Peter Bernstein Quotes

The information you have is not the information you want. The information you want is not the information you need. The information you need is not the information you can obtain. The information you can obtain costs more than you want to pay

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.

Our lives teem with numbers, but we sometimes forget that numberss are only tools. They have no soul; they may indeed become fetishes.

Time matters most when decisions are irreversible.

Game theory says that the true source of uncertainty lies in the intentions of others.

life is a collection of similarities rather than identities; no single observation is a perfect example of generality.

Fear of harm ought to be proportional not merely to the gravity of the harm, but also to the probability of the event.

Time matters most when decisions are irreversible. And yet many irreversible decisions must be made on the basis of incomplete information.

Vast ills have followed a belief in certainty.

We are prisoners of the future because we will be ensnared by our past.

This is the essence of risk aversion—that is, how far we are willing to go in making decisions that may provoke others to make decisions that will have adverse consequences for us.

The essence of risk management lies in maximizing the areas where we have some control over the outcome while minimizing the areas where we have absolutely no control over the outcome and the linkage between effect and cause is hidden from us.

So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand.[...]It is in those outliers and imperfections that the wildness lurks.

Nothing ventured, nothing gained, but don’t put all your eggs in one basket.

Markets look a lot less efficient from the banks of the Hudson than from the banks of the Charles.

In the first sense, probability means the degree of belief or approvability of an opinion—the gut view of probability. Scholars use the term “epistemological” to convey this meaning; epistemological refers to the limits of human knowledge not fully analyzable.

We are by now well into the eighteenth century, when the Enlightenment identified the search for knowledge as the highest form of human activity. It was a time for scientists to wipe the metaphysical dust from their eyes.

Shefrin and Statman hypothesize the existence of a split in the human psyche. One side of our personality is an internal planner with a long-term perspective, an authority who insists on decisions that weight the future more heavily than the present. The other side seeks immediate gratification. These two sides are in constant conflict.

[The] utility resulting from any small increase in wealth will be inversely proportionate to the quantity of goods previously possessed.

The prospect of getting rich is highly motivating, and few people get rich without taking a gamble.

The prevalence of surprise in the world of business is evidence that uncertainty is more likely to prevail than mathematical probability.

As Peter Bernstein has written, nature's pattern emerges only from the chaotic disorder of many random events.

We could turn this assertion around and state that a decision should involve the strength of our desire for a particular outcome as well as the degree of our belief about the probability of that outcome.

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.

One winter night during one of the many German air raids on Moscow in World War II, a distinguished Soviet professor of statistics showed up in his local air-raid shelter. He had never appeared there before. “There are seven million people in Moscow,” he used to say. “Why should I expect them to hit me?” His friends were astonished to see him and asked what had happened to change his mind. “Look,” he explained, “there are seven million people in Moscow and one elephant. Last night they got the elephant.

You never get poor by taking a profit." It would follow that cutting your losses is also a good idea, but investors hate to take losses, because, tax considerations aside, a loss taken is an acknowledgment of error. Loss-aversion combined with ego leads investors to gamble by clinging to their mistakes in the fond hope that some day the market will vindicate their judgment and make them whole.

So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand.[...]Even though many economic and financial variables fall into distributions that approximate a bell curve, the picture is never perfect.[...]It is in those outliers and imperfections that the wildness lurks.

God is, or he is not. Which way should we incline? Reason cannot answer.

We have gold because we cannot trust Governments.

the more refined and intellectual our needs become, the less they are capable of satiety.

The Commanding General is well aware that the forecasts are no good. However, he needs them for planning purposes.

Trade is also a risky business. As the growth of trade transformed the principles of gambling into the creation of wealth, the inevitable result was capitalism, the epitome of risk-taking.

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,

His local campaigns around Macedonia also augmented that absolutely essential economic resource: slaves-slaves to work the mines, slaves to work the fields, slaves to keep the whole economy humming.

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.3

The information you have is not the information you want. The information you want is not the information you need. The information you need is not the information you can obtain. The information you can obtain costs more than you want to pay.

If the satisfaction to be derived from each successive increase in wealth is smaller than the satisfaction derived from the previous increase in wealth, then the disutility caused by a loss will always exceed the positive utility provided by a gain of equal size.

Writing in 1921, the University of Chicago economist Frank Knight uttered strange words for a man of his profession: “There is much question as to how far the world is intelligible at all. . . . It is only in the very special and crucial cases that anything like a mathematical study can be made.

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.

In his 1996 book, Against the Gods: The Remarkable Story of Risk, Peter L. Bernstein wrote, “Regression to the mean motivates almost every variety of risk-taking and forecasting. It is at the root of homilies like ‘What goes up must come down,’ ‘Pride goeth before a fall,’ and ‘From shirtsleeves to shirtsleeves in three generations.

The earliest known work in Arabic arithmetic was written by al-Khowârizmî, a mathematician who lived around 825, some four hundred years before Fibonacci.11 Although few beneficiaries of his work are likely to have heard of him, most of us know of him indirectly. Try saying “al-Khowârizmî” fast. That’s where we get the word “algorithm,” which means rules for computing.12 It was al-Khowârizmî who was the first mathematician to establish rules for adding, subtracting, multiplying, and dividing with the new Hindu numerals. In another treatise, Hisâb al-jabr w’ almuqâbalah, or “Science of transposition and cancellation,” he specifies the process for manipulating algebraic equations. The word al-jabr thus gives us our word algebra, the science of equations.13

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

Why, given their advanced mathematical ideas, did the Arabs not proceed to probability theory and risk management? The answer, I believe, has to do with their view of life. Who determines our future: the fates, the gods, or ourselves? The idea of risk management emerges only when people believe that they are to some degree free agents. Like the Greeks and the early Christians, the fatalistic Muslims were not yet ready to take the leap.

If the random-walk view is correct, today's stock prices embody all relevant information. The only thing that would make them change is the availability of new information. Since we have no way of knowing what that new information might be, there is no mean for stock prices to regress to. In other words, there is no such thing as a temporary stock price-that is, a price that sits in limbo before moving to some other point. That is also why changes are unpredictable.

Thaler recounts an amusing real-life example of mental accounting.15 A professor of finance he knows has a clever strategy to help him deal with minor misfortunes. At the beginning of the year, the professor plans for a generous donation to his favorite charity. Anything untoward that happens in the course of the year—a speeding ticket, replacing a lost possession, an unwanted touch by an impecunious relative—is then charged to the charity account. The system makes the losses painless, because the charity does the paying. The charity receives whatever is left over in the account. Thaler has nominated his friend as the world’s first Certified Mental Accountant.

The Reformation meant more than just a change in humanity's relationship with God. By eliminating the confessional, it warned people that henceforth they would have to walk on their own two feet and would have to take responsibility for the consequences of their own decisions.

Consider this set of coin-tossing possibilities, proposed by Warren Buffet. Suppose 225 million Americans all join in a coin-tossing contest in which each player bets a dollar each day on whether the toss of a coin will turn up heads or tails. Each day, the losers turn their dollars over to the winners, who then stake their winnings on the next day’s toss. The laws of chance tell us that, after ten flips on ten mornings, only 220,000 people will still be in the contest, and each will have won a little over $1,000. After that, the game heats up. Ten days later, only 215 people will still be playing, but each of them will be worth over $1,050,000. Buffet suggests that this small group of winners will marvel at their own skills. Some of them will write books on “How I Turned a Dollar into a Million in Twenty Days Working Thirty Seconds a Morning.” Or, they will tackle skeptical professors of finance with “If it can’t be done, why are there 215 of us?” But, Buffet goes on to point out, “. . . then some business school professor will probably be rude enough to bring up the fact that if 215 million orangutans had engaged in a similar exercise, the results would be much the same—215 egotistical orangutans with 20 straight winning flips.”22

a Greek epigram about Diophantus states that "his boyhood lasted 1 /6th of his life; his beard grew after 1/12th more; he married after 1 /7th more, and his son was born five years later; the son lived to half his father's age, and the father died four years after his son." How old was Diophantus when he died?7

Whetstone of Witte introduced the symbol "_" because "noe 2 thynges can be more equalle than a pair of paralleles.

La palabra "riesgo" procede del italiano risicare, que significa "atreverse". En este sentido, el riesgo es más bien una elección que un destino.... La idea de la gestión de riesgos solo surge cuando las personas creen que hasta cierto punto son agentes libres.

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In December 1972, Polaroid was selling for 96 times its 1972 earnings, McDonald’s was selling for 80 times, and IFF was selling for 73 times; the Standard & Poor’s Index of 500 stocks was selling at an average of 19 times. The dividend yields on the Nifty-Fifty averaged less than half the average yield on the 500 stocks in the S&P Index. The proof of this particular pudding was surely in the eating, and a bitter mouthful it was. The dazzling prospect of earnings rising up to the sky turned out to be worth a lot less than an infinite amount. By 1976, the price of IFF had fallen 40% but the price of U.S. Steel had more than doubled. Figuring dividends plus price change, the S&P 500 had surpassed its previous peak by the end of 1976, but the Nifty-Fifty did not surpass their 1972 bull-market peak until July 1980. Even worse, an equally weighted portfolio of the Nifty-Fifty lagged the performance of the S&P 500 from 1976 to 1990.

All journalists stand on the shoulders of giants, whether they admit it or not. In many cases, my book was vastly enhanced by the superlative work of other journalists, writers, and financial historians, who have themselves explored some of the subjects and themes I have tried to knit together in one sweeping narrative. Peter Bernstein is a huge inspiration, and his books were of tremendous help for some of the earlier chapters, as was Colin Read’s The Efficient Market Hypothesists. Lewis Braham’s biography of Jack Bogle is essential reading for anyone interested in the tumultuous life of Vanguard’s founder. Ralph Lehman’s The Elusive Trade was exhaustively detailed on the genesis of ETFs, and Anthony Bianco’s The Big Lie vividly tells the story of WFIA/BGI in the Pattie Dunn era. I have also learned an enormous amount from working with or admiring from afar financial journalists like John Authers, Gillian Tett, James Mackintosh, Philip Coggan, and Jason Zweig, as well as industry experts such as Deborah Fuhr, Ben Johnson, Eric Balchunas, and David Nadig. They are all titans upon whose shoulders I nervously perch.

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.

Peter Bernstein and Robert Arnott reflected on this question in a recent article in the Journal of Portfolio Management: “Bull Market? Bear Market? Should You Really Care?” They concluded that “for most long-term investors, bull markets are not nearly as beneficial, and bear markets not nearly as damaging as most investors seem to think.” They noted, correctly, that “a bull market raises the asset value, but delivers a proportionate reduction in the prospective real yields that the portfolio can deliver from that point forward, while a bear market does the reverse, reducing portfolio value, which is largely offset by an increase in prospective yields, other things being equal.

But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand.

If they had kept quiet, and lain low for a time, things might have fizzled out as another unreal Wortstreist, blown up by a few ambitious authors of the party press. As it was, they decided to counter-attack the noisy, irrepressible outsiders--foreigners, to boot--and so forced a reluctant leadership to turn its full, slow, wrath against them; and against Bernstein too. For the most practical manifestation of revisionism was indiscipline and disobedience, a door opened to centrifugal forces of bourgeois influence.

[T]he “Law Of Frequency Of Error”. . . reigns with serenity and in complete self-effacement amidst the wildest confusion. The huger the mob . . . the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand . . . an unsuspected and most beautiful form of regularity proves to have been latent all along.13

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.

Without numbers, there are no odds and no probabilities; without odds and probabilities, the only way to deal with risk is to appeal to the gods and the fates. Without numbers, risk is wholly a matter of gut.

The story of numbers in the West begins in 1202, when the cathedral of Chartres was nearing completion and King John was finishing his third year on the throne of England. In that year, a book titled Liber Abaci, or Book of the Abacus, appeared in Italy. The fifteen chapters of the book were entirely handwritten; almost three hundred years would pass before the invention of printing. The author, Leonardo Pisano, was only 27 years old but a very lucky man: his book would receive the endorsement of the Holy Roman Emperor, Frederick II. No author could have done much better than that.1 Leonardo Pisano was known for most of his life as Fibonacci, the name by which he is known today. His father’s first name was Bonacio, and Fibonacci is a contraction of son-of-Bonacio. Bonacio means “simpleton” and Fibonacci means “blockhead.” Bonacio must have been something less than-a simpleton, however, for he represented Pisa as consul in a number of different cities, and his son Leonardo was certainly no blockhead.

Ingenious and original as Fibonacci’s exercises were, if the book had dealt only with theory it would probably not have attracted much attention beyond a small circle of mathematical cognoscenti. It commanded an enthusiastic following, however, because Fibonacci filled it with practical applications. For example, he described and illustrated many innovations that the new numbers made possible in commercial bookkeeping, such as figuring profit margins, money-changing, conversions of weights and measures, and—though usury was still prohibited in many places—he even included calculations of interest payments. Liber Abaci provided just the kind of stimulation that a man as brilliant and creative as the Emperor Frederick would be sure to enjoy. Though Frederick, who ruled from 1211 to 1250, exhibited cruelty and an obsession with earthly power, he was genuinely interested in science, the arts, and the philosophy of government. In Sicily, he destroyed all the private garrisons and feudal castles, taxed the clergy, and banned them from civil office. He also set up an expert bureaucracy, abolished internal tolls, removed all regulations inhibiting imports, and shut down the state monopolies. Frederick tolerated no rivals. Unlike his grandfather, Frederick Barbarossa, who was humbled by the Pope at the Battle of Legnano in 1176, this Frederick reveled in his endless battles with the papacy. His intransigence brought him not just one excommunication, but two. On the second occasion, Pope Gregory IX called for Frederick to be deposed, characterizing him as a heretic, rake, and anti-Christ. Frederick responded with a savage attack on papal territory; meanwhile his fleet captured a large delegation of prelates on their way to Rome to join the synod that had been called to remove him from power.

Fibonacci is best known for a short passage in Liber Abaci that led to something of a mathematical miracle. The passage concerns the problem of how many rabbits will be born in the course of a year from an original pair of rabbits, assuming that every month each pair produces another pair and that rabbits begin to breed when they are two months old. Fibonacci discovered that the original pair of rabbits would have spawned a total of 233 pairs of offspring in the course of a year. He discovered something else, much more interesting. He had assumed that the original pair would not breed until the second month and then would produce another pair every month. By the fourth month, their first two offspring would begin breeding. After the process got started, the total number of pairs of rabbits at the end of each month would be as follows: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233. Each successive number is-the sum of the two preceding numbers. If the rabbits kept going for a hundred months, the total number pairs would be 354,224,848,179,261,915,075. The Fibonacci series is a lot more than a source of amusement. Divide any of the Fibonacci numbers by the next higher number. After 3, the answer is always 0.625. After 89, the answer is always 0.618; after higher numbers, more decimal places can be filled in.a Divide any number by its preceding number. After 2, the answer is always 1.6. After 144, the answer is always 1.618. The Greeks knew this proportion and called it “the golden mean.” The golden mean defines the proportions of the Parthenon, the shape of playing cards and credit cards, and the proportions of the General Assembly Building at the United Nations in New York. The horizontal member of most Christian crosses separates the vertical member by just about the same ratio: the length above the crosspiece is 61.8% of the length below it. The golden mean also appears throughout nature—in flower patterns, the leaves of an artichoke, and the leaf stubs on a palm tree. It is also the ratio of the length of the human body above the navel to its length below the navel (in normally proportioned people, that is). The length of each successive bone in our fingers, from tip to hand, also bears this ratio.b

The journalist William Hoffer has remarked, “The great golden spiral seems to be nature’s way of building quantity without sacrificing quality.”2 Some people believe that the Fibonacci numbers can be used to make a wide variety of predictions, especially predictions about the stock market; such predictions work just often enough to keep the enthusiasm going. The Fibonacci sequence is so fascinating that there is even an American Fibonacci Association, located at Santa Clara University in California, which has published thousands of pages of research on the subject since 1962.

The abacus works by specifying an upper limit for the number of counters in each column; in adding, as the furthest right column fills up, the excess counters move one column to the left, and so on. Our concepts of “borrow one” or “carry over three” date back to the abacus.

This radical break with the analytical methodologies of other civilizations makes us wonder again why it was that the Greeks failed to discover the laws of probability, and calculus, and even simple algebra. Perhaps, despite all they achieved, it was because they had to depend on a clumsy numbering system based on their alphabet. The Romans suffered from the same handicap. As simple a number as 9 required two letters: IX. The Romans could not write 32 as III II, because people would have no way of knowing whether it meant 32, 302, 3020, or some larger combination of 3, 2, and 0. Calculations based on such a system were impossible.

Actually, one westerner had suggested a numbering system at least two centuries earlier than the Hindus. About 250 AD, an Alexandrian mathematician named Diophantus wrote a treatise setting forth the advantages of a system of true numbers to replace letters substituting for numbers.6 Not much is known about Diophantus, but the little we do know is amusing. According to Herbert Warren Turnbull, a historian of mathematics, a Greek epigram about Diophantus states that “his boyhood lasted l/6th of his life; his beard grew after l/12th more; he married after l/7th more, and his son was born five years later; the son lived to half his father’s age, and the father died four years after his son.” How old was Diophantus when he died?7

The centerpiece of the Hindu-Arabic system was the invention of zero—sunya as the Indians called it, and cifr as it became in Arabic.9 The term has come down to us as “cipher,” which means empty and refers to the empty column in the abacus or counting frame.c

According to Fitzgerald, Omar Khayyam was educated along with two friends, both as bright as he: Nizam al Mulk and Hasan al Sabbah. One day Hasan proposed that, since at least one of the three would attain wealth and power, they should vow that “to whomsoever this fortune falls, he shall share it equally with the rest, and preserve no preeminence for himself.” They all took the oath, and in time Nizam became vizier to the sultan. His two friends sought him out and claimed their due, which he granted as promised.

Hasan demanded and received a place in the government, but, dissatisfied with his advancement, left to become head of a sect of fanatics who spread terror throughout the Mohammedan world. Many years later, Hasan would end up assassinating his old friend Nizam. Omar Khayyam asked for neither title nor office. “The greatest boon you can confer on me,” he said to Nizam, “is to let me live in a corner under the shadow of your fortune, to spread wide the advantages of science and pray for your long life and prosperity.” Although the sultan loved Omar Khayyam and showered favors on him, “Omar’s epicurean audacity of thought and speech caused him to be regarded askance in his own time and country.

Despite Emperor Frederick’s patronage of Fibonacci’s book and the book’s widespread distribution across Europe, introduction of the Hindu-Arabic numbering system provoked intense and bitter resistance up to the early 1500s. Here, for once, we can explain the delay. Two factors were at work. Part of the resistance stemmed from the inertial forces that oppose any change in matters hallowed by centuries of use. Learning radically new methods never finds an easy welcome. The second factor was based on more solid ground: it was easier to commit fraud with the new numbers than with the old. Turning a 0 into a 6 or a 9 was temptingly easy, and a 1 could be readily converted into a 4, 6, 7, or 9 (one reason Europeans write 7 as 7).

Pontius Pilate’s soldiers cast lots for Christ’s robe as He suffered on the cross. The Roman Emperor Marcus Aurelius was regularly accompanied by his personal croupier. The Earl of Sandwich invented the snack that bears his name so that he could avoid leaving the gaming table in order to eat. George Washington hosted games in his tent during the American Revolution.4 Gambling is synonymous with the Wild West. And “Luck Be a Lady Tonight” is one of the most memorable numbers in Guys and Dolls, a musical about a compulsive gambler and his floating crap game.

Cardano was a lot more than a gambler and part-time mathematician. He was the most famous physician of his age, and the Pope and Europe’s royal and imperial families eagerly sought his counsel. He had no use for court intrigue, however, and declined their invitations. He provided the first clinical description of the symptoms of typhus, wrote about syphilis, and developed a new way to operate on hernias. Moreover, he recognized that “A man is nothing but his mind; if that be out of order, all’s amiss, and if that be well, the rest is at ease.” He was an early enthusiast for bathing and showering. When he was invited to Edinburgh in 1552 to treat the Archbishop of Scotland for asthma, he drew on his knowledge of allergy to recommend bedclothes of unspun silk instead of feathers, a pillowcase of linen instead of leather, and the use of an ivory hair comb. Before leaving Milan for Edinburgh, he had contracted for a daily fee of ten gold crowns for his services, but when he departed after about forty days his grateful patient paid him 1,400 crowns and gave him many gifts of great value.

Human beings have always been infatuated with gambling because it puts us head-to-head against the fates, with no holds barred. We enter this daunting battle because we are convinced that we have a powerful ally: Lady Luck will interpose herself between us and the fates (or the odds) to bring victory to our side. Adam Smith, a masterful student of human nature, defined the motivation: “The overweening conceit which the greater part of men have of their own abilities [and] their absurd presumption in their own good fortune.”1 Although Smith was keenly aware that the human propensity to take risk propelled economic progress, he feared that society would suffer when that propensity ran amuck. So he was careful to balance moral sentiments against the benefits of a free market. A hundred and sixty years later, another great English economist, John Maynard Keynes, agreed: “When the capital development of a country becomes the by-product of the activities of a casino, the job is likely to be ill-done.

Cardano’s great book on mathematics, Ars Magna (The Great Art), appeared in 1545, at the same time Copernicus was publishing his discoveries of the planetary system and Vesalius was producing his treatise on anatomy. The book was published just five years after the first appearance of the symbols “+” and “−” in Grounde of Artes by an Englishman named Robert Record. Seventeen years later, an English book called Whetstone of Witte introduced the symbol “=” because “noe 2 thynges can be more equalle than a pair of paralleles.”8 Ars Magna was the first major work of the Renaissance to concentrate on algebra.

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.

Time is the dominant factor in gambling. Risk and time are opposite sides of the same coin, for if there were no tomorrow there would be no risk. Time transforms risk, and the nature of risk is shaped by the time horizon: the future is the playing field. Time matters most when decisions are irreversible. And yet many irreversible decisions must be made on the basis of incomplete information. Irreversibility dominates decisions ranging all the way from taking the subway instead of a taxi, to building an automobile factory in Brazil, to changing jobs, to declaring war. If we buy a stock today, we can always sell it tomorrow. But what do we do after the croupier at the roulette table cries, “No more bets!” or after a poker bet is doubled? There is no going back. Should we refrain from acting in the hope that the passage of time will make luck or the probabilities turn in our favor? Hamlet complained that too much hesitation in the face of uncertain outcomes is bad because “the native hue of resolution is sicklied o’er with the pale cast of thought . . . and enterprises of great pith and moment . . . lose the name of action.” Yet once we act, we forfeit the option of waiting until new information comes along. As a result, not-acting has value.

Despite the emphasis that the Greeks placed on theory, they had little interest in applying it to any kind of technology that would have changed their views of the manageability of the future. When Archimedes invented the lever, he claimed that he could move the earth if only he could find a place to stand. But apparently he gave no thought to changing it. The daily life of the Greeks, and their standard of living, were much the same as the way that their forebears had subsisted for thousands of years. They hunted, fished, grew crops, bore children, and used architectural techniques that were only variations on themes developed much earlier in the Tigris-Euphrates valley and in Egypt. Genuflection before the winds was the only form of risk management that caught their attention: their poets and dramatists sing repeatedly of their dependence on the winds, and beloved children were sacrificed to appease the winds. Most important, the Greeks lacked a numbering system that would have enabled them to calculate instead of just recording the results of their activities.9 I do not mean to suggest that the Greeks gave no thought to the nature of probability. The ancient Greek word εικος (eikos), which meant plausible or probable, had the same sense as the modern concept of probability: “to be expected with some degree of certainty.” Socrates defines εικος as “likeness to truth.”10 Socrates’ definition reveals a subtle point of great importance. Likeness to truth is not the same thing as truth. Truth to the Greeks was only what could be proved by logic and axioms. Their insistence on proof set truth in direct contrast to empirical experimentation. For example, in Phaedo, Simmias points out to Socrates that “the proposition that the soul is in harmony has not been demonstrated at all but rests only on probability.” Aristotle complains about philosophers who, “. . . while they speak plausibly, . . . do not speak what is true.” Elsewhere, Socrates anticipates Aristotle when he declares that a “mathematician who argues from probabilities in geometry is not worth an ace.”11 For another thousand years, thinking about games and playing them remained separate activities.

Shmuel Sambursky, a distinguished Israeli historian and philosopher of science, provides the only convincing thesis I could find to explain why the Greeks failed to take the strategic step of developing a quantitative approach to probability.12 With their sharp distinction between truth and probability, Sambursky contends in a paper written in 1956, the Greeks could not conceive of any kind of solid structure or harmony in the messy nature of day-to-day existence. Although Aristotle suggested that people should make decisions on the basis of “desire and reasoning directed to some end,” he offered no guidance to the likelihood of a successful outcome. Greek dramas tell tale after tale of the helplessness of human beings in the grasp of impersonal fates. When the Greeks wanted a prediction of what tomorrow might bring, they turned to the oracles instead of consulting their wisest philosophers.

The old Talmudic Jewish philosophers may have come a bit closer to quantifying risk. But here, too, we find no indication that they followed up on their reasoning by developing a methodical approach to risk. Sambursky cites a passage in the Talmud, Kethuboth 9q, where the philosopher explains that a man may divorce his wife for adultery without any penalty, but not if he claims that the adultery occurred before marriage.13 “It is a double doubt,” declares the Talmud. If it is established (method unspecified) that the bride came to the marriage bed no longer a virgin, one side of the double doubt is whether the man responsible was the prospective groom himself—whether the event occurred “under him . . . or not under him.” As to the second side of the doubt, the argument continues: “And if you say that it was under him, there is doubt whether it was by violence or by her free will.” Each side of the double doubt is given a 50–50 chance. With impressive statistical sophistication, the philosophers conclude that there is only one chance in four (1/2 × 1/2) that the woman committed adultery before marriage. Therefore, the husband cannot divorce her on those grounds.

Trade is a mutually beneficial process, a transaction in which both parties perceive themselves as wealthier than they were before. What a radical idea! Up to that point, people who got rich had done so largely by exploitation or by plundering another’s wealth. Although Europeans continued to plunder across the seas, at home the accumulation of wealth was open to the many rather than the few. The newly rich were now the smart, the adventuresome, the innovators—most of them businessmen—instead of just the hereditary princes and their minions. Trade is also a risky business. As the growth of trade transformed the principles of gambling into the creation of wealth, the inevitable result was capitalism, the epitome of risk-taking. But capitalism could not have flourished without two new activities that had been unnecessary so long as the future was a matter of chance or of God’s will. The first was bookkeeping, a humble activity but one that encouraged the dissemination of the new techniques of numbering and counting. The other was forecasting, a much less humble and far more challenging activity that links risk-taking with direct payoffs.

According to the Canadian philosopher Ian Hacking, the Latin root of probability suggests something like “worthy of approbation.”10 This was the meaning the word carried for a long time. As an example, Hacking quotes a passage from Daniel Defoe’s novel of 1724, Roxana, or The Fortunate Mistress. The lady in question, having persuaded a man of means to take care of her, says, “This was the first view I had of living comfortably indeed, and it was a very probable way.” The meaning here is that she has arrived at a way of life that justifies the esteem of her betters; she was, as Hacking puts it, “a good leg up from her scruffy beginnings.”11

Hacking cites another example of the changing meaning of probability.12 Galileo, making explicit use of the word probabilità, referred to Copernicus’s theory of the earth revolving around the sun as “improbable,” because it contradicted what people could see with their own eyes—the sun revolving around the earth. Such a theory was improbable because it did not meet with approval. Less than a century later, using a new (but not yet the newest) meaning, the German scholar Leibniz described the Copernican hypothesis as “incomparably the most probable.” For Leibniz, Hacking writes, “probability is determined by evidence and reason.”13 In fact, the German word, wahrscheinlich, captures this sense of the concept well: it translates literally into English as “with the appearance of truth.

Semantics are important here. As Cardano put it, the probability of an outcome is the ratio of favorable outcomes to the total opportunity set. The odds on an outcome are the ratio of favorable outcomes to unfavorable outcomes. The odds obviously depend on the probability, but the odds are what matter when you are placing a bet.

Cardano begins Liber de Ludo Aleae in an experimental mode but ends with the theoretical concept of combinations. Above its original insights into the role of probability in games of chance, and beyond the mathematical power that Cardano brought to bear on the problems he wanted to solve, Liber de Ludo Aleae is the first known effort to put measurement at the service of risk.

Nearly forty years later, while Galileo was employed as the First and Extraordinary Mathematician of the University of Pisa and Mathematician to His Serenest Highness, Cosimo II, the Grand Duke of Tuscany, he wrote a short essay on gambling “in order to oblige him who has ordered me to produce what occurs to me about the problem.”17 The title of the essay was Sopra le Scoperte dei Dadi (On Playing Dice). The use of Italian instead of Latin suggests that Galileo had no great relish for a topic that he considered unworthy of serious consideration. He appears to have been performing a disagreeable chore in order to improve the gambling scores of his employer, the Grand Duke.

The story of the three Frenchmen begins with an unlikely trio who saw beyond the gaming tables and fashioned the systematic and theoretical foundations for measuring probability. The first, Blaise Pascal, was a brilliant young dissolute who subsequently became a religious zealot and ended up rejecting the use of reason. The second, Pierre de Fermat, was a successful lawyer for whom mathematics was a sideline. The third member of the group was a nobleman, the Chevalier de Méré, who combined his taste for mathematics with an irresistible urge to play games of chance; his fame rests simply on his having posed the question that set the other two on the road to discovery.

Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein

In 1738, the Papers of the Imperial Academy of Sciences in St. Petersburg carried an essay with this central theme: “the value of an item must not be based on its price, but rather on the utility that it yields.

A man is nothing but his mind; if that be out of order, all’s amiss, and if that be well, the rest is at ease.

but between reject and not—reject. You can decide that the probability that you are wrong is so small that you should not reject the hypothesis. You can decide that the probability that you are wrong is so large that you should reject the hypothesis. But with any probability short of zero that you are wrong—certainty rather than uncertainty—you cannot accept a hypothesis.

Stock prices in general follow changes in company fortunes. Investors who focus excessively on the short run are ignoring a mountain of evidence demonstrating that most surges in earnings are unsustainable. On the other hand, companies that encounter problems do not let matters slide indefinitely. Managers will set to work making the hard decisions to put their company back on track

There is a strong probability that the hot manager of today will be the cold manager of tomorrow, or at least the day after tomorrow, and vice versa. This

Peter Bernstein, John Kenneth Galbraith, Nassim Nicholas Taleb and Charlie Ellis.

that the opinion is a nonrational one.” (All quotes are from the frontispiece of Rethinking AIDS) Root-Bernstein subsequently backed away from his position challenging HIV,

After his meeting with Romney, Fonesca encountered Keith Flax, a local jeweler who was also speaker of the legislative council and a close friend of both Romney and Peters. It didn't take long for the Panamanian and the Belonger to recognize they shared a special bond. Both were members of the ancient order of Freemasons. Dating to the Industrial Revolution in England, Freemasonry appropriated the symbols of craft guilds like the stonemasons to forge a fraternal order kept alive through esoteric rituals and Masonic lodges. ¶ Fonseca had tapped into an underground network—a secret society within a secret society—that exists in tax havens, particularly the British ones. Knowledge of Freemasonry, its signs, symbols, and rites, often serves as a doorway into closed cultures. It provides instant solidarity and an opportunity for government and business interests to network privately. John Christensen [the Jersey island exposé cooperator] says he was approached multiple times on Jersey to join one lodge or another. He always declined the offer. Holding no particular animus toward Freemasonry or the elite hobnobbing in the lodges, Christensen nonetheless viewed it all as slightly creepy.

But in a cause-and-effect world, if we know the causes we can predict the effects. So “what is chance for the ignorant is not chance for the scientist. Chance is only the measure of our ignorance.

Ask yourself whether the letter K appears more often as the first or as the third letter of English words. You will probably answer that it appears more often as the first letter. Actually, K appears as the third letter twice as often. Why the error? We find it easier to recall words with a certain letter at the beginning than words with that same letter somewhere else.

people who start out with money in their pockets will choose the gamble, while people who start out with empty pockets will reject the gamble.

mental accounting,