routines, and material devices. An economic model that is incorporated into these can have effects even if those who use them are skeptical of the model's virtues, unaware of its details, or even ignorant of its very existence.

It is emphatically not my intention to imply that in respect to finance theory. For example, to say of Black-Scholes-Merton option-pricing theory that it was "performative" in the Barnesian sense is not to make the crude claim that any arbitrary formula for option prices, if proposed by sufficiently authoritative people, could have "made itself true" by being adopted. Most such formulas could not do so, at least other than temporarily.

The methodology offers not just "theoretical" prices but also a clear and systematic account of the economic process determining those prices. This account altered how economists conceived of a broad range of issues: the pricing not just of derivatives but also of more "basic" securities, such as bonds, and even the analysis of decisions outside of the sphere of finance that can be seen as involving implicit options. It affected how market participants and regulators thought about options, and it still does so, even if the phase of the Barnesian performativity of the original Black-Scholes-Merton model has passed.

Inquiring into Barnesian performativity thus involves more than an examination of the extent, the manner, and the general effects of the use of economics in economic practice. In investigating market conditions and prices and in judging whether they have moved toward (or away from) conformity to an aspect of economics, one is not just examining economics and those who develop and use it; inevitably one is also studying the "objects" that economics analyzes. That is something that the field to which much of my work has belonged the sociology of scientific knowledge has sometimes been reluctant to do.

Certainly one should not underestimate the complexity of judging whether patterns of market prices, for example, have moved toward greater conformity with a model such as Black-Scholes-Merton. One way of formulating the question is to examine the extent to which the model's predictions are borne out. However, what a model predicts is often not straightforward. The BlackScholes-Merton model, for example, yields an option price only after the characteristics of the option and the values of the parameters of the Black-Scholes equation have been set. One parameter, the volatility of the stock, is acknowledged not to be directly observable, so there is no unique theoretical price to compare with "actual" prices.

Furthermore, "actual" or "real-world" market prices are complex entities. As Koray Caliskan (2003, 2004) points out in a delightful ethnographic discussion of cotton trading, markets abound with prices and price quotations of many kinds. What gets reported as cotton's "world price," for instance, is a complicated construction involving not only averaging but also subjective adjustments.

Thus, Rubinstein had to analyze not "raw" prices of options, but weighted averages. He also filtered out large numbers of price records that he regarded as problematic. For example, he excluded any record that referred to either the first or the last 1,000 seconds of the options exchange's trading day. He removed transactions close to the start of the day because they often reflected the "execution of limit orders" held over from the previous day." He eliminated those in the final minutes before the close of trading because prices then were influenced by "trades to influence market maker margin" (1985, p. 463) in other words, the level of deposit that had to be maintained in order to be allowed to continue holding a position.

Replication and the reproducibility of results are at least as problematic in econometrics as the sociologist Harry Collins has shown them to be in the natural sciences. A later test will often contradict an earlier one see the extensive lists of examples in Goldfarb's 1995 and 1997 papers. In that situation, there may be no a priori way of knowing whether the original test was at fault, whether the new one is incompetent, or whether the discrepancy is to be explained by historical and geographical variation or other differences in the economic processes being studied.

For example, many efforts were made empirically to test two developments in finance theory: the Capital Asset Pricing Model and the efficient-market hypothesis. Normally it was not possible to disentangle these entirely so that only one was being tested at a time; typically the tests were of both the model and the hypothesis simultaneously. Tests of market efficiency usually involved examining whether investment strategies were available that systematically generated "excess" risk-adjusted returns. A criterion for what constitutes an "excess" return was thus needed, and in the early years of such testing the Capital Asset Pricing Model was usually invoked as the criterion. When "anomalies" were found in the results of the tests, how to interpret them was therefore debatable: were they cases of market inefficiency, or evidence against the Capital Asset Pricing Model?

Conversely, central to the Capital Asset Pricing Model was what the model posited about the returns expected by investors on assets with different sensitivities to market fluctuations, but typically no attempt was made to measure these expected returns directly for example, by surveying investors. (The results of any such survey would have been regarded as unreliable by most financial economists.) Instead, in empirical tests of the Capital Asset Pricing Model, more easily measurable after-the-fact realized returns were used as a proxy for expected returnsa substitution that rested on an efficient-market, rational-expectations view of the latter.

Rather than coding and punching all prices twice and then resolving discrepancies manually, we found a better procedure. We know that the change in the price of a stock during one month is very nearly independent of its change during the next month. Therefore, if a price changes a large amount from one date to a second date, and by a similar amount in the opposite direction from the second date to a third, there is a reason to believe that at the second date the price was misrecorded. A "large change" was rather arbitrarily taken to mean a change in magnitude of more than 10 per cent of the previous price plus a dollar.

Because of the complexities of econometric testing, the extent of the "fit" between a theoretical model and patterns of prices cannot be determined by simple inspection. "There just isn't any easy way to test a theory," said Fischer Black (1982, p. 32). Knowledge of whether patterns of prices have moved toward greater conformity with a theory is the outcome of a difficult, and often a contested, process. It is therefore tempting to set the issue aside, and to abandon the strongest meanings of performativity (Barnesian performativity and counterperformativity). However, to do that would involve also abandoning a central question: Has finance theory helped to create the world it posited for example, a world that has been altered to conform better to the theory's initially unrealistic assumptions?

As the economist and economic policy maker Alan Blinder has pointed out, in many respects global economies have in recent decades moved closer to the standard way in which economists model them, with, for example, its assumption of "single-minded concentration on profit maximization." Blinder suspects that "economists ... have bent reality (at least somewhat) to fit their models" (2000, pp. 16, 18). The anthropologist Daniel Miller likewise asserts that "economics has the authority to transform the world into its own image" (1998, p. 196).

"We have taken science for realist painting," writes Bruno Latour, "imagining that it made an exact copy of the world. The sciences do something else entirely paintings too, for that matter. Through successive stages they link us to an aligned, transformed, constructed world." (1999, pp. 78-79) If finance theory is one of Latour's sciences and this book's conjecture is that it is then simply to praise it is not to add much to humanity's conversations about markets, and simply to denounce it is to coarsen those conversations. To try to understand how finance theory has "aligned, transformed [and] constructed" its world which is also everyone's world, the world of investment, savings, pensions, growth, development, wealth, and poverty may, in contrast, contribute a little to conversations about markets.

Humanity's conversations about markets are not just intellectual; they bear on the question of the appropriate role for markets in our societies. Debates about that role sometimes remind me of debates about technology in the 1960s and the 1970s. Technology was then often taken as either to be adulated or to be condemned, and each of the apparent options frequently involved an implicit view of technological change as following an autonomous logic. The surrounding culture could choose to conform to that logic or to reject its products, but could not modify it fundamentally.

If the history and sociology of technology of the last 25 years have had a single dominant theme, it is that the view of technological change as following an autonomous logic is wrong, and the stark choice between conformity and refusal that it poses is an impoverished one. Technologies can develop in different ways according to circumstances, the design of technical systems can reflect a variety of priorities, and "users" frequently reshape technical systems in important ways. Ultimately, the development and the design of technologies are political matters.

Indeed, the core of the book-chapters 5, 6, and 7 -is in a sense a single, extended case study of the development of option theory, of its impact on markets, and of the empirical history of option pricing.

Oral-history interviews have well-known disadvantages. In particular, interviewees' memories of events, especially of specific events long in the past, may be fallible, and they may wish a particular version of events to be accepted. In consequence, I have tried to "triangulate" as much I can, checking one interviewee's testimony against that of others and (where possible) against the published record or econometric analyses of the markets they were describing. In the case of Long-Term Capital Management, for example, I checked for any "exculpatory" bias in insiders' views of the fund's 1998 crisis by interviewing others who had been active in the same markets at the same time.

The most significant early practical innovation to emerge from financial economics was the index fund. If, as financial economics suggested, managers' stock selections failed systematically to outperform broad market indices such as the S&P 500, then why not simply invest in the stocks that made up the index in such a way that the performance of one's portfolio would automatically track the level of the index? Such an index fund, its proponents suggested, would perform as well as the portfolios chosen by traditional managers, and it would not be hampered by the high fees those managers charged.

In what became the standard model of changes in stocks' prices, the statistical distribution of changes in the natural logarithms of stock prices is the normal distribution the canonical "bell-shaped" curve of statistical theory. This "lognormal" model is an example of what the mathematician and chaos theorist Benoit Mandelbrot calls "mild" randomness: the tails of the normal distribution, representing the probabilities of extreme events, are "thin." In the 1960s, Mandelbrot put forward a different model: one in which the tails are so "fat" that the standard statistical measure of a distribution's spread (the standard deviation or its square, the variance) is infinite.

Mandelbrot's model was of "wild" randomness: periods of limited price fluctuation can be interrupted unpredictably by huge changes. The model initially attracted considerable interest within financial economics (Eugene Fama, in whose work the efficient-market hypothesis crystallized, was the most prominent enthusiast for it), but, as chapter 4 describes, it also met fierce opposition because it undermined standard statistical procedures. In the words of one critic quoted in chapter 4, adopting Mandelbrot's model meant "consigning centuries of work to the ash pile."

In the period in which much of option theory was developed, options were "specialized and relatively unimportant financial securities" (Merton 1973a, p. 141) and were stigmatized by being associated widely with gambling and with market manipulation. However, option pricing seemed a tantalizingly straightforward "normal science" problem, in the terminology of Kuhn (1970). With an established model (the log-normal model) of how stock prices fluctuate, it did not seem too difficult to work out how much an option on that stock should cost.

Finding a satisfactory solution to the problem of option pricing turned out to be harder than it looked. In chapter 5 the development of the eventually successful solution by Fischer Black and Myron Scholes is contrasted with the work of Edward Thorp, a mathematician famous for showing how to beat the house at blackjack by "card counting" (that is, keeping a careful, systematic mental record of the cards that have been played). Black and Scholes were trying to solve a theoretical problem by applying the Capital Asset Pricing Model; Thorp was working on option pricing without use of the CAPM, and his chief goal was identifying arbitrage opportunities.

As they suggested, many other securities that on the surface did not look like options nevertheless had option-like features and so could be valued following the same approach, and, as noted above, the approach was also extended to the analysis of decisions as well as of securities.

Merton developed an approach to option pricing that led to the same equation that Black and Scholes had derived but which rested on different foundations. Merton's derivation did not invoke the Capital Asset Pricing Model, although it too involved assumptions about markets that were markedly at odds with the actual conditions of the early 1970s. Other contributions to option theory quickly followed, and their level of mathematical sophistication rapidly grew. Merton had introduced the use of rigorous stochastic calculus, and by the end of the 1970s the problem of derivatives pricing was reformulated in terms of martingale theory, an advanced area of "pure mathematics." The mathematical repertoire of Wall Street's quantitative finance specialists (first called "rocket scientists," then "quants") was being assembled.

Given the above discussion of econometric testing, it is worth remarking that a trader using spreading would have been exploiting and thus reducing precisely the discrepancies in options prices that were the focus of the most sophisticated econometric testing of the Black-Scholes-Merton model in this period. (As has been noted, this testing was conducted by the financial economist Mark Rubinstein.) It therefore seems plausible that the use of the model in spreading did more than add generally to its verisimilitude; spreading may have had a direct effect on specific features of price patterns examined in the model's econometric tests.

"I have conceived of a society," writes Barnes, "as a distribution of selfreferring knowledge substantially confirmed by the practice it sustains" (1988, p. 166). The Black-Scholes-Merton model informed practices such as spreading, and those practices in their turn helped to create patterns of prices of which the model was a good empirical description. In that sense, the performativity of the model was indeed Barnesian.

However, perhaps the Black-Scholes-Merton model succeeded because it was simply the right way to price options, but market participants learned that only slowly, with their markets only gradually becoming efficient? If that were so, "Barnesian performativity" would be an empty gloss on a process that could better be described in simpler, more conventional terms.

In chapter 7, however, I draw on the econometric literature on option pricing to note that after the 1987 crash the fit between the Black-ScholesMerton model and patterns of market prices deteriorated markedly. A "volatility skew" or "smile" at odds with Black-Scholes emerged, and it seems to be durable; it has not subsequently diminished or vanished. Option theory has left its permanent imprint on the options markets: the theory is embedded in how participants talk and in technical devices that are essential to their markets. But what is performed in patterns of prices in those markets is no longer classic option-pricing theory.

The volatility skew thus reveals the historicity of economics, at least of the particular form of economics examined here. The U.S. markets priced options one way before 1987 and have priced them differently since, and the change was driven by a historical event: the 1987 crash.

Since portfolio insurance was an application of option theory, this raises the issue of counterperformativity: perhaps the fit between option theory and reality was ended by an event in which one of its own applications was implicated?

Chapter 8 turns to an episode with echoes of 1987: the 1998 crisis surrounding the hedge fund Long-Term Capital Management (LTCM). Because the partners who ran the fund included the finance-theory Nobel laureates Robert C. Merton and Myron Scholes, its near-failure (it was re-capitalized by a group of the world's leading banks) has often been blamed on blind faith in finance theory's models and has been seen as suggesting fatal flaws in those models.

Merton, Scholes, and the other partners in LTCM were well aware of the status of finance theory's models as engines of inquiry rather than exact reproductions of markets, and the details of the models used by LTCM were often far less critical to its activities than is commonly imagined. The episode is interesting from the viewpoint of the relationship between models and "reality," but not by way of the banal observation that the former are imperfect approximations to the latter.

What is crucial is that LTCM conducted arbitrage, the central mechanism invoked by finance theory. To be sure, there are differences between the "arbitrage" that theory posits and arbitrage as market practice. However, some of what LTCM did was quite close to the paradigmatic arbitrages of finance theory. Aspects of its trading were similar to the arbitrage invoked in Modigliani and Miller's classic proof, and LTCM's option-market activities resembled the arbitrage that imposes Black-Scholes-Merton option pricing.

One way to pursue a better understanding of the relationship between financial models and "reality" is by means of empirical research on arbitrage as market practice, and the case of LTCM is of interest from that viewpoint. A social process imitation was at the heart of LTCM's crisis. The hedge fund and its predecessor group of bond-market arbitrageurs, led by LTCM's founder John Meriwether at the investment bank Salomon Brothers, were extremely successful. That success led others to begin similar trading, to devote more capital to it, or (in the case of mortgage-backed securities) even to adjust the models they were using in order to bring them into harmony with the features that they inferred the model being used by Meriwether's group must possess.

Finally, in September 1998, LTCM itself became the subject of a self-fulfilling prophecy of failure strikingly similar to the classic example of such a process given in 1948 by Robert K. Merton.

The eventual result was what chapter 8 calls a "superportfolio": a large, unstable structure of partially overlapping arbitrage positions. An event that was in itself less than cataclysmic the Russian government's default on its ruble-denominated bonds on August 17, 1998 caused that superportfolio to begin to unravel. Arbitrageurs who suffered losses in Russia had to begin selling other assets in the superportfolio; in an increasingly illiquid market, those sales caused prices to move sharply against the holders of the superportfolio, forcing further sales; and so on.

In the 1950s, finance was a well-established part of the curriculum in the business schools of U.S. universities. A typical course would cover matters such as "institutional arrangements, legal structures, and long-term financing of companies and investment projects" (Whitley 1986a, pp. 154-155). What Weston (1966, p. 4) calls "the chief textbook of finance" had for several decades been The Financial Policy of Corporations by Arthur Stone Dewing, a professor of finance at Harvard University. The text had first appeared in 1919, and by 1953 its 1,500 pages required two separate volumes.

Dewing began by presenting corporations as institutional and legal entities. He then discussed the ways in which corporations raise money by issuing securities, and described the different varieties of such securities. One main category was (and, of course, still is) stocks: those who buy a corporation's stock gain rights of ownership in it, and if circumstances are favorable they receive periodic dividend payments. The other main category was and is bonds, a tradable form of debt. (A corporation's bonds normally commit it to pay a set capital sum at a given date, and until then to pay set amounts in interest.) Dewing discussed the overall valuations of public utilities and of corporations, the basic techniques of accountancy, the causes and forms of business expansion, and the necessity sometimes to "remold the capital structure of the corporation" (Dewing 1953, p. 1175).

The journal of Finance, which began publication in 1946, was the field's leading periodical. "Most of the articles the journal published," Bernstein writes, "had to do with Federal Reserve policy, the impact of money on prices and business activity, taxation, and issues related to corporate finance, insurance, and accounting. The few articles that appeared under the rubric `Investments' dealt with topics like liquidity, dividend policy, and pension funding. In issues up to 1959, I was unable to find more than five articles that could be classified as theoretical rather than descriptive. The rest contain plenty of numbers but no mathematics."

John Muth, the initial proponent of the theory of rational expectations referred to in chapter 1, formulated the theory at Carnegie Tech and presented it explicitly as a response to Simon's accusation that economists presumed too much rationality in individuals and firms. The hypothesis of rational expectations "is based on exactly the opposite point of view" to Simon's, wrote Muth (1961, p. 316): "dynamic economic models do not assume enough rationality."

Modigliani, a refugee from Italian fascism, was broadly a Keynesian. Miller's mentor "a great influence in my life and in bringing me ... to serious modern economics" (Miller interview) was George Stigler, a University of Chicago colleague, ally, and close friend of Milton Friedman. (For example, Stigler and Friedman had traveled together in 1947 to the initial meeting of the Mont Pelerin Society, crossing the Atlantic by ocean liner and stopping off in London and Paris.)

Despite their differences, Modigliani and Miller, who had adjoining offices, found they had enough in common to build a productive, albeit temporary, partnership. Its products were not a direct response to Simon's "behavioral" critique of economics. Their first joint paper "was meant to upset my colleagues in finance," Modigliani recalled (1995, p. 153), not to upset Simon, whom they both respected despite the fact that they were both on the opposite side to him in the intellectual dispute that split the Graduate School of Industrial Administration.

In the paper, they agued that in what they called a "perfect market" (Modigliani and Miller 1958, p. 268) neither the total market value of a corporation (the sum of the market values of its stocks and bonds) nor the average cost' to it of capital was affected by its "capital structure" that is, by the extent to which it finances its activities by borrowing (issuing bonds) rather than by issuing stock.

It therefore seemed plausible that there should be an optimum balance between the issuing of stocks and of bonds. One might expect that this optimum balance would depend on investors' attitudes to risk and on matters such as the "psychological and institutional pressures" (Modigliani and Miller 1958, p. 279) on investors to hold investment portfolios of bonds rather than stocks. Those pressures were still strong in the 1950s.

The argument (outlined in more detail in appendix A) by which Modigliani and Miller sought to sweep aside such behavioral and institutional issues was as follows. Suppose that two investments are "perfect substitutes" (Modigliani and Miller 1959, p. 656), in other words that they are entitlements to identical income streams. If the prices of the two investments are not the same, then any holder of the dearer investment can benefit by selling it and buying the cheaper. Nothing need be assumed about investors' willingness to take on risk, or about any "psychological" or "institutional" matters, other than that "investors always prefer more wealth to less" (Miller and Modigliani 1961, p. 412). "The exchange" of the dearer investment for the cheaper, Modigliani and Miller wrote, would be "advantageous to the investor quite independently of his attitudes to risk" (1958, p. 269).

Modigliani and Miller knew perfectly well that they were assuming a world that did not exist. Taxation was the most obvious difference between their assumed world and empirical reality. American corporations were (and are) allowed to set interest payments on their bonds and other debts against their tax liabilities, but cannot do so for dividends on their stock. Until 2003, almost all individual investors in the United States faced a higher rate of tax on dividend income than on capital gains, and they can postpone the tax on capital gains until they actually sell their stock, so they may have good reasons to receive the benefits of a firm's earnings as capital gains rather than as dividends.

Having shown the irrelevance of capital structure and of dividend policy in their simple assumed world, Modigliani and Miller then investigated the consequences of allowing some more realism (especially in regard to taxes) back in. Just how far to go in adjusting their model to "reality" and the exact consequences of doing so became matters of dispute between Modigliani and Miller. Attuned, as Keynes had been, to the imperfections of markets, Modigliani was the more cautious. Indeed, when first describing the irrelevance of capital structure to a class at Carnegie Tech, he distanced himself: "I announced the theorem and said `I don't believe it."' (Modigliani interview) Miller, in contrast, was prepared more radically to set aside the question of the validity of assumptions, in the manner advocated by Friedman (Miller interview).

Miller, in contrast, was prepared more radically to set aside the question of the validity of assumptions, in the manner advocated by Friedman (Miller interview). Modigliani and Miller's published joint work trod a middle path they explored the consequences of the simple assumptions of a "perfect market," but also attended carefully to the effects of relaxing those assumptions but private disagreement between them emerged over the range of conditions under which their propositions would hold, in particular in respect to the tricky question of the effects of corporate and personal taxes (Miller interview; Modigliani interview).

Despite these incipient disagreements, Modigliani and Miller found themselves on the same side with respect to traditional finance scholarship, just as they had with respect to Herbert Simon's critique of orthodox economic reasoning. Their sharpest dispute was with David Durand, a prominent finance scholar of a more traditional, institutional bent who held a professorship of industrial management at MIT. Durand had himself examined what was in effect Modigliani and Miller's proposition about the irrelevance of capital structure, and had at least hinted that arbitrage might in principle enforce it. Ultimately, however, he had rejected the proposition.

Since many investors in the modern world are seriously circumscribed in their actions, there is an opportunity to increase the total investment value of an enterprise by effective bond financing. Economic theorists are fond of saying that in a perfectly fluid world one function of the market is to equalize risks on all investments. If the yield differential between two securities should be greater than the apparent risk differential, arbitragers would rush into the breach and promptly restore the yield differential to its proper value. But in our world, arbitragers may have insufficient funds to do their job because so many investors are deterred from buying stocks or low-grade bonds, either by law, by personal circumstance, by income taxes, or even by pure prejudice. These restricted investors, including all banks and insurance companies, have to bid for high-grade investments almost without regard to yield differentials or the attractiveness of the lower grade investments. And these restricted investors have sufficient funds to maintain yield differentials well above risk differentials. The result is a sort of super premium for safety; and a corporation management can take advantage of this super premium by issuing as many bonds as it can maintain at a high rating grade.

What divided Modigliani and Miller from Durand was at root whether market processes, in particular arbitrage, were strong enough to overcome the effects of institutional restrictions. Modigliani and Miller held that they were. Durand did not believe that, and he published an extensive critique of Modigliani and Miller's claim of the irrelevance of capital structure. He did not deny the logic of their basic reasoning as noted above, he had himself explored the path they took but he claimed that their analysis held only in a "limited theoretical context." The situation of what Durand called "real corporations" (1959, p. 640) was quite different, and the market they had to interact with was far from Modigliani and Miller's assumption of perfection.

For example, investors could not buy stock entirely on credit: to do so was prohibited by the Federal Reserve's famous "Regulation T," introduced after the credit-fueled stock-market excesses of the 1920s. Regulation T restricted the extent to which brokers could lend investors money to buy stock. From time to time the Federal Reserve altered the percentage of the cost of a stock purchase that could be borrowed, but in the period discussed here it was typically no more than 50 percent, and sometimes much less. The "arbitrage" operation of switching between investments that Modigliani and Miller invoked might therefore not be available to most investors, and was not free of risk: price fluctuations might lead stocks bought on credit no longer to be worth enough to serve as collateral for the loan, leading an investor's broker forcibly to sell such stock.

Modigliani and Miller's basic conceptual device, homogeneous "risk classes" (see appendix A), had no empirical referent, argued Durand: "To the practically minded, it is unthinkable to postulate the existence of two or more separate and independent corporations with income streams that can fluctuate at random and yet be perfectly correlated from now until doomsday." Modigliani and Miller had started "with a perfect market in a perfect world," wrote Durand.

A chance conversation with a broker pointed Markowitz toward the stock market as the subject for his Ph.D. thesis (Markowitz interview). Nowadays, this might seem a natural topic for an ambitious young graduate student, but that was not the case at the start of the 1950s. For example, the elite students of the Harvard Business School shunned Wall Street: in the early 1950s, only 3 percent of them took jobs there. "The new generation considered it unglamorous. Outside its gargoyled stone fortresses, black limousines waited for men with weary memories. Inside, it was masculine, aging, and unchanged by technology."

Wall Street's low prestige spilled over into academic priorities. At the Harvard Business School, the course on investments was unpopular with students and was allocated an undesirable lunchtime slot, earning it the unflattering sobriquet "Darkness at Noon" (Bernstein 1992, p. 110). "[A]cademic suspicion about the stock market as an object of scholarly research" was sufficiently entrenched that in 1959 the statistician Harry Roberts of the University of Chicago could describe it as "traditional" (1959, p. 3).

The value of a corporation's stock is ultimately as an entitlement to the future stream of dividends paid to the stockholders by the corporation, argued both Williams and the market practitioners on whom he drew. The emphasis on dividends seems to be contradicted by the later Miller-Modigliani assertion of the irrelevance of dividend policy, but Williams anticipated the objection that dividend policy was arbitrary by arguing that if corporate earnings that are not paid out as dividends can profitably be reinvested then they will enhance future dividends, and so be taken account of in his model (Williams 1938, pp. 57-58).

Expected future dividend payments cannot, however, simply be added up in order to reach a value for a corporation's stock. In part, that is because of the effect of inflation, but even without inflation the value of a dollar received in a year's time is less than that of a dollar received now, because the latter can be invested and earn interest. To work out the value of a stock, expected future dividends have therefore to be "discounted": their present value has to be calculated using an appropriate interest rate." Hence the name "dividend discount model."

When Markowitz read The Theory of Investment Value in the library of the University of Chicago's Graduate School of Business in 1950, he was struck by a different objection to Williams's dividend discount model, one rooted in the operations research that Koopmans was teaching him. … What would happen, Markowitz asked himself, if one applied Williams's way of tackling uncertainty not to a single stock but to an investor's entire portfolio? "If you're only interested in the expected value of a stock, you must be only interested in the expected value of a portfolio" (Markowitz interview). Simple reasoning based on the operations-research technique of linear programming quickly convinced Markowitz that an investor who focused only on expected value would put all his or her money into the single stock with the highest expected rate of return.

Markowitz quickly saw that once risk as well as return was brought into the picture the problem of finding efficient portfolios was not a linear one. The formula for the standard deviation or variance of returns involves squaring rates of return, so the problem could not be solved using existing linear programming techniques: it fell into what was then the little-explored domain of quadratic programming. Koopmans liked Markowitz's term paper, giving it a grade of A, and encouraged him to take the problem further, telling him: "It doesn't seem that hard. Why don't you solve it?" (Markowitz interview) Solve the problem of selecting efficient portfolios was precisely what Markowitz went on to do.

Of the set of attainable portfolios, a subset (shown by the thicker "southeast" edge of the attainable set) is going to be efficient. From points in this subset one cannot move down (to a portfolio with the same expected return but lower variance) or to the right (to a portfolio with the same variance but greater expected return) without leaving the attainable set. The subset therefore represents the portfolios that offer "minimum Vfor given E or more and maximum E for given Vor less" (Markowitz 1952, p. 82): it is what was later to be called the "efficient frontier" of the set of portfolios that can be constructed from the given securities.

Markowitz's graphical representation was, however, only a way of explaining the underlying idea. To calculate the "efficient frontier" in any particular case (given a set of securities and estimates of their expected returns, variances, and correlations) is computationally demanding. When the set of securities is even moderately large, it is beyond the capacity of an unaided human being. Because the problem fell into a mathematical domain that operations researchers were only beginning to explore, there was no "off-the-shelf" algorithm Markowitz could turn to: it was difficult, innovative work.

Markowitz's 1952 paper in the journal of Finance describing his portfolioselection method (though not the detail of the critical line algorithm) was later to be seen as the "harbinger" of the "new" finance, of "the mathematical and model-building revolution."" It certainly stood out: "No other article in the issue [of the journal of Finance] that carried Markowitz's paper contains a single equation." (Bernstein 1992, p. 42) Indeed, Markowitz's contribution to the Naval Research Logistics Quarterly, with its matrix algebra and its careful analysis of the mathematical properties of the critical line algorithm, inhabited an epistemic culture quite different from that traditional in the academic study of finance: essentially the culture of applied mathematics.

His argument rests on the concept of the Rational Man, who must act consistently with his beliefs. But the history of Wall Street suggests that such consistency may be unwise. ... His ideal is a Rational Man equipped with a Perfect Computing Machine.... Of course, he admits that the Rational Man does not exist at all and that the Perfect Computing Machine will not exist in the foreseeable future, but the image of these nonentities seems to have colored his whole work and given it an air of fantasy 19 It was not even clear that what Markowitz had done counted as economics.

Markowitz agreed to become the informal supervisor of Sharpe's UCLA Ph.D. thesis. Despite Markowitz's sense that his work was a "closed logical piece," there was one issue that he had broached but not fully pursued. His full version of portfolio selection required getting securities analysts to estimate the correlation of every pair of securities among which selection was to be made. The number of such correlations increased rapidly with the number of securities being analyzed. Selection among 1,000 securities, for example, would require estimation of 499,500 correlations (Baumol 1966, pp. 98-99).

No stock analyst could plausibly estimate half a million correlations. Statistical analysis of past correlations was not enough, even if the data for it had been easily available, which in the 1950s they were not, because what was needed for portfolio selection were future correlations. Even if estimates of the latter could somehow be produced, the limited sizes of computer memories in the 1950s and the early 1960s put the resultant computation well beyond the bounds of the feasible.

Markowitz had realized, however, that the difficulties of estimation and computation when selecting among large numbers of securities would be alleviated if it could be assumed that the correlation between securities arose because they were each correlated with "one underlying factor, the general prosperity of the market as expressed by some index" (Markowitz 1959, p. 100). Instead of asking securities analysts to guess a huge array of crosscorrelations, they would have to estimate only one correlation per security: its correlation with the index.

Sharpe's development of Markowitz's "underlying factor" model could still be seen as operations research rather than economics: it was published in Management Science (Sharpe 1963) rather than in an economics journal. At root, though, Sharpe was an economist, and Armen Alchian had taught him microeconomics-the foundational part of the discipline that studies how production and consumption decisions by rational firms and individuals shape market prices, giving rise to equilibrium in competitive markets.

Although the concept of "equilibrium" is complex, a simple notion of "equilibrium price" is the price at which the quantity of a commodity that suppliers will sell is equal to the quantity that buyers will purchase. If the market price is below that equilibrium level, there is excess demand: purchasers want to buy more than suppliers will sell, allowing the latter to raise prices. If the price is above equilibrium, there is excess supply: purchasers will not buy the full amount that suppliers want to sell, forcing the latter to lower their prices in order to clear their stocks.

In equilibrium, securities prices would be such that there would be a simple straight-line relationship between the expected return on a security and the extent of its covariation with the posited underlying factor. "Following the conventions" of the standard statistical technique of regression analysis, Sharpe used the Greek letter (3 (beta) to designate the extent of the sensitivity of the returns on a stock or other security to changes in the underlying factor. "Thus the result could be succinctly stated: securities with higher betas will have higher expected returns." (Sharpe 1995, p. 218) The logic of the diversification of investment portfolios gave an intuitive explanation of the dependence of expected return on beta.

If investors are guided only by risk and return, and if they all have the same estimates of assets' expected returns, risks, and mutual correlations, 26 then, Sharpe's analysis showed, the prices of assets had to adjust such that in equilibrium there was a straight-line relationship between the expected return on an asset and its beta, the extent of its sensitivity to the return on an optimal portfolio. This result was at the core of what was soon to become known as the Capital Asset Pricing Model (CAPM .

More than 40 years later, Sharpe can still recall the Darwinian analogy that Alchian used to convey the irrelevance of the verisimilitude of assumptions: `Assume that creatures crawled up from the primordial slime, looked around and decided that for maximum effect they should grow opposable thumbs." The assumption that anatomical change resulted from conscious judgment of usefulness was plainly absurd, but "the prediction of the model [the development of opposable thumbs] would be correct, even though the actual mechanism (evolution) was very different."

The fact that Sharpe was in this respect "very much in the Friedman camp at the time" meant that he did not allow making unrealistic assumptions to disturb him as he practiced what Alchian had taught in respect to modeling. As he puts it, his approach was to "take the problem, try to distil out the two or three most important things, build a logically coherent model ... that has those ingredients in it and then see whether or not this can help you understand some real phenomenon" (Sharpe interview).

Clearly, this implication of Sharpe's model was empirically false. Sharpe balked "I thought, well, nobody will believe this. This can't be right" and he tweaked his mathematics to avoid the unpalatable conclusion. "I wanted ever so much for there to be multiple risky portfolios that were efficient ... it does not come naturally" out of the mathematics (Sharpe interview). In the analysis in his published paper, multiple optimal portfolios albeit all perfectly correlated with each other are indeed possible, and Sharpe told his readers that "the theory does not imply that all investors will hold the same combination" of risky assets (Sharpe 1964, p. 435).

If there was a single optimal portfolio, it was clear what that portfolio had to be. Prices would adjust such that no capital asset remained without an owner and every investor would hold every risky capital asset every stock, for instance in proportion to its market value. Sharpe: "When I finally broke out of [the view that there had to be more than one optimal portfolio of risky assets] I said `If there's only one, it's got to be the market portfolio. It's the only way you can get everything to add up."

Although Sharpe did not know it at first, a model essentially the same as his Capital Asset Pricing Model was being developed at about the same time by an operations researcher namedJack Treynor. Very similar models were being developed by John Lintner at the Harvard Business School economist (Lintner 1965a,b) and byJan Mossin at the Norwegian School of Economics and Business Administration (Mossin 1966).

With the market itself taken to be the unique optimal portfolio of risky assets (a conclusion on which Sharpe, Treynor, Linter, and Mossin concurred"), the Capital Asset Pricing Model's parameter, beta, had a simple interpretation: it was the sensitivity of returns on the asset to overall market fluctuations. That sensitivity was the risk that could not be diversified away, and the extent of that "market risk" or "systematic risk" determined the relative prices of risky capital assets such as stocks.

The reasoning that had led Sharpe, Treynor, Linter, and Mossin to the Capital Asset Pricing Model was sophisticated. However, the model predicted an equilibrium relationship between an asset's beta and its expected return that was simplicity itself. (See figure 2.2.) An asset with a beta of zero has no correlation to the market as a whole, so any specific risk in holding such an asset can be eliminated by diversification. Hence, the asset can be expected to yield only the riskless rate of interest: the rate an investor could earn by holding until its maturity an entirely safe asset such as a bond issued by a major government in its own currency. As beta and thus market risk rises, so does expected return, in a direct straight-line relationship.

The theory of investment had been transformed. If the reasoning of Sharpe and of the other developers of the Capital Asset Pricing Model was correct, beneath the apparently bewildering complexity of Wall Street and other capital markets lay a simple tradeoff between systematic risk and return that could be captured by a straightforward, parsimonious, and elegant mathematical model.

The third main strand in the transformation of the study of finance in the United States in the 1950s and the 1960s was the most general. It involved two closely related notions: that prices of stocks and similar securities follow a random walk, and that financial markets at least the main markets in the United States and similar countries are efficient.

The idea that the movements in the prices of financial securities are in some sense random and therefore that the mathematical theory of probability can be applied to them received its decisive development in the 1950s and the 1960s, but did not originate then. As financial markets blossomed in the nineteenth century, a popular "science of investing" developed and was incorporated into manuals of investment aimed at a readership of middle-class men with worries that investing in securities was gambling (Preda 2001 a, 2004a). In 1863, the French broker Jules Regnault published one such text. (See Jovanovic 2000; Jovanovic and le Gall 2001.) Regnault sought to demonstrate to his readers the distinction between gambling on securities and legitimate, patient longer-term investment. He applied a simple probabilistic model to show that those who made frequent bets on short-term movements in prices faced eventual inevitable ruin.

Regnault argued that short-term price movements were like coin-tossing: upward and downward movements will tend to have equal probabilities (of 1/2), and subsequent movements will be statistically independent of previous movements (Regnault 1863, pp. 34-38). That was a fair game, but even in a fair game a player with finite resources playing an opponent with unlimited resources will eventually lose the entirety of those resources, and if that happens in a financial market the game is over from the player's viewpoint.

The market, "that invisible, mysterious adversary," had effectively infinite resources. Thus, even if "chances were strictly equal" those who indulged in frequent short-term speculation faced "an absolute certainty of ruin." Furthermore, brokers' commissions and other transaction costs meant that in practice the game was less than fair.

As a follower of the "social physics" of the pioneering statistician Adolphe Quetelet, Regnault sought regularities underlying the market's apparent randomness. What was from his viewpoint the central regularity could have been derived mathematically from his model, but Regnault seems to have found it empirically (and he certainly tested it empirically).

The regularity was that the average extent of price deviations is directly proportional to the square root of the length of the time period in question (Regnault 1863, pp. 49-50). Modern random-walk theory leads to the same conclusion, and there are passages in Regnault's work (especially Regnault 1863, pp. 22-24) that bring to mind the efficient-market hypothesis. However, Regnault's comments on his square-root law remind us that he inhabited a different intellectual world. For him, the regularity was an ultimately theological warning to "earthly princes ... kings of finance" to be humble in the face of what was, at root, Providential order.

Regnault's work has only recently been rediscovered. More celebrated as a precursor of modern random-walk theory has been Louis Bachelier, a student of the leading French mathematician and mathematical physicist Henri Poincare (on whom see, for example, Galison 2003). While Regnault drew on existing and relatively elementary probability theory, Bachelier developed a model of a random or "stochastic" process in continuous time. In Bachelier's model, the price of a security can change probabilistically in any time interval, however short. (The coin-tossing model is, in contrast, a stochastic process in discrete time: at least implicitly, the model is of a coin tossed only at specific moments, and not between those moments.)

In 1900, despite the currency of the popular "science of investing," the financial markets were an unusual topic for an aspirant academic mathematician. "Too much on finance!" was the private comment on Bachelier's thesis by the leading French probability theorist, Paul Levy (quoted in Courtault et al. 2000, p. 346). Bachelier's contemporaries doubted his rigor, and his career in mathematics was modest: he was 57 before he achieved a full professorship, at Besancon rather than Paris.

If it were indeed the case that "what looks like a purposive movement over a long period" in an economic time series was "merely a kind of economic Brownian motion," then any "trends or cycles" apparently observed in such series would be "illusory" (ibid., pp. 13, 18).

Later, Samuelson put this way: "If one could be sure that a price will rise, it would have already risen." (1965b, p. 41) If it is known that the price of a stock will go up tomorrow, it would already have gone up today, for who would sell it today without taking into account tomorrow's rise? Thus, Kendall's results could indicate that "speculation is doing its best because it leaves everybody with white noise" in other words, with randomness (Samuelson interview).

For Samuelson, in contrast, Kendall's findings suggested that it might be worthwhile devoting at least part of his professional attention to the financial markets.

Kruizenga had been employing as his asset price model a discrete random walk analogous to Regnault's, rather than Bachelier's continuous-time random walk, and must have been discomfited to discover "after most of my analysis had been completed" (Kruizenga 1956, p. 180) that someone else had analyzed the same topic, half a century before, in a mathematically more sophisticated way.

Bachelier's model was an "arithmetic" Brownian motion: it had the symmetry of the Gaussian or normal distribution. If the price of a bond was, for example, 100 francs, the probability on Bachelier's model of a one-franc upward movement was the same as that of a one-franc downward movement. Given the pervasiveness of the normal distribution, employing such a model was a natural step for someone with a background in mathematics or physics.

In a randomwalk model, he pointed out, the average return on stocks probably had to be "sweeter" than the rate of interest that could be earned from "riskless securities," for otherwise risk-averse investors could not be persuaded to hold stocks at all (Samuelson n.d., p. 11). However, after allowing for that "fair return," stock-price changes had to be a "fair game" or what mathematicians call a "martingale," because "if everyone could `know' that a stock would rise in price, it would already be bid up in price to make that impossible." In consequence, "it is not easy to get rich in Las Vegas, at Churchill Downs, or at the local Merrill Lynch office."

Although Samuelson was by far the best-known economist to embrace the random-walk model, other analysts did so too. They included Harry V. Roberts, a statistician at the University of Chicago Graduate School of Business, and M. F. M. Osborne, an astrophysicist employed by the U.S. Naval Research Laboratory. Roberts knew of Working's and Kendall's papers, but Osborne reached the conclusion that there was "Brownian motion in the stock market" empirically, apparently without knowing of Bachelier, Working, or Kendall. Like Samuelson, Osborne concluded that a log-normal random walk was a better model of stock-market prices than the physicists' arithmetic Brownian motion.

That view was that financial markets were "efficient" in other words, that "prices always `fully reflect' available information" (Fama 1970, p. 383). Drawing on a distinction suggested by his colleague Harry Roberts, Fama distinguished three meanings of "available information," the first two of which correspond roughly to successive phases in the history of the relevant research.

Different authors meant somewhat different things by "random walk," but the most common meaning was that "successive price changes are independent, identically distributed random variables. Most simply, this implies that the series of price changes has no memory, that is, the past cannot be used to predict the future in any meaningful way." (Fama 1965, p. 34) That property implied "weak form" efficiency. However, the latter was also implied by martingale ("fair game") models that were more general than the original conception of random walks. After these martingale formulations were introduced in the mid 1960s by Samuelson (and also by Benoit Mandelbrot) they tended to replace random walks as the preferred mathematical formulations of weakform efficiency.

The third category of "available information" was that to which only certain groups, such as corporate insiders, were privy. If this kind of information was always reflected in prices, and insiders could not make excess profits on the basis of it, a market was "strong form" efficient. "We would not, of course, expect this [strong form] model to be an exact description of reality," wrote Fama (1970, p. 409), and indeed there was already evidence against it.

Fama's Ph.D. student Myron Scholes had examined the effects on prices of large sales of stock. While Scholes's findings were broadly consistent with "semi-strong" efficiency, they also suggested that a corporate insider could have "higher expected trading profits than others because he has monopolistic access to some information."

By the late 1960s, the descriptive, institutional study of finance had in the United States been eclipsed by the new, analytical, mathematical approaches discussed in this chapter. The financial markets had been captured for economics, so to speak. Other disciplines Dewing's invocations of history and psychology, "behavioral" studies of organizations in the tradition of Herbert Simon were left on the margins. Modigliani, Miller, and the authors of the Capital Asset Pricing Model and the efficient-market hypothesis shared the view that "securities prices are determined by the interaction of self-interested rational agents" (LeRoy 1989, p. 1613). They were, likewise, all convinced that the processes involved had to be analyzed, not simply described, and that the necessary analytical tools were those of economics, not those of other disciplines.

CRSP's tapes soon joined by other data sources, notably the "Compustat" tapes of accounting data sold by Standard & Poor's-gave U.S. finance academics from the mid 1960s an advantage over their predecessors: easy access to massive volumes of data in a format that facilitated analysis. Even at the start of the 1960s, researchers such as the Chicago Ph.D. student Arnold B. Moore were still having to construct stock-price series by hand from runs of the Wall Street journal (Moore 1962, p. 47). Once the CRSP tapes became available, that tedious effort was no longer needed.

Another indicator of the successful emergence of a new specialty is incorporation into teaching curricula and textbooks. As the developments described in chapter 2 were consolidated and extended, they entered the curricula of the leading business schools in the United States. In the mid 1960s, for example, Eugene Fama and Merton Miller began to collaborate in the teaching of finance at the University of Chicago's Graduate School of Business, a collaboration that led to their 1972 textbook The Theory of Finance. "To make the essential theoretical framework of the subject stand out sharply," wrote Fama and Miller, "we have pruned away virtually all institutional and descriptive material."

The intellectual world of Arthur Stone Dewing had been swept away. Standard aspects of "managerial finance" such as "cash flow forecasting, cash budgeting ... [and] credit management" were set aside by Fama and Miller because work on them was "ad hoc" and "largely unrelated" to the emerging theory of finance (Fama and Miller 1972, p. vii). Replacing those topics was a broadly unified theoretical structure encompassing the topics of chapter 2 of this book: the Modigliani-Miller propositions, the work of Markowitz and Sharpe, and the efficient-market hypothesis. In the next two decades, The Theory of Finance was joined by many other textbooks building on the same core material. By the end of the 1990s, if one walked into almost any large university bookshop in Western Europe or in the United States, one could find shelves of textbooks whose contents had their roots in the finance scholarship described in chapter 2 and in option theory.

The Chicago and MIT groups differed in approach: as was discussed in chapter 1, Miller and his Chicago colleagues shared Friedman's view that the realisticness of assumptions was irrelevant, while Samuelson regarded that attitude as cavalier. In the background also lay political differences. Chicago was overwhelmingly "free market" in its politics. That was most famously so in the writings of Milton Friedman, but Miller also developed a highly visible, activist commitment to a free-market approach. Samuelson and Modigliani were more skeptical of the virtues of unfettered markets and more favorable to government action.

Economics departments were usually in the prestigious faculties of arts and sciences, while finance was often seen as an appropriate topic for universities' vocationally oriented business schools, which were gaining academic status only slowly. The older descriptive, institutional, "unscientific" approach taken in those business schools to the study of finance may have left its mark on economists' attitudes. The economist Stephen Ross, who began research in finance while an assistant professor at the University of Pennsylvania at the start of the 1970s, recalls being warned that "finance is to economics as osteopathy is to medicine" (Ross interview).

Nevertheless, in the 1960s and the 1970s the new financial economics gradually became a recognized, reasonably high-status, enduring part of the academic landscape, one that could, and did, successfully reproduce itself and grow Economists might continue to harbor doubts about the value of the research being done, but business schools, not economics departments, were the main institutional base of the new specialty. Within those schools, the mathematical modeling and computerized statistical testing that the "new finance men" employed were unquestionably state-of-the-art.

The attempt in the 1950s by Herbert Simon and his colleagues at Carnegie Tech to shift education for business from a vocational to a "science-based" approach was a harbinger of a wider transformation. In 1959, an influential report for the Ford Foundation titled Higher Education for Business noted the pedestrian, descriptive courses, the academic mediocrity, and the absence of a culture of research at many American business schools. Business, the authors of the report commented, "finds itself at the foot of the academic table, uncomfortably nudging those two other stepchildren, Education and Agriculture" (Gordon and Howell 1959, p. 4).

In response to the perception that they were not rigorous enough, American business schools sought to "academicize" themselves, a goal whose achievement was assisted by the availability of funds for the task from the Ford Foundation and by the general expansion in higher education. Academicization proceeded rapidly in the 1960s and the 1970s.

In a context of self-conscious "academicization," the new financial economists who worked on a traditional business school topic, but in a sophisticated, mathematical, academic, discipline-based way were attractive targets for recruitment. In consequence, the new generation of finance academics could find jobs outside the Chicago-MIT axis.

Success had come, said Cootner, because finance academics had been able to look not directly at the firm but at the market. "The areas within finance that have progressed more slowly are either those internal to the firm and most immune to market constraint, or those in which financial institutions' very raison d'etre [sic] arises from the imperfection of markets."

The focus as well as the methodology of finance scholarship had shifted: from the corporation, as in Dewing's classic focus on the Financial Policy of Corporations (Dewing 1953), to the rational investor, the market, and the way in which "an individual's optimal behavior is strongly constrained by the competitive efforts of others" (Cootner 1977, p. 553). Take the Modigliani-Miller propositions, discussed in chapter 2. They concerned matters about which firms made decisions (capital structure and dividend policy); however, instead of looking inside the firm for the determinants of these decisions, Modigliani and Miller looked at the firm from the outside: from the viewpoint of investors and the financial markets.

The shift of attention from corporation to market was in part a matter of finding a focus that was tractable mathematically. It was also a shift encouraged by the application to finance of orthodox microeconomic ways of thinking: recall Sharpe's testimony, quoted in chapter 2, that he "asked the question microeconomists are trained to ask. If everyone [that is, all investors] were to behave optimally ... what prices will securities command once the capital market has reached equilibrium." The shift was most likely also helped for example, in the attractiveness to students of the research topics involved by the gradual recovery in prestige of the stock market in the United States from a nadir that lasted from 1929 to the 1940s.

The Wall Street crash, the Great Depression, and World War II had left U.S. financial markets focused largely on bonds, especially government war debt.' However, as investors became more confident that the postwar prosperity would continue, stocks began to seem attractive. Stock prices rose markedly in the 1950s, and in February 1966 the DowJones industrial average reached, albeit briefly, the unprecedented level of 1,000 (Brooks 1973, pp. 102-103). The "blue chip" corporations that traditionally made up the Dow had to jostle for attention with alluring high-technology corporations such as Xerox, Polaroid, Litton Industries, Ling-Temco-Vought, and perhaps most strikingly of allH. Ross Perot's Electronic Data Systems. Investment, Wall Street, the financial markets in the 1960s, all these were once again interesting, even exciting.

The new generation of investors often chose to entrust their money to the managers of the fast-growing, seductively advertised mutual funds, rather than themselves directly buying stocks and other securities. With other investment intermediaries such as bank trust departments, pension funds, and insurance companies also expanding, the proportion of stocks held by "institutional" investors grew, for example increasing between 1969 and 1978 from 34.2 percent of holdings of stocks traded on the New York Stock Exchange to 43.4 percent (Whitley 1986a, p.

The quantitative, analytical skills that financial economists taught their students were certainly likely to be of practical benefit in their future employment. However, the relatively smooth institutionalization of finance theory within academia contrasts with an often quite different reaction to it outside universities. As financial-market practitioners gradually became aware of the views and the techniques that the theorists were developing, their response was frequently one of hostility, on occasion extreme hostility.

The overall causes of practitioner ire were, above all, the random-walk hypothesis and the efficient-market hypothesis. They were a direct challenge to the two dominant schools of thought among investment professionals: "chartism" (or "technical analysis") and "fundamentals analysis." Chartism was in a sense a by-product of the rapid development in the late nineteenth century of the technology for recording and disseminating securities prices, notably the stock "ticker," in which prices were recorded on exchanges' floors, transmitted telegraphically, and printed out on paper tape in brokers' offices. With prices available in close to real time, it became possible to construct charts of hour-by-hour fluctuations.

Chartism never achieved institutionalization in academia, but it became a lasting component of how many financial practitioners think about markets. It offered a vernacular theory of markets (one rooted not in economics but in speculations about investor psychology and perhaps even in the sociology of "herd behavior") and a way of making sense of markets that was, and is, attractive (Preda 2004b). Much mass-media presentation of markets with its citation of "trends," "reversals," "corrections," "resistance levels," and so, and with its fascination with salient round-number index levels such as a DowJones level of 10,000 is in a sense a diluted form of chartism. Even in Chicago's derivatives markets, heavily influenced as they are by finance theory, I encountered chartists.

Random-walk theory and efficient-market theory challenged the chartist worldview by suggesting that the patterns that the chartists believed they saw in their graphs were being read by them into what were actually random movements. For example, the University of Chicago Business School statistician Harry V. Roberts used a table of random numbers to simulate a year in a market, and found that the resultant graph (figure 3.1) contained the most famous of all chartist patterns, the "head-and-shoulders": a "peak" with two lower peaks on either side of it, regarded by many chartists as the unequivocal signal of the start of a prolonged decline. "Probably all the classical patterns of technical analysis [chartism]," Roberts asserted, "can be generated artificially by a suitable roulette wheel or random-number table."

The successive editions of Security Analysis, written by Graham and his Columbia colleague David L. Dodd, taught that stocks and other securities had an "intrinsic value," a value "which is justified by the facts, e.g., the assets, earnings, dividends, definitive prospects, as distinct, let us say, from market quotations established by artificial manipulation or distorted by psychological excesses" (Graham and Dodd 1940, pp. 20-21). Graham and Dodd admitted that there was no simple, rote way of determining what that intrinsic value was, but they believed that careful analysis could reveal cases in which a market price differed from any plausible estimate of intrinsic value.

Efficient-market theorists agreed with fundamentals analysts that securities had an intrinsic value that was rooted in the reality of the economic situations of the corporations that issued them. However, efficient-market theory posited that market prices were the best available estimators of that intrinsic value: that was part of the meaning of the statement that "prices always `fully reflect' available information" (Fama 1970, p. 383). Corporate fundamentals mattered, but, precisely because there were many skilled and intelligent analysts scrutinizing their implications for stock prices, such implications would already have been incorporated into prices. In consequence, if markets were efficient, fundamentals analysts were wasting their time looking for cases in which intrinsic value differed knowably from market price.

Was the practical investment success of some fundamentals analysts, notably of the enormously successful Warren Buffett, evidence against efficient-market theory? Buffett's investment record certainly commanded respect: Buffett told his biographer, Roger Lowenstein, that Paul Samuelson had hedged his intellectual bets by making a large investment in Buffett's holding company, Berkshire Hathaway (Lowenstein 1995, p. 311). In 1984, Columbia University celebrated the fiftieth anniversary of the original publication of Graham and Dodd's Security Analysis by staging a debate between Buffet and the efficientmarket theorist Michael Jensen. Jensen argued that such success as had been enjoyed by followers of Graham and Dodd, such as Buffet, might be sheer chance: "If I survey a field of untalented analysts all of whom are doing nothing but flipping coins, I expect to see some who have tossed two heads in a row and even some who have tossed ten heads in a row" (quoted on p. 317 of Lowenstein 1995) Replying to Jensen, Buffet did not dismiss the latter's unflattering analogy out of hand.

Replying to Jensen, Buffet did not dismiss the latter's unflattering analogy out of hand. If all the inhabitants of the United States were to begin a cointossing game in which those who called wrongly, even once, were thrown out of the game, after twenty rounds there would still remain some 215 players who had called successfully twenty times in a row It would be easy to imagine that this successful few had superior predictive skills.

Their most damning piece of evidence in this respect was an analysis by Michael Jensen of the performance of mutual funds from 1945 to 1964. … Diversification was indeed valuable, Jensen concluded, but there was no evidence that fund managers had systematic predictive skills. Even after the funds' large sales commissions were removed from the analysis, investing in a mutual fund was typically less rewarding than simply buying and holding a "market portfolio" in the form of all the stocks in the Standard and Poor's 500 index: "The evidence on mutual fund performance ... indicates not only that these ... mutual funds were on average not able to predict security prices well enough to outperform a buy-the-market-and-hold policy, but also that there is very little evidence that any individual fund was able to do significantly better than that which we expected from mere random chance."

There was a sense in which Jensen's result was theory-laden: the Capital Asset Pricing Model was used to eliminate the effects of differences in performance resulting from different levels of beta. … Even that, though, was scant comfort to the traditional "stock-picking" investment manager: without the correction, mutual funds would have underperformed by an even greater margin.

The existence of an increasingly authoritative theory of finance might be thought helpful in gaining professional status. The trouble, though, was that the theory suggested that much of the apparent expertise of members of the putative profession was either spurious (as in the case of chartists) or of little or no direct practical benefit (as in the case of most fundamentals analysts).

What, for example, was the point of certifying that someone had mastered the skills necessary for security analysis in the style of Graham and Dodd if the results of such analysis did not, in general, improve investment decisions? James Lorie, director of the University of Chicago's Center for Research in Security Prices, told a reporter for the magazine Institutional Investor that money managers should "give up conventional security analysis. Its occasional triumphs are offset by its occasional disasters and on the average nothing valuable is produced" (Welles 1971, p. 58). David Goodstein, an investment manager who was a convert to the new ideas, put the same point more bluntly: `A lot of people are simply going to be put out of business. I mean, what are they really doing? What value are they adding to the process? What passes for security analysis today, in my opinion, is 150,000 percent bullshit."

To practitioners, finance theory especially random-walk theory and efficient-market theory appeared to be claiming that "the value of investment advice is zero," as one such advisor, Pierre Rinfret of Rinfret-Boston Associates, told a 1968 conference of 1,500 money managers. To Rinfret, the theory that led to this conclusion was fundamentally flawed: ". . . random-walk theory is irrelevant, it is impractical, it is logically inconsistent, it is conceptually weak, it is limited in scope, and it is technically deficient." Finance academics seemed to be saying, in an analogy drawn by Gilbert E. Kaplan, who chaired the conference, that one might just as well select stocks by throwing darts at the financial pages of a newspaper as take professional advice.

Financial economists would not have accepted that the dartboard analogy was entirely fair -a portfolio selected by dart-throwing might, for example, not be diversified well enough to be optimal or near-optimal but it was a simple, memorable image that endured and seems to have captured for many investment managers what they objected to in efficient-market theory. In 1988, the Wall Street journal began regular contests in which the performance of a small number of stocks selected by investment managers was compared to a similar number of stocks selected by throwing darts. The managers indeed tended to outperform the darts, although the consistency with which they did so was less than fully reassuring. Managers' choices outperformed those of the darts in 83 of the 135 contests from 1990 to 2001, but the darts did better than the apparent experts 52 times (Jasen 2001).

If finance academics were believed to be saying that "the value of investment advice is zero," it is no wonder that, as the economist Burton Malkiel of Princeton University put it, proponents of efficient-market theory were "greeted in some Wall Street quarters with as much enthusiasm as Saddam Hussein addressing a meeting of the B'nai B'rith" (Malkiel 1996, p. 159). The investment adviser Peter Bernstein "found the new theories emerging from the universities during the 1950s and the 1960s alien and unappealing, as did most other practitioners. What the scholars were saying seemed ... to demean my profession as I was practicing it."

James Vertin of the Wells Fargo Bank, a leading member of the Financial Analysts Federation, wrote: "You just don't win friends ... by appearing to tell sincere, dedicated, intelligent people that they are useless dolts who could and should be replaced by computers.... Rightly or wrong, most practitioners feel themselves to be objects of academic ridicule, and most feel bound to resist this assault."

Take the Capital Asset Pricing Model, for example. It had aspects that were broadly compatible with how practitioners thought about stocks. When the computers and data sets of the 1960s and the 1970s were used to calculate betas, it usually turned out that low-beta stocks were those that practitioners regarded as stable, "defensive" investments, whereas a high beta generally indicated a riskier "growth" stock. So far so good, from a traditional practitioner's viewpoint. The CAPM could, however, also be turned into a disciplinary device, subjecting investment managers' results to mathematical scrutiny.

When Treynor stepped down as editor of the Financial Analysts journal, in 1981, his last editorial was pointed. The journal, he wrote, has "enemies" because "it encourages investors to distinguish between good research and bad research." The former often led to the efficient-market conclusion that "securities are correctly priced, with nothing to be gained by buying or selling." However, no transactions meant no income for brokers or market makers, so "a few greedy exceptions to the generally high-minded people in the securities industry consider they have a vested interest in bad research"-research that claimed to identify what were in reality non-existent opportunities for profit (Treynor 1981). The Financial Analysts journal, said Treynor, could be seen as "one small, unimportant front in a much larger war."

The idea of systematic evaluation of investment performance by using the Capital Asset Pricing Model was slow to take off. At first O'Brien could find only one client: the investment committee of the Aerospace Corporation, made up as it was of quantitatively minded "rocket scientists" (O'Brien interview). Another firm that began to offer a similar service, Becker Securities, even suspected that some of its former investment manager clients were diverting business away from it in retaliation for its move into performance measurement (Welles 1977, p. 41).

As the 1960s ended, however, the stock boom of the decade's middle years began to evaporate. The DowJones industrial average fell 15 percent in 1969, and continued to slide in the early months of 1970. By May, it was 36 percent below the level of December 1968. The favored "growth" stocks of the 1960s major components of the high-beta portfolios whose risk Treynor had diagnosed suffered far worse, many falling by 80 percent or more. The initial public offering of Electronic Data Systems in September 1968 had been one of the decade's stock-market highlights, but in a single day (April 22, 1970) its stock lost one-third of its value."

The reviving fortunes and renewed glamor of the stock market in the 1950s and the 1960s may have increased its attractiveness as an academic research topic. The sharp reversal of those fortunes at the start of the 1970s seems greatly to have increased practitioner interest in the practical results of this research. After what had happened, for institutional investors to know the beta values of their portfolios began to seem sensible. Well-established firms began to move into the field, realizing that betas could, literally, be sold.

Both Michael Jensen's work and the findings of performance measurement firms such as Becker (Ehrbar 1976) suggested that active, stockpicking investment managers did not outperform stock-market indices systematically. Indeed, once such managers' high costs were taken into account they typically did worse than those indices. … So why not turn Jensen's comparator buying and holding every stock in an index into an investment strategy? If conventional investment analysis had to be "throw[n] away" (McQuown interview) because markets were efficient, then why not simply invest in a portfolio that encompassed the market, for example by including every stock in the S&P 500 index in proportion to its market value?

Those who believed themselves to be skilled stock pickers, able to identify investment opportunities that the other participants in the market had not seen, often despised index funds. One such firm modified the classic Uncle Sam recruiting poster so that the caption read "Indexing is un-American." Soon a copy of the poster was "nailed behind [the] trading-room doors of practically every money manager in the country, replacing Marilyn Monroe" (Fouse interview).

Samsonite's initial $6 million in 1971 grew to around $9 billion in U.S. index funds by 1980, $47 billion in 1985, $135 billion in 1988, and $475 billion in 1996.

Some of the overt resistance to indexing by active, stock-picking managers turned to covert concession. If, as was increasingly the case, a manager's performance was judged relative to an index such as the S&P 500, then there was some safety in selecting a portfolio that closely resembled the makeup of the index. Of course, doing so meant little or no chance of a dramatic overperformance. However, it also greatly lessened the chances of a career-killing relative underperformance: if one's portfolio did badly, those of other managers would most likely be doing badly too, so the fault would be seen to lie with the market, not the manager.

The pension fund and endowment trustees who employed investment managers also had to worry whether, with efficient-market theory becoming academic orthodoxy and beginning to influence regulators, they might be held to have behaved imprudently if they allowed stock portfolios to diverge too much from coverage of the overall market. A particular spur in this respect was the 1974 Employee Retirement Income Security Act (Whitley 1986a, p. 169). Section 404 of the act laid down the "prudent man" test: `A fiduciary shall ... discharge his duties with the care, skill, prudence and diligence ... that a prudent man ... would use in the conduct of an enterprise of like character." (quoted by Brown 1977, p. 37) Following modern portfolio theory could be a defense against the charge of imprudence, while diverging too radically from its precepts might even leave one open to such a charge.

Increasingly, those who appeared to be active, risk-taking, stock-picking managers (and who charged the corresponding high fees) were in fact "closet indexers." Becker Securities regularly tracked the beta values of a sample of apparently actively managed portfolios relative to the S&P 500 index. A portfolio that tracked the index exactly would have a beta of precisely 1.0. From 1967 to 1971, the median beta was 1.09, indicating the taking on, on average, of somewhat more than simply overall market risk. By the end of 1974, the median beta was down to 1.07, and at the end of 1976 it was a mere 1.02 (Welles 1977, p. 51).

The growing sense that the findings of financial economics implied that one should simply "buy and hold the market" was possibly one reason why economists found the CAPM's "egregious" implication that there was only one optimal portfolio, the entire market, less shocking than Sharpe had feared, helping give him the confidence to abandon his earlier, strained alternative of multiple optimal portfolios. In that respect at least, the emergence of indexing meant that the world of investment practice came closer to that posited by finance theory.

Because a significant body of practitioner opinion came gradually to embrace at least some of the conclusions of financial economics, it is tempting to tell the latter's story within the familiar frame of scientific "discovery," practitioner resistance, and then eventual acceptance. Such a framing, however, would fail to capture the historical process involved in several respects. Most importantly, it would be misleading to present the development of financial economics as simply the discovery of what was out there all along, waiting to be discovered.

Bringing finance theory into confrontation with reality turned out to be a complex matter. The results of empirical testing were often equivocal, and argument broke out over whether the Capital Asset Pricing Model could be tested at all. The efficient-market hypothesis seemed empirically the sturdiest of finance theory's central propositions, but it too began to encounter anomalies. "Reality" was not a stable backdrop against which testing could take place: finance theory's effects on its object of study were growing.

Merton Miller put it this way: "The M&M [Modigliani and Miller] model was much harder to implement empirically [than the Capital Asset Pricing Model].... It's very difficult to prove `empirically' the M&M propositions holding even as approximations. You ... can't hold everything else constant." (Miller interview) In other words, you can't empirically identify in an unequivocal way the "risk classes" described in appendix A.

The Modigliani-Miller propositions provide those pages with their central organizing themes, but the text's authors treat the empirical validity of those propositions as still an open question. Indeed, my impression is that a significant strand of opinion in financial economics does not regard the propositions as empirical claims, viewing them more as "benchmarks" against which deviations can be analyzed.'

There was, Fama later recalled, "a brief euphoric period in the 1970s when market efficiency and the [capital asset pricing] model seemed to be a sufficient description of the behavior of security returns" (Fama 1991, p. 1590). However, there too difficulties soon began to accumulate.

Of the early attempts empirically to test the Capital Asset Pricing Model, the most supportive major study was by Fama and his Chicago colleague James D. MacBeth (1973), who used the data tapes of monthly stock returns from 1926 to 1968 constructed by the Center for Research in Security Prices (CRSP). Even Fama and MacBeth's support for the model was qualified in some respects, and other studies found significant discrepancies. For example, Michael Jensen, Myron Scholes, and Fischer Black also used the CRSP tapes on the monthly returns on all stocks on the New York Stock Exchange, in their case for the years from 1931 to 1965. They constructed ten hypothetical portfolios with betas (calculated against the "market" in the sense of all New York-listed stocks) ranging from 0.5 to 1.5. They found that the low-beta portfolios had higher returns than the CAPM predicted, and the high-beta portfolios had lower returns.

Black experimented with the theoretical consequences of dropping the assumption of unrestricted borrowing. He found that he could explain the pattern of stock returns identified in his work with Jensen and Scholes by "an equilibrium in which borrowing at the riskless rate is either fully or partially restricted" (Black 1972, p. 454).

Wells Fargo Bank supported Black, Jensen, and Scholes's research financially and sponsored the conference at which it was first presented, held at the University of Rochester (where Jensen then taught) in August 1969. Probably at Black's suggestion, McQuown's group at Wells Fargo saw a way to exploit the result of the research. If the anomalous finding was the result of restrictions on borrowing, perhaps it could be exploited by an investment company, which could borrow more easily and more cheaply than an individual could? The idea was to invest in low-beta stocks, with what the study by Black, Jensen, and Scholes had suggested was their high return relative to risk, and to use "leverage" (in other words, borrowing) to increase the portfolio's level of risk to somewhat more than the risk of simply holding the overall market, so also magnifying returns (McQuown interview).

Had the strategy of investing in leveraged low-beta portfolios been pursued on a large scale it might have had the performative effect of increasing the attractiveness of low-beta stocks, thus raising their prices, reducing the returns they provided, and minimizing the discrepancy between the model and the market.

Roll had begun by sharing the "euphoria" of the early 1970s about the model: "I was pretty much a believer in this being a panacea for everything, for asset pricing." (Roll interview) However, while Roll was doing theoretical work on asset pricing in the mid 1970s, his doubts began to grow.

In 1977, Richard Roll, who had been Eugene Fama's Ph.D. student at the University of Chicago, went beyond specific empirical criticisms to cast into doubt whether it was possible to test the Capital Asset Pricing Model at all.

There is one piece of empirical content" to the CAPM, says Roll, "which is that the true market portfolio should be on the efficient frontier [see chapter 2], if Sharpe's ideas are right, and maybe it is, but we'll never know that.... We'll never be able to measure it [the market portfolio] sufficiently when you think about all the stuff that's missing. I mean certainly it's not the American S&P 500. I mean that would be foolish to think that's a proxy for the worldmarket portfolio, which includes human capital and real estate." (Roll interview) Roll's methodological critique was interpreted by some, just as Fama and French's later empirical criticism was to be, as fatal blow to the Capital Asset Pricing Model.

Robert F Stambaugh, a Ph.D. student at the University of Chicago, countered Roll's critique by testing the consequences of including assets such as "corporate bonds, government bonds ... housefurnishing, automobiles, and real estate" in measures of the "returns on portfolios of aggregate wealth" (Stambaugh 1982, pp. 244 and 237). The performance of the Capital Asset Pricing Model was affected, Stambaugh concluded, by the specifics of how it was tested, and some of Stambaugh's tests implied that it should be rejected.

William Sharpe himself conceded that Roll's critique of the tests of his model was essentially correct. Sharpe told Institutional Investor's reporter: "We cannot, without a shadow of doubt, establish the validity of the capital asset pricing model." (Wallace 1980, p. 24) Stambaugh's study meant that the Capital Asset Pricing Model is "maybe OK after all," says Sharpe (interview). Nevertheless, in his view that kind of empirical defense against criticism of the model misses two deeper points. First, "nobody can confirm a hypothesis" such as the CAPM. "You can only fail to disconfirm it." (Sharpe interview) Second, statistical difficulties (such as the large sampling errors in estimating the average return on a stock), economic and historical change, and variation across countries render empirical findings in this area unstable.

There is a sense in which the efficient-market hypothesis and its predecessor, the random-walk hypothesis, always co-existed with contrary evidence. Holbrook Working, for example, believed it was possible to find at least some structure in the apparently random fluctuations of stock prices (Working 1958). So did another early formulator of the random-walk hypothesis: Alfred Cowles III, founder (and funder) of the Cowles Commission.

However, research by financial economists in the 1970s and the 1980s pointed to a wider range of phenomena that potentially were inconsistent with the efficient-market hypothesis. By 1978, there were enough of these phenomena to merit a special issue of the new journal of Financial Economics devoted to them.

Banz divided firms in the CRSP data tapes for 1926 to 1975 into five quintiles by the total market value of their stocks. On average, the monthly returns on the smallest 20 percent of firms the bottom quintile exceeded the returns on the remainder by around 40 basis points (0.4 percentage points). Cumulate an average monthly difference of that magnitude over years and decades, and the returns on holdings of small stocks were substantially greater than on holdings of larger stocks. Banz found that the difference was not due to different levels of market risk as measured by beta values. "There is no theoretical foundation for such an effect," he commented (Banz 1981, p. 16): it was indeed an anomaly.

A plausible account of the turn-of-the-year effect is that holders of stocks that have fallen in price tend to sell them in December, before their tax year ends, in order to realize a tax loss that can be set against gains in other parts of their portfolios. The stocks then "jump back up" in January. The effect might be particularly strong for small stocks because of their typically high volatilities (Roll 1983, p. 20).

But although an explanation in terms of tax incentives might satisfy market practitioners, who knew of the turn-of-the-year effect's existence, though apparently not of its concentration in small stocks, before academics identified it (Branch 1977), it was "ridiculous" from the viewpoint of efficient-market theory (Roll 1983, p. 20). Surely any effects of temporary sales pressures and purchase pressures would be minimized by arbitrageurs exploiting those effects. If the market was efficient, surely other investors not subject to turnof-the-year tax incentives would make use of the effect to earn excess returns.

Anomalies such as the small-firm and turn-of-the-year effects could, therefore, be construed as evidence against the efficient-market hypothesis. In Kuhn's analysis of the natural sciences, "a background of firm expectation makes anomalies and exceptions stand out and take on significance" (Barnes 1982, p. 20), and the accumulation of such anomalies was seen by Kuhn as the precursor of a scientific revolution. Jensen indeed suggested that the growing list of anomalies pointed in Kuhnian fashion to "a coming minirevolution in the field" (Jensen 1978, p. 95).

As Barry Barnes points out, however, anomalies do not speak for themselves. "What one scientist sees as an anomaly," necessitating a revolutionary new paradigm, "another sees as a puzzle" to be solved without radical conceptual change (Barnes 1982, p. 100). WhatJensen envisaged was indeed no more than a "mini-revolution": one likely to involve "more precise and more general theories of market efficiency and equilibrium models of the determination of asset prices under uncertainty," but not "abandonment of the `efficiency' concept" (Jensen 1978, pp. 96 and 100).

The dominant response of Eugene Fama and his University of Chicago students to the growing list of anomalies was to suggest that the fault lay in the Capital Asset Pricing Model, not in the efficient-market hypothesis.

In the Fama-French model, beta plays no role. In its place are two different factors: firm size (the total market value of a corporation's stocks) and "book-to-market" ratio (the ratio of a corporation's net assets as recorded in its balance sheet to its market value).

In many cases, the identification of finance's anomalies was the precursor to their attenuation or disappearance. That was so not just in the sense that explanations of them consistent with efficient-market theory were put forward, but because the anomalies were exploited in practice, often by the theory's adherents, and this exploitation seems to have reduced their size.

Paul Samuelson suggests that its diminution was due to the fact that "pretty soon [after the effect's identification] the assistant professors of finance were beginning to operate on this," in other words to exploit it (Samuelson interview). The first of the index futures that began to be traded in the 1980s was the Kansas City Board of Trade's futures on the Value Line index, which were launched in 1982. The Value Line index includes small firms, and each firm is given equal weight in the index's composition (rather than weighting firms by their total market value), so the performance of small firms has a substantial effect on the level of the index. Every December, the "assistant professors of finance" would "buy the Kansas City futures" and "sell the S&P futures" (in the construction of the S&P 500 index firms are weighted by market capitalization, so the index reflects primarily the behavior of very large stocks). The "professors" would thus benefit from the turn-of-the-year anomaly, while being insulated from overall market fluctuations.

Matters are more complex in respect to the small-firm effect. As was noted in chapter 3, a former University of Chicago MBA student, Rex Sinquefield, led the index-fund effort at the American National Bank in Chicago. In 1976 or 1977, Sinquefield learned of Banz's as yet unpublished Ph.D. work identifying the small-firm effect. He phoned Banz at the University of Chicago and asked "Could you come downtown for lunch?" The "preliminary numbers" that Banz showed Sinquefield and his colleagues persuaded them to extend American National's index funds to encompass stocks outside the S&P 500 (Sinquefield interview), and Banz's work informed the original central strategy of Dimensional Fund Advisors, an investment firm set up in Santa Monica in 1981 by Sinquefield and David Booth (also a Chicago MBA).

Dimensional's first product was "designed literally on Banz's paper," Sinquefield said in an interview "It was the fifth quintile he talked about." In 1982, Dimensional launched what was almost an index fund covering the smallest 20 percent of the stocks traded on the New York Stock Exchange. … Sinquefield rejected Banz's proposed "arbitrage," which involved holding small stocks and taking short positions on large stocks, because of its high volatility. … "Frankly, that's all that could have been sold to the pension community anyway."

Sinquefield did not believe that the small-firm effect that had inspired Dimensional Fund Advisors was a market inefficiency. "I'm sort of the Ayatollah of efficient markets," he jokes, "pretty hard line." (Sinquefield interview) If investing in small-capitalization stocks brought enhanced returns, it must be because it also brought greater risk, though exactly what that risk consisted in remained unclear, even when elaborated into the Fama-French model discussed above. "There's no free lunch here."

Dimensional avoided an exact index-tracking strategy that would have left it little or no discretion over the content and timing of sales and purchases. Instead of being a customer, paying in order to trade, it successfully positioned itself as in effect a market maker, making money out of trading (Keim 1999; Cohen 2002). It encouraged other participants in the market for small stocks to offer it blocks of stock that they wanted to sell, so that it was able to buy at a discount rather than paying a premium.

Since the start of the 1980s, there has thus been a mechanism whereby the identification of anomalies prompts practical action, often by efficient-market theorists or those close to them, which exploits and therefore tends to eliminate those anomalies. Indeed, if that cannot be done if there seems to be no way of exploiting an apparent anomaly there is a sense in which it is not an anomaly, for what the efficient-market hypothesis rules out is not non-random "structure" of any kind, but structure from which excess risk-adjusted profits can be made.

Market practitioners had long suspected the existence of a momentum effect. The paper that seems to have convinced even "orthodox" financial economists that such an effect was real was "Returns to Buying Winners and Selling Losers" (Jegadeesh and Titman 1993). One reason the effect is of interest is that among possible explanations is the "behavioral finance" conjecture that market participants "underreact" to new information, so the market "responds only gradually to new information" (Chan, Jegadeesh, and Lakonishok 1996, p. 1681).

The "momentum effect" is exploited widely in trading it is, for example, a familiar hedge-fund strategy but that does not seem to have eliminated it (Jegadeesh and Titman 2001). Roll and Ross Asset Management, for example, found that the effect has "been a pretty long-term thing" (Roll interview). In the case of other anomalies, exploitation seems to tend to diminish their size, but that may not be so with the momentum effect, which conceivably may be intensified by the trading that exploits it. For example, buying a "winner" to exploit its momentum may have the effect of making it more of a winner, encouraging other "momentum traders" likewise to buy.

The testimony of arbitrageurs (in, for example, my interview with David Shaw) is that in addition to the anomalies discussed in the literature of financial economics that are exploitable market inefficiencies that are not publicly known. Naturally, arbitrageurs are reluctant to say exactly what they are: others' exploitation of them would very likely reduce or eliminate them. Even in 1965 it was clear to James Lorie, founder of the Center for Research in Security Prices, that such anomalies might exist: ". . . there is a haunting fear that those with the best arguments [against the random-walk hypothesis] are silently sunning and swimming at St. Tropez" (Lone 1965, p. 18).

Furthermore, one practical application of efficient-market theory, index funds, seems to have created an anomaly, rather than identifying a pre-existing anomaly. The composition of the S&P 500 and similar indices is not fixed. Periodically, firms are added to and deleted from them, because of mergers and bankruptcies and to reflect changes in the market values of corporations and in the overall makeup of the stock market. From an efficient-market viewpoint, the inclusion of a corporation in an index or its deletion from it should not affect the price of its stock: it seems to convey no information about the corporation that was not previously known. … However, Andrei Shleifer, who was to become a leader of behavioral finance, found that from 1976 to 1983 the inclusion of a stock in the S&P 500 index was associated with an average rise in its price on the day of the announcement of its inclusion of just under 3 percent (Shleifer 1986, p. 582). The effect survived its identification: between 1976 and 1996, the average increase was 3.5 percent. To take an extreme case, the price of stock of AOL (America Online) went up by 18 percent when its inclusion in the S&P 500 was announced (Shleifer 2000, p. 22).

At one level, the cause of an increase in price following a stock's inclusion in the S&P 500 or similar indices seems straightforward: index funds, which as noted in chapter 3 have become an extremely large category of investor, do not hold the stock before its inclusion, and when it is included they have to buy it. Again, though, such an explanation is unsatisfactory from the viewpoint of efficient-market theory. It runs directly against a central tenet of finance theory, which goes back to Modigliani, Miller, Markowitz, and Sharpe but which was expressed perhaps most clearly by Myron Scholes on the first page of his Ph.D. thesis: "The shares a firm sells are not unique works of art, but abstract rights to an uncertain income stream for which close counterparts exist either directly or indirectly via combinations of assets of various kinds."

If a purchase or sale of stock conveys no information if it is not, for instance, the result of a corporate insider unloading stock before bad news becomes public then even a large purchase or sale should have an effect on price that is "close to zero" (Scholes 1972, p. 182). For example, if a stock is selected for inclusion in the S&P 500 then large purchases by index funds are necessary, but those purchases are "informationless." Present holders of the stock in question should not need any significant inducement to sell it and to invest instead in one or more of its close substitutes. … That there was an effect could therefore be seen as an anomaly whose existence was evidence against efficient-market theory (Shleifer 2000, pp. 21-23, 48-50). The "investment advice implied by the Efficient Market Hypothesis" that is, to invest in index funds "may itself be undermining the efficiency of the stock market" (Morck and Yang 2001, p. 32).

In recent years, however, the "index inclusion" anomaly seems to have diminished considerably (Cusick 2001) as the familiar process of identification, exploitation, and eventual attenuation or elimination takes hold. For example, analysis by the investment bank J. P. Morgan suggests that in the late 1990s and in 2000 it was fairly reliably profitable to buy stock if it seemed probable that a company might be added to the United Kingdom's leading stock index, the FTSE (Financial Times -Stock Exchange) 100, while selling those companies at risk of being deleted. Since 2000, however, the strategy's profitability "has been eroded as it has become increasingly arbitraged" (Loeys and Fransolet 2004, p. 16).

Beyond the anomalies (and earlier than them in its emergence) lay another kind of problem for efficient-market theory a problem that seems technical but is deep in its ramifications. If changes in security prices were in some sense "random," how was that randomness to be characterized mathematically? Was it a "mild" randomness that could be treated by standard statistical techniques, or a "wild" randomness not susceptible to those techniques?

The proponent of wildness versus mildness was Benoit Mandelbrot. His challenge to the mathematical foundations of much of modern economics was so fundamental that unlike most of the topics discussed in this book it has attracted the attention of historians of economics, notably Philip Mirowski (1989, 1990, 1995) and Esther-Mirjam Sent (1998, 1999).

Mandelbrot saw the possibility of applying to the topic a more sophisticated mathematical formulation derived from the work of his undergraduate professor Paul Levy. Among the topics investigated by Levy was probability distributions that are "stable" in the sense that if two independent variables follow a probability distribution of a given form, their sum also follows that probability distribution (Levy 1925, pp.

The parameter that is most important in distinguishing between different members of the Levy family of distributions is the "characteristic exponent," which Levy denoted by the Greek letter a (alpha). Alpha is always greater than zero and no greater than 2. The lower the value of alpha, the more cases fall in the tails of the distribution: in other words, the higher the proportion of events that are extreme, "wild," deviations from the average.

A value for alpha of 2 corresponds to the normal distribution, with its "nonmonstrous," well-understood, mathematically tractable properties and rapidly diminishing tails. It is a form of "mild" randomness: the rapidly diminishing tails mean that extreme events are very infrequent. If alpha is less than 2, however, the tails of the distribution are sufficiently "fat" that the statistician's standard ways of measuring the extent of a distribution's "spread" (the standard deviation and its square, the variance) no longer exist: the integral expression that defines them does not converge, and so they have no finite value and are in that sense infinite.

Infinite variance plays havoc with standard statistical procedures. Levy distributions with values of alpha other than 2 could thus seem to be theorists' oddities, of little or no value to practical statisticians. I was taught statistics as an undergraduate in 1970-1972. Levy distributions were never mentioned explicitly, though one member of the family the "Cauchy distribution," for which a = 1 was described briefly, perhaps as a warning to students not unthinkingly to assume that a distribution's "moments" its mean, its variance, and so on always exist.

For Mandelbrot, the failure of many existing statistical techniques in a world of Levy distributions with infinite variances was an incentive, not a deterrent. He relished the challenge of examining situations in which the "causally structural features" of systems "are likely to be very much more hidden by noise" than if the central limit theorem applied. With established analytical approaches failing, one might have to turn, for example, to geometrical investigations and to visual intuition. Standard notions of mathematical rigor might have to be set aside: "... when one works in a field where the background noise is [Levy-distributed], one must realize that one faces a burden of proof that is closer to that of history and autobiography than to that of physics" (Mandelbrot 1963b, pp. 422 and 433).

On Houthakker's blackboard were data about changes in the price of cotton. What Mandelbrot-champion of the role of the "eye" in science saw in Houthakker's data was a sign of his monsters, indications of the joint distribution of two Levy variables (figure 4.1) that exhibited a particular form of dependence. In the latter, if the two variables indicate the changes in prices in two successive time intervals, "large changes tend to be followed by large changes of either sign and small changes tend to be followed by small changes" (Mandelbrot 1963a, p. 418). If we were in the non-monstrous world of the normal distribution, the "probability isolines" of the joint distribution would be circles or ellipses. Instead, in Houthakker's data, Mandelbrot saw the cross-shaped isolines of figure 4. 1: the mark, to his eye, of his monsters.

The pattern that Mandelbrot glimpsed on Houthakker's blackboard shifted his focus from the distribution of income (a peripheral problem in the mainstream economics of the 1960s) to the distribution of price changes, which as we saw in chapter 2 was becoming a central topic. Mandelbrot started working with cotton prices, taking Houthakker's price data back to the IBM Research Center at Yorktown Heights "in a box of computer cards" (Gleick 1988, p. 85), obtaining further prices going back to 1880 from the U.S. Department of Agriculture, and analyzing all these data on the powerful IBM 7090 computer at Yorktown Heights. Soon he was working on the prices of wheat and of other grains, on the prices of nineteenth-century railroad stocks, and on interest rates. Everywhere, he found evidence that price changes in "very active speculative markets" (Mandelbrot 1963a, p. 404) followed Levy distributions.

First, Levy distributions had been shown mathematically to occupy a certain privileged position. A generalization of the central limit theorem that was known well enough to be found in the more advanced textbooks of probability theory was that "if a sum of independent random variables with common distribution tends toward any limiting distribution, that distribution will be a member of the [Levy] class" (Roll 1970, p. 63, summarizing Feller 1966, p. 168). The random-walk hypothesis suggested that price changes were indeed sums of independent random variables, so this theorem might well apply.

Levy distributions have the elegant property that we now call "selfsimilarity." Price changes in longer time periods are simply the sum of changes in shorter time periods, and Levy distributions are invariant under addition. If changes in short time periods were independent and all followed the same Levy distribution, then so would changes over longer periods. The "scale" used in the analysis time periods of a minute, an hour, a day, a week, a month, a year would therefore not matter: the form of the distribution would be unchanged.

Early in 1962, Mandelbrot was in Chicago and took the opportunity to visit the Graduate School of Business. Merton Miller and his colleagues were impressed "We all wanted to make him an offer [of a professorship]" (Miller interview) and a productive collaboration, albeit an informal and largely long-distance one, ensued. … "Benoit had a great influence on a lot of us, not just the fat tails but the first really rigorous treatment of expectations [Mandelbrot 1966], and so on.... I'm, to this day, a Mandelbrotian." (Miller interview) The University of Chicago financial economist who took up Mandelbrot's work most actively was Eugene Fama, still a graduate student in 1962.

Fama concluded that the distributions of stock-price changes were unequivocally fat-tailed. Were they Levy distributions? Were their variances infinite? Those were harder questions to answer. In any sample of finite size, the sample variance will always be finite even if the underlying distribution has an infinite variance, so these questions cannot be answered by calculating a variance.

Cootner attacked Mandelbrot's "messianic tone" and expressed his discomfort with what he said was Mandelbrot's "disturbingly casual" use of evidence, noting that much of the evidence was "graphical and involves slopes of lines which are not given precise numerical values" (Cootner 1964, p. 333). Cootner marshaled his own evidence against the Levy hypothesis, and ended with an impassioned plea to consider the possible costs (the "loss functions," as he put it) involved in the acceptance or rejection of the hypothesis: Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil, and tears.

Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil, and tears. If he is right, almost all of our statistical tools are obsolete-least squares, spectral analysis, workable maximum-likelihood solutions, all our established sample theory, closed distribution functions. Almost without exception, past econometric work is meaningless. Surely, before consigning centuries of work to the ash pile, we should like to have some assurance that all our work is truly useless. If we have permitted ourselves to be fooled for as long as this into believing that the Gaussian [normal-distribution] assumption is a workable one, is it not possible that the [Levy] revolution is similarly illusory?

One trigger of the loss of support was the work of the University of Chicago Ph.D. student Robert R. Officer, who applied Fama and Roll's improved methods of estimating alpha and found that its value rose as daily stock-price data were aggregated into longer time periods, behavior that was at odds with self-similarity or invariance under addition (Officer 1972).

If they [price changes] were really stable [Levy-distributed], the way Mandelbrot describes them, they maintained the same properties under addition. So if you start with a stable distribution of log returns, it's going to be of the same type [the same value of alpha] when you look at monthly returns, and that wasn't true. They tend to converge towards normality.... I think people just kind of because they couldn't explain the slow convergence stuff, so they kind of became disinterested in the fat tails. (Fama interview) If one was dealing with stock or portfolio returns over periods as long as a month, Fama concluded, the tails became slim enough that "the normal distribution is a good working approximation."

If one was dealing with stock or portfolio returns over periods as long as a month, Fama concluded, the tails became slim enough that "the normal distribution is a good working approximation." The "costs of rejecting normality for securities returns in favor of [Levy] non-normal distributions are substantial," Fama wrote. Although "most of the models of the theory of finance" could be reconstructed on the basis of Levy distributions, the "exposition" of those models became more complicated and "statistical tools for handling data from [Levy] non-normal ... distributions are primitive relative to the tools that are available to handle data from normal distributions."

For Roll, too, the appearance of evidence at odds with self-similarity (in his case, in particular in Hsu, Miller, and Wichern 1974) suggested that further investment of his time in work on Levy distributions would be mistaken: "I started thinking ... that maybe I shouldn't waste too much effort trying to go further on the Levy laws. I worked a long time trying to derive closed-form density formulas [see appendix B] and stuff like that, and I could have done that the rest of my life, I suppose. So I decided to quit that and do other things."

Mandelbrot agrees that Officer's and similar work showed that "simple scaling did not apply." However, he questions the conclusions drawn from that work ("They were hasty and indefensible"), and he regards the notion that "somehow things become Gaussian [normal]" as an "arrant" misinterpretation.

Nor is the failure of an empirical prediction, even a central one, in itself enough to explain the abandonment of the Levy model. As we saw in chapter 2, the Capital Asset Pricing Model made, at least once Sharpe had the confidence to embrace it, a prediction that was manifestly false that all investors would hold portfolios of risky assets that were identical in their proportionate composition but that did not stop the model being adopted widely. What was at least as important as the empirical doubt cast on self-similarity or invariance under addition in explaining the abandonment of the hypothesis of Levy distributions was that a variety of other ways of modeling distributions with high frequencies of extreme events were becoming available (see, for example, Clark 1973).

For all the apparent technicality of the issue of infinite variance, Levy distributions had aroused strong passions. One mathematically sophisticated interviewee, Oldrich Vasicek, told me that he thought that Mandelbrot "must just have pulled everybody's legs the whole time.... I just cannot believe he would actually take it [Levy distributions with infinite variance] seriously himself.... It has consequences so brutal that nobody would be able to live with that." If the logarithm of a stock price varied according to a Levy process with infinite variance, as Mandelbrot had hypothesized, then the expected value of the price itself would be infinite. "So you'd be saying with straight face that you have an infinite expectation for tomorrow's Xerox price."

Options are contracts that give their holder the right, but do not oblige their holder, to buy (or to sell) an asset at a set price on, or up to, a given date. They are old instruments. Puts (options to sell) and calls (options to buy) on the stock of the Dutch East India Company were being bought and sold in Amsterdam when Joseph de la Vega discussed its stock market in 1688 (de la Vega 1957), and subsequently options were traded widely in Paris, London, New York, and other financial centers.

Before the 1970s, age had not brought options respectability. Sometimes they were seen simply as wagers on stock-price movements. Options also seemed the perfect tool for the speculator. Because the cost of an option was and is typically much less than that of the underlying stock, a speculator who correctly anticipated price increases could profit considerably by buying calls, or benefit from decreases by buying puts. Sometimes such speculators themselves caused prices to move in the direction they wanted by spreading false rumors, for example so options also became associated with market manipulation.

The focus on options did not arise because they were important financial instruments: they were not. The Great Crash of 1929 reignited the traditional hostility to options, which were widely seen as implicated in the excesses and abuses of the 1920s. An outright federal ban on stock-option trading was only just averted (Filer 1959), and such trading continued only in a small, illiquid, ad hoc market based in New York. In general, only brokers' price quotations could be obtained from that market, not the actual prices at which options were bought and sold. The absence of robust price data was a disadvantage of the options traded in New York from the viewpoint of financial economists.

Instead, the main focus of attention was on warrants, a particular form of call options that were traded in more liquid, organized markets particularly the American Exchange and for which market prices were available. Like an ordinary call option, a warrant gives its holder the right to buy stock at a fixed price. However, ordinary call options are written (that is, issued) by investors or traders, and if the holder of such an option exercises it, option writers supply the holder with existing stock that the writer either must already possess or must buy in the market. Warrants, in contrast, are issued by corporations, and if the holder of a warrant exercises it, the corporation creates new stock to issue to the warrant holder.

Even warrants were of limited substantive importance. Rather, developing a theory of option and warrant pricing was a way of elaborating the randomwalk model of stock prices: a form of "normal science" in Kuhn's (1970) terms. As Cootner put it, "options obtain their value from the price of the underlying shares" (1964, p. 373). If one had a well-defined mathematical model of the fluctuations of stock prices (and, the issues discussed in chapter 4 aside, the log-normal random walk seemed to offer such a model), then it appeared as if all one had to do was some relatively easy mathematical analysis to reach a formula for the expected value of a warrant or option.

Sprenkle then argued that this expected value would be a warrant's value to an investor only if the investor was indifferent to risk or "risk neutral." To get a sense of what this means, imagine being offered a fair bet with a 50 percent chance of winning $1,000 and a 50 percent chance of losing $1,000, and thus an expected value of zero. If you would require to be paid to take on such a bet you are "risk averse"; if you would pay to take it on you are "risk seeking"; if you would take it on without inducement, but without being prepared to pay to do so, you are "risk neutral." A risky investment is worth exactly the expected value of its payoff only to a risk-neutral investor. It is worth less than that to a risk-averse investor, and more than that to a risk-seeking one.

Warrants and other forms of option are riskier than the underlying stock because of their leverage, in other words because "a given percentage change in the price of the stock will result in a larger percentage change in the price of the option" (Sprenkle 1961, p. 189). An investor's attitude to risk could be conceptualized, Sprenkle suggested, as the "price" the investor was prepared to pay for leverage.

Sprenkle's formula for the value of a warrant to an investor (equation 2 in appendix C) involved three unknowns: the expected extent of the stock's appreciation in price by the warrant's expiry date; the standard deviation of the stock's anticipated price distribution at expiry; and the "price" the investor was prepared to pay for a warrant's leverage. The price of leverage would be negative for a risk-averse investor, zero for a risk-neutral investor, and positive for a risk-seeking investor.

Sprenkle (1961, pp. 199-201) assumed that the values of his three unknowns, and thus the value of a warrant, would vary from investor to investor: `Actual prices of the warrant then reflect the consensus of marginal investors' opinions the marginal investors' expectations and preferences are the same as the market's expectations and preferences."

Sprenkle examined warrant and stock prices for the "classic boom and bust period" of 1923-1932 and for the relative stability of 1953-1959, hoping to estimate from those prices "the market's expectations and preferences," in other words the levels of expected stock prices and their anticipated standard deviations, and also investors' attitudes to risk as expressed by the price of leverage. His econometric work, however, hit considerable difficulties: "it was found impossible to obtain these estimates." Only by arbitrarily assuming no expected appreciation in prices and testing out a range of arbitrary values of the price of leverage could Sprenkle make partial progress. His theoretically derived formula for the value of a warrant depended on parameters whose empirical values were hard to estimate empirically (Sprenkle 1961, pp. 204, 212-213).

The most sophisticated theoretical analysis of warrants in the early and mid 1960s was by Paul Samuelson, the MIT economist discussed in previous chapters. Samuelson developed a collaboration with the MIT mathematician Henry P. McKean Jr, a world-class specialist in stochastic calculus (the theory of stochastic processes in continuous time), which in the years after Bachelier's work had become an important area of probability theory. Samuelson's model also depended, like Sprenkle's, on parameters that seemed to have no straightforward empirical referents the expected rate of return on the underlying stock, and the expected rate of return on the warrant and Samuelson offered no way of directly estimating these parameters (Samuelson 1965a; McKean 1965).

Herbert Simon, whose "behavioral" criticism of financial economics was discussed in chapter 2, would no doubt have felt that option theory in the 1960s was a perfect manifestation of his point. The theoretical formulas for the values of options and warrants always involved unobservable parameters, in particular the parameter on whose unobservability Simon had focused, a stock's expected rate of return. Furthermore, attempts to work backward from observed option prices to estimate expected stock returns and other underlying parameters had proved frustrating: no entirely convincing estimates had been generated.

Warrants and the corresponding stock tended to move together: if the stock price increased, then so did the warrant price; if the stock fell, so did the warrant. So one could be used to offset the risk of the other. If, for example, warrants seemed overpriced relative to the corresponding stock, one could sell them short (in other words, borrow and sell them), hedging the risk of stock-price increases by buying some of the stock. Trading of this sort, conducted by Kassouf in parallel with his Ph.D. research, enabled him "to more than double $100,000 in just four years" (Thorp and Kassouf 1967, p.

In 1959-1961, while at MIT, Thorp had collaborated with the celebrated information theorist Claude Shannon on a tiny, wearable analog computer system that could predict where the ball would be deposited on a roulette wheel (Thorp interview). Thorp went on to devise the first effective methods for beating the casino at blackjack by keeping track of cards that had already been dealt and thus identifying situations in which the probabilities were favorable to the player (Thorp 1961; Tudball 2002).

Thorp and Shannon's use of their wearable roulette computer was limited by easily broken wires, but card counting was highly profitable. In 1961, during MIT's spring recess, Thorp traveled to Nevada equipped with a hundred $100 bills provided by two millionaires with an interest in gambling. After 30 hours of blackjack, Thorp's $10,000 had become $21,000. He went on to devise, with computer scientist William E. Walden of the nuclear weapons laboratory at Los Alamos, a method for identifying favorable side bets in the version of baccarat played in Nevada.

Thorp found, however, that beating the casino had disadvantages as a way of making money. At a time when American casinos were controlled largely by organized criminals, there were physical risks. (In 1964, while playing baccarat, Thorp was nearly rendered unconscious by "knockout drops" in his coffee.) The need to travel to places where gambling was legal was a further disadvantage to an academic with a family (Thorp interview).

Thorp and Kassouf's 1967 book Beat the Market examined the relationship between the price of a warrant and of the underlying stock. (See figure 5.1.) No warrant should ever cost more than the underlying stock, since it is simply an option to buy the latter, and this constraint yields a "maximum value line." If at any time the price of the stock exceeded the warrant's strike or exercise price (the price at which it gave one the right to buy the stock) by more than the price of the warrant, an instant arbitrage profit could be made by buying the warrant, exercising it, and selling the stock thus acquired at its market price. So a warrant can never cost less than the stock price minus the strike or exercise price, and this determines the "minimum value line" in figure 5. 1.

Thorp decided to approximate it by assuming that the expected price of the stock rose at the riskless rate of interest (the rate paid by a borrower who creditors are certain will not default, for which a usual indicator is the yield of bonds issued in their own currencies by major governments). He had no better estimate, and he "didn't think that enormous errors would necessarily be introduced" by the approximation.

Thorp's expression for the value of a warrant or call option was formally equivalent to that of Fischer Black and Myron Scholes (equation 2 in appendix D), except for one feature: unlike Black and Scholes, Thorp did not discount the expected value of the option at expiration back to the present. (In other words, his value for the option price did not take into account the fact that the seller of an option could earn interest on the proceeds of its sale.)

In the warrant markets in which Thorp traded, the proceeds of the short sale of a warrant were retained in their entirety as collateral by the broker from whom the warrant had been borrowed until the warrant was repurchased and returned. The proceeds were therefore not available immediately to the seller, as Black and Scholes assumed.

Treynor specialized in the analysis of the financial aspects of business decisions such as whether to buy or to lease machine tools (Treynor and Vancil 1956). Those decisions typically involve working out the present value of projected future income and expenditures. Such calculations depend critically on the choice of interest rate at which to discount future cash flows.

The main difficulty was how to deal with future cash flows that were uncertain. The guidance Treynor had received from his professors at the Harvard Business School (from which he graduated with an MBA in 1955) seemed to him to fudge the issue. It "wasn't very satisfactory. They were basically saying `well, choose the discount rate to take risk into account.' It was obvious to anybody that, depending on which risk discount rate you chose, you could get ... radically different present values and that would either lean you toward going ahead with a project or not, and so that troubled me. It just didn't seem like an adequate answer."

Treynor first made a serious effort to solve the problem of how to discount uncertain cash flows in the summer of 1958. His parents owned a cottage in the Rocky Mountains, which they used to escape from the oppressive heat and humidity of the summers in Treynor's native Iowa, and he joined them for a vacation from his job at Little that turned into a working holiday. He drove down from his parents' cottage to the University of Denver to work in its library, and there he read Modigliani and Miller's 1958 paper on the irrelevance of capital structure to total market value. In any problem in operations research it is necessary to know what one is seeking to maximize, and in Modigliani and Miller's paper Treynor found his answer.

What Modigliani and Miller's paper taught Treynor to do, in other words, was to look outside the corporation to the capital markets in order to solve problems in decision making like the choice of discount rate to use in making investment decisions. Mathematically, Treynor based his analysis "on the kind of work that I had seen the senior guys doing in the operations research group" of Arthur D. Little: they would first "try to solve the problem for a single [time] period ... drive that ... solution to an infinitesimally small time period, turn it into a partial differential equation and then integrate that thing out over finite time" (Treynor interview).

This was a reformulation of the later, less successful, steps in Treynor's approach to the mathematics of capital asset pricing (Treynor 1963), and the aspect of it on which Black and Treynor collaborated had involved Treynor writing an expression for the change in the value of a cash flow in a short, finite time interval At; expanding the expression using the standard calculus technique of Taylor expansion; taking expected values; dropping the terms of order AP and higher; dividing by At; and letting At tend to zero so that the finite-difference equation became a differential equation. Treynor's original version of the latter was in error because he had left out "some terms involving second derivatives" that did not vanish, but Black and he worked out how to correct the differential equation.

The hedged portfolio had been the central idea of Thorp and Kassouf's book Beat the Market, which Scholes had not yet read (Scholes interview). Scholes's goal, in any case, was different. Thorp and Kassouf's hedged portfolio was designed to earn high returns with low risk in real markets. Scholes's was a desired theoretical artifact. He wanted a portfolio with a beta of zero: that is, with no correlation with the overall level of the market. If such a portfolio could be created, the Capital Asset Pricing Model implied (as noted above) that it would earn, not high returns, but only the riskless rate of interest. It would thus not be an unduly enticing investment, but knowing the rate of return on the hedged portfolio might solve the problem of warrant pricing.

What Scholes could not work out, however, was how to construct a zerobeta portfolio. He could see that the quantity of shares that had to be sold short must change with time and with changes in the stock price, but lie could not see how to determine that quantity. `After working on this concept, off and on, I still couldn't figure out analytically how many shares of stock to sell short to create a zero-beta portfolio." (Scholes 1998, p. 480) Like Black, Scholes was stymied.

Then, in "the summer or early fall of 1969," Scholes told Black of his efforts, and Black described the different approach he had taken, in particular showing Scholes the Taylor-series expansion of the warrant price that echoed his work with Treynor (Scholes 1998, p. 480).

Black and Scholes could see how a zero-beta portfolio would have to be constructed. If the stock price x changed by the small amount Ax, the warrant or option price w would alter by Ax multiplied by aw/ax, the partial derivative of w with respect to x and thus the rate at which the warrant or option price changes as the stock price changes. (This partial derivative-" delta," as it was to become known to the option traders discussed in chapter 6 would vary with time and with stock-price changes, but would be calculable if w could be expressed as a differentiable function of x and of the other parameters of the problem.) So the necessary hedge was to short-sell a quantity aw/ax of stock for every warrant held. That was in a sense the same conclusion Thorp and Kassouf had arrived at: aw/ax is their hedging ratio, expressed in their case as the slope of the empirically derived curves of warrant price plotted against stock price as in figure 5.1.

The risk of the hedged portfolio was, therefore, the kind of risk that could be diversified away. Therefore, according to the Capital Asset Pricing Model, the hedged portfolio could earn only the riskless rate of interest. With the expected return on the hedged portfolio known, simple manipulation led to a finite difference equation that could be transformed into a differential equation (again, equation 1 in appendix D), the Black-Scholes option-pricing equation, as it was soon to be called.

Like Black, Scholes was "amazed that the expected rate of return on the underlying stock did not appear" in the equation (Scholes 1998, p. 481). This prompted Black and Scholes to experiment, as Thorp had done, with setting the expected return on the stock as the riskless rate of interest. They substituted this rate for the expected rate of appreciation of the stock price in Sprenkle's formula for the expected value of the payoff of a warrant at expiration (equation 1 in appendix Q. To get the option or warrant price, they then had to discount that expected payoff, in other words to work out its present value.

"Rather suddenly, it came to us," Black later recalled. "If the stock had an expected return equal to the [riskless] interest rate, so would the option. After all, if all the stock's risk could be diversified away, so could all the option's risk. If the beta of the stock were zero, the beta of the option would have to be zero too.... The discount rate that would take us from the option's expected future value to its present value would always be the [riskless] interest rate."

Black and Scholes's tinkering with the formula for the expected value of an option's payoff was in one sense no different from what Boness or Thorp had done. However, Boness's justification for his choice of expected rate of return on stock was empirical he chose "the rate of appreciation most consistent with market prices of puts and calls" (Boness 1964, p. 170) and Thorp freely admits that he "guessed" that the right thing to do was to set the stock's rate of return equal to the riskless rate: it was "guesswork, not proof" (Thorp interview). Black and Scholes, on the other hand, could prove mathematically that their call option formula was a solution to their differential equation, and the latter had a clear theoretical, economic justification.

Neither Black nor Scholes knew the mathematical theory needed to do calculus rigorously in a stochastic environment, but the Capital Asset Pricing Model provided an economic justification for what might otherwise have seemed dangerously unrigorous mathematics. "We did not know whether our formulation was exact," says Scholes, "but intuitively we thought investors could diversify away any residual risk that was left."

As was noted above, Black had been a close colleague of the Capital Asset Pricing Model's co-developer, Jack Treynor. Scholes had done his graduate work at the University of Chicago, where in the 1960s and the early 1970s the model was seen as an exemplary contribution to the field. (The "Chicago" criticism of the model discussed in chapter 4 was a later development.) However, at the other main site of financial economics, MIT, the original version of the Capital Asset Pricing Model was regarded much less positively. The model had been developed using a "mean-variance" view of portfolio selection: investors were modeled as guided only by the expected value or mean of the returns on investments, and by investments' risks as measured by the expected standard deviation or variance of their returns.

Unless the changes in prices of securities followed a joint normal distribution (which was regarded as ruled out, because it would imply, as Samuelson had noted, a non-zero probability of negative prices), mean-variance analysis seemed to rest on a specific form of the "utility function" characterizing the relationship between the return, y, on an investor's portfolio and his or her preferences. Mean-variance analysis seemed to imply that investors' utility functions were quadratic: that is, they contained only terms my andy2. Special cases aside, a rational investor with a utility function whose mathematical form differed from this would not be guided by the expected mean and variance alone.

Quadratic utility implied that beyond a certain level of wealth, increasing levels of wealth meant decreasing utility, so investors would "pay you to cart away their wealth" (Samuelson interview).

Robert C. Merton had been an amateur investor since the age of 10 or 11, had graduated from stocks to options and warrants, and had come to realize that he had "a much better intuition and `feel' into economic matters than physical ones." In the spring of 1968, Samuelson appointed the mathematically talented young Merton as his research assistant, even allocating him a desk inside his MIT office (Merton interview; Merton 1998, pp. 15-16).

Compared with "discrete-time" models, "the continuous-time models are mathematically more complex," says Merton. He quickly became convinced, however, that "the derived results of the continuous-time models were often more precise and easier to interpret than their discrete-time counterparts" (Merton 1998, pp. 18-19). His "intertemporal" Capital Asset Pricing Model (Merton 1973b), for example, did not necessitate the "quadratic utility" assumption of the original.

In a letter, Merton (1972b) told Fischer Black: "I ... do not understand your reluctance to accept that the standard form of CAPM just does not work." "What I sort of argued with them [Black and Scholes]," says Merton, "was, if it depended on the [capital] asset pricing model, why is it when you look at the final formula [equation 1 in appendix D] nothing about risk appears at all? In fact, it's perfectly consistent with a risk-neutral world."

"I looked at this thing," says Merton, "and I realized that if you did ... dynamic trading ... if you actually [traded] literally continuously, then in fact, yeah, you could get rid of the risk, but not just the systematic risk, all the risk." Not only did the hedged portfolio have zero beta in the continuous-time limit (Merton had initial doubts on this point but they were assuaged), "but you actually get a zero sigma" that is, no variance of return on the hedged portfolio (Merton interview).

Because it offers returns that are certain, the hedged portfolio can therefore earn only the riskless rate of interest, "not for the reason of [the capital] asset pricing model but ... to avoid arbitrage, or money machine": a way of generating certain profits with no net investment (Merton interview). For Merton, then, the "key to the Black-Scholes analysis" was an assumption Black and Scholes did not initially make: continuous trading, the capacity to adjust a portfolio at all times and instantaneously. "Only in the instantaneous limit are the warrant price and stock price perfectly correlated, which is what is required to form the `perfect' hedge." (Merton 1972a, p. 38) Black and Scholes were not initially convinced of the correctness of Merton's approach.

Black and Scholes were not initially convinced of the correctness of Merton's approach. Merton's additional assumption his world of continuoustime trading was a radical abstraction, and in a January 1971 draft of their paper on option pricing Black and Scholes even claimed that aspects of the world posited by Merton were incompatible with equilibrium in capital markets (Black and Scholes 1971, pp. 20-21). Despite this disagreement, Black and Scholes used what was essentially Merton's revised form of their arbitragebased derivation in the final, published version of their paper (Black and Scholes 1973), though they also presented Black's original derivation, which drew directly on the Capital Asset Pricing Model.

Emanuel Derman, who worked closely with Black at the investment bank Goldman Sachs, recalls Black becoming "quite excited" when a simulation with which Derman was experimenting seemed to show that Merton's continuously adjusted hedge did not yield precisely the Black-Scholes price of an option. According to Derman, Black "said something like, `You know, I always thought there was something wrong with the replication method."' It turned out that the discrepancy arose because of error in the simulation, but, says Derman, "in his heart ... Fischer [Black] mistrusted the Merton derivation and preferred his original proof" (Derman 2004, pp. 170-171).

Black, indeed, came to express doubts even about the central intuition of orthodox financial economics: that modern capital markets were efficient, with prices in them incorporating all available price-relevant information. Efficiency held, he suggested, only in a diluted sense: "... we might define an efficient market as one in which price is within a factor of 2 of value." Black noted that this position was intermediate between that of Merton, who defended the efficient-market hypothesis, and that of the "behavioral" finance theorist Robert Shiller: "Deviations from efficiency seem more significant in my world than in Merton's, but much less significant in my world than in Shiller's." (Black 1986, p. 533; see Merton 1987 and Shiller 1989) Viewed from a distance, however, the differences between Black, Scholes, and Merton diminished Black's doubts about Merton's derivation were not public and the common core of their arguments became more salient.

In Sharpe's binomial model, an option can be hedged perfectly, just as in the Black-Scholes-Merton model. The theoretical price of an option is then determined, as in the Black-Scholes-Merton analysis, by the argument that a perfectly hedged portfolio must earn the riskless rate of interest. If the market price of an option deviates from that theoretical price, arbitrage is possible. Investors' attitudes to risk need not be considered, and there is no need to know the probabilities that the stock will move "up" or "down" in price. It is arbitrage, not those probabilities or investors' beliefs about them, that determines the price of an option.

However, the emerging new breed of financial economists quickly saw the elegance of the Black-Scholes-Merton solution. The expected return on the underlying stock and investors' levels of risk aversion did not appear in the Black-Scholes equation: their arbitrage-based arguments did not require knowledge of those. Herbert Simon's jibe that finance was a field dependent on unobservable variables seemed to have been answered decisively, at least as far as expected returns and risk aversion were concerned.

"What got Black, Scholes and Merton there," Samuelson recalled in 2000, "was their courage to take a final step that I was squeamish about: namely, I was loathe to accept the idealization of truly instantaneous rebalancings; always, I insisted, for finite time intervals, however small, no perfect hedge was possible."

One particular product of the work of Cox and Ross was to take on a special practical significance, as we shall see in chapter 7. This arose from a collaboration between them and Mark Rubinstein, a finance academic at the University of California at Berkeley who had particular expertise in the applications of computing to finance. The Cox-Ross-Rubinstein model (sketched in appendix E) was an attractive practical alternative to Black-Scholes. It was especially suited to implementation on a digital computer, and if the computer was powerful enough the Cox-Ross-Rubinstein model allowed option-pricing problems that were difficult or impossible to solve by analytical techniques to be solved numerically.

Harrison and Kreps showed that in a "frictionless" market with no opportunities for arbitrage there existed an "equivalent martingale measure," a way of assigning probabilities to the path followed by the price of an asset such that the value of an option or other derivative contract on that asset was simply the expected value of its payoff discounted back to the present.

However, "the martingale stuff brought the hypermathematicians in" (Ross interview). Building on the work done by Black, Scholes, and Merton, other theorists Sharpe, Cox, Ross, Rubinstein, and especially Harrison and Kreps had constructed a bridge between financial economics and martingale theory, an advanced, high-prestige area of pure mathematics. Things that probability theorists within pure mathematics knew about-measure-theoretic notions of probability, the Radon-Nikodym theorem, the martingale representation theorem, the martingale convergence theorem, the Girsanov theorem became relevant to finance. "There's this whole literature on martingales and stochastic processes so people doing that suddenly said `yeah, I can get a job on Wall Street.' That's what brought them all into it." (Ross interview) By the 1990s, it had become possible for probability theorists to teach courses that were both rigorous by the standards of pure mathematics and attractive to students looking forward to well-paid jobs in finance.

For all the diversity and elaboration of option theory after 1973, the work of Black, Scholes, and Merton remained paradigmatic. None of what followed contradicted their approach; it was all consistent with it. For example, the Black-Scholes-Merton model is a limit case of the Cox-Ross-Rubinstein model.

The Black-Scholes-Merton model was not transcended, but supplemented. It was brilliant, productive theoretical work. But was it empirically valid? After constructing their formula for the pricing of call options (equation 2 in appendix D), Black and Scholes tested its empirical validity for the ad hoc New York options market, using a broker's diaries in which were "recorded all option contracts written for his customers." They found only an approximate fit: "in general writers [the sellers of options] obtain favorable prices, and ... there tends to be a systematic mispricing of options as a function of the variance of returns of the stock" (Black and Scholes 1972, pp.

In their paper on the theory of option pricing, Black and Scholes spelled out their assumptions. These included not just the basic assumption that the "stock price follows a [log-normal] random walk in continuous time," but also assumptions about market conditions: that there are "no transaction costs in buying or selling the stock or the option"; that it is "possible to borrow any fraction of the price of a security to buy it or to hold it," at the riskless rate of interest; and that there are "no penalties to short selling" (Black and Scholes 1973, p.

In the 1960s and at the start of the 1970s, these assumptions about market conditions were wildly unrealistic. Commissions (an important transaction cost) were high everywhere. Investors could not purchase stock entirely on credit (in the United States this was banned by the Federal Reserve's "Regulation T"), and such loans would be at a rate of interest in excess of the riskless rate. Short-selling was legally constrained and financially penalized: stock lenders retained the proceeds of a short sale as collateral for the loan, and refused to pass on all (or sometimes any) of the interest earned on those proceeds (Thorp interview).

In these and other respects, however, the world of the early 1970s was starting to change. Even before it had altered much, Black-Scholes-Merton option theory began to affect the fortunes of options exchanges and even the patterns of prices on them.

Agriculture thrived on the Midwest's endless prairies, but the exchanges that traded futures on the produce of those prairies the Chicago Board of Trade and the Chicago Mercantile Exchange did not always benefit. Government guarantees set minimum prices for agricultural products, while surpluses prevented prices from rising much. The need to hedge the risk of price fluctuations diminished, and speculation on those fluctuations became unattractive.

At the Merc, Leo Melamed had seen the trade in egg futures collapse, and onion futures were banned by Congress in August 1958 after one of the periodic scandals that rocked the commodities futures markets. In 1961, the Merc launched a futures contract on frozen pork bellies, and other futures on meat followed. They formed a viable market one that was later to come to wider attention when Hillary Rodham Clinton's success in the 1970s speculating in the Merc's cattle futures was scrutinized' but Melamed knew that "a oneproduct line was a very dangerous way for an exchange to live." As he rose to leadership of the Mere, he explored the possibility of futures on other commodities such as shrimp, potatoes, apples, and turkeys (Melamed interview).

Plywood and shrimp did not, however, seem to guarantee a genuine revival of the Board of Trade and the Merc, and in the late 1960s a more radical departure began to be canvassed: financial futures. They could serve the same interlocked interests in hedging and speculation as agricultural futures did, but their pursuit encountered barriers that were essentially moral, like the earlier barriers to life insurance (Zelizer 1979).

Stock options and futures were integral to nineteenth-century exchanges (Weber 2000a,b), but the 1929 crash and the subsequent Great Depression reignited hostility to "speculation" in derivatives that looked like wagers on price movements. Even in the 1960s, market regulators such as the Securities and Exchange Commission (founded in response to the excesses and abuses of the 1920s) remained deeply suspicious of derivatives.

Futures trading had always been contentious farmers, for example, often blamed speculators on futures exchanges for the low price of their produce and a crucial plank of its opponents' efforts to ban it was the argument that futures contracts were wagers. If its critics could succeed in making this identification, they would push futures trading outside the law, since gambling was illegal in most of the United States.

For much of the late nineteenth century and the early twentieth century, courts in the United States had struggled to find a clear distinction between legitimate futures trading and gambling. Their efforts were complicated and sometimes contradictory (Swan 2000). However, a test that commanded wide agreement was whether or not a futures contract could be settled by physical delivery of the underlying commodity, for example grain. … If a futures contract could be settled by delivery of the underlying asset, courts generally ruled that it was legal and enforceable. If it could not if the contract could be settled only in cash it was in general held to constitute a wager.' Hence, as noted in chapter 1, even if delivery was seldom demanded, it had to be possible. If it was not, a futures contract was against the law of Illinois and of any other state in which gambling was prohibited.

Since an index was an abstraction, there was no straightforward way in which an index future could be settled other than in cash. In 1968, Sullivan and two leading members of the Chicago Board of Trade consulted securities lawyer Milton Cohen about the feasibility of a Dow Jones futures contract. Cohen advised against proceeding: the contract would violate Illinois law (Falloon 1998, pp. 209-210).

Melamed, however, had a different idea: futures on currencies. "Currencies had been ... really dear to my heart," he says (Melamed interview). He remembered his father explaining to him the differences between the currencies of the countries they traveled through: Poland, Lithuania, Russia, Japan, and the United States.

The thousands of often desperately poor Jewish refugees in Japan had been kept from destitution by a currency arbitrage. Japanese citizens were forbidden from owning any foreign currency, and in consequence a black market existed, particularly in dollars. … The Jewish Labor Committee would open bank accounts for refugees in Japan such as Melamed's family, and deposit yen in them. When refugees received a U.S. visa, they would take the visa to the bank, and they were then allowed to convert the yen in their account to dollars at the official rate. They would take these dollars on board the ship taking them from Japan (Melamed still remembers the "little briefcase" in which his father did this) and register them with the ship's purser to prove they were not penniless. After doing so, they would then return the dollars to a representative of the Labor Committee, who would take them back onshore and convert them back to yen at the much more favorable black-market rate (Melamed interview).

With exchange rates fluctuating only in very limited bands, trading currency futures would be unattractive: there would be no need to hedge against adverse fluctuations, and little point in speculating.

The 1953 book that contained Friedman's essay on "The Methodology of Positive Economics" also contained a chapter titled "The Case for Flexible Exchange Rates." In it, Friedman argued that "current economic and political conditions" demanded "a system of flexible or floating exchange rates exchange rates freely determined in an open market primarily by private dealings and, like other market prices, varying from day to day." Such a regime, he claimed, was "absolutely essential for ... the achievement and maintenance of a free and prosperous world community engaging in unrestricted multilateral trade" (Friedman 1953b, p. 157).

Among the contributors in the 1960s to the academic literature on options discussed in chapter 5 were the Princeton economists Burton Malkiel and Richard Quandt. They argued that options' reputation as "the `black sheep' of the securities field" was undeserved. Their use was "a very desirable strategy for most investors" and "wholly rational," although the ad hoc New York options market was "relatively inefficient" (Malkiel and Quandt 1969, pp. 6, 163, 165, and 167).

It seems to have been reading about Malkiel and Quandt's favorable economic analysis of options in an article in the magazine Institutional Investor (Malkiel and Quandt 1968) that drew the attention of a leading member of the Board of Trade: the grain trader Edmund O'Connor. Options were desirable but traded only ad hoc. Might the Board not profitably standardize them and trade them in a busy, efficient Chicago pit?

As Friedman was preparing his paper, desperate efforts were being made at government level to reconstruct a system of fixed exchange rates, but it was already clear that even if that was successful the allowable bands of fluctuation would be wider than 1 percent permitted under Bretton Woods. Those involved in foreign trade would, therefore, be exposed to far greater risks of currency fluctuation than they had been in the 1950s and the 1960s. Bringing hedgers and speculators together in a currency futures market would make that market large and liquid, making it possible "to hedge at low costs and at market prices that move only gradually and are not significantly affected by even large commercial transactions" (Friedman 1971, p.

Shultz, though, had been a colleague of Friedman: he had been a professor in and then dean of the University of Chicago's Graduate School of Business. "If it's good enough for Milton," he told Melamed and Harris, "it's good enough for me."

In their contribution to the Nathan Report, Baumol, Malkiel, and Quandt argued that options "enrich the investor's repertoire of strategies by allowing him to realize a different set of payoffs than he would have realized in their absence." Just as the possibility of carrying an umbrella was an advantage to the pedestrian, "the more strategies are available to the investor, the better off he is likely to be" (Nathan Associates 1969, vol.

The Nathan Report, in turn, made it possible for the proposal for an options exchange to gain its single most crucial recruit, Milton Cohen. The Chicago lawyer had originally not wished to be associated with the proposal, but the report made it "legitimate enough" that he agreed to become Special Counsel to the Board of Trade and to lead its negotiations with the SEC (Sullivan interview). Cohen had been a senior official at the SEC and was arguably the preeminent securities lawyer in the United States. No one was better placed to "make a record" with the SEC: putting proposals and getting responses.

Casey's attitude to "speculation" was quite different from that of his predecessor Manuel Cohen, and he held Milton Cohen in high regard, trying to lure him back from private practice to become his "personal mentor" (Sullivan interview; Rissman interview). Casey's respect for Milton Cohen meant that the latter was able to secure a meeting with him to go through the arguments in favor of an organized options exchange. Although members of his staff were still skeptical, Casey was convinced, saying to Cohen: "Tell me what kind of order you need from the Commission to get started." (Milton Cohen, in CBOE/OCC 1998b) On April 26, 1973, the Chicago Board Options Exchange opened.

On the Mercantile Exchange, similarly, Leo Melamed devoted large amounts of time he could otherwise have spent on profitable trading to leading its move into financial derivatives. He continued to trade in the pits (part of his authority came from the fact that he led the Merc from there), but his duties chairing the Merc often kept him from paying full attention to trading, and he suffered losses. … However, Melamed rejected all proposals to pay him until the need to respond to the crisis of 1987 made clear that "the demand on my time was such that I could no longer trade effectively" (Melamed and Tamarkin 1996, p. 281). Furthermore, although the Merc's financial derivatives trading became profitable and self-sustaining, there were as discussed below periods in which Melamed had to encourage the Merc's members to take part in it even if their profits were likely to be low He could not instruct them to do so: he was their elected representative, not their employer. All he could do was to seek to persuade them to act for the collective good of the exchange.

As Olson (1980) famously argued, collective action cannot satisfactorily be explained simply by the fact that it was in the collective interest of all those involved, in this case the memberships of the Board of Trade and the Merc. All their members benefited, even those who stood aside from it entirely. In such a situation, rational egoists the individuals posited in much of orthodox economic theory will free ride, leaving it to others to bear the costs of collective action, which will therefore not take place, even if it would foster the interests of all involved. Hence the possibility of a delightful paradox: the very markets in which Homo economicus, the rational egoist, appears to thrive cannot be created (if they require the solution of collective action problems, as in Chicago) by Homines economici.

Certainly, the accounts of their motivation provided by central actors in the move to financial derivatives are not of rational egoism. Leo Melamed's admiration for Friedman sat alongside a political inheritance of quite a different sort. When I asked him why he devoted effort to collective projects, Melamed cited the influence of his father, a member of the Jewish revolutionarysocialist Bund (Melamed interview). Even as a child, Melamed recalls, he was "able to sense the intense feelings [the Bund] generated" in his parents (Melamed and Tamarkin 1996, p. 22). "I will never forget," he says, "being wedged between them standing rigidly erect at Bund meetings in Bialystok that opened with the Shvue, the Bund's anthem an oath of allegiance. My mother held my hand tightly as she and my father sang, and I could feel the emotional choking that gripped both of them as they fervently swore never to forsake the battle on behalf of the working class. There among the mass of people with the decibels ringing in my ears, I knew something was going on, something big, something awe-inspiring, something eternal."

Had it not been for the escape route offered by Sugihara's letter of transit, Melamed's parents would have joined the Bundist partisans in the forests of Lithuania in armed resistance: it was, for example, members of the Bund who led the heroic, doomed uprising of the Warsaw ghetto in April 1943. Melamed disavowed his parents' socialism "Adam Smith taught me that you serve society best by caring for yourself" (Melamed interview) but he never abandoned their sense of the moral demands of the collective. … "My father had instilled in me [the] idea that you gain immortality by tying yourself up with an idea, or a movement, or an institution that transcends mortality" (Melamed interview). The very name of the world's first successful modern financial derivatives exchange, the Merc's "International Monetary Market," was a private homage to a socialist. It shared its initials with Melamed's father, Isaac Moishe Melamdovich.

"We... never thought of even asking for reimbursement [of expenses involved in creating the options exchange]," says Gorky Eisen of the Board of Trade. "This was part of the concept that was inculcated into all of us: `You owe it to your community.' We had all done very nicely, thank you ... and we felt that we had an obligation to the exchange and this is how you pay your obligations." (Eisen, interviewed by Millo10) Of course, avowals of altruism sometimes mask self-interest, but for a rational egoist to embark on a project like the creation of the International Monetary Market or the Chicago Board Options Exchange, in a context in which all others are rational egoists, is implausible.

Of course, avowals of altruism sometimes mask self-interest, but for a rational egoist to embark on a project like the creation of the International Monetary Market or the Chicago Board Options Exchange, in a context in which all others are rational egoists, is implausible. A risk-neutral egoist would need to be confident that the expected personal benefits of the creation of the new markets exceeded the total costs of establishing them (others must be expected to free-ride, so the founder must expect to bear all these costs); for a risk-averse egoist, the excess might have to be considerable. Given the considerable ex ante uncertainty whether the new markets would prosper many members of the Board of Trade opposed the options exchange as a likely waste of money these conditions are unlikely, and my interviews give no suggestion that they were met.

Actions that are seen as unduly opportunistic are punished by "freezing out," and actions that are perceived as in the common good are rewarded with "respect" (Melamed interview). Generosity gives rise to obligation, sometimes between generations rather than in the form of mutual reciprocity.

"Corky" Eisen, Power's second "godfather," reports: … I ... came to the Board of Trade as a clerk at the age of twenty.... One of my mentors was an Irishman by the name of Jim McKerr.... He brought me in as a clerk, financed me, loaned me ... the money to buy the membership.... When I came back from the service (Korea), things were tough then. I went to work for another Irishman, Bill Haggerty senior.... They were wonderful to me and when I got my membership back he wanted me to clear through him. I told him ". . . I have an obligation to Jim McKerr, and I'm going to clear and be his customer, not yours." I expected him to say "That's very nice, here's the door, goodbye." Instead he said "I can understand that. As a matter of fact, I respect you for it, your job here is secured." . . . So I remained McKerr's customer. I felt obligated. In about two years I developed into a pretty good trader ... but I realized the only way I could survive and compete was to become a [clearing] member. I still didn't have any money because in those two years I was paying lots of debts. I was now even. I went to Jim McKerr (that was in 1956) and said "I'm going to start clearing." He said "That's wonderful ... but what are you going to do for money?" ... My share was $15,000 in order to start a clearing firm and Jim said "Okay" and reached in his pocket and wrote me a check for $15,000. I didn't even ask. I said "How in the world can I ever thank you?" And he said "You have a debt, but the debt is to youngsters that come on after you. You can repay me by helping other kids." . . . Many years later, when the Options Exchange was in existence, I was a clearing member and I was taking a lot of young floor traders as customers. One day Jim McKerr came visiting from Florida ... he was 80 years old.... One of the kids jumped and gave him a big hug. Jim looked at him he was rather reserved and said "What's that for?" And the guy said "Dlr. McKerr, I owe my career to you. Whenever I came to Corky [Eisen] to thank him, he told me about you and he said that he was returning your help." When I took him down to lunch there must have been twenty people who shook his hand, people he had never seen or heard of. But this was his legacy and we have passed it on. (Eisen, interviewed by 1\1i11o) "Respect" and "obligation," in their turn, are resources for moral suasion.

"Respect" and "obligation," in their turn, are resources for moral suasion. The need for collective action did not cease once financial derivatives began to be traded. Members of the Board of Trade and of the Mere had to be persuaded to spend some time, and devote some money, to trading the new products, even though they might not at first offer the same opportunities as more familiar commodities: as the new markets were established, trade in agricultural futures was reviving, for example with the beginning of grain sales to the Soviet Union.

When the Mere launched the S&P 500 index futures discussed below, Melamed was similarly active in pressuring and persuading its members to trade the new product. Other traders would show him their time-stamped trading tickets to demonstrate that they had done the 15 minutes of trading per day on the nascent market that Melamed demanded. They would be "ashamed not to" do this minimum for the collective good, says Melamed (interview).

Nor did the social structure of the Chicago exchanges cease to matter once the International Monetary Market and Chicago Board Options Exchange became large and successful (by 1978, more than 100,000 options contracts, each corresponding to 100 shares, were traded on an average day on the latter).' Baker (1981; 1984a,b) examined the pattern of trading and the behavior of prices in two options trading "crowds," one large and one small. After taking account of the volatility of the underlying stocks, Baker found that contrary to standard economic predictions, option prices were more volatile in the larger crowd, an effect he explained by the tendency of this crowd to fragment into subnetworks when trading was intense.

Viewed from the galleries from which (before September 11, 2001) visitors could watch, Chicago's pits could appear to be places of frenzied chaos. Those who trade in them, however, do so day after day, and, especially in the smaller pits, they are normally trading repeatedly with the same people. Traders often stand in the same spot every day, and where one stands is consequential. There is a spatial hierarchy in Chicago's pits, as Caitlin Zaloom (2004) found in the pits of the Board of Trade and as Cari Lynn (2004) found at the Mercantile Exchange. Novice traders begin at the bottom, in what is sometimes called "the soup," and as they gain in seniority, in capital, and in ability to take on larger trades, they are allowed gradually to move up the steps of the pit.

This, then, is the environment into which Black-Scholes-Merton option theory was launched in 1973 (I will return below to the simpler theory of futures prices). The theory's abstract mathematics might seem to inhabit a world quite different from the deeply social, intensely bodily interaction of trading pits. The Black-Scholes-Merton model, however, began to have effects on the Chicago Board Options Exchange almost immediately. Even more effectively than the economics of Baumol, Malkiel, and Quandt, the Black-Scholes analysis enabled the Options Exchange to rebut the charge that options were morally disreputable.

The former counsel of the Chicago Board Options Exchange, Burton R. Rissman, told me that even after it opened it still faced the stigma of the association with gambling. For example, he visited a senior official of the Federal Reserve to try to persuade her to interpret its Regulation T, which restricts the extension of credit for the purchase of stocks, in a way that would facilitate the hedging of options by the exchange's market makers. On her desk was spread out a Wall Street journal article on options, "and I could see, as I sat there, that some places were underlined in red ... Everywhere that was underlined was the word `gambling."'

As the work of Black and Scholes became well known, it undermined the long-standing cultural association between options and gambling: … Black-Scholes was really what enabled the exchange to thrive.... It gave a lot of legitimacy to the whole notions of hedging and efficient pricing, whereas we were faced in the late 60s-early 70s with the issue of gambling. That issue fell away, and I think BlackScholes made it fall away. It wasn't speculation or gambling, it was efficient pricing. I think the SEC very quickly thought of options as a useful mechanism in the securities markets and it's probably that's my judgment the effects of Black-Scholes. I never heard the word "gambling" again in relation to stock options traded on the Chicago Board Options Exchange. (Rissman interview) That the theoretical work of Black and Scholes could effectively be deployed to defend options' legitimacy did not, however, mean that the theory was adequate as an empirical description of prices.

That the theoretical work of Black and Scholes could effectively be deployed to defend options' legitimacy did not, however, mean that the theory was adequate as an empirical description of prices. As we saw in chapter 5, when Black and Scholes tested their formula against prices in the ad hoc New York options market, they found only approximate agreement (Black and Scholes 1972).

Galai had, of course, all the advantages of the academic. He was investigating hypothetical trading strategies using past price data supplied on punched cards by the Chicago Board Options Exchange. He had available to him programming assistance and the University of Chicago's powerful computers. Could the Black-Scholes-Merton model be used not in these favorable circumstances but in the bodily hubbub of a trading floor?

The Black-Scholes-Merton model's core was a differential equation that would have been opaque to anyone without college-level training in mathematics. Even in the simplest case, a call option on a stock that pays no dividend (appendix D, equation 2), an unaided human being cannot realistically be expected to calculate a Black-Scholes price. At the very least, a table of natural logarithms and of the distribution function of a normal distribution are needed.

In the 1970s and for most of the 1980s, it would have been against the rules of the Chicago Board Options Exchange to use a computer on the trading floor, and to my knowledge no one tried: the computers of the period were too cumbersome. … Most traders seem to have regarded calculators as too slow for use in a pit. Even the few seconds it would take to input parameter values and wait for a solution could mean a loss of profitable trading opportunities. Furthermore, making the necessary adjustment to take into account the payment of dividends was "difficult and time-consuming." In consequence, few "use [programmable calculators] regularly for option evaluation after the initial novelty wears off" (Gastineau 1979, pp.

Instead, an old technology paper was the most important mediator between the mathematics of the Black-Scholes-Merton model and what was sometimes the scrum of human bodies on trading floors. Away from the hubbub, computers were used to generate Black-Scholes prices. Those prices were reproduced on sets of paper sheets which floor traders could carry around, often tightly wound cylindrically with only immediately relevant rows visible so that a quick squint would reveal the relevant price.

At first sight, Black's sheets look like monotonous arrays of numbers. They were, however, beautifully designed for their intended role in "distributed cognition" (Hutchins 1995a,b). Black included what options traders using the Black-Scholes-Merton model needed to know, but no more than they needed to know There was virtually no redundant information on his sheets hence the sheets' easy portability. Black devoted particular care to the crucial matter of the estimation of volatility.

Even the physical size of Black's sheets was well judged. They had first to be printed on the large computer line-printer paper of the period, but they were then photo-reduced onto standard-size paper, differently colored for options traded on different exchanges. The resultant sheets were small enough for easy handling, but not so small that the numbers became too hard to read.

The care that Black put into his sheets does not, of course, explain why they were bought and used. Not all options traders believed using sheets was necessary. The options trader Blair Hull reports that he was mocked for using them. Fellow traders "would laugh at you and try to intimidate you out of the pit, saying `You're not a man if you're using those theoretical value sheets.' They'd take your sheets and throw them down on the floor and say Be a man. Trade like a man.... You shouldn't be here. You're not a trader. You can't trade without those."

Why might a participant in the options market in the 1970s have chosen to use Black's sheets or another material implementation of the Black-ScholesMerton model? One factor could have been the authority of economics. Financial economists quickly came to see the Black-Scholes-Merton model as superior to its predecessors. It involved no non-observable parameters except for volatility, and it had a clear theoretical basis, one closely linked to the field's dominant viewpoint: efficient-market theory.

However, while there were a number of participants with links to academia, Chicago floor traders in general were and are not in awe of professors. From their viewpoint, however, the model had the advantage of "cognitive" simplicity. The mathematics of the solutions to the Black-Scholes equation might be off-putting (especially when one had to consider dividend-bearing stocks and American puts), but the model could be talked about and thought about relatively straightforwardly.

The Black-Scholes-Merton model's one free parameter (volatility) was easily grasped, discussed, and reasoned about. Other models including some of the variants of and modifications of Black-Scholes-Merton that were offered by other financial economists typically involved a mental grasp of, and estimation of, more than one free parameter often three or more. As The Stock Options Manual put it, "the user of these complex models is called upon to deal with more unknowns than the average human mind can handle" (Gastineau 1979, p.

Another factor underlying the success of the Black-Scholes-Merton model was simply that it was publicly available in a way many of its early competitors were not. As U.S. law stood in the 1960s and the 1970s, it was unlikely that an options pricing model would be granted patent or copyright protection, so there was a temptation not to disclose the details of a model. Black, Scholes, and Merton, however, did publish the details, as did Kassouf (whose model was described in his Ph.D. thesis, and thus was available for use by options pricing services). Keeping the details private may have been perfectly sensible for those who hoped to make money from their models, but it was a barrier to the adoption of those models by others.

The situation was perhaps akin to the triumph of the publicly available IBM PC architecture over rival architectures, especially Apple's. The architecture of IBM personal computers may well not have been better than Apple's proprietary architecture, but IBM's design (like the Black-Scholes-Merton model) was available for others to adopt while Apple's was not.

The options traders who used Black's sheets or other implementations of the Black-Scholes-Merton model hoped, of course, to make money. The most obvious way of doing that was to put into practice the arbitrage strategy inscribed in the model's derivation. One could use the model to identify options that were overpriced (or underpriced) relative to their theoretical values, sell them (or buy them), and hedge the risk by taking and adjusting a position in the underlying stock. Black's sheets included not only theoretical prices but also the "delta" values that told subscribers how big that hedging position in stock should be.

However, any floor trader on the Chicago Board Options Exchange could practice "spreading" (Black 1975a, pp. 39-40; Galai 1977, pp. 189-194). This operation which appears to have been practiced widely involved using the model to identify pairs of options on the same underlying stock, in which one option was, according to the model, underpriced relative to the other. Traders could then buy the underpriced option and sell its overpriced counterpart, and applying some simple arithmetic to the numbers on Black's sheets showed how to minimize exposure to the risk of fluctuations in the price of the underlying stock: one made the sizes of purchases and sales inversely proportional to the deltas of the options in question.

The "Introduction" to his options service that Black circulated gave simple instructions how to identify and to exploit opportunities for spreading (Black 1975b, p. 7). Spreading avoided both the difficulties of the more basic BlackScholes arbitrage strategy described above. It was "less sensitive to the estimated volatility of the stock" because "an increase in the volatility estimate will increase the value of all the options on a stock" (Black 1975a, p. 40), and it did not require purchases or sales of stock: it required only purchases and sales of options.

At first, the correspondence between the Black-Scholes-Merton model and patterns of prices on the Chicago Board Options Exchange was fairly poor. Soon, however, it began to improve. The most thorough tests of fit were conducted by Mark Rubinstein (1985), using a subset of a huge data base of nearly all Chicago Board Options Exchange price quotations and transactions between August 1976 and August 1978.

A fundamental aspect of what Rubinstein did was, therefore, to check the empirical validity of a basic feature of the Black-Scholes-Merton model: "that all options on the same underlying asset with the same time-to-expiration but with different striking prices should have the same implied volatility" (Rubinstein 1994, p. 772). In other words, Rubinstein checked whether the graph of implied volatility against strike price was a flat line, as it should be on the model. There was thus a homology between the econometric testing of the Black-Scholes-Merton model and the trading-floor use of the model in "spreading." When spreaders used the model (for example, by following the instructions that accompanied Black's sheets) to look for discrepancies, it would be precisely deviations from that flat line that they would have identified and that their activities would have tended to "arbitrage away." It seems, therefore, that the model may have been helped to pass its central econometric test "with remarkable fidelity" (Rubinstein 1994, p. 772) by the market activities of those who used it.

If my conjecture is correct (and though it is plausible, the available evidence does not permit certainty), it would constitute a form of performativity that is, in the terminology of chapter 1, Barnesian. There, I quoted Barry Barnes's succinct summary of his viewpoint: "I have conceived of a society as a distribution of self-referring knowledge substantially confirmed by the practice it sustains" (Barnes 1988, p. 166). The Black-Scholes-Merton model was used in the practice of arbitrage especially, but not exclusively, in "spreading" and the effects of that arbitrage seem to have been to move patterns of prices toward the postulates of the model, in particular on Rubinstein's test. The "practice" that the Black-Scholes-Merton model sustained helped to create a reality in which the model was indeed "substantially confirmed."

The effects of the use of the Black-Scholes-Merton model in arbitrage thus seem to have formed a direct performative loop between "theory" and "reality." Markets were, however, also changing toward greater conformity to the model for reasons in which the model was not directly implicated. In 1973, Black, Scholes, and Merton's assumptions were wildly unrealistic. Stock, for example, could not be bought entirely on credit: it had been the constraint this placed on market makers' capacity to hedge using stock that Rissman had been trying to have removed during his unsuccessful visit to the Federal Reserve.

If an options trader did not belong to a member firm of the New York Stock Exchange, stock transactions incurred, as noted above, significant commissions. The information on stock prices needed to price an option and to create and adjust a hedge was often not available quickly: at first, the electronic "feed" conveying prices from New York to Chicago was relatively slow. Purchases and sales of stock took time, and "to place a stock order, a marketmaker must leave the options trading crowd (or at least momentarily divert his attention from options trading activity), and, as a result, may lose the opportunity to make an advantageous options trade" (SEC 1979, pp. 139-140).

Gradually, though, many of the Black-Scholes-Merton model's assumptions gained greater verisimilitude. Stock borrowing became easier, for example as the trust departments of U.S. banks began to be prepared to lend out stocks owned by their clients (Faulkner 2004, p. 47), and the balance of market power began to shift, with borrowers obtaining increasing proportions of the interest on the proceeds of short sales (Thorp interview). A protracted struggle over the New York Stock Exchange's fixed commissions ended with their abolition in May 1975. The speed of transmission of stock prices from New York to Chicago was increased, and better communications and increasing automation made it quicker and easier to adjust the replicating portfolio.

It was even proposed that if the limit on the extension of credit to purchase stocks laid down by the Federal Reserve were to be removed for hedging by market makers on options exchanges, the Black-Scholes model would be used, performatively, to determine the quantity of stock purchases that constituted a bona fide hedge and that were therefore eligible for unrestricted credit. Had this proposal been accepted, it would have been another delightfully direct loop of performativity the Black-Scholes model deployed to make one of its assumptions a reality but the Federal Reserve rejected the idea. The Federal Reserve nevertheless permitted options market makers unrestricted use of credit for their options positions and, at least in some cases, 75 percent credit for stock bought as a hedge.

Gradually, too, the culture of the Chicago Board Options Exchange changed. Initially, it was (as noted above) allowed to trade only call options, and it did so in a bear market, in which calls with high strike prices seemed always to expire unexercised, because the stock price remained below the strike price. A good income could therefore apparently be earned by selling those calls without bothering with theory or hedging. "Sell the 280s and drive a Mercedes" became the motto of at least some traders, referring to high-strikeprice ($280) calls on IBM, then the stock on which options were most heavily traded (Doherty interview).

One manager, Michael Greenbaum, tried to teach option theory to market makers: "He'd stay late to give seminars and two people would show up, and it would be Joe Doherty [Sullivan's deputy, who became an options trader] and somebody else, and they were already fully sold disciples.... He's trying to bring in some new technology [option-pricing theory] and nobody would use it or pay for it." (Carusillo and Struve interview 1) However, a sudden surge in stock prices in April 1978 caused huge losses to market makers who had sold large numbers of insufficiently hedged calls, and some were forced out of the market: those who had sold the 280s lost their Mercedes, so to speak.

However, a sudden surge in stock prices in April 1978 caused huge losses to market makers who had sold large numbers of insufficiently hedged calls, and some were forced out of the market: those who had sold the 280s lost their Mercedes, so to speak. Gradually, Chicago options market makers began to develop a distinct self-identity in which careful pricing and hedging were important. On the agricultural futures exchanges, the stereotypical belief was "I got the trade 'cause I'm faster than you, buddy." In New York, it was "I got the trade 'cause I'm here" that is, because I am the designated specialist. In the Chicago Board Options Exchange's growing self-perception, it was "I got the trade 'cause I thought it out" (Doherty interview).

As the options markets grew, and the SEC relaxed, options were traded on more stocks, some no longer "blue chip" corporations but instead highly volatile newcomers. More expensive errors made pricing models seem indispensable: "I'll stand in a pit with [options on] 16 stocks that each trade two [expiration] months and five strike prices and I'll take anybody on: turn off the lights, I want to trade with no electronics. But when you get to multiple expirations, strike prices, higher volatility stocks ... volatility changes by 10 percent. Arco goes from a 15 to a 13.5 [annualized percentage implied volatility]. I can do that math in my head. [With a highly volatile stock] 150 to 135 seems like it ought to be similar, but ... I've got too much money at risk if I'm wrong in my mental calculations."

The gradual "mathematicization" of options trading did not mean abstraction from the dense, bodily, spatial social structures of Chicago pit trading: mathematicization took place through those structures, not despite them.

The socio-spatial structures of different exchanges, however, affected the ease with which the mathematical relation between put and call prices was maintained. The first exchange to join Chicago in trading options was the American Stock Exchange (Amex). The social structure of trading on the Amex differed from that in Chicago. Like the New York Stock Exchange, the Amex had "specialists" who maintained "books" of buy and sell orders and matched those orders. When options trading began at the Amex, the specialist system was extended to it, while in Chicago the privileges of the specialist were anathema because of the tradition of competitive market makers with equal formal rights. … In Chicago, market makers quickly learned how to profit from discrepancies between put and call prices, and violations of put-call parity were typically evanescent. In busy classes of options at the Amex, however, it was found necessary to have two specialists (both members of the same firm), one taking responsibility for trading in calls and the other for trading in puts. … Apparently there were many more breaches of put-call parity on the Amex, and these could be exploited by traders who stood between the two specialists monitoring the prices at which each would deal. "What a dream world that was.... They [the specialists] didn't know ... what [the other specialists were] doing. They were doing okay on their own, but they didn't coordinate.... He's the call specialist, you're the put specialist. And you don't even stand real close to each other."

It remained the case that, in the words of judge George H. Painter in 1976, "the possibility of delivery on the exchange is the single element distinguishing futures trading from wagering" (Tamarkin 1993, p. 172). So an index future that could be settled only in cash was still illegal.

Melamed's main motivation, however, was that a federal agency could "give that edict about cash settlement" (Melamed interview). The original 1974 charter of the Commodity Futures Trading Commission preempted the laws of individual states, so if it approved cash-settled futures contracts they would no longer conflict with state gambling laws (there was no federal prohibition on gambling).

Philip McBride Johnson, who in 1974 was Counsel to the Chicago Board of Trade, and who later chaired the Commodity Futures Trading Commission, said that this broad, apparently vague phrasing was deliberate: "To have offered the word securities' would have set off alarms through the SEC [Securities and Exchange Commission], which was at best a casual observer through most of the legislative process. Instead we offered a definition of 'commodity' that would include the phrase services, rights and interests,' believing one or more of those words would capture securities (to which the courts have subsequently agreed). This seemingly benign phrase was readily adopted."

The careful wording kept the financial derivatives traded by the Merc and the Board of Trade in the 1970s under the jurisdiction of the Commodity Futures Trading Commission, and away from that of the SEC. But despite having failed to notice the threat to its "turf" contained in the 1974 wording, the SEC could not fail to be aware of and unhappy about the emergence of new financial derivatives outside its jurisdiction. Allowing its regulatory rival authority over futures on stock indices would have been yet a further incursion into its "turf."

The problematic feature of stock index futures from the viewpoint of the gambling laws cash settlement turned into a resource from the viewpoint of negotiating the jurisdictional dispute between the Commodity Futures Trading Commission and the SEC. "We aren't delivering stocks, you know," argued Melamed. "We are never going to deliver stocks. This is cash settlement.... It's not necessarily a security. It isn't anything, in fact." (ibid.) … In December 1981, John Shad of the SEC and Philip McBride Johnson of the Commodity Futures Trading Commission agreed that a cash-settled futures contract on a sufficiently broad stock index fell within the latter's jurisdiction, and the Shad Johnson Accord was enacted into law by the U.S. Congress in 1982 (Brady Commission 1988, pp.

The Merc's lawyers had told Melamed that no agreement was needed: "... they [the Standard & Poor's Corporation] don't own the index. Nobody owns an index.... It's ... public domain." (Melamed interview) Indeed, when Melamed went to see Brenton W. Harries, the president of Standard & Poor's, "he looked at me as if I was ... from Mars," asking Melamed "You want to pay me for something we're giving away for free?" (Melamed interview) … The Merc's apparently unnecessary expense turned out to be a wise investment. The Board of Trade decided to offer futures on the Dow Jones industrial average, and took the stance that the index was in the public domain, but then lost a court battle with Dow Jones. So it ended up trading futures on the Amex's much less well known Major Market Index, which was only a partial proxy for the Dow Jones.

Kansas City was a peripheral market that needed a boost, so Susan M. Phillips of the Commodity Futures Trading Commission (CFTC) requested that the Merc not insist on its priority over it and over the New York Stock Exchange's newly established futures exchange. After a decade plotting the path to the "ultimate contract," Melamed must have been tempted to insist on being the first to trade it, but he knew that "a favor of this kind to the CFTC would pay many dividends in the years ahead" (Melamed and Tamarkin 1996, p. 295). So Kansas City, not the Merc, was the first to trade index futures.

A market, says Melamed, "is more than a bright idea. It takes planning, calculation, arm-twisting, and tenacity to get a market up and going. Even when it's chugging along, it has to be cranked and pushed." (Melamed and Tamarkin 1996, p. 295) Even once the Merc's S&P index futures were launched (on April 21, 1982) the political work of market construction did not end. Financial derivatives exchanges are subject to virtuous and vicious cycles: if trading volumes are high, exchanges are liquid and attractive places to trade, further enhancing volume; if volume starts to slip, liquidity can dry up and exchanges become fatally unattractive.

Melamed worried in particular about the competition from the futurestrading offshoot of the New York Stock Exchange, the world's most powerful exchange: "I tell you that I was scared of them." So "all chits were ... called in" by Melamed to ensure the success of the Merc's S&P futures. All those for whom he had done favors over the years were asked to return them by trading the new contract. Every member of the Mercantile Exchange was asked to spend at least 15 minutes every day trading in the S&P pit, and Melamed led the way by spending as much of every day as he could in the pit himself. "I used to meet with them in groups.... I would meet with them one on one. Whatever it took. Get 'em in the pit. Get 'em in the pit." (Melamed interview) A cash-settled index future contract worked and, some details aside, still works as follows.

A cash-settled index future contract worked and, some details aside, still works as follows. (I draw my example from Martin 1988, pp. 139-140.) Suppose the S&P 500 index level was 285.00, and a future on the index, maturing in three months, can be bought at 286.40. The "contract multiplier" in the 1980s was $500, so a single contract had a notional value of the index level (285) multiplied by $500, or $142,500. The purchaser of such a contract, however, had to deposit with the Mercantile Exchange's clearinghouse only an "initial margin" of $10,000 (which could, for example, be in the form of U.S. Treasury bills, so one does not have to forgo interest on the margin payment). The seller also had to deposit a similar margin.

The theoretical value of a future was not a "discovery" of finance theory; the analogous relationship between the value of a future, the price of the underlying asset, interest rates, and storage costs had long been understood by participants in commodity futures markets. The relationship between futures prices and index levels was, nevertheless, a relatively strict mathematical relationship-a "theorem," so to speak.

Index arbitrage thus has the potential to create an objective link between index futures and stocks. The theoretical value of an index future has nothing to do with opinions as to whether the price of stocks will rise or fall; like the theoretical value of an option, it is imposed by arbitrage. Arbitrage, therefore, had the potential to stop index futures being "a figment of Melamed's imagination," yoking them firmly to the prices of the underlying stocks.

In the early months of index futures trading, futures tended to be below their theoretical value. Stock prices were rising in retrospect, " 82 ... was the beginning of the big 80s bull market" but nobody, futures traders included, believed it. `As a result, the index futures, which weren't yet pegged to their correct value by lots of people doing arbitrage ... were cheap."

What is even more striking, because of the much greater complexity of the mathematical relationship involved, is the closeness with which the index options that also began to be traded in the early 1980s clustered around the Black-Scholes flat-line relationship between strike price and implied volatility. … The establishment of the Commodity Futures Trading Commission had freed the futures exchanges from the grip of state anti-gambling laws, but the options exchanges were still subject to them.

A floor below which the value of an asset cannot fall is, in effect, a put option on the asset: an option to sell the asset at the guaranteed price level. In principle, therefore, the value of a portfolio can be insured by buying a put on the portfolio with a strike price equal to the desired floor.

What Leland had seen, however, was that although suitable actual puts were not available, a pension fund or other investor that desired portfolio insurance could use option theory to "manufacture" a synthetic put. Qualitatively, what was needed was to shift between stocks and cash (or government bonds) as stock prices fluctuated, buying stocks as prices rose and selling them as prices fell. If the value of the stock portfolio fell toward its floor, more and more of it would be sold, so the overall impact on the portfolio of further declines in stock prices became less because fewer stocks and perhaps eventually no stocks were held. Option theory could provide quantitative guidance as to how to do that in such a way that the desired put would be replicated precisely.

In February 1981 the trio established Leland O'Brien Rubinstein Associates, Inc. (LOR) with "two part-time secretaries, one computer, and no clients" (Leland and Rubinstein 1988, p. 7).

Leland, O'Brien, and Rubinstein knew they did not live in what Leland called "a Black-Scholes world" (Leland 1980, p. 580), a world in which market conditions were as posited by option theory. As portfolio insurance was molded from idea to product, the underlying theory was developed to incorporate some of reality's imperfections.

However, as described in chapter 6, in April 1982 the Chicago Mercantile Exchange launched a futures contract on the S&P 500 index, the benchmark most widely used by portfolio managers. The introduction of index futures provided LOR with a far simpler way of implementing portfolio insurance, one that did not require interference with fund managers' holdings.

The close, arbitrage-imposed link between the price of futures and the level of the underlying index made it possible to implement portfolio insurance by buying and selling futures, rather than by buying and selling stocks, at least so long as the portfolio to be insured was highly correlated with the S&P 500, as well-diversified U.S. stock portfolios would be. As noted in chapter 6, a futures position equivalent to a huge position in stock could be constructed by making margin deposits that were a small fraction of the value of the underlying stock.

If index levels then fell, LOR would telephone instructions to Chicago to sell more futures; if they rose, it would buy futures. Futures traded in large volumes and could readily be bought and sold with low transaction costs, making "the protection of very large [portfolios] feasible for the first time.... As of the end of 1986, roughly 80 percent of the dollar value of LOR accounts was protected using futures." (Leland and Rubinstein 1988, p. 8) During the mid 1980s, portfolio insurance became big business.

During the mid 1980s, portfolio insurance became big business. By the autumn of 1987, the portfolio-insurance programs of LOR and its licensees covered $50 billion of stock (Mason et al. 1995, p. 786) with perhaps almost as much again covered by firms not affiliated with LOR (Voorhees 1988, p. 57). This success, however, began to cause Leland and Rubinstein to have misgivings. Although they had coined the term "portfolio insurance," they had reservations about it, preferring the broader and more neutral phrase "dynamic asset allocation." They knew that for all their technical innovations they had not freed themselves completely from the assumptions of a BlackScholes world.

"The analogy with insurance breaks down," they warned, if stock prices "gapped" downward, plunging discontinuously: there would not be "sufficient time to adjust the replicating portfolio" (Rubinstein and Leland 1981, p. 72). Such discontinuities were excluded, mathematically, from the Black-Scholes log-normal random walk, but could not be ruled out in practice.

LOR therefore added an "override" check to the Black-Scholes strategy. "Every day we would say `if we were to take all the money out of the market and put it in cash and hold it through the expiration date, would we be able to deliver the floor?"' (Rubinstein interview). For certain clients-such as the Aetna Life Insurance Company, which was literally, not just figuratively, insuring portfolios-LOR added "jump protection," working out whether their positions would meet the conditions of the above override check if markets fell by a set amount (around 6 percent) so quickly that the portfolio could not be adjusted at all (Rubinstein interview).

It was accepted by all involved that, at least in the absence of jump protection, portfolio insurance would fail if a dreadful external event caused the market to fall discontinuously if, as Leland warned pension fund officials, "one morning, we learn that the Russians have invaded Iran and all the Mideast oil supplies are being cut off" (Leland interview). What gradually became more salient, however, was a risk "internal" to the markets. In a BlackScholes world, adjustment of the replicating portfolio does not affect the price of the underlying stock, the market for which was implicitly taken to be large, liquid, and efficient: the Black-Scholes option-pricing equation "assumes that you can't affect either stock or options prices, by placing orders," wrote Fischer Black (1990, p. 13). Would that still be the case as portfolio insurance became big business?

Sales by a portfolio insurer as prices fell were an "informationless," mechanical response to changing prices, so in an efficient market they should not affect stock prices, which should be determined by the tradeoff of risk and expected return discussed in chapter 2. That prices were governed by that tradeoff was the reasoning of Myron Scholes's Ph.D. thesis, but it was not peculiar to Scholes; it was a fundamental tenet of finance theory.

When portfolio insurance was small-scale, the assumption that the stock and futures markets were external "things" in which prices would not be affected significantly by the insurers' purchases or sales was plausible enough. But what if portfolio insurance was adopted widely? In January 1983, after attending an LOR presentation, Bruce Jacobs of the Prudential Insurance Company of America wrote in a memo to his employers (reproduced in Jacobs 1999, pp. 301-304) that "if a large number of investors utilized the portfolio insulation technique, price movements would tend to snowball. Price rises (falls) would be followed by purchases (sales) which would lead to further price appreciation (depreciation)."

By June 1987, the portfolios "insured" by LOR and its licensees were sufficiently large that Leland was pointing out that "if the market goes down 3 percent, which, in those days, would have been a very large one-day move, we could double the volume [of trading] in the New York Stock Exchange" (Leland interview). (Although by then LOR's portfolio insurance was implemented primarily with futures, index arbitrage would transmit selling pressure from the futures to the stock market.) With sales on that scale, would informationless selling really have no effect on prices?

"We had one client come to us who had a huge pension plan," says Rubinstein. "We wanted to tell that client that was too much money for us to handle. We were just too worried about the impact that the trading would have on the markets." If LOR refused the client's business, however, "he'd go somewhere else" to one of the growing number of other firms also offering portfolio insurance (Rubinstein interview).

"It was as if Pandora's box had been open [ed]" (Rubinstein interview): "we could shut our doors, but that wasn't going to stop anything" (O'Brien interview). LOR's principals did not envisage a catastrophic crash they assumed, as had Jacobs, that "savvy investors" (Jacobs 1999, p. 303) would step in to exploit and thus limit the mispricings induced by positive feedback but they suspected that market volatility could be increased. "If that's what people want to do [purchase portfolio insurance]," they thought, "then the market should be more volatile. There's nothing necessarily bad about it" (Rubinstein interview).

Rubinstein's concerns were, however, brought into focus by a sharp market decline on September 11 and 12, 1986. On September 11, the Dow Jones industrial average fell 4.6 percent, its largest one-day fall for nearly 25 years (SEC 1987, p. 1). The Securities and Exchange Commission (SEC) investigated, and "concluded that the magnitude of the September decline was a result of changes in investors' perception of fundamental economic conditions, rather than artificial forces arising from index-related trading strategies."

Rubinstein believed (but could not prove) that the SEC was wrong, and that the pressure of futures selling by portfolio insurers had been critical. He told the SEC, but did not publish his concerns: "for the first time in my career I had a conflict of interests.... I wasn't sure about it and I didn't want to stick my neck out and do a thing that would have hurt the business."

The events of September 1986 were followed by another sharp decline on January 23, 1987, but those falls seemed minor reversals in a prolonged international bull market that saw the S&P 500 index almost triple between 1982 and September 1987, with a similar rise in London and an even greater rise in Tokyo. The demons of the 1970s high inflation, oil shocks, bitter labor disputes, stagnation seemed to be receding, banished by liberalized markets, monetarism, Reaganism, Thatcherism, and by the vogue for aggressive financial management, exemplified by the audacious acquisitions of big, staid corporations by raiders with good access to the market in "junk" (lowerthan-investment-grade) bonds.

On Wednesday October 14, disappointing data on the trade deficit and moves by the Ways and Means Committee of the House of Representatives to remove tax advantages that had contributed to the mergers and acquisitions boom led to what was then the largest number of points ever lost by the Dow Jones average in a single day.

On Monday October 19 the London market fell some 11 percent (Anonymous 1988a, p. 52), and in New York where the trading day is several hours later than London's, because of the time zone difference the Dow fell 22.6 percent. It was its largest one-day fall ever, worse even than its worst individual days in the Great Crash: the 12.8 percent fall on October 28, 1929, and 11.7 percent fall on October 29, 1929 (Schwert 1990; Brady Commission 1988, p. 1).

As alarming as the size of the crash were the breakdowns in markets that accompanied it. The printers at the specialists' booths on the New York Stock Exchange could not keep up with the waves of sell orders arriving through the semi-automated DOT (Designated Order Turnaround) system, and there were also serious network delays and software problems (Brady Commission 1988, pp. 48 and VI-47).

In Chicago, extraordinarily sharp declines in index futures prices began. Brokers acting for external customers, notably for portfolio insurers, had to implement large "sell orders." As they did, index futures prices plunged far below the theoretical values implied by the levels of the index. … Normally, if the futures price fell substantially below its theoretical value, the discrepancy would be corrected by index arbitrage. However, the trading disruptions in New York broke the link that arbitrage established between the stock and futures markets.

The network delays on October 19 hampered index arbitrage, and at 9:30 A.M. on October 20 the New York Stock Exchange imposed what was in effect a prohibition on use of DOT for arbitrage (Brady Commission 1988, p. III22). In addition, the ends of the automated chain were human beings: the specialists on the floor of the exchange. It was they who had to turn an index arbitrageur's DOT order, arriving on printers at all the specialists' posts at which S&P 500 stocks were traded, into completed transactions. Many were unable or unwilling do to so. They could not find buyers to match with sellers and, with their own capital evaporating, they feared bankruptcy if they stepped in to remedy the imbalance (as their regulatory obligations said they should).

For example, Edward O. Thorp, whose work on option pricing was discussed in chapter 5, was involved in the 1980s in index arbitrage via the firm he co-founded, Princeton Newport Partners. He recalls great difficulty in getting his firm's trader even to attempt arbitrage on October 20. He was able to persuade him only by threatening to do it on his own account and telling him "I'm going to hang you out to dry" because the firm would then get no share of the profit. The trader was able to make only around 60 percent of the short sales Thorp had instructed, but Thorp had anticipated this by telling him to attempt twice the theoretical quantity (Thorp interview).

Although it was the price falls on Monday October 19, 1987 that hit the headlines, the hours of greatest systemic danger came that night and on Tuesday morning. The events with which I began this book were not public knowledge at the time, but enough leaked out for "rumors about the financial viability" of the Mercantile Exchange's clearinghouse to sweep the markets on the Tuesday morning (Brady Commission 1988, p. 40). Since the clearinghouse stood behind all the billions of dollars of futures traded by the Mere, it was a central part of the financial infrastructure of the United States, and the possibility of its failure was a source of deep alarm.

Later, there was speculation that the purchases were "part of a desperate attempt to boost the Dow and save the markets" (Stewart and Hertzberg 1987, p. 23). If that were so, the choice of instrument was shrewd. Like the other stock-index futures, Major Market futures had been trading far below their theoretical values. Their rapid rise took them to a premium, to prices above theoretical values. As the news reached New York, it was a much-needed fillip to morale. Within a few minutes, at around 12:45 P.M., it was followed by some orders to buy stocks, as arbitrageurs began to restart trading to lock in the profits that the premium offered despite, as one of them later put it, feeling "terrified of the market" (Stewart and Hertzberg 1987, p. 23). 17 of the Major Market Index's 20 stocks were also in the Dow Jones 30-stock industrial average, so the purchases were largely in the stock of corporations whose prices shaped the publicly most salient market index.

As arbitrageurs' purchases began, the programs, noted in chapter 1, that corporations were announcing to buy back their stock also started to have effects. Gradually, New York's specialists received enough "buy" orders to resume trading. Phelan had wanted to keep the New York Stock Exchange open. That morning he had received a private appeal from the White House not to shut the exchange, and he also feared that closure might be permanent. "If we close it," he later recalled thinking, "we [will] never open it."

Portfolio insurers performed quite credibly in protecting their clients' "floors" in the exceptional conditions of October 19 and 20. Although slow futures sales meant LOR was "underhedged by 50 percent" on October 19, it "still met its floor for 60 percent of its clients" with the rest of its accounts suffering "floor violations that ranged between 5 and 7 percent" (Voorhees 1988, p. 57).

The problem, though, was that many portfolio insurance accounts were then "stopped out." They were in effect completely in cash (the futures sales needed to try to protect "floors" had been equivalent to the entire insured portfolio), and the only way in which LOR or the other portfolio insurers could continue to guarantee the "floor" was to leave them in that condition (see, for example, Rubinstein 1988, p. 40). Unless insurers' clients were prepared to accept an ad hoc downward revision of their floors, they thus had entirely to forgo the benefits of subsequent stock-price rises. Given the extent to which stock prices recovered, that turned out to be a significant cost.

The crash was a grotesquely unlikely event on the log-normal model of stock-price movements underpinning that theory. In terms of the log-normal model, the fall on October 19 of "the two month S&P 500 futures price ... is a -27 standard deviation event with probability 10-160" (Jackwerth and Rubinstein 1996, pp. 1611-1612).

Detailed analysis by the task force led by Nicholas Brady found that on October 19 portfolio insurers directly sold almost $2 billion in stocks (nearly 10 percent of that day's volume of trading on the New York Stock Exchange). They also sold S&P 500 index futures equivalent to stocks worth $4 billion, more than 40 percent of externally generated trading in those futures (Brady Commission 1988, p. 36).

By 1987, the technique was beginning to be adopted outside the United States, but nowhere else had it achieved anything like its scale in the United States. Since all of the world's major stock markets crashed, by amounts often similar to or in some cases even worse than in the United States (Roll 1988), specific features of the U.S. market such as portfolio insurance might seem to be incidental.

To the extent that fears of a crash had been widespread in the months preceding October 1987 and Shiller's survey suggests they were they would help to explain the growing popularity of portfolio insurance, and also would add an element of self-fulfilling prophecy to the October events: large numbers of investors who feared a crash responded to price declines by all running for the exit and finding "it was large enough to accommodate only a few" (Brady Commission 1988, p. 57).

It is also perfectly possible that to inquire into the causes of the crash is to ask the wrong question. The fundamental challenge posed by the October events to efficient-market theory is to explain why such large price movements took place in the absence of major new information about economic prospects and the situation of America's corporations. From this viewpoint, it may be the rebound in the afternoon of October 20 and on October 21 that is more challenging to explain than the price declines on October 19, for which reasonably plausible explanations, broadly compatible with economic orthodoxy, can be found.

The question of what caused the crash of October 19 was important as events unfolded, not just retrospectively: how participants behaved on the Tuesday and Wednesday was affected by their beliefs as to the cause of Monday's events.

Given the ambiguity of the evidence and the depth of the underlying issues, it is interesting that the developers of portfolio insurance do not take the easy option of denying that it had a significant role in the 1987 crash. Leland and Rubinstein are both broadly "orthodox" economists and efficient-market theorists (see, for example, Rubinstein 2001). How do they reconcile this with their acceptance that it "isn't ridiculous to say that portfolio insurance was a significant factor in the market crash" (Rubinstein interview)?

Apart from in one feature to be discussed below, Gennotte and Leland's is a "rational-expectations" model: it posits investors who have a correct understanding of the price dynamics presumed in the model. The model is of the determination by supply and demand of the price, p°, of a single risky asset, which can be "interpreted as the stock market portfolio" (Gennotte and Leland 1990, p. 1006). Part of the demand for the asset comes from "uninformed investors ... who observe only p0" in other words, whose only source of information about the future price of the asset is inference from its current observed price (Gennotte and Leland 1990, p. 1002). Part of the supply of the asset results from the activities of portfolio insurers, who sell increased quantities of it as its price falls. That supply is it(po), a deterministic, decreasing function of p°.

Because portfolio insurance can create positive feedback (as the price of the risky asset falls, portfolio insurers will sell more of it), price discontinuities or `crashes' can occur" (Gennotte and Leland 1990, p. 1008). The main determinant of their likelihood in Gennotte and Leland's model is whether or not 7t(po), the function describing the extent of portfolio insurers' sales at different price levels, is known to the economic agents posited by the model. (The possibility that it(po) is known to no participant is the key departure from a full rational-expectations model.)

Sales of the asset by portfolio insurers will lead to lower prices, but if Tc(p°) is not known in other words, if investors do not know the proportion of sales that are "mechanical" responses to lower prices price falls will be greater "as a consequence of investors inferring information from prices. A supply shock leads to lower prices, which in turn (since the shock is unobserved) leads uninformed investors to revise their expectations downward. This limits these investors' willingness to absorb the extra supply and causes a magnified price response" (Gennotte and Leland 1990, p. 1001).

When Gennotte and Leland set the parameters of their model to values roughly corresponding to the U.S. stock market in 1987, the effects of whether or not 7t(po) is observed were dramatic. "The unobserved hedging which created a 30 percent crash in market prices, would have less than a 1 percent impact on prices if it were observed by all investors" (Gennotte and Leland 1990, p. 1016).

For Leland, then, the key factor in the 1987 crash was not portfolio insurance per se but lack of awareness of the true extent of portfolio insurance's "mechanical" sales. "If everybody knows that we're uninformed traders, then people don't revise their expectations downward when the price falls. They just say things are on sale. Then they will take the other side [i.e. buy] more willingly. If everyone thinks the price is falling because somebody has information, then they won't take the other side." (Leland interview) The price fall will then be much larger.

A fifth of individual investors, and two-fifths of institutional investors, reported experiencing such symptoms on October 19 (Shiller 1989, pp. 388-389). Almost all were aware of falling prices during that day Shiller's institutional respondents "checked the prices of stocks" an average of 35 times on October 19 (1989, p. 388) and those falls provoked emotion consistent with there being "something fundamentally wrong."

LOR heard rumors that "suggested portfolio insurance trading was going to be three or four times larger than in fact it was" (Norris 1988, p. 28) they might have felt less afraid.

Unlike many other discussions of the 1987 crash (for example, by the Brady Commission), Leland and Gennotte's explanation of the role of portfolio insurance in the crash involves an explicit economic model. Ultimately, however, it is no more provable (or disprovable) than other explanations of the crash. It has, however, an important aspect: its explicit link to "sunshine trading," a means of repairing the rational market.

The idea of sunshine trading predated the crash. It emerged from a conversation between John O'Brien and the futures broker Steven Wunsch of Kidder Peabody, who were discussing the fact that LOR's futures trades were large and that they had to be made. O'Brien puts it this way: "If the market drops this much, we have to trade. It's not a matter of us saying Well, gee, this is not a good time to trade."' The solution O'Brien and Wunsch came up with "was something [for which] we then came up with the name sunshine trading.' We said, what we'll do, we'll go down to the floor of the futures exchange, we'll announce an hour beforehand that we're going to sell $10 million of futures at 11 o'clock." (O'Brien interviewL2) The obvious objection was that a sunshine trader would be "front run": others would sell futures ahead of them, in order to profit from a decline in price brought on by the pre-announced sale.

The obvious objection was that a sunshine trader would be "front run": others would sell futures ahead of them, in order to profit from a decline in price brought on by the pre-announced sale. However, the proponents of sunshine trading reckoned that if news of the intended sale was disseminated widely, competition among would-be front runners would tend to eliminate the adverse price effects of front running.

LOR's pre-crash experiments with sunshine trading were successful: "We made 13 large trades this way ... and it was our belief that, on average, we got better prices." (Rubinstein interview) The goal at that point was to reduce LOR's transaction costs, but after the crash Leland and O'Brien saw sunshine trading as attractive for another reason. Instead of pre-announcing just one trade, portfolio insurers could make known "the table of trades that we would make at various market levels" (O'Brien interview), in effect publishing Gennotte and Leland's it(po).

If Gennotte and Leland's account of the crash were correct, disseminating knowledge of portfolio insurers' sales in advance would greatly reduce the risk of those sales destabilizing the market. With 7c(p0) not known, large sales produced "shock ... nobody knowing how big ... how much more would be coming." In contrast, with Tc(p0) known the market could "prepare itself" for portfolio insurers' informationless trades and "clear ... just fine" (O'Brien interview; see also Grossman 1988, pp. 278-279).

Sunshine trading could, in other words, be seen as an attempt to reconstruct a Black-Scholes world, to recreate a world in which the mere placing of "informationless" orders did not affect prices.

That mattered less than it might have, because after October 1987 the market for the type of portfolio insurance sold by LOR, its licensees, and its competitors dwindled rapidly. In part that was because the costs of portfolio insurance in situations of high volatility (forgone gains and risks of being "stopped out") became evident, but it may also have been because the managers of "respectable" institutions such as pension funds wished to avoid overt pursuit of a strategy that was "tainted" by its association with the crash.

It was not that the desire for what portfolio insurance promised a floor to losses vanished. Instead, those who wished such a floor seem to have turned from portfolio insurance's synthetic puts to actual puts. Such puts were purchased either "over-the-counter" (by direct institution-to-institution negotiation) from investment banks or bought on organized options exchanges, notably the Chicago Board Options Exchange.

In addition, the price of actual puts has to be paid explicitly and "up-front," rather than primarily by forgone gains, as in portfolio insurance. As we shall see, after 1987 the price of the index puts most likely to be attractive as a floor to losses has consistently been high higher than it would be in a Black-Scholes world. These "up-front premium" costs could cause "sticker shock" (Voorhees 1988, p. 58), limiting the scale of the purchase of puts.

The overall consequences of the 1987 crash for the U.S. economy were remarkably limited. Central parts of the financial system broke down, but only briefly. The rise in stock prices of the 1980s was reversed only temporarily (the 1990s were to see an extraordinary boom), and even in the short run the effects of the reversal on the wider economy were not huge. The crash did have its effects, and those effects have persisted, but they are not evident on the surface.

In the 1980s, human beings had been still at the center of the market, and technical systems were their aids. By 2000, the balance had shifted. The Chicago Board Options Exchange traded 104,000 classes of option. Inevitably, trading in some was quiet in 2000, despite record overall trading volumes the average class was trading only 13 contracts per day but the exchange's Autoquote system, now pervasive, continuously generates prices for all classes of options, no matter how sporadic the actual transactions in those classes, and distributes those prices to the vast array of electronic displays on the trading floor and through worldwide computer networks.

Such was the array of screens, computers, and communication systems on the Chicago Board Options Exchange's trading floor at the end of the 1990s that other heating was needed only when the Chicago temperature dropped below -10°F (Options Institute 1999, p. 232).

Two words at the top of each screen revealed how Autoquote updated prices: "Cox-Ross." The Cox-Ross-Rubinstein model discussed in appendix E was used to generate prices. Human beings remained in ultimate command: by pressing on the section of the screens marked "lean," traders could manually override model values, and, furthermore, the ebb and flow of orders in actively traded option classes did move prices. Nevertheless, such human interaction was now merely one aspect of a larger technosystem.

By 2000, however, a crucial aspect of the BlackScholes-Merton model was almost never present. As we saw in chapter 6, in that model the relationship between the strike price and the implied volatility of options on the same underlying asset with the same time to expiration is a flat line. In the fall of 1987, however, the flat-line relationship, empirically manifest in the late 1970s and the early 1980s, disappeared, and was replaced by a distinct "skew" Figure 7.

The earlier flat line has not returned subsequently (see, for example, Jackwerth 2000); indeed, the skew continued to grow at least until 1992 (Rubinstein 1994, pp. 772-774). The direction of the skew has been stable: puts with strike prices well below current stock index levels have higher implied volatilities are relatively more expensive than puts with higher strike prices, and the putcall parity relation discussed in chapter 6 means that the same is true of calls.

The empirical history of option pricing in the United States, therefore, falls into three distinct phases. The first two phases were described in chapter 6. Before the April 1973 opening of the Chicago Board Options Exchange, and in the first year or so of its operation, there were substantial differences between patterns of market prices and Black-Scholes values. A second phase had begun by 1976 and lasted until summer 1987. In it, the Black-ScholesMerton model was an excellent fit to market prices. … The third phase in the empirical history of option pricing is from autumn 1987 to the present, when the Black-Scholes-Merton model's fit has again been poor, especially for index options, in the crucial matter of the relationship between strike price and implied volatility. The Black-Scholes-Merton flat-line relationship vanished, and it has not returned.

There is little doubt that the 1987 crash is the event that separates the second and third phases of the history of option pricing, and there appears to be econometric consensus. No analysis now finds the Black-Scholes-Merton model to fit the observed pattern of prices of options well; all find a volatility skew that is variable in nature but, in general, has in the case of options on stock indices roughly the same pattern as in the lower graph in figure 7.1; and the skew is evident both in the index options traded on the Chicago Board Options Exchange and in the options on index futures traded on the Chicago Mercantile Exchange.

On the morning of every trading day on the Chicago Board Options Exchange, "Designated Primary Market Makers" set the skew for the options for which they are responsible. As the underlying stock price or index value changes, Autoquote uses this skew and the Cox-Ross-Rubinstein model to generate prices. If trading conditions shift markedly, the primary market maker can reset the skew during the day, but this by no means always happens.

The econometrician David Bates concludes that "the substantial negative skewness and leptokurtosis16 implicit in actively traded short-maturity option prices appear fundamentally inconsistent with an absence of large weekly movements in S&P 500 futures returns over 1988-93" (Bates 2000, p. 227). "The parameter values necessary to match the smirk [skew] in S&P 500 futures options appear inconsistent with the time series properties of the stock index futures and of option prices" (Bates 2003, p. 399).

To explain observed index-option prices since 1988 thus requires the artificial addition to the actual price record of crashes of almost 1987's severity more frequent than one every four years, when "even a 20% [one month] crash every eight years seems to be a rather pessimistic outlook" (Jackwerth 2000, p. 447). (Between 1802 and 1988 there were only seven calendar months in which the U.S. stock market fell by more than 20 percent [Schwert 1990, p. 80, table 1].) "The most likely explanation," Jackwerth concludes (2000, p. 450), "is mispricing of options in the market."

If Jackwerth is right, and options are indeed mispriced, this is a striking finding: participants in one of high modernity's most sophisticated markets have been behaving irrationally. Such a conclusion, however, seems to me to involve too narrow a view of rationality. Because of the limited wider effects of the 1987 crash, it is hard now to recapture just how traumatic it was to those most centrally involved. The arbitrageur Eric Rosenfeld, then at the investment bank Salomon Brothers, recalls "sitting at the [trading] desk and wondering about the end of the whole financial system" (quoted in Dunbar 2000, p. 97).

Option prices rose to levels that defeated the nascent automated systems, many of which could cope only with double-digit dollar prices. When option prices rose to $106, "it appeared on your sheets as ... $6.... So your account [with the clearing firm] was off by $20 million the next day... Nobody knew where they stood."

The sudden, huge rise in the prices of index put options some rose eightfold (Brady Commission 1988, p. VI-19), with implied volatilities, normally around 20 percent or less, soaring to 170 percent (Bodie and Merton 1995, p. 217, figure 6-1)-meant that enormous margin payments were owed to clearing firms by market makers who had sold options that had shot up in value, and by the firms to the Options Clearing Corporation. First Options, the leading clearing firm, absorbed huge losses from market makers who could not meet their obligations. Its failure would have been a calamity, but it had shortly before been bought by Continental Illinois, and the Federal Reserve permitted the bank to draw on its capital reserves to replenish First Options' funds.

Nor were all the effects of the crash short-lived; it was 1995 before stock options trading on the Chicago Board Options Exchange recovered to pre-crash volumes (CBOE/OCC 1998a, p. 12). It is this collective trauma, I conjecture, that sustains the skew It is, for example, noteworthy that the skew in index options appears initially to have been largely an American phenomenon.

It is, for example, noteworthy that the skew in index options appears initially to have been largely an American phenomenon. L9 The British options market, for example, does not seem to have responded to 1987 by developing a similar skew (Gemmill 1996). Although stock markets in the United Kingdom and elsewhere also crashed, the effects on the then-tiny British derivatives markets were nowhere near as devastating as in the United States. When a consistent skew did emerge in the U.K. in the first half of the 1990s, it seems to have been only a third as intense as in the U.S. In Japan, too, the skew may have been less marked (Gemmill and Kamiyama 2001).

Furthermore, to hedge index options by using the Black-Scholes "delta hedging" procedure (outlined in chapters 5 and 6) might well be insufficient if an index fell sharply: it might not be possible to adjust the hedge fast enough. In a Black-Scholes world there are no "jumps" no discontinuous price movements and no changes in volatility. 1987, however, taught options market makers that indices could go down effectively discontinuously while volatility could leap upward. If that happened, "delta hedging" would fail adequately to protect a market maker who had sold puts.

While no analysis of the skew is yet definitive, the explanation most consistent with my interviews is Bates's suggestion that the index options markets in the United States have come to resemble the markets in catastrophe risk: … The stock index options markets ... appear to be functioning as an insurance market. A large clientele of assorted institutional investors predominantly buy stock index options, whereas a relatively small number of specialized option market making firms predominantly write them. These firms can delta-hedge their positions against small market fluctuations, but are perforce exposed in aggregate to jump and volatility risks. ... Consequently, market makers limit their exposure to these risks by risk management techniques such as value at risk [see glossary] and worst-case scenario analysis. The limited capitalization of the market makers implies a limited supply of options, and the pricing of the extra risks spanned by options at the shadow prices of investors with relatively high aversions to those risks.

The moral obloquy arises because the 1987 crash taught the options market that unrestrained, unhedged or inadequately hedged put sales threatened not just the seller but the market as a whole. A collective response to the danger came in two phases. First, options clearing firms themselves changed their riskmanagement practices in response to 1987, for example by starting to check the consequences for each trader who cleared via them of a repetition of the crash (Hinkes interview 2).

Individual memory of the 1987 crash and of the possible systemic risks posed by put sales is fading as older traders are replaced by a new generation. However, there is a sense in which that memory has been institutionalized in the U.S. options markets' risk-management systems. One delicious nuance is that part of that institutionalized memory is now Mandelbrot's Levy distributions, which were, as discussed in chapter 4, the "path not taken" by financial economics.

Our [OCC's] research found that [Levy] distributions provided estimates of future distributions that were much more consistent (stable) over time than those that either ignored higher moments than variance or relied solely on past extreme instances that had occurred during a past data sampling window. While on average the typical stock alpha was about 1.65, there was a wide distribution about that average (1.3 to virtually 2.0). So OCC uses stock specific values for all four parameters of a stable [Levy] distribution (including non-symmetry) and assesses the critical tail values (I% and 99% cutoffs) individually. This led to different likely movements across stocks and larger down moves than up moves as well.

There is an intriguing counterperformative aspect to this use of Levy distributions. They are, as noted in chapter 4, a form of "wild randomness." Tim Hinkes, their key Chicago proponent, believes however that by assuming wild randomness one reduces the impact, and possibly even the likelihood, of disastrous manifestations of such randomness: "we want to set [a] relatively high bar [margin requirements] and relatively consistent bar for all our firms" (Hinkes interview 1).

Even quite substantial fluctuations in market volatility have limited, slow effects on statistical estimators of the parameters of Levy distributions with infinite variance. In calm periods, estimates of the probabilities of extreme events do not go down much, so margin requirements are not reduced substantially. When extreme events do happen, Levy estimators are also affected only relatively modestly, because Levy distributions with infinite variance "assume" that the probabilities of such events happening are substantial.

In consequence, the use of Levy distributions means that extreme events do not suddenly increase margin requirements, which would be what would happen if the latter were based on more conventional econometric estimation. The danger of a sudden increase in margin requirements is that it may trigger forced sales, worsening the events that have caused the increase: "Suddenly there is some volatility in the market and suddenly your value-at-risk [see glossary] blows up, and `Oh, now I've got to do something.' So [I've] got to liquidate.... It's almost likely a secondary feedback effect that adds to the volatility."

The 1987 crash has not been repeated. Up to the time of writing, no subsequent event (not even the attacks of September 11, 2001) has presented the danger to the financial system it posed. Yet 1987 has left its traces. It ended the period of the Barnesian performativity of classic option-pricing theory and replaced it with a seemingly permanent volatility skew.

LTCM practiced arbitrage on an unprecedentedly large scale. Its trading was "arbitrage" in the sense in which the term is used in financial markets: it sought to make low-risk profits by exploiting discrepancies in prices, for example when an unduly large "spread" had opened up between the prices of similar assets.

However, the safety of government bonds does not preclude trading opportunities. Indeed, the U.S. bond markets of the 1980s attracted aggressive traders. The expanding government deficits during the presidency of Ronald Reagan meant that increasing numbers of Treasury bonds had to be issued. Trading volumes increased more than fivefold between 1980 and 1988, to levels in excess of $100 billion a day (Hughes 2004).

More subtly, however, anomalies can arise in the pricing of bonds, and these anomalies sometimes become large enough that sophisticated traders can exploit them profitably. For example, the market in newly issued ("on-the-run") U.S. Treasury bonds is more liquid than the market in less recently issued ("offthe-run") bonds: many off-the-run bonds are in the relatively static portfolios of pension funds and insurance companies. Investors concerned with liquidity are therefore prepared to pay a premium for on-the-run bonds.

Because of the risk of pre-payment, and because the federal bodies involved are agencies, not the government itself, mortgage-backed securities trade at a discount to (or, to put it in other words, offer higher yields than) government bonds. Typically, the yield of mortgage-backed securities is about one percentage point higher than the yield of government bonds, and there can, for example, be profit opportunities if that difference widens or narrows for temporary reasons.

From the mid 1970s on, the arbitrage opportunities offered by bonds and mortgage-backed securities were expanded by the emergence of markets in derivatives of these securities. The Chicago Board of Trade began trading futures on mortgage-backed securities in October 1975 and futures on U.S. Treasury bonds in August 1977. Markets also began to develop in derivatives (such as bond options and swaps) sold "over the counter" that is, by direct, institution-to-institution negotiations. (Swaps are contracts to exchange income streams, such as fixed-rate and floating-rate interest on the same notional principal sum.)

To identify arbitrage opportunities involving mortgage-backed securities, for example, one has to examine the extent of the "spread" of their yields over government bonds after taking into account the mortgage holders' prepayment option. It is also necessary to work out how to hedge the pre-payment risk, for instance by purchasing interest-rate options.

Bonds are more complicated than stocks from the viewpoint of mathematical modeling. There is no single dominant model of interest-rate fluctuations equivalent to the log-normal random walk for stocks. The value of a bond at maturity is a deterministically fixed, not a stochastic, sum of money, and yield curves are both complex and subject to radical changes in shape.

At first the arbitrage activities of the Salomon group had focused exclusively on the United States. But as other countries also began to deregulate their financial systems, arbitrage opportunities began to appear in capital markets overseas. Japan, for example, partially liberalized its financial system in the 1980s, and Salomon became heavily involved in arbitrage involving convertible bonds. (A convertible bond is one that includes an option to exchange it for another asset, in most cases for stock of the corporation that has issued it. Often such bonds trade at prices different from those implied by the value of the option as calculated by Black-Scholes or other models of option pricing.) The bank made almost $1 billion in two years of arbitrage trading of this kind in Japan (Meriwether interview).

By 1986, realizing the need for greater sophistication in order to keep ahead of his competitors, Meriwether had developed "a pronounced game plan to interact with academia," indeed to "evolve into a quasi-university environment" (Meriwether interview). He sent Salomon employees to visit universities and to attend the conferences of the American Finance Association.

Repo, Rosenfeld recalls, was not a prominent or a prestigious business: "In the 1970s and 1980s, it wasn't done by the top people at the firm; it was ... almost like a clerk's job." Rosenfeld and his Salomon colleagues "always spent a lot of time with those guys and that was very important to us." Equally important was discovering what bonds could be borrowed for short sale, and on what terms.

As Salomon's arbitrage activities began to expand overseas, Meriwether who, like the traders at Dimensional Fund Advisors, was a good practical economic sociologist realized that it would not be enough simply to send Americans, however sophisticated mathematically, into overseas markets. "Knowing the culture," he says, "was more important than just quantitative knowledge."

LTCM, which began trading in February 1994, was based in Greenwich, Connecticut. It also had an office in London and a branch in Tokyo. Its primary registration like that of many other hedge funds was in the Cayman Islands.

LTCM's basic strategy was "convergence" and "relative-value" arbitrage: the exploitation of price differences that must be temporary or that have a high probability of being temporary. Typical were its many trades involving "swaps." By the time of LTCM's crisis, its swap book consisted of some 10,000 swaps with a total notional value of $1.25 trillion.

As has already been noted, a swap is a contract to exchange two income streams for example, fixed-rate and floating-rate interest on the same notional sum. Swaps are a recent invention they date only from the early 1980s but they have become important financial derivatives, widely used to manage the risks of interest-rate fluctuations. Around 47 percent of the $273 trillion in total notional amounts of derivatives contracts outstanding worldwide at the end of June 2004 was made up of interest-rate swaps.

The "swap spread" is the difference between the fixed interest rate at which swaps can be entered into and the yield of a government bond with a similar maturity denominated in the same currency. Swap spreads can indicate arbitrage opportunities because the party to a swap who is paying a floating rate of interest while receiving a fixed rate is in a situation similar to that of someone who has borrowed money at a floating rate and used it to buy a bond that pays fixed interest. If there is enough of a discrepancy between the terms on which swap contracts can be entered into and on which positions in bonds in the same currency and of similar maturities can be financed, arbitrage may be possible.

High levels of leverage, however, did not necessarily imply huge risk (as much subsequent commentary suggested). For example, the risks of swapspread trades are rather limited. Bond prices and the terms on which swaps are offered fluctuate considerably, particularly as interest rates vary. LTCM, however, almost always neutralized that risk by constructing "two-legged" trades, in which the effects on one "leg" of a change in interest rates would be canceled by its equal-but-opposite effect on the other "leg." (The trade in appendix G is an example.) The chief "market risk" of swap-spread trading is of the spread temporarily moving in an unfavorable direction, but if that happens the arbitrageur can simply continue to hold the position and wait until liquidating it becomes profitable.

Indeed, a swap-spread position such as that described in appendix G can be held until the bond matures and the swap expires. That feature was taken to be the essence of convergence arbitrage: if held to maturity, a convergence arbitrage position has to make a profit, whatever the market's fluctuations along the way.

Any "credit risk" (risk of default) associated with swap-spread arbitrage like the trade in appendix G is typically small. The risk of the U.S. government's defaulting on its bonds is regarded as negligible; bond futures contracts are guaranteed by the clearinghouse of a derivatives exchange such as the Chicago Board of Trade; and LTCM's swap contracts were typically with major banks. Even major banks may fail, but because the principal sum in a swap is not exchanged, it is only notional and is at no risk: the credit risk involved is only of the loss of future net differences between fixed-rate and floating-rate interest.

Although the risks were limited, the profits from LTCM's swap-spread trading were impressive. The trade described in appendix G earned a profit of $35 million, which was a return of 28-35 percent achieved in eight months or less. Nor was this untypical. Between February and December 1994, LTCM's returns before fees were 28.1 percent (un-annualized); after management and incentive fees were deducted, investors received 19.9 percent (unannualized). Gross returns in 1995 were 59.0 percent, and returns after fees 42.8 percent; in 1996, the corresponding percentages were 61.5 and 40.8.

Although LTCM was active in the American and Japanese markets, it had particularly heavy involvement in European markets. In the 1990s, financial deregulation in Europe proceeded apace, but arbitrageurs such as LTCM initially found much less competition than in the United States or Japan. "The Japanese banks," according to Costas Kaplanis (who in 1998 was Salomon Brothers' head of global arbitrage), "were the ones who were terribly interested in setting up proprietary [trading] desks. The European banks were still a bit hesitant."

The risks involved in LTCM's positions were carefully calculated and controlled using the "value-at-risk" approach, a standard practice of the world's leading banks (Meriwether interview). Value-at-risk is a measure of the exposure of a portfolio to adverse price movements. In the case of the dollar swap spread, for example, historical statistics and judgments of likely future values led LTCM to estimate that the spread had an "equilibrium value" of around 30 basis points, with a standard deviation of about 15 basis points per annum (Rosenfeld interview; a "basis point" is a hundredth of a percentage point). Using those estimates, it was then possible to work out the relationship between the magnitude of possible losses and their probabilities, and thus to work out the value-at-risk in the trade.

LTCM's positions were geographically dispersed, and in instruments of very different kinds. (See table 8.3 below for an example of the typical range of its major positions.) At the level of economic fundamentals, little if anything connected the spread between U.S. government bonds and mortgage-backed securities to the difference between the prices of the stock of pairs of companies such as Royal Dutch and Shell, the idiosyncrasies of the Italian bond market, the bulges in the yen yield curve, or the chances of specific mergers' failing. LTCM was aware that its own and other arbitrageurs' involvement in these diverse positions would induce some correlation, but nevertheless the observed correlations, based on five years' data, were very small-typically 0.1 or lower.

The standard deviations and correlations that went into LTCM's aggregaterisk model were, however, not simply the empirically observed numbers; they were deliberately conservative estimates of future values. The observed standard deviation of the U.S. dollar swap spread, for example, was around 12 basis points a year, while, as noted above, the risk model assumed it would be 15 (Rosenfeld interview). Past correlation levels, likewise, were "upped" to provide a safety factor: despite observed correlations being 0.1 or less, LTCM was "running analyses at correlations at around 0.3" (Meriwether interview).

Clearly, LTCM's trading involved risk. It is therefore, tempting to conclude that what LTCM did although it was unquestionably "arbitrage" in financial-market usage of the term was not arbitrage as it is conceived within finance theory. However, LTCM's index option positions were quite close to the arbitrage that finance theory posits as imposing Black-Scholes option pricing.

More generally, beginning with the work of Modigliani and Miller, it was fundamental to finance theory that, in the words of Myron Scholes, "the market will price assets such that the expected rates of return on assets of similar risk are equal." If the market did not do so, Modigliani, Miller, and their successors reasoned, "investors seeing these profit opportunities would soon arbitrage them away" (Scholes 1972, p. 182). LTCM's "relative value" arbitrage can be seen as precisely this kind of arbitrage.

On August 17, 1998, Russia defaulted on its ruble-denominated bonds and devalued the ruble. This triggered a "flight to quality" in the financial markets -a sudden greatly increased preference for financial assets that were safer (less prone to default) and more liquid (more readily bought and sold).

The first explanation-consciously reckless risk-taking is entirely inadequate as an account for LTCM's 1998 disaster. The partners in LTCM believed themselves to be running the fund conservatively, and in the modest volatility of its returns they had evidence for the correctness of this belief. After the fund's crisis, it was commonly portrayed as wildly risk-taking, but it is hard to find anyone inside or outside LTCM who can be proved to have expressed that view before the crisis.

Nor does the second hypothesis advanced in the commentary blind faith in mathematical models explain the crisis. Models were much less critical to LTCM's trading than commonly thought. Many of the pricing anomalies it sought to exploit (such as the premium of shares in Royal Dutch over those in Shell, or the swap-spread example discussed in appendix G) could be identified without sophisticated modeling. Although models were important to how LTCM's trades were implemented and to assessing the risks involved, all those involved knew that models were approximations to reality and a guide to strategy rather than a determinant of it.

LTCM's traders had often themselves developed the models they used: no one was more aware than they of the models' likely deficiencies. The way in which the standard deviations and correlations in the most important model of all LTCM's overall risk model were increased by explicitly judgmentbased "safety factors" is indicative of that.

LTCM's pre-crisis leverage ratios were not, in fact, egregious when compared, for example, to those of investment banks. In the early months of 1998, LTCM's leverage ratio was around 27: 1 (Perold 1999, pp. C 11-C 12). 27: 1 was the average ratio of the five biggest investment banks at the end of 1998 (President's Working Group on Financial Markets 1999, p. 29).

Blaming LTCM's crisis on leverage is similar to attributing a plane crash to the fact that the aircraft was no longer safely in contact with the ground: it identifies the source of overall vulnerability but not the specific cause. That cause was the financial crisis of August and September 1998, and in particular the way in which the adverse price movements of those months exceeded LTCM's, or anyone else's, expectations.

However, the interviews drawn on here suggest that overlaying the increased preference for safer, more liquid assets were the effects of a different, more directly sociological process. Meriwether's group at Salomon and at LTCM earned remarkable profits, and were known to have earned those profits. This had encouraged others in other investment banks, and increasingly in other hedge funds to follow similar strategies.

Meriwether's group had been imitated even in its days at Salomon Brothers. In the market for mortgage-backed securities, a crucial issue, as noted above, is calculating the impact of homeowners' "pre-payment" option. The calculation was a non-trivial modeling task that typically took the form of adjusting the "spread" of the yield of mortgage-backed bonds over the yield of Treasury bonds of similar maturities to take the pre-payment option into account. … "The people making more money," he says, "were the ones with the better models, the Meriwethers of the world." Those who were less sophisticated in their modeling learned from the Salomon group by what Roll calls "mimicry": by inferring from Salomon's trading the features its model must have. Roll puts it this way: "If you saw Meriwether going long [that is, buying a mortgage-backed bond] with an option-adjusted spread you thought was five basis points, you knew that his model said it's 100 basis points." In consequence, less experienced participants in the market would ask themselves what they would have to do to their pre-payment model to generate a larger spread, saying to themselves, in Roll's words, "Let's tinker with [the model] and see if we can get that."

Imitation seems to have intensified after LTCM's success became public. Other traders were being told "LTCM made $2 billion last year. Can't you?" (Meriwether interview). For example, LTCM's success meant that it rapidly became largely closed to new investors, and in January 1998 a new fund, Convergence Asset Management, "raised $700 million in a single month purely from disgruntled investors denied a chance to buy into LTCM" (Dunbar 2000, p. 197).

Even if the details of LTCM's trading could not be discovered, its basic strategy convergence and relative-value arbitrage had to be disclosed to potential investors, and others seeking to follow that strategy would often be led to take positions similar to LTCM's. It "[didn't] take a rocket scientist" to discover the kinds of arbitrage opportunities being pursued by LTCM (Rosenfeld interview), especially when discovering one leg of an LTCM trade through being a counterparty to it would greatly narrow the range of likely other legs.

Some of LTCM's trades were well known to market insiders before LTCM became involved. The Royal Dutch/Shell trade, for example, was the "classic European arbitrage trade" (Wenman interview), and the relationship between Royal Dutch and Shell shares had even been discussed in the academic literature before LTCM was founded (Rosenthal and Young 1990). News or speculation about other LTCM trades circulated freely. "I can't believe how many times I was told to do a trade because the boys at Long-Term deemed it a winner," says the hedge-fund manager James Cramer (2002, p. 179).

As a result of conscious and unconscious imitation, many of LTCM's positions became, in the words of an arbitrageur who was not affiliated to LTCM, "consensus trades" (Kaplanis interview). Of course, the growing number of arbitrage traders in investment banks and hedge funds did not sit down together in a room to identify good arbitrage opportunities. Rather, "the arbitrage philosophy ... had been disseminated, well disseminated by August '98; it was there in quite a few hedge funds, it was there in quite a few firms. So Salomon [and LTCM] lost their uniqueness in doing these things. There were many, many others that could do them." (Kaplanis interview) There was some communication: "If you talk[ed] to another arb trader in the street, they'd say `Oh yes, I have this as well, I have that as well."'

In the summer of 1998, imitation switched to become a disastrously negative factor because of two decisions, neither of which had anything directly to do with LTCM. In 1997, Salomon Brothers had been taken over by the Travelers Corporation, whose chairman, Sanford I. Weill, was building the world's largest financial conglomerate, Citigroup (Booth 1998). According to Kaplanis, Salomon's U.S. arbitrage desk had not consistently been successful since the departure of Meriwether and his group, and in the first half of 1998 it was loss making: by June, "U.S. was down about 200 [million dollars]. ... So Sandy [Weill] ... closed it [Salomon's U.S. arbitrage desk] down" (Kaplanis interview). The closing of the desk was announced on July 7.

Though Kaplanis, promoted to head of global arbitrage for Salomon, advised against it, the decision was taken to liquidate the U.S. arbitrage desk's portfolio as quickly as possible, and responsibility for the liquidation was passed to Salomon's U.S. customer desk. Since the latter was "not accountable for the losses generated as a result of the liquidation, the speed of the latter was faster than would otherwise have been the case." This caused losses not just to Travelers/Citicorp but also to all of those who had similar positions: "Not only did we lose money as the positions went against us as we were selling them, but all the other funds that also had these consensus trades also started losing money." (Kaplanis interview) If the liquidation of Salomon's arbitrage positions was a background factor in the problems of the summer of 1998, the immediate cause of the 1998 crisis was, as noted above, Russia's August 17 default on its ruble-denominated debt.

If the liquidation of Salomon's arbitrage positions was a background factor in the problems of the summer of 1998, the immediate cause of the 1998 crisis was, as noted above, Russia's August 17 default on its ruble-denominated debt. That Russia was in economic trouble was no surprise: what was shocking was that it (unlike previous debtor governments) should default on debt denominated in domestic currency.

True, some investors in ruble-denominated bonds had hedged against the risk of Russia defaulting by short-selling Russian hardcurrency bonds (Shleifer 2000, p. 108). For those investors, however, even the good news of August 17 Russia's avoidance of a hard-currency default was damaging, because it meant their hedge failed to protect them to the extent it should have.

In the days that followed, however, it became increasingly clear that Russia's default had triggered what Kaplanis calls an "avalanche." The default was combined with a de facto devaluation of the ruble of 25 percent and a threemonth moratorium on the "foreign obligations" of Russian banks (Marshall 2001, p. 4). Since Western investors used foreign-exchange forward contracts with these banks to hedge against the declining value of the ruble, widespread losses were incurred.

LTCM had known perfectly well that a flight to quality could happen and that this would be its consequence. Indeed, it was of the very essence of convergence and relative-value arbitrage that spreads could widen relative prices could move against the arbitrageur before a trade finally converged. For that reason, LTCM had required investors to leave their capital in the fund for a minimum of three years: it was in part this restriction that made the fund LongTerm Capital Management.

In some circumstances, such a decision by management might even be anticipated by the traders: "You know that if ... your manager sees that you're down $10 million ... the likelihood that lie will ask you to get out of this position is very high. It's not a formal stop-loss but ... it's there." (Kaplanis interview) In the case of hedge funds, the issue was investor rather than manager queasiness.

In the case of hedge funds, the issue was investor rather than manager queasiness. Most funds did not have LTCM's long capital lockup: "they knew that investors were starting to drain money if they saw more than 15 percent [loss] or whatever.... They knew that if they showed big losses a lot of investors would want to get out. They wouldn't wait until they lost 80 percent of their money ... so that was the behavioral constraint that led to people unwinding positions even though they knew that those positions had value in the long run. They just had no choice." (Kaplanis interview) (The fourth quarter of 1998 saw net withdrawals from hedge funds of about $6 billion.)

Paradoxically, another factor may have been modern risk-management practices, particularly value-at-risk. This allows senior management to control the risks incurred by trading desks by allocating them a risk limit, while avoiding detailed supervision of their trading. When a desk reaches its value-at-risk limit, it must start to liquidate its positions.

The freedom to use value-at-risk models in calculating capital requirements was attractive to banks because it generally reduced those requirements. However, it could have the consequence that as market prices move against a bank and become more volatile, they may eventually either have to liquidate positions or to raise more capital to preserve them, a slow and often unwelcome process. Even if banks were not close to being forced to make this choice, the increased prominence of value-at-risk may have contributed to pressure to liquidate positions in the face of adverse price movements and of increased volatility (Dunbar 2000; Meriwether interview).

As people were forced to sell, that drove the prices even further down. Market makers quickly became overwhelmed, where the dealers, who would [normally] be willing to buy or sell those positions were simply unwilling to do it, and they either said just go away: I'm not answering my phone' or set their prices at ridiculous levels.

In a single day (August 21, 1998), LTCM lost $550 million as swap spreads in the United States and the United Kingdom widened dramatically and the planned merger between Ciena Corporation and Tellabs, Inc., in which LTCM had a large position that would profit if the merger was completed, was canceled (Perold 1999, pp.

Consider, for example, the premium of Royal Dutch stock over Shell stock, which, as noted above, LTCM expected to decline. In 1997, the premium had been around 8 percent. During the early months of 1998 it started to rise for unclear reasons, and during the crisis it shot up, at times exceeding 17 percent.

Assets that LTCM was believed to hold in large quantity became impossible to sell at anything other than "fire sale" prices. Beliefs about LTCM's portfolio were sometimes incorrect or exaggerated: after the crisis, LTCM was approached with an offer to buy six times the position it actually held in Danish mortgage-backed securities (Meriwether interview). Nevertheless, presumptions about its positions were accurate enough to worsen its situation considerably, and as September went on, and LTCM had to divulge more information to its counterparties, those presumptions became more accurate.

As the prices of the options that LTCM had sold rose (in other words, as their implied volatilities increased), LTCM had to transfer collateral into accounts held by its counterparty banks. If LTCM failed, those banks would lose the hedge LTCM had provided them with (in other words, they would be "short volatility") but they would now own the collateral in the accounts. So it was in their interest that the implied volatility of the index options LTCM had sold should be as high as possible.

"When it became apparent they [LTCM] were having difficulties, we thought that if they are going to default, we're going to be short a hell of a lot of volatility. So we'd rather be short at 40 [at an implied volatility of 40 percent per annum] than 30, right? So it was clearly in our interest to mark at as high a volatility as possible. That's why everybody pushed the volatility against them, which contributed to their demise in the end."

A remarkable analysis by Cai (2003) of Board of Trade data obtained from the Commodity Futures Trading Commission via the Freedom of Information Act shows that market makers seem (perfectly legitimately) to have anticipated such purchases, buying futures a minute or two before Bear Stearns did, alerted perhaps by the arrival in the pit of brokers for Bear Stearns or by the behavior of traders acting on the firm's behalf" LTCM kept its counterparties and the Federal Reserve informed of the continuing deterioration of its financial position.

McDonough brokered a meeting of LTCM's largest counterparties, which concluded that a re-capitalization of LTCM would be less damaging to them than a "fire sale" of its assets. Fourteen banks contributed a total of $3.6 billion, in return becoming owners of 90 percent of the fund. LTCM's investors and partners were not "bailed out." They were left with only $400 million, a mere tenth of what their holdings had recently been worth.

If the "superportfolio" explanation advanced in this chapter is correct, then superimposed on the flight to quality should be distinctive price movements reflecting the unraveling of the positions held by LTCM's conscious and unconscious imitators. The composition of the superportfolio is not known with any precision, but if the imitation-based explanation is correct, LTCM's portfolio should be a reasonable proxy, and its main components are known from Perold 1999 and from the testimony of interviewees. The hypothesized specific characteristic of September 1998-"run-on-the -bank" declines in the prices of assets believed to be held by LTCM-is identical in its predicted consequences to the "unraveling superportfolio" explanation.

Convergence and relative value arbitrage as conducted by LTCM and its imitators typically involves short-selling an asset with low default risk and/or high liquidity while holding a similar asset with higher default risk and/or lower liquidity. In many cases, therefore, price movements caused by a flight to quality and by the forced sales of components of an arbitrage superportfolio cannot be distinguished.

In cases of two types, however, the predictions of the two explanations differ. Type one is cases in which there is a range of similar spreads or implied volatilities in only some of which LTCM had positions. The superportfolio explanation would then predict greater increases in the spreads or implied volatilities in which LTCM had positions than in those in which it did not (assuming that, as was in general the case, LTCM held the less liquid instrument or was short volatility, in other words had sold the options in question). If the spreads or implied volatilities genuinely are similar, the flight-to-quality explanation would, in contrast, predict similar movements of them all.

The second type of case in which the predictions of the flight-to-quality and superportfolio explanations differ is the minority of arbitrage positions in which LTCM held the more liquid instrument and was short the less liquid one (the swap-spread example discussed in appendix G is an example of this kind of situation). In such a situation, the flight-to-quality interpretation predicts a rising spread; the superportfolio explanation predicts a more slowly rising, or possibly even a falling, spread.

Swap spreads encompass two "type two" cases (France and Germany) and also an overall "type one" comparison. Because the market in swaps is less liquid than that in government bonds, and because a crisis may prompt fears of bank failures (and did so in 1998), a flight to quality should increase swap spreads. Table 8.2 contrasts the behavior of swap spreads in four countries. In France, LTCM was "long" the swap spread in 1998 (that is, had a position, akin to that described in the swap spread example in appendix G, which would increase in value if the spread rose). That makes France a "type two" case, one in which the effect of the superportfolio unraveling (downward pressure on the swap spread) would be opposite in direction to the effect of a flight to quality (upward pressure). … As table 8.2 shows, spreads widened markedly in the United States and the United Kingdom. (The same happened in Sweden, where arbitrageurs were also short the swap spread.) In contrast, in France and Japan, swap spreads widened only more modestly during the crisis; that was also the case in Germany, another type two case in which LTCM had a long position in the swap spread akin to that in France. I know of no plausible flight-to-quality explanation of these international contrasts, while they are broadly consistent with the superportfolio explanation. … A flight to quality did take place in August and September 1998, but these data do indeed suggest that overlaying it (and sometimes acting in contradiction to it) was an unraveling superportfolio.

The overall pattern in table 8.3 seems clear. In all the cases for which data are available, the relative price movements of the crisis are consistent with the "superportfolio" explanation, while in five cases they are inconsistent (and in a further four, possibly inconsistent) with the flight-to-quality explanation. … A simpler piece of evidence consistent with the superportfolio hypothesis is the contrast between the market reaction to the August 1998 Russian default and to the attacks of September 11, 2001, which also sparked a flight to quality. LTCM's successor fund, JWM Partners, was active then too, but its capital base was smaller and its leverage levels lower, so its arbitrage positions were considerably smaller (Silverman and Chaffin 2000). The amount of capital devoted to convergence and relative value arbitrage by other market participants such as investment banks was also much smaller (interviewees estimate possibly only a tenth as large in total).

One way of expressing the forms currently taken by the inextricable interweaving of the "economic" and the "social" is Knorr Cetina and Bruegger's notion of "global microstructure." The financial markets are now global in their reach, but interaction within them still takes the form of "patterns of relatedness and coordination that are ... microsocial in character and that assemble and link global domains" (Knorr Cetina and Bruegger 2002a, p. 907).

What happened in August and September 1998 was not simply that international markets fell in concert (that would have had little effect on LTCM), but that very particular phenomena, which at the level of economic "fundamentals" had seemed quite unrelated, suddenly started to move in close to lock-step: swap spreads, the precise shape of yield curves, the behavior of equity pairs such as Royal Dutch/Shell, and so on.

The "nature of the world had changed," says John Meriwether, "and we hadn't recognized it" (Meriwether interview). LTCM's wide diversification, both internationally and across asset classes, which lie had thought kept aggregate risk at acceptably modest levels, failed to do so, because of the effects of a global microstructure rooted in one of the most basic of social processes: imitation.

Often technology develops in a cascade. An initial success provides a basis for further improvements and new developments, and those improvements and developments are in their turn built on. Soon, the technology has outstripped potential rivals and seems to have a momentum of its own. … The emergence of finance theory also has something of the character of a cascade. Markowitz provided Sharpe with his basic model; Modigliani and Miller inspired Treynor; Sharpe and Treynor gave Black and Scholes their crucial intellectual resource; Merton rebuilt Black and Scholes's model on new foundations; Cox, Ross, Rubinstein, Harrison, and Kreps built on Black, Scholes, and Merton; Wall Street's "quants" translated what the academics had done into forms more suited to the exigencies of practice; and so onward into trading rooms.

At times, steps in the cascade involved one researcher's reading the works of previous researchers, as when Treynor read Modigliani and Miller. At other times, especially in the early stages of the cascade, extensive personal contact was involved, as in the cases of Sharpe's relation to Markowitz, Black's relation to Treynor, Merton's relation to Black and Scholes, and Emanuel Derman's relation to Black.

As with cascades in technology, cascades in the social sciences are not selfexplaining. In Britain, the economist A. D. Roy produced a mathematical analysis of portfolio selection (Roy 1952) that was contemporaneous with and similar to Markowitz's, while the statistician M. G. Kendall (1953) put forward the view of price changes as random walks. Unlike Markowitz's work, however, Roy's was not carried on by the equivalent of a Sharpe. Kendall's work was built upon, but in the United States, by Samuelson, not in the United Kingdom.

Chance no doubt played a role, but Whitley (1986a,b) is surely right to see the academicization of American business schools as having facilitated the development of modern financial economics in the United States. As he points out, the slow development in the U.K. of business schools comparable to those in the United States, and the fact that in the U.K. finance was often taught in departments of accounting and finance that were dominated by accountants, created an institutional context that was much less supportive of theoretical, mathematical approaches to the subject.

Financial economics was never simply an academic endeavor, and putting finance theory to practical use was seen as entirely legitimate. The interweaving of innovation in financial economics and developments in the financial markets meant that, despite the hostility of many in the markets to finance theory, attractive consultancies were available from the 1960s on. Before long, there were tempting job opportunities in the finance sector. In 1984, for example, Fischer Black resigned his professorship at MIT's Sloan School of Management for a post at Goldman Sachs, where he remained until his death in 1995. In 1990, Scholes became a consultant to Salomon Brothers, and later he became joint head of the group at Salomon that traded and sold bond derivatives, though he also maintained an academic attachment to Stanford University.

However, despite the many links between financial economics and market practice, the changed priorities of American business schools had the consequence that central aspects of the field's reward system and epistemic culture remained distinctively academic and research-focused. While teaching contributions within business schools were no doubt of some importance, recognition by academic peers for research achievements was indispensable for financial economists who remained within university settings.

For a finance theorist, the key to achieving peer recognition was the development of good models. "Good" meant economically plausible, innovative, and analytically tractable. A model that neither its developer nor anyone else could solve was unlikely to be seen as good. The most influential models, notably the Capital Asset Pricing Model and the Black-Scholes-Merton model, yielded as their solutions relatively simple equations. However, a good model also could not be "obvious" and thus at risk of being seen by theorists' peers as trivial (as Sharpe had feared would happen to the first equilibrium model he produced in his work on capital asset pricing).

When research productivity, peer recognition, and publication are prized, another essential quality of a "good" model is that it can be the foundation for further research that is itself tractable without being trivial. All the "orthodox" models centrally considered here had that feature. Consider, in contrast, Mandelbrot's infinite-variance Levy distributions, another case of a cascade that began (with Fama building on Mandelbrot's work, and Fama's students, especially Richard Roll, then taking up the Levy model in their turn) but then lost almost all momentum. Infinite variances undercut standard components of the economist's and econometrician's intellectual toolkit, while what Levy distributions had to offer in their stead could seem dauntingly intractable.

Over and above questions of the analytical tractability of models lay a central theoretical commitment. Orthodox financial economics was, and is, committed strongly to a view of financial markets as efficient. That commitment has now been challenged forcibly by the rise of "behavioral finance," which emphasizes investors' propensity to systematic errors in reasoning. Behavioral finance is, however, a relatively recent development. The work by the psychologists Daniel Kahneman and Amos Tversky that inspired behavioral finance dated from the late 1970s, but not until the 1990s did behavioral finance become prominent. In the 1960s and the 1970s, the commitment to market efficiency faced no serious challenge within financial economics, for all that it aroused practitioners' ire.

However, while Black and Scholes were trying to solve the problem of option pricing by deploying the Capital Asset Pricing Model, Thorp had little interest in the latter; he was aware of it, but not "at the expert level." Indeed, for him the proposition (central to the mathematics of Black and Scholes, and in a different way to Merton's analysis as well) that a properly hedged portfolio would earn only the riskless rate of interest would have stood in direct contradiction to his empirical experience. The entire point of his and Kassouf's book Beat the Market (Thorp and Kassouf 1967) was that its authors had found they could earn far more than that from hedged portfolios.

For Thorp, then, to have put forward Black and Scholes's or Merton's central argument would have involved overriding what he knew of empirical reality. For Scholes, trained as he was in Chicago economics, and even for Black (despite his doubts as to the precise extent to which markets were efficient), it was reasonable to postulate that markets would not allow money-making opportunities such as a riskless portfolio that earned more than the riskless rate of interest.

Ultimately, though, what divided Thorp from Black, Scholes, and Merton was not empirical. Black's, Scholes's, and Merton's practical actions are evidence that they too accepted that mispricings that offered opportunities for profit did sometimes exist. While looking for ways of testing their model empirically, Black and Scholes identified apparently unduly cheap warrants issued by a corporation called National General. "Scholes, Merton, and I and others jumped right in and bought a bunch of these warrants" (Black, 1989, p. 7), just as Thorp might have done.

What divided Thorp from Black, Scholes, and Merton was a difference in goals. Thorp was not trying to pursue a career in academic financial economics. His aim was to find arbitrage opportunities, and his modeling work was mainly a means to that end. In contrast, Merton and (at least at that stage of their careers) Black and Scholes were oriented above all to their academic peers: seeking to make money from National General warrants was a sideline. Their model was designed to offer an elegant, economically insightful account of the processes determining option prices. They did not see modeling, as Thorp did, primarily as a tool for identifying opportunities for profitable trading.

The purchase by Black, Scholes, and Merton of the National General warrants indicates that the theoretical commitments of the financial economists discussed here, strong as they were, did not always take the form of conviction that the field's models were empirically entirely accurate. Some degree of conviction of verisimilitude is perhaps inevitable when a model becomes incorporated centrally into the work of a successful research specialty and researchers have a "shared sense of the group as having achieved a satisfactory, working routine" (Bloor 2004, pp. 24-25).

Probably a majority of the finance theorists discussed in this book have had some involvement in practical activity that would make no sense if the efficient-market hypothesis were taken to be an entirely accurate model of markets. This activity ranged from simple, small-scale private investment like the purchase of National General warrants, to the more demanding exploitation of anomalies such as the "turn-of-the-year" effect, and, on the largest scale, the massive arbitrage trading by Long-Term Capital Management.

Finance theorists believed that markets were made efficient by the actions of arbitrageurs and other knowledgeable investors, so there was no contradiction in those theorists seeking to take these actions themselves. Nevertheless, that they did so shows that they did not construe market efficiency as an already-achieved fact. Rather, the achievement of efficiency was a process perhaps an endless process' in which they could themselves sometimes take part and from which they could profit.

Similar ambivalence the capacity both to be committed to a model and, simultaneously, to doubt the extent of its empirical validity can be found in regard to more specific models. Black and Scholes, for example, drew crucially on the Capital Asset Pricing Model. However, they also knew (indeed, they had themselves showed in their collaboration with Jensen) that the empirical accuracy of the model, at least in its original form, was questionable, and they were involved in the proposal discussed in chapter 4 for an investment fund that would exploit this.

Another facet of ambivalence is, however, present here too. The failure to profit from National General warrants might have been a private disappointment, but there was a sense in which it was a vindication of market efficiency: an apparent profit opportunity turned out not to be real, because market prices were incorporating a piece of information that was not known to Black and his colleagues. `Although our trading didn't turn out very well, this event helped validate the [Black-Scholes] formula," wrote Black: "The market price was out of line for a very good reason" (Black 1989, p. 7). Paradoxically, theorists' practical failure could thus be cited as evidence of theory's robustness.

When I discussed the crisis of Long-Term Capital Management (LTCM) with interviewees, the same aspect of ambivalence was sometimes manifest. Because of the prominent role of finance theorists in LTCM, its crisis was embarrassing to the field, but the debacle could also be read as a vindication of market efficiency. The large, apparently safe arbitrage profits that LTCM had been making contradicted the efficient-market hypothesis, and thus there was a sense in which LTCM's crisis resolved the contradiction by showing that those profits had not been as safe as they seemed.

However, all of the finance theorists centrally discussed in this book would both strongly defend the virtues of their models and agree with Fama's assertion, quoted in chapter 4, that any model is "surely false" in the sense of not being an exact description of market realities. Finance theory is an epistemic culture that makes knowledge using models, but there is a deep ambivalence in the field's attitude to the extent to which its models can be taken as realistic.

Through it flowed money, people, procedures, devices, and ideas. Despite the fact that its claims were controversial, financial economics received funding from the burgeoning finance industry in the United States, such as the stream of support that made possible the crucial stock-price databases produced by the University of Chicago's Center for Research in Security Prices.

Finance theory has become incorporated into the infrastructures of financial markets first in the United States, and increasingly worldwide as well in at least three ways: technical, linguistic, and legitimatory. All three are most evident in the case of financial derivatives, the emergence and development of which have been perhaps the most dramatic change in global finance since the start of the 1970s. The huge derivatives-market trading volume mentioned in chapter I -a total of $273 trillion in notional amounts of outstanding contracts in June 2004 would effectively be inconceivable without a guide to the pricing and hedging of such derivatives, and that is surely a case of theory's technical incorporation into market infrastructure.

A second way in which finance theory has been incorporated into the infrastructures of financial markets is linguistic. The theory offers a way of talking about markets, especially about markets whose complexity might otherwise be baffling. Much of the attractiveness to practitioners of the Capital Asset Pricing Model's "beta" was that it seemed to offer a simple way of summarizing the relative riskiness of different stocks.

Investment analysts might sometimes not have understood "beta" as Sharpe had intended. They often took beta to be a direct measure of a stock's individual riskiness rather than a measure of a stock's covariance with the overall market, and thus of the stock's contribution to the overall risk of a diversified portfolio. Nevertheless, "beta" became a lasting feature of how sophisticated practitioners talked, and still talk, about financial markets.

Again, though, derivatives offer the best example of the incorporation of finance theory into the linguistic infrastructures of markets. Options market participants talk all the time about "implied volatility": indeed, option prices are sometimes quoted not in dollars but in implied volatilities. "Implied volatility" is an entirely theoretical notion, calculated by running an option-pricing model such as Black-Scholes "backwards" to determine the volatility of the underlying asset implied by option prices.

As was emphasized in chapter 6, the notion of "implied volatility" takes a multiplicity of market prices (the prices of puts and calls with different expiry dates and different strike prices, and the prices of more complicated options as well) and reduces them to a single number or small set of numbers. Options market participants may no longer perform Black-Scholes pricing, but their constant invocation of "implied volatility" -a notion that did not exist before the work of Black, Scholes, and Merton shows that work's permanent imprint on their culture.

"Efficient," in the sense in which the term is used in financial economics, does not equate to "desirable": one could, for example, imagine a market in human kidneys that was efficient in the speed with which prices incorporate available information, but that does not imply that it would be good to construct such a market. Nevertheless, that our wider culture's most authoritative source of knowledge of markets has declared financial markets to be "efficient" a word with almost entirely positive connotations in ordinary speech has surely been of some importance.

The legitimatory role of economics in regard to the development of derivatives markets has been particularly clear-cut. As chapter 1 noted, as recently as 1970 markets in financial derivatives were either non-existent or (by today's standards) small-scale, and many current financial derivatives were illegal. Derivatives were haunted by the impression, held not only by lay people but by many market regulators, that they were simply wagers on the movement of prices. This was not merely a general obstacle to the development of derivatives markets. The way in which the legal distinction between gambling and legitimate futures trading had been drawn in the United States made cashsettled derivatives contracts illegal, and, as noted in chapter 6, until the 1980s this blocked the emergence of stock-index derivatives such as index futures and index options.

Economists (Baumol, Malkiel, and Quandt in the case of the Chicago Board Options Exchange; Friedman in the case of the Chicago Mercantile Exchange) helped make the Chicago financial derivatives markets possible by providing initial legitimacy. Black, Scholes, and Merton provided the capstone, decisively undermining the regulatory view that derivatives were morally dubious instruments of gambling. The modern derivatives markets might have developed even in the absence of this legitimatory role of economics futures markets and at least sporadic markets in options had emerged in previous centuries without much in the way of academic legitimation but there can be little doubt that economics eased their path.

There are clearly cases probably many cases in which finance theory was invoked but in which the invocation had little or no effect on market processes. In the 1970s, for example, many U.S. investment managers learned to talk plausibly about "betas" and paid for beta books, but, as noted above, a good number of them may have understood "beta" in a different way from how finance theorists understood it. Many such managers also seem to have continued in their investment practice much as they always had done, trying to pick "winners," to "buy low," and to "sell high."

Even for managers who were doing no more than paying lip service to finance theory, the theory's incorporation into market infrastructure mattered. As chapter 3 suggested, stock-picking managers knew that their investment performance was increasingly being monitored by software-implemented measurement systems. They might not fully have understood those systems' foundations in the Capital Asset Pricing Model, but their behavior changed nonetheless. Many became "closet" index trackers, their self-perceived stockpicking skills limited to modest over-weighting or under-weighting of particular stocks or sectors.

Overall, there is little doubt that finance theory's incorporation into market infrastructure was consequential: in the terminology sketched in chapter 1, it constituted "effective performativity." The stock market itself was affected first in the United States and then overseas by the growth of index funds, which were, as chapter 3 noted, inspired in part by ideas of market efficiency' Again, though, it has been in the derivatives markets that the effects of finance theory have been the most profound. As emphasized above, those markets simply could not function on anything like the scale that they currently do without a technical and communicative infrastructure incorporating models that can be traced back to option theory.

When the Modigliani-Miller proposition on the irrelevance of capital structure was adjusted to take into account the tax advantages of debt financing, it suggested that the American corporations of the 1950s and the 1960s were operating at levels of debt that were too low Similarly, the tax disadvantages of dividends by comparison with capital gains suggested that corporate emphasis on the former was irrational.

What is crucial from the viewpoint of Barnesian performativity is that the agreement between the Capital Asset Pricing Model and empirical data does not seem to have improved after the model was formulated. If anything, tests on later data suggested poorer agreement than the original tests, which were conducted using price series stretching back into the period before the Capital Asset Pricing Model was formulated.

What is crucial from the viewpoint of Barnesian performativity is that the agreement between the Capital Asset Pricing Model and empirical data does not seem to have improved after the model was formulated. If anything, tests on later data suggested poorer agreement than the original tests, which were conducted using price series stretching back into the period before the Capital Asset Pricing Model was formulated. It is thus difficult to find in the econometric literature any persuasive evidence for the Barnesian performativity of the model.

In one specific set of contexts, however, the Capital Asset Pricing Model has the power of government behind it. In the United States, the United Kingdom, and other countries, privately owned utilities (such as the suppliers of electricity natural gas, and water) are often regulated by government-appointed commissions that set the maximum prices that utilities can charge or the maximum rates of profit that they can earn. In so doing, those commissions are typically required to ensure that, in the words of the crucial U.S. legal judgment, the 1949 Hope decision, "the return to the equity owner should be commensurate with returns on investments and other enterprises having corresponding risks."

If the use of the model in this way actually generated model-compliant rates of return (I know of no empirical study of the issue), it would be an instance of Barnesian performativity.

The case for the Barnesian performativity of the efficient-market hypothesis seems stronger than for the performativity of the Capital Asset Pricing Model. The hypothesis provided a systematic framework within which researchers identified "anomalies": market phenomena at variance with the hypothesis. Most of those researchers had an efficient-market viewpoint, and many were Ph.D. students at the University of Chicago's Graduate School of Business, where Fama had formulated the hypothesis and where support for it was strong. Once anomalies were identified, they were often made the object of trading strategies that, in general, seem to have had the effect of reducing their size or even of eliminating them.

However, there is one major exception to this pattern. Efficientmarket theory's most important practical product was the index fund, and the growth of indexing created an anomaly from the viewpoint of the theory: the sharp increases in price that typically followed a stock's inclusion in a major index, which is an essentially "informationless" event that should not affect prices.

Option pricing is the aspect of finance theory whose performativity has been examined most closely in the previous chapters. The fit between the BlackScholes-Merton model and empirical patterns of option prices was originally only approximate, but it improved rapidly after the model was published and adopted by market practitioners. There is no way of being certain that the improved fit was due to the practical adoption of the model: the year of its publication also saw the opening in Chicago of the first modern options exchange, and the development of organized options trading would have had an effect on patterns of prices quite independent of the model.

Nevertheless, the availability of convenient material implementations of the Black-Scholes-Merton model (notably Black's "sheets"), and their use to identify arbitrage opportunities particularly opportunities for "spreading" most likely had the effect of reducing discrepancies between empirical prices and the model, especially in the econometrically crucial matter of the flat-line relationship between implied volatility and strike price. As was noted in chapter 6, there was thus a homology between the way the model was tested econometrically and options market practices based on the model. Use of the model does indeed seem to have helped to create patterns of prices consistent with the model.

Gradually, too, the financial markets changed in a way that made the BlackScholes-Merton model's assumptions, which at first were grossly at variance with market conditions, more realistic. In part, this was a result of technological improvements to price dissemination and transaction processing. It was also a result of the general liberalizing influence of free market economics. At least a small part of the process, however, was the way in which, by making options trading seem legitimate, option theory contributing to the emergence of the high-volume, efficient, low-transaction-cost liquid market the theory posited.

If the discrepancy between Black-Scholes prices and market prices was seen (as Scholes persuaded Mathew Gladstein: see chapter 6) as a flaw in the market, not in the model, then adoption of the model would have had the effect of reducing prices: it would give the confidence to keep selling options, as Gladstein did, until prices dropped. To the extent that others did this (just how widespread it was isn't clear), the availability of the Black-Scholes formula and of its associated hedging technique gave options market participants the confidence to write options at prices lower in relative terms than in previous markets.

Keenly priced options in their turn helped the new U.S. options exchanges of the 1970s to grow, to prosper, and to become more efficient, rather than to falter as their predecessors had. Since the Black-Scholes-Merton analysis posits a liquid, zero-transaction-cost options market, this would again be an effect of the model that was performative in the Barnesian sense.

As noted above, the theory of derivatives also enables the risks involved in derivatives portfolios to be decomposed mathematically, and in the case of large investment banks, many of these risks turn out to be mutually offsetting. In consequence, the residual risk to be hedged is often quite small in relation to the overall derivatives portfolio of a major financial intermediary such as a big investment bank (Merton 1992, pp. 450-457). Such banks can thus "operate on such a scale that they can provide liquidity as if they had no transaction costs" (Taleb 1998, p. 36). … As a result, the Black-Scholes-Merton model's assumption of zero transaction costs is now close to true for the hedging of derivatives by major investment banks, in part because the use of that model and its descendants by those banks allows them to manage their portfolios in a way that minimizes transaction costs.

That the distributions of price changes over short time periods had fat tails (high frequencies of extreme events) was known before 1987: Mandelbrot and Fama had made the point vigorously in the 1960s. Furthermore, as discussed in chapter 7, there is a sense in which the options market has "over-learned": the magnitude of the skew is greater than can be accounted for simply by the extent to which the empirical distributions of price changes have fatter tails than the log-normal model underpinning Black-Scholes-Merton.

Given the three-phase history, it is hard to sustain the view that the second phase of the empirical history of option pricing, the close fit between the model and empirical patterns of market prices from the mid 1970s to the summer of 1987, was simply the discovery by market participants of the correct way to price options. It is more plausible to see the third phase, the emergence of the skew, as rational learning from the near-catastrophe of October 1987 (the huge price movements of October 19 can be seen as an emphatic rejection of the null hypothesis of log-normality), but even here there are difficulties.

The empirical success of the Black-Scholes-Merton model was a historically contingent process in which the model itself played a constitutive role. To say that is in no way to diminish the brilliant achievement of Black, Scholes, and Merton; it would be a curious prejudice to see a theory that changed the world (as their theory did) as inferior to one that merely reported on it. Rather, it is to assert that the model was a theoretical innovation, not simply an empirical observation; that the model's relation to the market was not always passive, but sometimes active; that its role was not always descriptive, but sometimes performative, even in the strongest, Barnesian sense. An engine, not a camera.

This book has, however, also emphasized that counterperformativity is possible: that practical action based on economic models can undermine the empirical validity of those models. One instance noted above is the way in which the development of index funds an expression of the efficient-market view that systematic success in stock picking is unlikely seems to have created an anomaly from the viewpoint of efficient-market theory: the increases in price that typically followed inclusion of a stock in a major index. However, by far the most significant possible instance of counterperformativity is the role of portfolio insurance (which was based, albeit loosely, on a Black-Scholes world, in other words a world in which the assumptions of the Black-Scholes-Merton model were valid) in exacerbating the 1987 crash and thus undermining the Black-Scholes world.

The extent of portfolio insurance's role in the 1987 crash is not clear. Nevertheless, if it did play a role, it would indeed be a case of counterperformativity. First, on the log-normal model underpinning Black-Scholes-Merton the crash was, as already noted, an event whose probability was vanishingly small. Second, both the crash and, paradoxically, perhaps to an even greater extent the partial recovery that took place immediately afterward are hard to account for in standard efficient-market terms as rational responses to new information. Third, the crash was the historical trauma that, at least in U.S. options markets, gave rise to the volatility skew and thus ended the Barnesian performativity of the classic form of option theory.

It is conceivable that models of the stochastic dynamics of asset price movements may have a general counterperformative aspect if large amounts of practical action (especially in the form of risk-control measures) are based on them. In most of its forms, portfolio insurance depended on continuity in price movements; to the extent that it played a role in the 1987 crash, it generated a discontinuity. While the role of value-at-risk models in the 1998 crisis described in chapter 8 is also unclear, it is possible that sudden, widespread efforts to liquidate similar trading positions in the face of rising value-at-risk estimates contributed to price movements well beyond those envisaged in the models on the basis of which the estimates had been calculated.

In both 1987 and 1998, practical action involving models that incorporated the assumption that randomness is "mild" may thus have helped to generate "wild" randomness. The adoption by the Options Clearing Corporation of Mandelbrot's wildly random infinite-variance Levy distributions can also be seen as counterperformative, although in this case deliberately so. By assuming wild randomness, the Options Clearing Corporation hopes to keep randomness mild.

Between the 1950s and the 1990s, the attention paid by corporations to financial markets greatly increased, above all in the United States and the United Kingdom, but increasingly in other countries too. Corporate leaders for whom the financial markets were one concern among many Roger Lowenstein points out that Alfred P. Sloan Jr., who headed General Motors for four decades, never mentions in his autobiography the price of its stock "as a factor in his decision making" (Lowenstein 2004, p. 29) were replaced by a generation for whom their corporations' stock prices were an obsession.

In the first contribution to finance theory discussed in chapter 2, Modigliani and Miller asked what it was that the managers of a corporation should be seen as maximizing. Their answer was the corporation's market value: ". . . any investment project and its concomitant financing plan must pass only the following test: Will the project, as financed, raise the market value of the firm's shares? If so, it is worth undertaking; if not, its return is less than the marginal cost of capital to the firm." (Modigliani and Miller 1958, p. 264) There is no reason to think that in emphasizing the maximization of market value Modigliani and Miller saw themselves as acting politically.

There is no reason to think that in emphasizing the maximization of market value Modigliani and Miller saw themselves as acting politically. They (Modigliani in particular) were exercised, rather, by an academic issue: the incoherence of the traditional criterion of profit maximization in a world of uncertainty. If "profit outcome" is "a random variable," they wrote, "its maximization no longer has an operational meaning" (Modigliani and Miller 1958, p. 263). However, as Jack Treynor (for whom this aspect of Modigliani and Miller's work was central) realized, the assertion of the centrality of market-value maximization could be read as a statement of how things ought to be.

Finance theory looked at the corporation from the "outside": from the viewpoint of the investor and of the financial markets. There is, therefore, an affinity between finance theory's view of the corporation and the way in which the governance of corporate life, especially of American corporate life, evolved. The economist Alan Blinder (2000, p. 18) puts it well: ". . . the stark assumption of [market] value maximization comes much closer to the mark today than it did a decade or two ago."

It certainly was not the only factor. A different area of economics, agency theory, was the main academic source of legitimacy for a crucial aspect of the change, the greatly increased proportion of corporate executives' rewards that came in the form of stock and stock options.

The "market for corporate control" sparked by the hostile acquisitions of the 1980s was another cause of the financialization of American corporations, and financial economics played only a minor part in the emergence of this market. (See the discussion of Michael Milken above.) The wider political and economic changes both symbolized and encouraged by the presidency of Ronald Reagan and the accommodation with those changes reached in the 1990s by the Democrats were clearly important too. Free-market economics was of obvious importance to those changes, but financial economics specifically did not play a prominent role.

The case for seeing the growing priority given by American corporations to market-value maximization as a direct performative effect of financial economics is therefore weak. However, once the students in American business schools realized the strength of the influence of the financial markets on the fate of the corporations that were going to employ them and increasingly on their own personal wealth too they would be likely to be far keener to learn about those markets than they had been in the 1950s, when the Harvard Business School's course on investments was the despised "darkness at noon" described in chapter 3.

It is also plausible though I know of no direct evidence on the point that when the students who graduated with their MBAs from American business schools from the 1960s on came to occupy senior positions in corporations, they would have remembered at least some of what they had been taught in courses on the new financial economics. They would thus know that the goal of market-value maximization could be defended as being right, as well as being career-enhancing and wealth-enlarging. Many people were exposed to financial economics in the course of studying for the MBA degree. By the end of the 1990s, U.S. business schools were awarding about 100,000 MBAs a year (Skapinker 2002). The growing prestige of financial economics and the increasing emphasis in American corporate life on market-value maximization may thus have been to at least some degree mutually self-reinforcing.

Furthermore, corporations in the United States and elsewhere seem increasingly to be becoming "financialized" in a sense additional to that of marketvalue maximization. The use of derivatives to manage financial risks such as exchange-rate and interest-rate fluctuations is established, but corporations now also have available to them derivatives of a growing range of physical substances and processes: for example, oil and gasoline derivatives, natural gas derivatives, even weather derivatives. … Derivatives of this kind allow risks that traditionally had to be managed by physical or organizational means to be hedged financially. Oil companies, for example, traditionally sought to control risk by vertical integration-ownership of an entire supply chain from oil fields, through transportation and refining, and into retail but the availability of oil and gasoline derivatives offers another route to the same goal (Merton 1998, p. 59).

However, one of the most famous of the corporate catastrophes was the crippling $1.3 billion loss suffered in the early 1990s by Metallgesellschaft AG as a result of the over-ambitious but sensibly motivated use of oil and gasoline futures to hedge fixed-price contracts with the corporation's customers. The difficulties of Enron, a pioneer of energy derivatives and of the "assetlight" virtualized corporation, are also notorious. (See MacKenzie 2003a.) Nevertheless, the use of derivatives is one factor making possible corporate structures in which the ownership of physical assets is of decreasing importance, risks are hedged financially, and the ownership of "virtual" assets such as intellectual property rights is more important.

Michel Gallon's critic Daniel Miller argues that economic sociology and anthropology should "radically separate out the market as a ritual and ideological system constructed by economists and the actual practice of economies" (D. Miller 2002, p. 224). In the sections above, we have seen a range of performative effects of financial economics. They vary in importance and in the extent to which they approximate to strong, Barnesian performativity. Nevertheless, it is clear that in at least some contexts most obviously in the derivatives markets the radical separation called for by Miller is impossible. The economic theory of derivatives and the "actual practice" of derivatives markets are interwoven too intimately.

However, when in pursuit of a theme such as the performativity of economics, one should not give in to the temptation to exaggerate its significance. In particular, attention to performativity does not render redundant economic sociology's focus on the embedding of economic action in cultures, in political systems, and in networks of interpersonal connections. Especially in chapter 6, we saw performativity articulating with these matters, rather than displacing them.

The market participants discussed in earlier chapters were certainly economically calculative, and as Gallon's formulation would suggest their calculations were often conducted using procedures and devices made possible by finance theory. However, they did not become Homines economics in the sense of atomistic, amoral egotists.

The networks of connections to personally known others on which the economic sociologist Mark Granovetter (1973, 1985) has focused are also in evidence in respect to the legitimatory role of economics in facilitating the emergence of derivatives markets. The persuasive power of economics did not on its own create the Chicago Board Options Exchange and the Merc's International Monetary Market. That persuasive power flowed through a network of interpersonal connections: in the case of the Options Exchange, from Baumol, Malkiel, and Quandt, via Edmund O'Connor and Nathan Associates, to Milton Cohen, and, crucially, to William Casey; in the case of the Mere, from Milton Friedman to Arthur Burns, George Shultz, Bill Simon, and others in Washington.

Furthermore, wider cultural-political issues also mediate the legitimatory role of economics. In the United States in the late 1960s and the early 1970s, economics had persuasive force, particularly with the Nixon Administration, committed as it was to freeing markets from their Rooseveltian shackles. In contrast, in Malaysia in the late 1990s and the early 2000s a similar battle to permit derivatives trading was fought, but those engaged in it appealed for legitimacy to Islamic jurisprudence, not to neoclassical economics (Kamali 1997; Maurer 2001).

Part of the significance of the performativity of economics arises from the fact that individual human beings tend to have quite limited powers of memory, information-processing, and calculation." Those limitations explain the centrality especially in complex markets of simplifying concepts (e.g., "implied volatility") and of material means of calculation (e.g., Black's sheets and the Chicago Board Options Exchange's Autoquote system).

That concepts and material means are therefore constitutive of economic action that economic action involves distributed cognition in the sense of Hutchins (1995a,b) implies that the economic theory crystallized in concepts and devices is performed. Sometimes, I have suggested, this performativity is Barnesian: it helps to create the phenomena the theory posits.

There is thus a sense in which the capacity for economics to be performative arises from the cognitive limitations of human beings limitations that require standard models of the rational actor to be weakened. However, in order better to understand economic behavior, even in financial markets, it is also necessary to enrich standard models of the rational actor to encompass ways in which we affect each other that are not reducible to calculation in the ordinary sense of the word. We are often profoundly influenced by anticipation of how our behavior will appear to others, even if their approval or their disapproval has no direct material consequences.

The weakening of standard views of rational economic actors is currently prominent in "behavioral finance," which portrays investors as prone to systematic biases.2" For instance, the "prospect theory" put forward by Daniel Kahneman and Amos Tversky (1979) points to the way in which attitudes to a risky decision are affected by how the decision is framed in relation to subjectively important reference points. When psychologists confront experimental subjects with risky decisions, those subjects are typically risk averse with respect to perceived gains, but risk seeking with respect to what are seen as losses. They are prepared to "gamble" to recoup a perceived loss, but are less willing to endanger gains.

In the case of professional traders in financial markets, the relevant subjective reference point may be an anticipated level of bonus, and Kahneman and Tversky's prospect theory would suggest that "a trader expecting a good performance (and thus bonus) outcome will be reluctant to put those anticipated gains at risk whereas a trader anticipating a poor outcome will be more willing to take risks to avoid that negative outcome" (Fenton- O'Creevy, Nicholson, Soane, and Willman 2005, p. 181).

One factor is the lore of traders, in which perhaps the most common maxim "run your profits and cut your losses" (Fenton-O'Creevy Nicholson, Soane, and Willman 2005, p. 192) directly contradicts the predisposition posited by prospect theory. The maxim enjoins traders to continue to hold risky positions when in the domain of gains and to liquidate those in the domain of losses. The need for the maxim suggests that prospect theory's diagnosis of the typical predisposition is correct, but if the maxim is influential it will counter the predisposition. A second factor again may provide both evidence of the predisposition and a mechanism countering it: the role of traders' managers, part of whose job is often to discourage undue risk aversion while also detecting and stopping the dangerous "doubling up" of loss-bearing trades (Fenton- O'Creevy, Nicholson, Soane, and Willman 2005).

Indeed, markets themselves can be seen as prostheses in the sense that they enable human beings to achieve outcomes that go beyond their individual cognitive grasp. … The classic examples are the demonstrations that when placed in a double-auction market akin in its structure to open-outcry trading, both untutored human beings and even computerized "zero-intelligence traders" submitting "random bids and offers" achieve economic outcomes close to those predicted by theories that posit fully rational economic actors (Smith 1991; Gode and Sunder 1993, p. 119).

In emphasizing human cognitive limitations, as behavioral finance rightly does, we therefore need also to remember the interactions between those limitations and the mechanisms, both "social" and "technological," that constitute markets. The interactions by no means always eliminate the effects of the limitations the crises of 1987 and 1998 can be seen as cases in which they exacerbated them but I suspect they are always important.

Arbitrage is also a crucial mechanism by which finance theory affects markets. For example, the most important channel by which the Barnesian performativity of finance theory is achieved is the use of the theory to identify, exploit, and thus diminish discrepancies between "model" and "reality." Examples include the "spreading" arbitrage in options markets that seems to have contributed to moving price patterns toward the Black-Scholes-Merton model, and the arbitrage-like exploitation of "anomalies" that helped to eliminate them.

I, for one, never thought that people myself included were all that rational in their behavior. To the contrary, I am always amazed at what people do. But, that was never the point of financial theory.

The absence of arbitrage requires that there be enough well financed and smart investors to close arbitrage opportunities when they appear.... Neoclassical finance is a theory of sharks [arbitrageurs] and not a theory of rational homo economicus, and that is the principal distinction between finance and traditional economics. In most economic models aggregate demand depends on average demand and for that reason, traditional economic theories require the average individual to be rational. In liquid securities markets, though, profit opportunities bring about infinite discrepancies between demand and supply. Well financed arbitrageurs spot these opportunities, pile on, and by their actions they close aberrant price differentials.... Rational finance has stripped the assumptions [about the behavior of investors] down to only those required to support efficient markets and the absence of arbitrage, and has worked very hard to rid the field of its sensitivity to the psychological vagaries of investors. (Ross 2001, p. 4) If, in contrast, the potential for arbitrage is constrained, then discrepancies between finance-theory models and "reality" may persist, and the effects on patterns of prices of the phenomena pointed to by behavioral finance may not be eliminated.

If, in contrast, the potential for arbitrage is constrained, then discrepancies between finance-theory models and "reality" may persist, and the effects on patterns of prices of the phenomena pointed to by behavioral finance may not be eliminated.

However, two partners in LTCM independently pointed out to me the impossibility of making arbitrage profits from exaggerated valuations. Suppose they had been vouchsafed a little peek into the future: that they knew, with absolute certainty, that at a particular point in time the stock price of company X would be zero. Could they now, they asked me, make money with certainty from this knowledge? Their question was rhetorical; they knew the answer to be "No." Of course, they could sell the stock short. If they could hold their position until the stock price became zero, they could indeed profit handsomely. But if in the interim the price continued to rise, they could still exhaust their capital and be forced to liquidate at a loss.

Perhaps the most interesting single line of work in behavioral finance pioneered especially by Andrei Shleifer has been the modeling of situations of the kind referred to by my LTCM interviewees. These are situations in which the powers of arbitrage are limited, for example because arbitrageurs have access to only finite amounts of capital, and temporarily adverse price movements can generate margin calls and other demands on capital.

If arbitrageurs are constrained by finite supplies of capital, even an arbitrage trade that is certain to converge profitably may nevertheless have to be abandoned at a loss, for instance because those who provide arbitrageurs with capital withdraw it prematurely in the face of adverse price movements. The analysis of this risk in Shleifer and Vishny 1997 was prescient: as chapter 8 suggests, a flight of arbitrage capital of this kind was integral to the crisis surrounding Long-Term Capital Management.

Firms and other economic actors do not choose their courses of action in isolation: they monitor each other, and make inferences about the uncertain situation they face by noting the success or failure of others' strategies. When this leads to diversity to firms selecting different strategies and coming to occupy different "niches" -a stable market structure can result. But if firms imitate, each choosing the same strategy, potentially disastrous "crowding" can occur.

"Crowding" is what appears to have taken place in global arbitrage in the 1990s. As discussed in chapter 8, it seems to have been driven at least in part by imitation of Long-Term Capital Management. The consequence was the sudden appearance in the crisis of 1998 of substantial correlations between arbitrage positions that had little or nothing in common at the level of economic fundamentals and which previously had manifested very low correlations.

The possibility of imitation-induced correlation tightens the limits to arbitrage caused by the risk, discussed above, of the "flight" of capital-constrained arbitrageurs in the face of temporarily adverse price movements. If correlations between different arbitrage positions could be relied upon to remain low, the risk of forced flight could be reduced considerably by holding a large portfolio of diverse arbitrage positions, as Shleifer and Vishny acknowledge (1997, p. 47). However, as LTCM found, diversification is of little avail if correlation can suddenly appear around the world and across asset classes when things "go bad."

That was the lesson that LTCM's successor fund, JWM Partners, drew from its predecessor's crisis. In JWM Partners' risk model, all the fund's positions, no matter how diversified geographically or how unrelated in asset type, are now assumed to have correlations of 1.0 "to the worst event" (Meriwether interview). In other words, it is assumed that in an extreme crisis all the fund's positions may move in lock-step and adversely, even those positions that would in the abstract be expected to rise in relative value in a crisis (in other words, the cases in which it holds the more liquid or more creditworthy of two instruments and has a short position in its less liquid or less creditworthy counterpart).

JWM Partners' revised risk model thus incorporates the possibility that an imitative, overlapping arbitrage "superportfolio" will again come into being, and that its unwinding will not merely exacerbate a crisis but will even override the "flight to quality" that typically accompanies crisis. The new risk model was informed by the experience of LTCM's 1998 crisis, not by economic sociology or by the social studies of finance, but it is an acknowledgement of the social, imitative aspect of financial risk.

I raise the topic of the uptick rule not to express a view on its desirability, but because it is an example of a general point: the financial and other markets of high modernity are to a significant extent entities subject to deliberate design, and the details of their design are consequential.

Markets, like technologies, are surely means to be tinkered with, modified, redesigned, improved, and on occasion delimited not ends that can only be embraced or be rejected. They are not forces of nature, but human creations.

Performativity has, however, three virtues. First, when confronted with a theory or model it is natural to ask: is it accurate? Keeping performativity in mind reminds us also to ask: if the model is adopted and used widely, what will its effects be? What will the use of the model do? Second, because performativity often resides not just in "big ideas" but also in apparently small technicalities, the notion reminds us also to pay attention to the latter, and to consider the role they play in the infrastructures of markets: in the material devices, procedures, routines, rules, and design features that make markets what they are. And, finally, the notion of performativity prompts the most important question of all: What sort of a world do we want to see performed?

Black then assumed that the Capital Asset Pricing Model applied both to the stock and warrant, so that E(Ax) and E(Aw) would depend on, respectively, the beta of the stock and the beta of the warrant. He also assumed that the stock price followed a log-normal random walk and that he could eliminate those terms that are "second order" in At. In addition, Black seems to have simplified the problem by assuming that, as he and Scholes put it (1973, p. 640): "The stock pays no dividends or other distributions."

A simple numerical example (based on Sharpe 1978, pp. 366-373) captures important features of option pricing in a model that is extremely straightforward but nevertheless possesses essential aspects of more complex models. The setting in the model is "binomial": in any given time period, the price of a stock can only do two things, rise by a set amount or fall by a set amount. (To make the model more realistic, we would have to examine the path of a stock price over many such periods, as in the Cox-Ross-Rubinstein model discussed below, but the main points emerge when considering a single period.) In the model it is assumed that investors can both lend and borrow at the riskless rate of interest of, let us say, 5 percent a year that the stock pays no dividends and can be sold short without penalty, and that buying or selling stock or options incurs no transaction costs.

Thus far, the argument used to determine the option price is simply the binomial analogue of Black-Scholes-Merton option pricing. Risk-neutral valuation as put forward by Cox and Ross involves assuming (a) that all investors are risk neutral, and so the value to them of risky investments is the present value of the expected payoff of these investments; and (b) that "the expected returns on both stock and option must equal the riskless rate" of interest (Cox and Ross 1976, p. 153). Cox and Ross's claim was that the price of an option as worked out under these assumptions must be its arbitrage-determined price in our original world (in which we assumed nothing about expected returns or attitudes to risk).

To see the equivalence of the two ways of determining option price in the example discussed here, we first work out the probabilities of a rise to $200 and fall to $50 that would make the expected return on the stock equal to the riskless rate of interest of 5 percent (these probabilities are what are called the "martingale probabilities"). Let the probability of a rise to $200 bep; the probability of a fall to $50 is thus 1 - p. The initial stock price is $100, so if the stock's expected return is 5 percent, the expected value of its price after a year must be $105. Hence, 200p + 50 (1 -p) = 105 and p = 55/150.

If the stock's price rises to $200, the call option is worth $50; if the price falls to $50, the option is worthless. So the expected value of the option's payoff is $50 x p = $50 x (55/150) = $18.33. The option's present value to a riskneutral investor is thus $18.33 discounted at the riskless interest rate of 5 percent: $18.33/1.05 = $17.46, which is equal to the price as determined by arbitrage.

The "tree" can be elaborated to take into account dividends, and `American" as well as "European" options can be treated (the former can be exercised at any time up to their expiration, raising the need to examine when early exercise may be rational). Such problems can become intractable analytically, but the Cox-Ross-Rubinstein model allows them to be solved numerically and recursively by working "backwards" through the tree.

The Black-Scholes-Merton model is a limit case of the Cox-RossRubinstein model. If the time periods become infinitely many and infinitesimally small, a "multiplicative" binomial process like that in figure E. becomes the Black-Scholes-Merton log-normal random walk in continuous time, but other stochastic processes can also be modeled using the Cos-Ross-Rubinstein approach.

Suppose party A wishes to buy a security such as a bond using borrowed money. It approaches party B with a request to "repo" the bond. If the repo is agreed to, party B lends party A an amount of money close to the value of the bond. Party A buys the bond on the market and transfers it to the custody of party B for safekeeping. The two parties (A and B) also agree that on a specified future date party A will repay the amount of money lent by party B, plus interest, and party B will return the bond to A. The bond is thus serving as collateral for the loan from B to A. The interest rate that A pays B is called the "repo rate."

The reason that this arrangement is called a "repurchase" (repo) agreement is that it can often be executed in another form, also known as a "buy-sell." In this equivalent form of the transaction, party A "sells" the bond to B, and B simultaneously agrees to "sell it back" to A (that is, A agrees to repurchase it) at a future date. The difference between the future price and the initial price represents the "repo" interest charged by B for in effect lending the money to A.

The chief risk to B is if A defaults in a situation in which the price of the bond has fallen, but B can mitigate this risk by imposing a "haircut," in other words lending less than the market price of the bond. In the markets within which Salomon and LTCM operated, haircuts of 2 percent were standard for long duration U. S. Treasury bonds: in other words, B would lend A only 98 percent of the bond's market price. Haircuts, however, vary with market conditions, with the type of and maturity date of the security, and with B's assessment of the likelihood of A defaulting.

That legal status was clarified only in the 1980s. Previously, the conduct of repo had been remarkably informal: there was no clearly established legal definition of "repo." Sometimes "two parties will do a repo but sign no agreement; they may be just sloppy, but more likely, party A's lawyer doesn't like party B's agreement and vice versa" (Stigum 1989, p. 5, emphasis in original).

"The lack of concern that money market people displayed about dotting [sic] the legal i's and is with respect to repo reflected ... their notion that they were afforded much protection by the standards of the business in which they operated. Money market folk have always felt, at least until recently, that they are in a business in which people say My word is my bond' and mean it; a business in which, if someone says something is done,' it is done." (Stigum 1989, p. 218) It should be noted that "repo" has uses quite other than those discussed above.

The interest rate at which repo can be used to borrow money to buy bonds is called "repo rate." (See appendix F.) Because the bonds are held by the creditor as collateral, and because a "haircut" protects against the consequences of default, repo rate is typically lower than Libor (by 20 basis points at the time we are discussing).

A tiny positive cash flow could thus be obtained by buying bonds yielding 6.77 percent, funding the purchase at repo rate, and paying fixed interest in a swap while receiving Libor in return. The incoming cash flow would be in effect 6.77 percent + Libor, while the outgoing flow would be repo rate + 6.94 percent. Since Libor was 20 basis points above repo rate, the net annual cash flow was thus three basis points.

Crucially, however, a swap spread of 17 basis points was unusually low: between May 1994 and February 1997 the 20-year US. dollar swap spread had fluctuated between 17 and 33 basis points (Perold 1999, p. A20). If the spread widened again, LTCM's bond position would be worth more than its swap position, and it could profit perhaps substantially by selling the bonds and entering into a swap contract "canceling out" the original.

LTCM would not enter into a trade such as a swap-spread arbitrage without an understanding of why an apparently attractive opportunity had opened up. In early 1997, LTCM believed that there were identifiable, temporary reasons why the swap spread had become unusually narrow (See Perold 1999, p. A5.) Accordingly, it gradually built its position, using repo to buy bonds (and also buying bond futures), while entering into swap contracts in which it paid fixed interest and received dollar Libor. By July 1997, the predicted increase in the swap spread had indeed taken place, and the fund was able over the summer to liquidate its position, with a total net gain of about $35 million.

Libor The London interbank offered rate: the average rate of interest at which a panel of major banks report other banks as being prepared to lend them funds in a particular currency for a particular period. Other interest rates are often set with Libor as the benchmark.

The figure of $273 trillion is the sum of the total notional amounts of exchangetraded and over-the-counter derivatives contracts at the end of June 2004, as calculated by the Bank for International Settlements (2004, p. 10, table A2). The Bank's estimate of the gross market value corresponding to the $220 trillion over-the-counter portion of this total is $6.4 trillion: the gross market value is the sum "of the absolute values of all open contracts with either positive or negative replacement values evaluated at market prices prevailing at the reporting date" (Bank for International Settlements 2003, p.

Friedman saw himself as defending the legacy of the great British economist Alfred Marshall, for example against the accounts of "imperfect" or "monopolistic" competition put forward by E. H. Chamberlin and Joan Robinson (Friedman 1953a, pp. 38-39). The sentence that I have drawn on in this book's title invokes Marshall: "Marshall took the world as it is; he sought to construct an `engine' to analyze it, not a photographic reproduction of it."

It should be stressed that the "camera" invoked here is a metaphor, not a comment on the actual process of photography, which is often not passive recording of an unchanged external world. See, for example, Dyer's (1997) elegant discussion of the process of "making white people white" for the purposes of film, or consider the question of the impact of photographic images of thin models on the propensity to diet (and thus to alter one's own body) or even to suffer eating disorders.

The degree of disentanglement of a futures contract from those who initially entered into it depends on the clearing mechanism in place (Mille, Muniesa, Panourgias, and Scott, forthcoming). Moser (2000) describes the evolution of clearing on the Chicago Board of Trade from "direct clearing" of bilateral contracts, via "ring clearing," to "complete clearing" in which the clearinghouse itself became the counterparty in all contracts. This last is now the standard situation in derivatives exchanges.

Before the recent decimalization, U.S. securities prices were quoted in binary fractions of dollars. Because the options contracts in question referred to 100 shares, a price of, for example, "3'4" translates into a cost of $325 per contract. A `July/40 call" gave the right to buy 100 Polaroid shares at $40 per share at any time up to its July expiration date.

As noted below, for Modigliani the spark was attendance at a 1950 conference organized by the National Bureau of Economic Research, at which he heard David Durand present the paper that became Durand 1952. As discussed in the text, Durand explored, but ultimately dismissed, the idea that capital structure might be irrelevant. Modigliani felt the proposition might hold despite Durand's belief that it did not. (Modigliani's own contribution to the meeting-Modigliani and Zeman 1952 was further from his eventual position than Durand's paper.) It took Modigliani several years of occasional reflection on the problem to come up with "a really convincing proof" that the proposition held (Modigliani interview). When he did, lie described the proposition that capital structure was irrelevant to a class lie was teaching at Carnegie that Miller was also attending. "Merton Miller said `I have the evidence for you."' (Modigliani interview) Miller had set his graduate students the task of finding empirically the best capital structure from the viewpoint of minimizing a corporation's cost of capital, and they had been unable to do so: "They couldn't find any optimum." (Miller interview) 7.

Thus Robert G. Wiese of Scudder, Stevens & Clark wrote in 1930: "Theoretically, the proper price of any security, whether a stock or a bond, is the sum of all future income payments discounted at the current rate of interest in order to arrire at the present value" (Wiese 1930, p. 5). Williams quoted Wiese's article to this effect (Williams 1938, p. 55).

In modern option theory, the price of options is seen as determined by considerations of arbitrage, not by beliefs about whether stock prices will rise or fall.

In later years, part of mutual fund underperformance seems to have resulted from arbitrageurs exploiting the fact that the prices of mutual fund shares were fixed once a day at a set time while the prices of the underlying portfolio fluctuated continuously. A study by Eric Zitzewitz of Stanford University estimated that in 2001 "stale-price arbitrage" cost the average shareholder in an internationally diversified mutual fund 1.1 percent of the value of his/her holding (Plender 2003). That this "stale-price arbitrage" was practiced in the 1960s is, however, doubtful. The much higher transaction costs of stock trading in the 1960s would probably have made it unattractive.

Dennis Tito, the main competitor to BARRA (Barr Rosenberg and Associates) commented: "Despite all we're doing, he gets all the coverage. Somebody came up to me the other day and said That Rosenberg's fantastic. Did you know he runs four miles a day?' Well, I run four miles a day, too, and nobody knows about it. I'm sure he has an interesting lifestyle, but I have an interesting lifestyle also, and nobody knows about that either." (Welles 1978, p. 66) Rosenberg was not simply applying the Capital Asset Pricing Model but deploying statistically more elaborate models of risk and return.

The problem with equal dollar weights, however, is that to maintain them as stock prices fluctuate requires frequent rebalancing of the portfolio, which incurs transaction costs. Later index funds tended to seek to track the S&P 500 index, which includes stocks not traded on the New York Stock Exchange and, crucially, weights them by market capitalization, so the need for rebalancing is greatly reduced.

Fouse criticized the idea of the leveraged low-beta fund within Wells Fargo, earning Black's ire: "I said `Well, Jeez, there's something wrong here, guys. We're going to end up levering utilities and food stocks, and the future earnings developments of these groups can wander away from what was expected and you're going to find yourself in trouble.' ... Fischer Black got so angry with me ... he got up and left the conference room." (Fouse interview) 5.

On the efficient-market view expressed by Scholes, however, the demand curve for a corporation's stock is flat: "... the demand curve facing individual shareholders is essentially horizontal" (Scholes 1972, p. 182). Equivalently, the price elasticity of demand "the percentage change in the quantity of a good demanded divided by the corresponding percentage change in its price" (Begg, Fischer, and Dornbusch 1997, p. 57) is in the case of stock "virtually infinite" (Scholes 1970, p. 1). Above a certain price level, the stock would not be purchased at all; below that level, there would be effectively infinite demand for it. The view that the demand curve for a stock is flat seems to have been deeply counterintuitive to traditional finance scholars, and I suspect remains so to many practitioners, yet Scholes concluded that his Ph.D. research, an empirical study of "secondary distributions" (sales of large blocks of already-issued stock), was consistent with this view (Scholes 1970, 1972).

Officer happens to have observed empirically something I was predicting with the new more general model. (True, I did not publish this prediction until much later.)

No one would have reacted badly to a distribution with an infinite fifth moment; nevertheless its exponential would also have an infinite expectation. Altogether, it used to be safe for scientists to believe that the universe is organized for simplicity and the conveniences of the mathematicians. But my fifty-year long study of complexity suggests otherwise. … For example, what can you deduce from knowing the average sales of a US software firm in 2003? It is the ratio with a numerator somewhat higher than the sales of Microsoft and a denominator that is meaningless because it is overly dependent on the smallest sales used in taking the average. What about the expectation of a `nearly' log-normal variable? It is so extremely sensitive to inevitable deviations from lognormality that it hardly matters. … The lesson for finance: divergences may or may not be significant, but must not be papered over in advance.

The core of arbitrage pricing theory is well described by Perry Mehrling. In the theory, "a capital asset ... represents a portfolio of exposures to different risk factors whose prices are determined by the preferences of wealth holders. The price of the capital asset is then, so goes the argument, equal to the weighted sum of the risk factor prices, with the weights proportional to the exposures to each factor. The argument depends on something called the principle of no arbitrage. If the capital asset were at any other price, then some component risk factor must have an implied price that is different from its price as implied by other capital assets, and riskless arbitrage profits must be attainable by buying the risk factor at the lower price and selling it at the higher price" (Mehrling 2000, p. 83). The risk factors are not specified in the arbitrage pricing model itself, but in its empirical applications they are identified by statistical techniques. The model is in a sense a generalization of the Capital Asset Pricing Model's single risk factor, and it predicts an overall equilibrium relationship of an analogous form: "every equilibrium will be characterized by a linear relationship between each asset's expected return and its return's response amplitudes, or loadings, on the common factors" (Roll and Ross 1980, p. 1074).

I am extremely grateful to Emily Schmitz of the Chicago Board Options Exchange for providing me with a copy of the Nathan Report. Like Baumol, Malkiel, and Quandt, Merton Miller also contributed an appendix to the Nathan Report. He felt that some of the case being made for options trading such as Malkiel and Quandt's conclusion that institutions such as university endowments could earn enhanced investment returns by selling options on stocks they held violated the efficient-market hypothesis. "Organized option trading in stocks is not the greatest invention since sliced bread as some of the puffing by spokesmen for the Board [of Trade] often seems to suggest," wrote Miller. Such trading was only "a modest marginal improvement in the structure of the capital markets," albeit "one still very much worth making" (Nathan Associates 1969, vol. 2, p. 51).

Merton (ibid., pp. 143-144) showed, under quite general conditions, that the early exercise of an American call on a non-dividend-bearing stock is never optimal, so its theoretical value is equal to that of a European call.

25. Consider, for example, these two positions on a stock that pays no dividends: (a) a call option with a strike price equal to the current stock price, plus cash equivalent to the stock price; and (b) buying the stock in question plus a put with the same strike price as the call. (The call and the put have the same expiration date, and both are European: they can be exercised only at their expiration.) The payoff of the two positions is equal. If the stock price rises above the strike price, the payoff from exercising the call is just the stock's gain in price, while if the stock price falls below the strike price, exercise of the put eliminates the loss on the stock. Factoring in the capacity to earn interest on the cash yields a simple equation connecting put and call prices.

The arbitrage's profitability was enhanced by a quirk of U.S. tax law, which meant that 60 percent of profits on futures were treated as long-term capital gains, "regardless of how long you hold them" (Weinberger interview).

In the analysis by Roll, "computer-designed trading" is judged to have been present in five of the 23 national markets examined: Canada, France, Japan, U.K., and U.S. (Roll 1988, pp. 29-30). This judgment, however, masks large differences in scale. For example, the Bank of England reported that: "In contrast to the US markets, the use of stock-related derivative products in the United Kingdom is very limited and the volume of stock-index-related business is very small" (Anonymous 1988a, p. 58).

Financial economists refer to the possibility that prices may reflect the subjective probability of an event that does not in fact take place in the time period studied as a "peso problem." The reference is to the influence on the prices of Mexican assets in the period of managed exchange rates of the possibility of a sudden, large devaluation of the peso.

The German options market did manifest a skew after 1987, but it was opposite in direction to that in the U.S. (Bates 2000, p. 225).

Many swaps "cancel out" other swaps (see the previous note), and the replacement cost of a swap is usually much less than the notional principal, which does not change hands. So chapter l's caveats about the way in which total notional amounts overstate the economic importance of derivatives certainly apply to swaps.

A particular idiosyncrasy identified by LTCM was that restrictions on many Italian banks meant that they had to hold Italian government short-maturity bills, Buoni Ordinari del Tesoro (BOTs), which were therefore anomalously expensive. LTCM expected this difference to reduce in size and entered into swap trades accordingly.

5. "[There] seems little evidence of the `publish or perish' syndrome in this area [finance] before 1960" (Whitley 1986b, p. 173). Regression-based analysis of the determinants of academic economists' salaries found that in the 1980s "a publication in the top journal was worth an increase in salary of $1602," an amount equivalent to roughly 4 percent of the average salary of an academic economist in the period (Colander 1989, p. 143, drawing on Sauer 1998). The top journal identified by Sauer was the Journal of Political Economy; other studies suggest that the American Economic Review held first rank (Grubel and Boland 1986, p. 425).

7. That markets cannot achieve full informational efficiency that "there is an equilibrium degree of disequilibrium" is the claim of Grossman and Stiglitz (1980, p. 393), but their work was not orthodox financial economics.

9. There is a sense in which it was the Capital Asset Pricing Model that "ought" to have inspired index funds (because it posits that the market portfolio is mean-variance efficient), but, as noted in chapter 3, in practice the inspiration tended to be the simpler intuition that "you can't systematically beat the market."

12. Bruck 1989, pp. 11, 28; Milken 2000; Hickman 1958; Atkinson 1967. The one piece of academic research by Milken that I have been able to trace is a Wharton School working paper (Walter and Milken 1973), which Celso Brunetti kindly located for me. It discusses capital structure, but does not cite Modigliani and Miller. A representative of Mr. Milken declined my request for an interview with him.

The prominent financial economists Michael Jensen and Stephen Ross played leading roles in the development of agency theory. (See, e.g., Jensen and Meckling 1976; Ross 1973.) The theory posited that agents (in this context, managers) could be relied upon only to pursue their own interests, not those of their principals (the stockholders). The solution was thus to design contracts in such a way that managers would maximize their rewards by doing what was in their principals' interest. Consultants seized on agency theory in particular on an article in the Haraard Business Review Jensen and Murphy 1990) that called for tighter links between managers' performance and their rewards and drew from it the lesson that alignment of interests could be achieved by making a larger proportion of managers' rewards take the form of the stock of the corporations they managed or options to buy that stock (Lowenstein 2004, pp. 13-21). To the extent that rewards geared to stock prices fueled the managerial deceit and wrongdoing of the 1990s and early 2000s, agency theory might be seen as having a perverse performative effect: forms of reward based on the agency-theory presumption that managers would pursue their own self-interest without scruples may have helped to generate a context in which managers did just that.

Metallgesellschaft's hedging program was in principle perfectly feasible, and (as in the case of LTCM) it appears as if the firm's losses would largely have been temporary had it not liquidated its futures market positions. However, price fluctuations generated large margin calls and cash outlays. These damaged Metallgesellschaft's credit rating and under accounting practice in Germany they had to be reported as huge losses (rather than deferred as they could have been under U.S. "hedge accounting" rules). The large size and predictability of the corporation's futures market activities also seem to have made those activities vulnerable to exploitation by other market participants.

Shiller, Robert J. 1988. "Portfolio Insurance and Other Investor Fashions as Factors in the 1987 Stock Market Crash." NBER Macroeconomics Annual: 287-295. … Shiller, Robert J. 2002. From Efficient Market Theory to Behavioral Finance. Discussion Paper 1385, Cowles Foundation for Research in Economics, New Haven.