Introduction
What is it that distinguishes the thousands of years of history from what we think of as modern times? The answer goes way beyond the progress of science, technology, capitalism, and democracy.
The distant past was studded with brilliant scientists, mathematicians, inventors, technologists, and political philosophers. Hundreds of years before the birth of Christ, the skies had been mapped, the great library of Alexandria built, and Euclid’s geometry taught. Demand for technological innovation in warfare was as insatiable then as it is today. Coal, oil, iron, and copper have been at the service of human beings for millennia, and travel and communication mark the very beginnings of recorded civilization.
The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature. Until human beings discovered a way across that boundary, the future was a mirror of the past or the murky domain of oracles and soothsayers who held a monopoly over knowledge of anticipated events.
This book tells the story of a group of thinkers whose remarkable vision revealed how to put the future at the service of the present. By showing the world how to understand risk, measure it, and weigh its consequences, they converted risk-taking into one of the prime catalysts that drives modern Western society. Like Prometheus, they defied the gods and probed the darkness in search of the light that converted the future from an enemy into an opportunity. The transformation in attitudes toward risk management unleashed by their achievements has channeled the human passion for games and wagering into economic growth, improved quality of life, and technological progress.
By defining a rational process of risk-taking, these innovators provided the missing ingredient that has propelled science and enterprise into the world of speed, power, instant communication, and sophisticated finance that marks our own age. Their discoveries about the nature of risk, and the art and science of choice, lie at the core of our modern market economy that nations around the world are hastening to join. Given all its problems and pitfalls, the free economy, with choice at its center, has brought humanity unparalleled access to the good things of life.
The ability to define what may happen in the future and to choose among alternatives lies at the heart of contemporary societies. Risk management guides us over a vast range of decision-making, from allocating wealth to safeguarding public health, from waging war to planning a family, from paying insurance premiums to wearing a seatbelt, from planting corn to marketing cornflakes.
In the old days, the tools of farming, manufacture, business management, and communication were simple. Breakdowns were frequent, but repairs could be made without calling the plumber, the electrician, the computer scientist—or the accountants and the investment advisers. Failure in one area seldom had direct impact on another. Today, the tools we use are complex, and breakdowns can be catastrophic, with far-reaching consequences. We must be constantly aware of the likelihood of malfunctions and errors. Without a command of probability theory and other instruments of risk management, engineers could never have designed the great bridges that span our widest rivers, homes would still be heated by fireplaces or parlor stoves, electric power utilities would not exist, polio would still be maiming children, no airplanes would fly, and space travel would be just a dream.a Without insurance in its many varieties, the death of the breadwinner would reduce young families to starvation or charity, even more people would be denied health care, and only the wealthiest could afford to own a home. If farmers were unable to sell their crops at a price fixed before harvest, they would produce far less food than they do.
If we had no liquid capital markets that enable savers to diversify their risks, if investors were limited to owning just one stock (as they were in the early days of capitalism), the great innovative enterprises that define our age—companies like Microsoft, Merck, DuPont, Alcoa, Boeing, and McDonald’s—might never have come into being. The capacity to manage risk, and with it the appetite to take risk and make forward-looking choices, are key elements of the energy that drives the economic system forward.
The modern conception of risk is rooted in the Hindu-Arabic numbering system that reached the West seven to eight hundred years ago. But the serious study of risk began during the Renaissance, when people broke loose from the constraints of the past and subjected long-held beliefs to open challenge. This was a time when much of the world was to be discovered and its resources exploited. It was a time of religious turmoil, nascent capitalism, and a vigorous approach to science and the future.
In 1654, a time when the Renaissance was in full flower, the Chevalier de Méré, a French nobleman with a taste for both gambling and mathematics, challenged the famed French mathematician Blaise Pascal to solve a puzzle. The question was how to divide the stakes of an unfinished game of chance between two players when one of them is ahead. The puzzle had confounded mathematicians since it was posed some two hundred years earlier by the monk Luca Paccioli. This was the man who brought double-entry bookkeeping to the attention of the business managers of his day—and tutored Leonardo da Vinci in the multiplication tables. Pascal turned for help to Pierre de Fermat, a lawyer who was also a brilliant mathematician. The outcome of their collaboration was intellectual dynamite. What might appear to have been a seventeenth-century version of the game of Trivial Pursuit led to the discovery of the theory of probability, the mathematical heart of the concept of risk.
Their solution to Paccioli’s puzzle meant that people could for the first time make decisions and forecast the future with the help of numbers. In the medieval and ancient worlds, even in preliterate and peasant societies, people managed to make decisions, advance their interests, and carry on trade, but with no real understanding of risk or the nature of decision-making. Today, we rely less on superstition and tradition than people did in the past, not because we are more rational, but because our understanding of risk enables us to make decisions in a rational mode.
At the time Pascal and Fermat made their breakthrough into the fascinating world of probability, society was experiencing an extraordinary wave of innovation and exploration. By 1654, the roundness of the earth was an established fact, vast new lands had been discovered, gunpowder was reducing medieval castles to dust, printing with movable type had ceased to be a novelty, artists were skilled in the use of perspective, wealth was pouring into Europe, and the Amsterdam stock exchange was flourishing. Some years earlier, in the 1630s, the famed Dutch tulip bubble had burst as a result of the issuing of options whose essential features were identical to the sophisticated financial instruments in use today.
These developments had profound consequences that put mysticism on the run. By this time Martin Luther had had his say and halos had disappeared from most paintings of the Holy Trinity and the saints. William Harvey had overthrown the medical teachings of the ancients with his discovery of the circulation of blood—and Rembrandt had painted “The Anatomy Lesson,” with its cold, white, naked human body. In such an environment, someone would soon have worked out the theory of probability, even if the Chevalier de Méré had never confronted Pascal with his brainteaser.
As the years passed, mathematicians transformed probability theory from a gamblers’ toy into a powerful instrument for organizing, interpreting, and applying information. As one ingenious idea was piled on top of another, quantitative techniques of risk management emerged that have helped trigger the tempo of modern times.
By 1725, mathematicians were competing with one another in devising tables of life expectancies, and the English government was financing itself through the sale of life annuities. By the middle of the century, marine insurance had emerged as a flourishing, sophisticated business in London.
In 1703, Gottfried von Leibniz commented to the Swiss scientist and mathematician Jacob Bernoulli that “[N]ature has established patterns originating in the return of events, but only for the most part,”1 thereby prompting Bernoulli to invent the Law of Large Numbers and methods of statistical sampling that drive modern activities as varied as opinion polling, wine tasting, stock picking, and the testing of new drugs.b Leibniz’s admonition—”but only for the most part”—was more profound than he may have realized, for he provided the key to why there is such a thing as risk in the first place: without that qualification, everything would be predictable, and in a world where every event is identical to a previous event no change would ever occur.
In 1730, Abraham de Moivre suggested the structure of the normal distribution—also known as the bell curve—and discovered the concept of standard deviation. Together, these two concepts make up what is popularly known as the Law of Averages and are essential ingredients of modern techniques for quantifying risk. Eight years later, Daniel Bernoulli, Jacob’s nephew and an equally distinguished mathematician and scientist, first defined the systematic process by which most people make choices and reach decisions. Even more important, he propounded the idea that the satisfaction resulting from any small increase in wealth “will be inversely proportionate to the quantity of goods previously possessed.” With that innocent-sounding assertion, Bernoulli explained why King Midas was an unhappy man, why people tend to be risk-averse, and why prices must fall if customers are to be persuaded to buy more. Bernoulli’s statement stood as the dominant paradigm of rational behavior for the next 250 years and laid the groundwork for modern principles of investment management.
Almost exactly one hundred years after the collaboration between Pascal and Fermat, a dissident English minister named Thomas Bayes made a striking advance in statistics by demonstrating how to make better-informed decisions by mathematically blending new information into old information. Bayes’s theorem focuses on the frequent occasions when we have sound intuitive judgments about the probability of some event and want to understand how to alter those judgments as actual events unfold.
All the tools we use today in risk management and in the analysis of decisions and choice, from the strict rationality of game theory to the challenges of chaos theory, stem from the developments that took place between 1654 and 1760, with only two exceptions:
In 1875, Francis Galton, an amateur mathematician who was Charles Darwin’s first cousin, discovered regression to the mean, which explains why pride goeth before a fall and why clouds tend to have silver linings. Whenever we make any decision based on the expectation that matters will return to “normal,” we are employing the notion of regression to the mean.
In 1952, Nobel Laureate Harry Markowitz, then a young graduate student studying operations research at the University of Chicago, demonstrated mathematically why putting all your eggs in one basket is an unacceptably risky strategy and why diversification is the nearest an investor or business manager can ever come to a free lunch. That revelation touched off the intellectual movement that revolutionized Wall Street, corporate finance, and business decisions around the world; its effects are still being felt today.
The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on quantification and numbers, determined by the patterns of the past, and those who base their decisions on more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved.
The issue boils down to one’s view about the extent to which the past determines the future. We cannot quantify the future, because it is an unknown, but we have learned how to use numbers to scrutinize what happened in the past. But to what degree should we rely on the patterns of the past to tell us what the future will be like? Which matters more when facing a risk, the facts as we see them or our subjective belief in what lies hidden in the void of time? Is risk management a science or an art? Can we even tell for certain precisely where the dividing line between the two approaches lies?
It is one thing to set up a mathematical model that appears to explain everything. But when we face the struggle of daily life, of constant trial and error, the ambiguity of the facts as well as the power of the human heartbeat can obliterate the model in short order. The late Fischer Black, a pioneering theoretician of modern finance who moved from M.I.T. to Wall Street, said, “Markets look a lot less efficient from the banks of the Hudson than from the banks of the Charles.”2
Over time, the controversy between quantification based on observations of the past and subjective degrees of belief has taken on a deeper significance. The mathematically driven apparatus of modern risk management contains the seeds of a dehumanizing and self-destructive technology. Nobel laureate Kenneth Arrow has warned, “[O]ur knowledge of the way things work, in society or in nature, comes trailing clouds of vagueness. Vast ills have followed a belief in certainty.”3 In the process of breaking free from the past we may have become slaves of a new religion, a creed that is just as implacable, confining, and arbitrary as the old.
Our lives teem with numbers, but we sometimes forget that numbers are only tools. They have no soul; they may indeed become fetishes. Many of our most critical decisions are made by computers, contraptions that devour numbers like voracious monsters and insist on being nourished with ever-greater quantities of digits to crunch, digest, and spew back.
To judge the extent to which today’s methods of dealing with risk are either a benefit or a threat, we must know the whole story, from its very beginnings. We must know why people of past times did—or did not—try to tame risk, how they approached the task, what modes of thinking and language emerged from their experience, and how their activities interacted with other events, large and small, to change the course of culture. Such a perspective will bring us to a deeper understanding of where we stand, and where we may be heading.
Along the way, we shall refer often to games of chance, which have applications that extend far beyond the spin of the roulette wheel. Many of the most sophisticated ideas about managing risk and making decisions have developed from the analysis of the most childish of games. One does not have to be a gambler or even an investor to recognize what gambling and investing reveal about risk.
The dice and the roulette wheel, along with the stock market and the bond market, are natural laboratories for the study of risk because they lend themselves so readily to quantification; their language is the language of numbers. They also reveal a great deal about ourselves. When we hold our breath watching the little white ball bounce about on the spinning roulette wheel, and when we call our broker to buy or sell some shares of stock, our heart is beating along with the numbers. So, too, with all important outcomes that depend on chance.
The word “risk” derives from the early Italian risicare, which means “to dare.” In this sense, risk is a choice rather than a fate. The actions we dare to take, which depend on how free we are to make choices, are what the story of risk is all about. And that story helps define what it means to be a human being.
a The scientist who developed the Saturn 5 rocket that launched the first Apollo mission to the moon put it this way: “You want a valve that doesn’t leak and you try everything possible to develop one. But the real world provides you with a leaky valve. You have to determine how much leaking you can tolerate.” (Obituary of Arthur Rudolph, in The New York Times, January 3, 1996.)
b Chapter 7 describes Jacob Bernoulli’s achievements in detail. The Law of Large Numbers says in essence that the difference between the observed value of a sample and its true value will diminish as the number of observations in the sample increases.
Notes
1. Quoted in Keynes, 1921, frontispiece to Chapter XXVIII.
2. Personal conversation.
3. Arrow, 1992, p. 46.