Against the Gods: The Remarkable Story of Risk

by Peter L. Bernstein

  There is no inherent reason why a hedging instrument should wreak havoc on its owner. On the contrary, significant losses on a hedge should mean that the company's primary bet is simultaneously providing a big payoff. If an oil company loses on a hedge against a decline in the price of oil, it must be making a large profit on the higher price that caused the loss in the hedging contract; if an airline loses on a hedge against a rise in the price of oil, it must be because the price has fallen and lowered its operating costs.

  These disasters in derivative deals among big-name companies occurred for the simple reason that corporate executives ended up adding to their exposure to volatility rather than limiting it. They turned the company's treasury into a profit center. They treated lowprobability events as being impossible. When given a choice between a certain loss and a gamble, they chose the gamble. They ignored the most fundamental principle of investment theory: you cannot expect to make large profits without taking the risk of large losses.

  In deep trouble in a series of derivative transactions with Bankers Trust, Gibson Greetings provided a perfect example of prospect theory in action. Bankers Trust told the treasurer at one point in 1994 that Gibson's losses stood at $17.5 million, but, according to the treasurer, Bankers Trust also told him the losses could be "potentially without limit." Gibson promptly signed a new arrangement that capped the loss at $27.5 million but, if everything worked exactly right, could reduce the loss to only $3 million. Prospect theory predicts that people with losses will gamble in preference to accepting a sure loss. Gibson could have liquidated out at $17.5 million for certain but chose the gamble instead. As a director of another company described what happens in such situations, "It's a lot like gambling. You get in deep. And you think `I'll get out of it with this one last trade."' But Gibson did not get out of it on one last trade. As the loss column headed toward $20.7 million, Gibson called it quits: it sued Bankers Trust for having violated a "fiduciary relationship."

  Procter & Gamble, as described by Carol Loomis, a reporter for Fortune magazine, was being "chewed up [during 1994] by derivatives that incorporated astounding leverage and confounding complexity." These derivatives also were created by Bankers Trust, whose full-page ads in business and financial publications proclaimed, "Risk wears many disguises. Helping you see beneath its surface is the strength of Bankers Trust."

  Procter & Gamble's management dutifully followed Gibson in acting out prospect theory. Whether Raymond Mains, the corporate treasurer, was doing a good job was not determined by the absolute level of interest rates that the company paid to borrow money; the company judged his performance on a what-have-you-done-for-us-lately basis. In other words, they looked only at how much less Mains was paying compared with what money had cost them the year before. The heat in that oven was hot. In a sarcastic comment on the company's disaster, Nobel Laureate Merton Miller joked, "You know Procter & Gamble? Procter is the widow and Gamble is the orphan."

  The deal that triggered all the trouble was extremely complicated in detail-fun in the negotiating, like analyzing a case at Harvard Business School. It was signed in the fall of 1993, following four years in which short-term interest rates declined almost without interruption from about 10% to less than 3%; the deal revealed P&G's belief that, after such an extended decline, a significant increase in interest rates was so unlikely as to be impossible. Clearly, nobody in the executive offices had read Galton-regression to the mean appears to have been unknown to them.

  They bet the ranch on what would have been no more than a modest saving if interest rates had remained stable or had fallen further. The deal involved a notional amount of $200 million in the form of a five-year loan from Bankers to P&G, but the maximum interest saving to the company compared with what it would have paid in a straight commercial-paper borrowing would have been $7.5 million over the life of the loan. According to the Fortune article, if things went wrong instead of right-if interest rates rose instead of continuing to fall-the exposure would put the company into the position of "covering the risks of interest rate earthquakes."

  On February 4, 1994, only four months after the deal was signed, the Federal Reserve startled the markets by raising short-term interest rates. As Loomis reported, "With remarkable fury, these quakes then occurred." It is obvious that the P&G executives had never heard of Kahneman and Tversky either, for on February 14, already showing losses, the company entered into yet another contract, this one for $94 million over years, that had them betting once again that interest rates would fall.

  Interest rates did not fall. The interest rate on commercial paper had climbed from 3 1/4% in February to 6 1/2% in December while the prime rate moved from 6% to 8 1/2%. It was a catastrophe for P&G. Under the initial contract, they were left with a commitment to pay Bankers Trust 14 1/2 percentage points in interest until late 1998 and, under the second contract, to pay 16.4 percentage points in interest over the same period.

  Bankers Trust is being sued here, too, and has received no payments from P&G at this writing. Mr. Mains is no longer with the company.

  What are we to make of all this? Are derivatives a suicidal invention of the devil or the last word in risk management?* Bad enough that fine companies like Procter & Gamble and Gibson Greetings can get into trouble, but is the entire financial system at risk because so many people are trying to shed risks and slough them off onto someone else? How well can the someone else manage that responsibility? In a more fundamental sense, as the twentieth century draws to a close, what does the immense popularity of derivatives tell us about society's view of risk and the uncertain future that lies ahead? I shall postpone my response to that last question to the next, and final, chapter.

  James Morgan, a columnist for the Financial Times, once remarked, "A derivative is like a razor. You can use it to shave yourself.... Or you can use it to commit suicide."10 Users of derivatives have that choice. They do not have to use derivatives to commit suicide.

  Precisely who persuaded whom to do what in the case of Procter & Gamble and the other companies remains obscure, but the cause of the disasters is clear enough: they took the risk of volatility instead of hedging it. They made the stability of their cash flows, and thereby the integrity of their long-term future, hostages to the accuracy of their interest-rate forecasts. While Bankers Trust and the other dealers in derivatives were managing their books on the basis of Pascal's Triangle, Gauss's bell curves, and Markowitz's covariances, the corporate risk-takers were relying on Keynesian degrees of belief. This was not the place to bet the corporate ranch or to act out failures of invariance.

  Speculators who think they know what the future holds always risk being wrong and losing out. The long history of finance is cluttered with stories of fortunes lost on big bets. No one needed derivatives in order to go broke in a hurry. No one need go broke any faster just because derivatives have become a widely used financial instrument in our times. The instrument is the messenger; the investor is the message.

  The losses at a few corporations in 1994 made banner headlines but posed no threat to anyone else. But suppose the errors had run in the other direction-that is, suppose the corporation had had huge winnings instead of losses. Would the counterparties to these transactions have been able to pay? The counterparties to most of the big tailormade derivatives contracts are major money-center banks and top-tier investment bankers and insurance companies. The big players all made a lot less money in 1994, the year of surprises, than they had made in 1993, but none of them was at any point in trouble. Bankers Trust, for example, reported that losses "were all within our capital limits and we knew the extent of our exposures all the time.... The risk control processes worked fine."

  The financial solvency of these institutions supports the financial solvency of the world economic system itself. Every single day, they are involved in millions of transactions involving trillions of dollars in a complex set of arrangements whose smooth functioning is essential. The margin for error is miniscule. Poor con
trols over the size and diversification of exposures are intolerable when the underlying volatility of the derivatives is so high and when so much is at stake beyond the fortunes of any single institution.

  Everyone is aware of the dangers inherent in this situation, from the management of each institution on up to the governmental regulatory agencies that supervise the system. So-called "systemic risk" has become a parlor word in those circles and is the focus of attention at central banks and ministries of finance around the world. The measurement of the overall risk exposure in the system has been progressing in both comprehensiveness and sophistication.*

  But there is only a fine line between guaranteeing absolute safety and stifling the development of financial innovations that, properly handled, could reduce the volatility of corporate cash flows. Corporations that shelter their cash flows from volatility can afford to take greater internal risks in the form of higher levels of investment or expenditures on research and development. Financial institutions themselves are vulnerable to volatility in interest rates and exchange rates; to the extent that they can hedge that volatility, they can extend more credit to a wider universe of deserving borrowers.

  Society stands to benefit from such an environment. In November 1994, Alan Greenspan, Chairman of the Federal Reserve Board, declared:

  There are some who would argue that the role of the bank supervisor is to minimize or even eliminate bank failure; but this view is mistaken, in my judgment. The willingness to take risk is essential to the growth of a free market economy.... [I]f all savers and their financial intermediaries invested only in risk-free assets, the potential for business growth would never be realized."

  he great statistician Maurice Kendall once wrote, "Humanity did not take control of society out of the realm of Divine Providence ... to put it at the mercy of the laws of chance."' As we look ahead toward the new millennium, what are the prospects that we can finish that job, that we can hope to bring more risks under control and make progress at the same time?

  The answer must focus on Leibniz's admonition of 1703, which is as pertinent today as it was when he sent it off to Jacob Bernoulli: "Nature has established patterns originating in the return of events, but only for the most part." As I pointed out in the Introduction, that qualification is the key to the whole story. Without it, there would be no risk, for everything would be predictable. Without it, there would be no change, for every event would be identical to a previous event. Without it, life would have no mystery.

  The effort to comprehend the meaning of nature's tendency to repeat itself, but only imperfectly, is what motivated the heroes of this book. But despite the many ingenious tools they created to attack the puzzle, much remains unsolved. Discontinuities, irregularities, and volatilities seem to be proliferating rather than diminishing. In the world of finance, new instruments turn up at a bewildering pace, new markets are growing faster than old markets, and global interdependence makes risk management increasingly complex. Economic insecurity, especially in the job market, makes daily headlines. The environment, health, personal safety, and even the planet Earth itself appear to be under attack from enemies never before encountered.

  The goal of wresting society from the mercy of the laws of chance continues to elude us. Why?

  For Leibniz, the difficulty in generalizing from samples of information arises from nature's complexity, not from its waywardness. He believed that there is too much going on for us to figure it all out by studying a set of finite experiments, but, like most of his contemporaries, he was convinced that there was an underlying order to the whole process, ordained by the Almighty. The missing part to which he alluded with "only for the most part" was not random but an invisible element of the whole structure.

  Three hundred years later, Albert Einstein struck the same note. In a famous comment that appeared in a letter to his fellow-physicist Max Born, Einstein declared, "You believe in a God who plays with dice, and I in complete law and order in a world which objectively exists."2

  Bernoulli and Einstein may be correct that God does not play with dice, but, for better or for worse and in spite of all our efforts, human beings do not enjoy complete knowledge of the laws that define the order of the objectively existing world.

  Bernoulli and Einstein were scientists concerned with the behavior of the natural world, but human beings must contend with the behavior of something beyond the patterns of nature: themselves. Indeed, as civilization has pushed forward, nature's vagaries have mattered less and the decisions of people have mattered more.

  Yet the growing interdependence of humanity was not a concern to any of the innovators in this story until we come to Knight and Keynes in the twentieth century. Most of these men lived in the late Renaissance, the Enlightenment, or the Victorian age, and so they thought about probability in terms of nature and visualized human beings as acting with the same degree of regularity and predictability as they found in nature.

  Behavior was simply not part of their deliberations. Their emphasis was on games of chance, disease, and life expectancies, whose outcomes are ordained by nature, not by human decisions. Human beings were always assumed to be rational (Daniel Bernoulli describes rationality as "the nature of man"), which simplifies matters because it makes human behavior as predictable as nature's-perhaps more so. This view led to the introduction of terminology from the natural sciences to explain both economic and social phenomena. The process of quantifying subjective matters like preferences and risk aversion was taken for granted and above dispute. In all their examples, no decision by any single individual had any influence on the welfare of any other individual.

  The break comes with Knight and Keynes, both writing in the aftermath of the First World War. Their "radically distinct notion" of uncertainty had nothing whatsoever to do with nature or with the debate between Einstein and Born. Uncertainty is a consequence of the irrationalities that Knight and Keynes perceived in human nature, which means that the analysis of decision and choice would no longer be limited to human beings in isolated environments like Robinson Crusoe's. Even von Neumann, with his passionate belief in rationality, analyzes risky decisions in a world where the decisions of each individual have an impact on others, and where each individual must consider the probable responses of others to his or her own decisions. From there, it is only a short distance to Kahneman and Tversky's inquiries into the failure of invariance and the behavioral investigations of the Theory Police.

  Although the solutions to much of the mystery that Leibniz perceived in nature were well in hand by the twentieth century, we are still trying to understand the even more tantalizing mystery of how human beings make choices and respond to risk. Echoing Leibniz, G.K. Chesterton, a novelist and essayist rather than a scientist, has described the modern view this way:

  The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.'

  In such a world, are probability, regression to the mean, and diversification useless? Is it even possible to adapt the powerful tools that interpret the variations of nature to the search for the roots of inexactitude? Will wildness always lie in wait?

  Proponents of chaos theory, a relatively new alternative to the ideas of Pascal and others, claim to have revealed the hidden source of inexactitude. According to chaos theorists, it springs from a phenomenon called "nonlinearity." Nonlinearity means that results are not proportionate to the cause. But chaos theory also joins with Laplace, Poincare, and Einstein in insisting that all results have a cause-like the balanced cone that topples over in response to "a very slight tremor."

  Students of chaos theory reject the symmetry of the bell curve as a description of reality. They hold in contempt li
near statistical systems in which, for example, the magnitude of an expected reward is assumed to be consistent with the magnitude of the risks taken to achieve it, or, in general, where results achieved bear a systematic relationship to efforts expended. Consequently, they reject conventional theories of probability, finance, and economics. To them, Pascal's Arithmetic Triangle is a toy for children, Francis Galton was a fool, and Quetelet's beloved bell curve is a caricature of reality.

  Dimitris Chorafas, an articulate commentator on chaos theory, describes chaos as "... a time evolution with sensitive dependence on initial conditions."4 The most popular example of this concept is the flutter of a butterfly's wings in Hawaii that is the ultimate cause of a hurricane in the Caribbean. According to Chorafas, chaos theorists see the world "in a state of vitality... characterized by turbulence and volatility."5 This is a world in which deviations from the norm do not cluster symmetrically on either side of the average, as Gauss's normal distribution predicts; it is a craggy world in which Galton's regression to the mean makes no sense, because the mean is always in a state of flux. The idea of a norm does not exist in chaos theory.

  Chaos theory carries Poincare's notion of the ubiquitous nature of cause and effect to its logical extreme by rejecting the concept of discontinuity. What appears to be discontinuity is not an abrupt break with the past but the logical consequence of preceding events. In a world of chaos, wildness is always waiting to show itself.

  Making chaos theory operational is something else again. According to Chorafas, "The signature of a chaotic time series ... is that prediction accuracy falls off with the increasing passage of time." This view leaves the practitioners of chaos theory caught up in a world of minutiae, in which all the signals are tiny and everything else is mere noise.

  As forecasters in financial markets who focus on volatility, practitioners of chaos theory have accumulated immense quantities of transactions data that have enabled them, with some success, to predict changes in security prices and exchange rates, as well as variations in risk, within the near future.6 They have even discovered that roulette wheels do not produce completely random results, though the advantage bestowed by that discovery is too small to make any gambler rich.