Against the Gods: The Remarkable Story of Risk

by Peter L. Bernstein

  Early in this book we commented on the stability of the daily lives of most people century after century. Since the onset of the industrial revolution about two hundred years ago, so many "single other facts" have been added to the "Average" that defining the "Normal Scheme" has become increasingly difficult. When discontinuities threaten, it is perilous to base decisions on established trends that have always seemed to make perfect sense but suddenly do not.

  Here are two examples of how people can be duped by overreliance on regression to the mean.

  In 1930, when President Hoover declared that "Prosperity is just around the corner," he was not trying to fool the public with a sound bite or a spin. He meant what he said. After all, history had always supported that view. Depressions had come, but they had always gone.* Except for the period of the First World War, business activity had fallen in only seven years from 1869 until 1929. The single two-year setback during those years was 1907-1908, from a very high point; the average annual decline in real GDP was a modest 1.6%, and that included one decline of 5.5%.

  But production fell in 1930 by 9.3% and in 1931 by 8.6%. At the very bottom, in June 1932, GDP was 55% below its 1929 peak, even lower than it had been at the low point of the short-lived depression of 1920. Sixty years of history had suddenly become irrelevant. The trouble stemmed in part from the loss of youthful dynamism over the long period of industrial development; even during the boom of the 1920s, economic growth was below the long-term trend defined by the years from 1870 to 1918. The weakening of forward momentum, combined with a sequence of policy errors here and abroad and the shock of the stock market crash in October 1929, drove prosperity away from the corner it was presumably around.

  The second example: In 1959, exactly thirty years after the Great Crash, an event took place that made absolutely no sense in the light of history. Up to the late 1950s, investors had received a higher income from owning stocks than from owning bonds. Every time the yields got close, the dividend yield on common stocks moved back up over the bond yield. Stock prices fell, so that a dollar invested in stocks brought more income than it had brought previously.

  That seemed as it should be. After all, stocks are riskier than bonds. Bonds are contracts that specify precisely when the borrower must repay the principal of the debt and provide the schedule of interest payments. If borrowers default on a bond contract, they end up in bankruptcy, their credit ruined, and their assets under the control of creditors.

  With stocks, however, the shareholders' claim on the company's assets has no substance until after the company's creditors have been satisfied. Stocks are perpetuities: they have no terminal date on which the assets of the company must be distributed to the owners. Moreover, stock dividends are paid at the pleasure of the board of directors; the company has no obligation ever to pay dividends to the stockholders. Total dividends paid by publicly held companies were cut on nineteen occasions between 1871 and 1929; they were slashed by more than 50% from 1929 to 1933 and by about 40% in 1938.

  So it is no wonder that investors bought stocks only when they yielded a higher income than bonds. And no wonder that stock prices fell every time the income from stocks came close to the income from bonds.

  Until 1959, that is. At that point, stock prices were soaring and bond prices were falling. This meant that the ratio of bond interest to bond prices was shooting up and the ratio of stock dividends to stock prices was declining. The old relationship between bonds and stocks vanished, opening up a gap so huge that ultimately bonds were yielding more than stocks by an even greater margin than when stocks had yielded more than bonds.

  The cause of this reversal could not have been trivial. Inflation was the main factor that distinguished the present from the past. From 1800 to 1940, the cost of living had risen an average of only 0.2% a year and had actually declined on 69 occasions. In 1940 the cost-ofliving index was only 28% higher than it had been 140 years earlier. Under such conditions, owning assets valued at a fixed number of dollars was a delight; owning assets with no fixed dollar value was highly risky.

  The Second World War and its aftermath changed all that. From 1941 to 1959, inflation averaged 4.0% a year, with the cost-of-living index rising every year but one. The relentlessly rising price level transformed bonds from a financial instrument that had appeared inviolate into an extremely risky investment. By 1959, the price of the 2 1/2% bonds the Treasury had issued in 1945 had fallen from $1,000 to $820-and that $820 bought only half as much as in 1949!

  Meanwhile, stock dividends took off on a rapid climb, tripling between 1945 and 1959, with only one year of decline-and even that a mere 2%. No longer did investors perceive stocks as a risky asset whose price and income moved unpredictably. The price paid for today's dividend appeared increasingly irrelevant. What mattered was the rising stream of dividends that the future would bring. Over time, those dividends could be expected to exceed the interest payments from bonds, with a commensurate rise in the capital value of the stocks. The smart move was to buy stocks at a premium because of the opportunities for growth and inflation hedging they provided, and to pass up bonds with their fixed-dollar yield.

  Although the contours of this new world were visible well before 1959, the old relationships in the capital markets tended to persist as long as people with memories of the old days continued to be the main investors. For example, my partners, veterans of the Great Crash, kept assuring me that the seeming trend was nothing but an aberration. They promised me that matters would revert to normal in just a few months, that stock prices would fall and bond prices would rally.

  I am still waiting. The fact that something so unthinkable could occur has had a lasting impact on my view of life and on investing in particular. It continues to color my attitude toward the future and has left me skeptical about the wisdom of extrapolating from the past.

  How much reliance, then, can we place on regression to the mean in judging what the future will bring? What are we to make of a concept that has great power under some conditions but leads to disaster under others?

  Keynes admitted that "as living and moving beings, we are forced to act ... [even when]our existing knowledge does not provide a sufficient basis for a calculated mathematical expectation."14 With rules of thumb, experience, instinct, and conventions-in other words, gutwe manage to stumble from the present into the future. The expression "conventional wisdom," first used by John Kenneth Galbraith, often carries a pejorative sense, as though what most of us believe is inevitably wrong. But without conventional wisdom, we could make no long-run decisions and would have trouble finding our way from day to day.

  The trick is to be flexible enough to recognize that regression to the mean is only a tool; it is not a religion with immutable dogma and ceremonies. Used to make mechanical extrapolations of the past, as President Hoover or my older associates used it, regression to the mean is little more than mumbo jumbo. Never depend upon it to come into play without constantly questioning the relevance of the assumptions that support the procedure. Francis Galton spoke wisely when he urged us to "revel in more comprehensive views" than the average.

  'p to now, our story has focused on theories about probability and on ingenious ways of measuring it: Pascal's Triangle, Jacob Bernoulli's search for moral certainty in his jar of black and white balls, Bayes's billiard table, Gauss's bell curve, and Galton's Quincunx. Even Daniel Bernoulli, delving for perhaps the first time into the psychology of choice, was confident that what he called utility could be measured.

  Now we turn to an exploration of a different sort: Which risks should we take, which risks should we hedge, what information is relevant? How confidently do we hold our beliefs about the future? In short, how do we introduce management into dealing with risk?

  Under conditions of uncertainty, both rationality and measurement are essential to decision-making. Rational people process information objectively: whatever errors they make in forecasting the future are random errors rather than the result of a stu
bborn bias toward either optimism or pessimism. They respond to new information on the basis of a clearly defined set of preferences. They know what they want, and they use the information in ways that support their preferences.

  Preference means liking one thing better than another: tradeoff is implicit in the concept. That is a useful idea, but a method of measuring preferences would make it more palpable.

  That was what Daniel Bernoulli had in mind when he wrote his remarkable paper in 1738, boasting, "It would be wrong to neglect [his ideas] as abstractions resting upon precarious hypotheses." Bernoulli introduced utility as the unit for measuring preferences-for calculating how much we like one thing more than another. The world is full of desirable things, he said, but the amount that people are willing to pay for them differs from one person to another. And the more we have of something, the less we are willing to pay to get more.1

  Bernoulli's concept of utility was an impressive innovation, but his handling of it was one-dimensional. Today, we recognize that the desire to keep up with the Joneses may lead us to want more and more even when, by any objective standard of measurement, we already have enough. Moreover, Bernoulli built his case on a game in which Paul wins the first time Peter's coin comes up heads, but Paul loses nothing when Peter's coin comes up tails. The word "loss" does not appear in Bernoulli's paper, nor did it appear in works on utility theory for another two hundred years. Once it had appeared, however, utility theory became the paradigm of choice in defining how much risk people will take in the hope of achieving some desired but uncertain gain.

  Still, the power of Bernoulli's concept of utility is evident in the way his insights into "the nature of man" continue to resonate. Every advance in decision-making theory and in risk evaluation owes something to his efforts to provide definition, quantification, and guides to rational decisions.

  One might expect, as a result, that the history of utility theory and decision-making would be dominated by Bernoullians, especially since Daniel Bernoulli was such a well-known scientist. Yet such is not the case: most later developments in utility theory were new discoveries rather than extensions of Bernoulli's original formulations.

  Was the fact that Bernoulli wrote in Latin a problem? Kenneth Arrow has pointed out that Bernoulli's paper on a new theory of measuring risk was not translated into German until 1896, and that the first English translation appeared in an American scholarly journal as late as 1954. Yet Latin was still in common usage in mathematics well into the nineteenth century; and the use of Latin by Gauss was surely no barrier to the attention that his ideas commanded. Still, Bernoulli's choice of Latin may help explain why his accomplishments have received greater notice from mathematicians than from economists and students of human behavior.

  Arrow suggests a more substantive issue. Bernoulli dealt with utility in terms of numbers, whereas later writers preferred to think of it as a preference-setter: saying "I like this better than that" is not the same as saying "This is worth x utils to me."

  Utility theory was rediscovered toward the end of the eighteenth century by Jeremy Bentham, a popular English philosopher who lived from 1748 to 1832. You can still see him on special occasions at University College, London, where, under the terms of his will, his mummified body sits in a glass case with a wax head to replace the original and with his hat between his feet.

  His major work, The Principles of Morals and Legislation, published in 1789, was fully in the spirit of the Enlightenment:

  Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do.... The principle of utility recognizes this subjection, and assumes it for the foundation of that system, the object of which is to rear the fabric of felicity by the hands of reason and law.2

  Bentham then explains what he means by utility: "... that property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness .... when the tendency it has to augment the happiness of the community is greater than any it has to diminish it."

  Here Bentham was talking about life in general. But the economists of the nineteenth century fastened onto utility as a tool for discovering how prices result from interactive decisions by buyers and sellers. That detour led directly to the law of supply and demand.

  According to the mainstream economists of the nineteenth century, the future stands still while buyers and sellers contemplate the opportunities open to them. The focus was on whether one opportunity was superior to another. The possibility of loss was not a consideration. Consequently the distractions of uncertainty and the business cycle did not appear in the script. Instead, these economists spent their time analyzing the psychological and subjective factors that motivate people to pay such-and-such an amount for a loaf of bread or for a bottle of port-or for a tenth bottle of port. The idea that someone might not have the money to buy even one bottle of port was unthinkable. Alfred Marshall, the pre-eminent economist of the Victorian age, once remarked, "No one should have an occupation which tends to make him anything less than a gentleman."3

  William Stanley Jevons, a card-carrying Benthamite with a fondness for mathematics, was one of the prime contributors to this body of thought. Born in Liverpool in 1837, he grew up wanting to be a scientist. Financial difficulties, however, prompted him to take a job as assayer in the Royal Mint in Sydney, Australia, a gold-rush boom town with a population rapidly approaching 100,000. Jevons returned to London ten years later to study economics and spent most of his life there as Professor of Political Economy at University College; he was the first economist since William Petty to be elected to the Royal Society. Despite his academic title, Jevons was among the first to suggest dropping the word "political" from the phrase "political economy." In so doing, he revealed the level of abstraction toward which the discipline was moving.

  Nevertheless, his masterwork, published in 1871, was titled The Theory of Political Economy.' Jevons opens his analysis by declaring that "value depends entirely upon utility." He goes on to say, "[W]e have only to trace out carefully the natural laws of the variation of utility, as depending upon the quantity of a commodity in our possession, in order to arrive at a satisfactory theory of exchange."

  Here we have a restatement of Bernoulli's pivotal assertion that utility varies with the quantity of a commodity already in one's possession. Later in the book Jevons qualifies this generalization with a statement typical of a proper Victorian gentleman: "the more refined and intellectual our needs become, the less they are capable of satiety."

  Jevons was confident that he had solved the question of value, claiming that the ability to express everything in quantitative terms had made irrelevant the vague generalities that had characterized economics up to that point. He brushed off the problem of uncertainty by announcing that we need simply apply the probabilities learned from past experience and observation: "The test of correct estimation of probabilities is that the calculations agree with the fact on the average. ... We make calculations of this kind more or less accurately in all the ordinary affairs of life."

  Jevons takes many pages to describe earlier efforts to introduce mathematics into economics, though he makes no mention of Bernoulli. He leaves no doubt, however, about what he himself has achieved:

  Previous to the time of Pascal, who would have thought of measuring doubt and belief? Who would have conceived that the investigation of petty games of chance would have led to the creation of perhaps the most sublime branch of mathematical science-the theory of probabilities?

  Now there can be no doubt that pleasure, pain, labour, utility, value, wealth, money, capital, etc. are all notions admitting of quantity; nay, the whole of our actions in industry and trade certainly depend upon comparing quantities of advantage and disadvantage.

  Jevons's pride in his achievements reflects the enthusiasm for measurement that characterized the Victorian era. Over time, more and more aspects of life succu
mbed to quantification. The explosion of scientific research in the service of the industrial revolution added a powerful impulse to that trend.

  The first systematic population census in Britain had been carried out as early as 1801, and the insurance industry's use of statistics had grown more and more sophisticated throughout the century. Many right-thinking men and women turned to sociological measurement in the hope of relieving the ills of industrialization. They set out to improve life in the slums and to combat crime, illiteracy, and drunkenness among the newly poor.

  Some of the suggestions for applying the measurement of utility to society were less than practical, however. Francis Edgeworth, a contemporary of Jevons and an innovative mathematical economist, went as far as to propose the development of a "hedonimeter." As late as the mid-1920s Frank Ramsay, a brilliant young Cambridge mathematician, was exploring the possibility of creating a "psychogalvanometer."

  Some Victorians protested that the rush toward measurement smacked of materialism. In 1860, when Florence Nightingale, after consulting with Galton and others, offered to fund a chair in applied statistics at Oxford, her offer was flatly refused. Maurice Kendall, a great statistician and a historian of statistics, observed that "[I]t seems that our senior universities were still whispering from their towers the last enchantments of the Middle Ages... [A]fter thirty years of effort Florence gave it up."*s

  But the movement to bring the social sciences to the same degree of quantification as the natural sciences grew stronger and stronger as time passed. The vocabulary of the natural sciences gradually found its way into economics. Jevons refers to the "mechanics" of utility and self-interest, for example. Concepts like equilibrium, momentum, pressure, and functions crossed from one field to the other. Today, people in the world of finance use terms like financial engineering, neural networks, and genetic algorithms.