Robert Merton Delivers Block Community Lecture

September 15, 1998

Robert Merton (center), whose community lecture on mathematics in finance found a receptive audience in Toronto, is welcomed by SIAM president John Guckenheimer and Joyce McLaughlin, chair of the SIAM Board of Trustees.

James Case

SIAM's second annual I.E. Block Community Lecture was delivered in Toronto, at the 1998 SIAM Annual Meeting, by Robert Merton, last year's co-recipient (with Myron Scholes) of the Nobel Prize in economics. Along with Fisher Black, now deceased, the two had devised the famous Black-Scholes formula for pricing a (European) stock option. The combination of academic financial research with financial practice, Merton told the audience, has been "a central theme" of his professional life. Stochastic differential and integral equations, stochastic dynamic programming, and partial differential equations," he said, have become "the core tools" in a discipline that previously relied on "a collection of anecdotes, rules of thumb, and shuffling of accounting data." In the rapidly expanding universe of quantitative methods, the Black-Scholes formula stands alone as "the most influential development in terms of impact on financial practice."

Announcing that he would resist the temptation to derive "new financial models for practice" or "introduce any mathematical tools hitherto unknown to finance which might help to break new ground in the theory," he directed those in search of such enlightenment to the meeting's several related technical sessions. In this he was surely well advised, as those sessions played to SRO audiences in the university's large, well-equipped classrooms and reflected the rapid pace at which the field is progressing. Instead, Merton touched lightly in his address on the subject's remarkable but well-documented past, expressed mildly controversial opinions concerning the present, and ventured a few predictions about future interactions between mathematics and the world of finance. Without belittling the impact of quantitative models on financial practice-not to mention on the lives of ordinary citizens-he managed to convey the impression that the past was but prelude to even more startling developments.

Research Predicts Practice
Among Merton's better-known empirical studies is a 1981 paper (On Market Timing and Investment Performance, J. Business, Vol. 54, No. 3; see table 3, p. 378) in which he pointed out that $1000 invested in stocks on the New York Stock Exchange on January 1, 1927, and shifted back and forth at the beginning of each month between stocks and short-term (interest-bearing) bonds in such a way as to reap the higher of the two possible returns for the intervening month, would have been worth $5,362,212,000 by the end of 1978. Had those 624 binary decisions been impeccably made over the 52 eventful years in question, the initial investment would have appreciated at an average annual rate of 34.65%, compared with only 8.47% had the original stocks been held continuously! The point is that perfect foresight would have been required to make those 624 correct decisions, and money managers have nothing of the kind. The best might average 10% or even 11% growth in the long term, by shifting between stocks and bonds in a timely manner, but none achieves anything like 35% average rates of return. The inventor of a genuine crystal ball won't need to sell stocks and bonds for a living!

Merton, who believes that today's financial research predicts tomorrow's financial practice, and interprets a 1954 paper of Kenneth Arrow as foretelling the eventual development of derivative securities, traced the origins of mathematical finance to Louis Bachelier's 1900 dissertation on option pricing at the Paris Bourse (stock exchange). Kiyoshi It�, Merton told the audience as an aside, once confided to him that Bachelier's work had exerted far more influence on his own than did Norbert Wiener's subsequent-and more widely acclaimed-formalization of similar material. The same may be said of Paul Samuelson's 1965 theory of rational warrant pricing, perhaps the most direct precursor of the original Black-Scholes paper, which circulated in and around Cambridge, Massachusetts, for some years prior to publication in 1973.

Having been present at the creation, Merton could state with authority that the Black-Scholes model was developed entirely in theory, with "essentially no reference to empirical option pricing data as motivation for its formulation." Yet within two years of the opening of the Chicago Board of Options Exchange, in April 1973,

"traders there were using the model to both price and hedge their option positions. It was so widely used that Texas Instruments began selling a hand-held calculator specially programmed to produce Black-Scholes option prices and hedge ratios right in the trading pit. . . . The rapid adoption of the option model was all the more impressive, as the mathematics used in that model were not part of the standard mathematical training of either academic economists or practitioner traders."

Despite scattered attempts throughout the 1950s and 1960s to render quantitative methods useful to money managers, it was not until the mid-1970s that wholesale adoptions began. Merton attributed the abrupt about-face to "manifest need."

Describing the 1960s as a decade of "low volatility," during which the stock market rose rather steadily, interest rates were relatively stable, and international exchange rates remained fixed, he saw in those years little incentive for financial managers to adopt new and unproven technologies designed to insulate investors from the effects of unwanted risk.

Perceptions began to change, however, in the early 1970s. The abandonment of the Bretton Woods agreement, which had fixed international currency exchange rates since the end of World War II, the subsequent burgeoning of the price of gold, the concomitant devaluation of the U.S. dollar, the OPEC oil embargo of October 1973, the onset of double-digit inflation, and the Great Bear Market of 1974 combined---along with improved computer and telecommunications technology---to drive perceived levels of risk to record highs, thereby speeding the acceptance of "rocket science" by the investment community.

Other developments of that eventful decade included the emergence of the national mortgage market, featuring a wide variety of mortgage-backed securities; the passage of the Employee Retirement Income Security Act (ERISA) in 1974, which spurred the development of a vast pension-fund industry; the first money-market fund with check-writing privileges; and the explosive growth in mutual fund assets, from $48 billion 25 years ago to $4.3 trillion today (a 90-fold increase), with a single institution---Fidelity Investments---accounting for some $500 billion. In this same period, average daily trading volume on the New York Stock Exchange grew from 12 million to more than 300 million shares. Europe and Asia hosted even more dramatic change. The cumulative impact has affected all of us-as employers, employees, and overseers of the financial system---while stimulating the demand for ever more sophisticated financial products and models.

At present, the globalization process is far from complete, and, although its pace may slacken as Japan, Thailand, Korea, and the other "Asian Tigers" undertake needed reform, Merton considers a halt or reversal unlikely. As a result, demand for innovative financial products and services seems unlikely to weaken. On the contrary, he pointed out, so many potential efficiencies remain unrealized, and so much theoretical work remains to be done, that demand may in fact intensify. In particular, the portfolio-selection process needs to be purged of its reliance on "static" optimization techniques, which are incapable, by their very nature, of evaluating intertemporal tradeoffs. A fully satisfactory method of portfolio selection must come to grips with the large nonlinear systems of multivariate partial differential equations of dynamic optimality.

User-friendly Financial Products
Merton explained another need---for "user-friendly" financial services---by likening financial products to electronic entertainment centers. The first entertainment systems, he pointed out, were simple devices, standing waist high in a corner of the living room, featuring a rotary volume-control button, which doubled as a power button, and a channel (or frequency) tuner. More advanced models included record players and could be switched back and forth between radio and recorded sound. Later came Hi-Fi and stereo, with their bewildering varieties of mix-and-match components, not unlikely to occupy an entire wall of shelves. Yet today the trend is toward devices that pack the versatility of a 1980s-style stereo system into the space occupied by a 1930s-model radio and are almost as easy to operate.

The financial community, he suggested, should take note. Even now, it could be offering estate-planning packages tailored to individual needs, by requiring prospective customers to fill out a standard form specifying the number and ages of children to be educated, expected retirement age, the fraction of peak earnings desired thereafter, key tax liabilities, and so on. Providers would then be obliged to explain the tradeoffs required to attain an acceptable mix of the foregoing benefits, and to update each contract-holder's plan on a regular basis. All else being equal, it would then be possible to compare contracts on the basis of post-retirement benefits alone. Ordinary customers, he observed, would be far better served by such a system than by the present one, in which the responsibility for making important and technically complex decisions involving significant risk and long-term intertemporal exchange (of benefits issuing from, among other things, the seven thousand odd separate and distinct mutual funds now in existence) devolves upon individual households.

The individuals in question, he said, were not obliged to make such decisions in the past, are untrained to make them at present, and seem unlikely to execute them efficiently in the foreseeable future, despite elaborate and well-meaning proposals to furnish appropriate training! Paradoxically, the need to make financial products easier for the public to understand will make them more difficult to design. Merton likened the challenge awaiting the industry to that faced by a ballerina, who is expected to make even the most difficult jumps, attitudes, and pirouettes appear effortless to the audience. He expressed confidence, nevertheless, that the industry is or soon will be equal to the task.

To explain the role of derivative securities in the globalization process, Merton resorted to yet another analogy. Imagine commerce to be an ideal fluid---not unlike natural gas---coursing through complex pipeline networks in accordance with the laws of supply and demand. And imagine those pipelines to vary in cross-sectional geometry from one country to another, being square in one, round in the next, and triangular in yet a third. A wide variety of "adapters" would then be needed to interconnect one national pipeline system with another. With such adapters, the fluid could continue to flow as before in each individual nation, while crossing international borders with ease. Derivative securities, Merton suggested, constitute the very adapters needed to incorporate the global village, since they dilute the risks inherent in trade between national economies whose fortunes---and currency values---may diverge without warning. His analogy is particularly apt as applied to currency-backed derivatives, but it applies with almost equal force to many commodity futures, interest rate swaps, and so on.

If commerce were an ideal fluid. . . . Making one of several very effective analogies, Robert Merton explained the role of derivative securities in diluting the risks inherent in global trade.

Risk---Perceived and Objective
Several times during his talk, and again in the lively question-and-answer session that followed, Merton addressed the question of system safety. It is true, he conceded, that some observers perceive greater risks in the modern world, despite the presence of modern risk-management techniques, than lurked in the more staid and familiar world of the 1950s and 1960s. With everything connected to everything else, there is reason to doubt that one part of the world can be insulated against a recession or stock market crash occurring in another. Accordingly, defenders of the status quo are often asked how long the public can be quarantined against the effects of derivative-related disasters, such as those recently suffered by Orange County, California, Barings Bank, LTD, and Proctor and Gamble, as well as regional ills like those now plaguing Southeast Asia.

Merton responded to such doubts in several ways. Early in his address, he pointed out that the most damaging of recent financial disruptions, such as the American S&L crisis of the 1980s, the roughly contemporaneous third-world debt crisis, and the current Asian crisis, appeared to be the result of "traditional institutional risks such as commercial, real-estate, and less-developed-country lending, loan guarantees, and equity-share holdings; risks that are typically evaluated using relatively low-tech financial models." The very fact that we can attach specific names to the Barings Bank, Orange County, and Proctor and Gamble debacles suggests that they are less frequent and therefore less threatening than traditional disasters. Until data to the contrary are in hand, Merton seems content to view them as "unfortunate pathologies rather than indicators of systemic flaws." More emphasis, he added, should be placed on the "physiology" of this financial technology-the way it works when it works as it should-since it does exactly that most of the time.

Later he suggested that inadequate understanding of the new environment may lead to higher levels of perceived risk "even when the objective level of risk in the system remains unchanged or is actually reduced." If so, he suggests that the time to deal with the widening "knowledge gap" is now, since the pace of financial innovation seems likely to accelerate into the 21st century.

Finally, during the question-and-answer period, he likened global finance to air travel, the safety of which did not increase appreciably with the introduction of ultrasafe aircraft, like the European Airbus, which is equipped to land in zero-visibility conditions and carries a host of state-of-the-art safety features. Because such planes can and do land with zero visibility, they are allowed to take off in conditions previously deemed unsafe. As a result, more flights are completed in equal safety, rather than an equal number of flights in greater safety. Because safety levels are collectively chosen, it seems fair to conclude that the public is satisfied with the new arrangement. And, by analogy, the arrangement whereby more purchases are financed at traditional levels of risk, rather than the previous number at reduced risk, seems to be equally satisfactory.

What Merton did not address---in part because he was not asked about it---is the nagging suspicion that risk management is a kind of "protection racket" in which new risks are created by the same globalizing multinational elite that earns so much of its income by selling insurance against commercial risk. Merton seemed untroubled by such suspicions, and it would have been interesting---perhaps even reassuring---to know why.

James Case is an independent consultant who lives in Baltimore, Maryland.

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