GUEST SPEAKER

Risk as a History of IdeasPeter L. Bernstein

The perception of risk throughout history has reflected the temper and times in each society asthe emphasis has swung from gut to measurement and back to gut. As long as people sensedthey had no control over their futures, chance explained the entire outcome of risk taking.Then, the collection of ideas we call the Renaissance freed the human spirit for experimentationand exploration, demonstrating that choice is a valid human activity and that risk issomething to be taken as well as faced. Quantification became essential, leading to thedevelopment of the laws of probability. In more modern times, uncertainty has replaced manyof the neat concepts of probability and has even begun to attack the roots of the capital ideasof finance: mean-variance, the efficient market hypothesis, and the capital asset pricing model.

Risk has always been a matter ofmeasurement and gut. As mea-surement and gut intertwine inever-changing ways over time,they reflect the development ofthe most basic philosophical un-derpinnings of society. This shift-ing interaction is what makes riskas a history of ideas so importantand so exciting.

Risk as a history of ideas isespecially pertinent right now. Irefer to more than the parochialattack on the quantitative riskmeasurements featured in mean-variance theories and the capitalasset pricing model (CAPM). Thevery structure of the world as wehave known it seems to be trem-bling at its foundations, intensi-fying the search for novel riskmanagement techniques at alllevels of human activity.

I shall begin at the beginningand trace how^ risk evolved fromsuperstition to the theory ofprobability to the notion of un-certainty. Because the unknown

Peter L. Bernstein is president of Peter i.Bernstein, Inc., in New York. This paper wasoriginally presented to the Berkeley Programin Finance, Palm Springs, March 13, 1994.

is always with us, the way hu-mans have responded to the fogof the future can tell us a greatdeal about what has motivated usand shaped our beliefs about our-selves and the universe. Thestory goes in a straight line, withthree brief digressions.

For by far the largest part ofhuman history, the future was ablack hole. As long as peoplesensed that they had no controlover their futures, chance ex-plained the entire outcome of risktaking. Oracles and priests—especially priests—were the fore-casters of choice, because peoplebelieved that these seers had adirect line to the powers that con-trolled the elements. But the ran-dom track records and obscuremethodologies of these seers cre-ated little confidence in their pre-dictions; like Macbeth, their con-stituents believed what theywanted to believe and rejectedthe rest.

No one can study this longhistory without being astonishedby the absence of anything thatresembles the laws of probabilityas we know them today. After

all, evidence of gambling reachesall the way back to the earliestdays of human civilization. Yet,any form of systematic analysisof the likelihood of future eventsis less than 600 years old.

One can only speculate aboutwhy even the master mathemati-cians and philosophers of ancientGreece had no interest in thissubject. The entire Mediterra-nean basin from about 500 BC to300 BC was a hotbed of scientificresearch, much of which hasdominated the work of scientistsright up to our own time. Indeed,knowledge of these mattersreaches back even farther. Thepriests in the temples of Egyptand Babylon knew quite a bitabout geometry before Euclidcame upon the scene, and thePythagorean Theorem about thesquare of the hypotenuse pro-vided a strategic element to archi-tecture in the Tigris-EuphratesValley as early as 2000 BC.

The Greeks were special, lessbecause of their many remark-able discoveries than becausethey were the first civilization tobe free of the intellectual strait-

Financial Analysts Journal / January-February 1995

jackets imposed by secretive andall-powerful priesthoods. As aconsequence, the Greeks refusedto accept at face value the rules ofthumb that older societies passedon to them. The unique quality ofthe Greek spirit was their insis-tence upon logical proofs thatwould validate what they weretold.

Still, they shut their eyes to thelaws of probability. I do not meanto suggest that they were igno-rant of probability as a generalidea. The surprise is that theyturned their back on quantifica-tion.

The key to this puzzle is in theGreek view of the distinction be-tween heaven and earth. TheGreeks were great astronomerswho discovered order, regular-ity, and perfection in the skies. Incontrast, irregularity and unpre-dictability defined the earth forthem. The idea of laws of proba-bility for earthlings was a contra-diction in terms, an alien con-cept. There was no point inseeking order where no ordercould possibly exist. This view-point, which is articulated re-peatedly in all Greek drama, waspervasive in Greek civilization.

As long as people sensed thatthey had no control over theirfutures, chance explained the en-tire outcome of risk taking. Butthat view vanished abruptly withthe arrival of Christianity. Nowrandom chance was out; God'swill was in. "Thy will be done"became the dominant paradigmfor determining the future andexplaining the past. As a conse-quence, scientific research wascrushed. In Alexandria in 380AD, for example, the monks ofSt. Cyril murdered Hypatia, abrilliant mathematician, by scrap-ing her naked body with oystershells.

But even the Church, callingon the highest authority of them

all, could not stifle human curi-osity. The authority of religionultimately crumbled before theendless search for a better life onearth.

For the West, the definingevent was the Crusades, with theculture shock of Arabic civiliza-tion and, in particular, the num-bering system the Arabs had in-herited from the Hindus nearly athousand years earlier. This storyis worth an essay of its own, buthere I can only emphasize itsoverwhelming importance. Trywriting an algebraic equationwith Roman numerals or withoutregard to zero. How about II"?As the great philosopher AlfredNorth Whitehead put it.

The point about zero is that wedo not need to use it in theoperations of daily life. No onegoes out to buy zero fish. It isin a way the most civilized ofthe cardinals, and its use isonly forced on us by the mostcultivated modes of thought.Unlike the alphabetical num-

bering systems of the Hebrews,Greeks, and Romans, the Hindunumbers are the inputs to cal-culations and are only inciden-tally used to record calculation.As people were liberated fromthe constraints of the countingframe, or abacus, a whole newworld of mathematics becamepossible, offering the limitlesscharacter of the abstract, notmerely the tangible.

As digression number one, Iwant to mention the earliestknown work on Arabic arith-metic. It was written about 825 bya man whose name was al-KhowSrizmi. The name is thederivation of the word "algo-rithm," which with its unmistak-able diphthong, I had always as-sumed had a respectable Greekorigin. al-Khowariznii was thefirst mathematician to establishrules for adding, subtracting.

multiplying, and dividing withthe new Hindu numerals. Healso wrote a treatise on the sub-ject of al-jahr, which is the deri-vation of "algebra." Thanks toal-Khowarizmi, schoolchildrenhave been learning the multipli-cation tables for more than 1,000years.

The combination of the Cru-sades, the early development oftrade, and the beginning of seri-ous geographical explorationmade people explicitly aware, forthe first time in human history,that perhaps they did have somecontrol over their futures, thatchoice is a valid human activity,and that risk is something to betaken as well as something to befaced. After all, the word "risk,"so often defined in relation toloss, has its roots in the earlyItalian risicare, which means todare, or from the Greek rhiza,which pertains to sailing arounda cliff. That was what the Renais-sance was all about: the freeing ofthe human spirit for experimen-tation, innovation, exploration.

Now, measurement becamenot only interesting but also es-sential. A literature in mathemat-ics began to develop to explainthe new numbering system andhow to apply it to real-time prob-lems. {Again, I skip over fascinat-ing material such as the pioneer-ing work in algebra of the poetOmar Khayyam about 1100 ADand, a hundred years later, ofLeonardo Fibonacci of the myste-rious Fibonacci numbers.) Themost important book in mathe-matics to appear in the earlyyears of the Renaissance wasSumma de arithmetic, geometria etproportionalita, published in Ven-ice in 1494 and written by a cos-mopolitan and widely traveledFranciscan named Luca Paccioli.The Summa drew heavily on Fi-bonacci's work, but it was alsothe first serious effort to explain

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double-entry bookkeeping, an in-novation with economic conse-quences comparable to the dis-covery of the steam engine 300years later.

Paccioli also set out the basicprinciples of algebra, in thecourse of which he posed thefollowing problem:

A & B are playing a fair gameof balla. They agree to playuntil one has won six rounds.The game actually stops whenA has won five and B three.How should the stakes be di-vided?

This puzzle, which is knownas the problem of the points,sounds innocuous, but it is not. Itappears repeatedly in the writ-ings of the mathematicians of the16th and 17th centuries, withmany different variations but al-ways with the same question:How do we divide the stakes inan incomplete game? The an-swers were not obvious to themathematicians of those timesand led to heated disputes. Theproblem of the points turned outto be the origin of the calculus ofprobability. The definitive solu-tion had to wait for nearly 150years.

Before telling you how that so-lution came about, I must stopfor digression number two. Prob-ability, as a systematic concept,really started in the mid-1550swith an Italian who was a con-temporary of Benvenuto Celliniand Copernicus. His name wasGirolamo Cardano, and I fail tounderstand why so few peopleare acquainted with this fascinat-ing man. Cardano described him-self as "hot-tempered, single-minded, and given to women,"as well as "cunning, crafty, sar-castic, diligent, impertinent, sad,treacherous, magician and sor-cerer, miserable, hateful, lascivi-ous, obscene, lying, obsequious,fond of the prattle of old men."

Cardano wroee 131 printedworks, claims to have burned 170more, and left 111 in manuscriptform at his death. His writingsspanned math, astronomy, phys-ics, urine, teeth, the life of theVirgin Mary, lesus Christ's horo-scope, morality, immortality,Nero, music, and dreams. Hewrote a book on venereal dis-ease, but it was never publishedbecause, as he noted in his auto-biography, "Hi libri corrupti sunturina felis."

Cardano's great book in math-ematics, Ars Magyia {The GreatArt), appeared in 1545 and wasthe first major work to concen-trate on algebra. Cardano marchedright into the solutions to cubicand quadratic equations. He evenwrestled with square roots ofnegative numbers, totally un-known concepts before the intro-duction of the Hindu numberingsystem and still mysterious andinconceivable to many people.

Cardano was a passionate andcompulsive gambler, whose trea-tise on the subject. Liber de LudoAleae, appears to have been thefirst serious effort to develop theprinciples of probability. Car-dano wrote the book in 1525 andrewrote it in 1565, claiming to"have discovered the reason for athousand astounding facts."Note the use of the words "rea-son for." Cardano issued the the-oretician's customary lament that". . . these facts contribute agreat deal to understanding buthardly anything to practicalplay." The book was never pub-lished in Cardano's lifetime butwas found among his manu-scripts when he died. Its firstpublic appearance came muchlater, when it was printed inBasle in 1663.

Cardano's generalizationsabout the probabilities in gam-bling have high importance. Hesensed the concept of the law of

large numbers. He defined, forthe very first time, what is nowthe conventional format for ex-pressing probability as a fraction.He even had to teach his readersthat the probabilities on throwsof two six-sided dice were to bebased on 36 possibilities, not 12.

Now, return to the problem ofthe points. In 1654, at about themoment when Cardano's bookon gambling appeared, a wealthyFrench nobleman with an addic-tion to gambling put the questionto a religious freak who was alsoa great mathematician. This manthen turned to a provincial law-yer whom he had never met butwho played with the theory ofnumbers in his spare time. Thenoble gambler was the Chevalierde M^re; the mathematicianswere Blaise Pascal and Pierre deFermat. Between them, they setthe stage for all the work in prob-ability theory that was to follow,right up to Gauss's developmentof the normal distribution, basedupon his geodesic and astronom-ical studies from 1809 to 1816,and Galton's proposition of theregression to the mean and thecoefficient of correlation, basedon his explorations into genera-tions of sweetpeas in the 1880s.Where would finance theoristsand practitioners be withoutthese two men?

Galton was a wealthy Victorianand amateur scientist whose di-verse achievements included theinvention of eugenics and finger-printing. Measurement was Gal-ton's obsession. "Wherever youcan, count," was one of his favor-ite expressions.

Galton took note of the sizeof heads, noses, arms, legs^heights, and weights, and of thecolor of eyes, the sterility of heir-esses, the number of fidgetsmade by people listening to lec-tures, and the degree of colorchange as the audience at a derby

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watched the horses run a race.He classified the good looks ofgirls he passed on the street,pricking a hole in a left-pocketcard when the subject wascomely and pricking a right-pocket card when she was plain(the London girls scored highest;the girls of Aberdeen were at thebottom).

Galton's compulsion to mea-sure accompanied him even on atrip in darkest Africa in 1849 tohunt big game in what is nowknown as Namibia. When he ar-rived at a village of Hottentots,one of the women caught hisattention. As a scientific man, hereported, he was "exceedinglyanxious to obtain accurate mea-surements of her shape." Hecould speak no Hottentot andwas uncertain how to undertakethis urgent piece of research, buthe still accomplished his goal:

Of a sudden, my eye fell uponmy sextant; the bright thoughtstruck me, and I took a seriesof observations upon her fig-ure in every direction. . . .[T]his being done, I boldlypulled out my measuring tape,and measured the distancefrom where I was to the placewhere she stood, and havingthus obtained both base andangles, I worked out the re-sults by trigonometry and log-arithms.

Although the theory of proba-bility was developing into amighty tool to help humansgrasp at the unknown future, anunderground set of ideas was be-ginning to gain a foothold. Theprogenitor of these new conceptswas in Daniel Bernoulli's so-called Petersburg Paradox in1738. Bernoulli described a gamein which a player at coin flippinghas a chance to win an infiniteamount. What should the playerpay for this opportunity?

The Petersburg Paradox pro-

voked intense controversy thatcontinued long after Bernoullidied in 1782, but everyoneagreed that there are good argu-ments against paying an infiniteamount for the opportunity towin an infinite amount. That wasthe intellectual point of inflec-tion: If utility functions are con-cave rather than straight lines,then the number of utility func-tions you can draw is limitless. Inother words, gut has returned tothe scene and measurement re-cedes into the background. Un-certainty has begun to confrontprobability.

The big break in risk percep-tions, however, came whenWorld War I blasted into smith-ereens the conventional wisdomsof the Victorian and Edwardianeras. A world that had onceseemed predictable and orderlyturned out to be unpredictableand disorderly in the extreme. Itis no coincidence that FrankKnight's great book Risk, Uncer-tainty, and Profit appeared in 1921and that he chose these words toexpress his central theme: "Thereis much question as to how farthe world is intelligible at all. . . .It is only in very special andcrucial cases that anything like amathemat ica l s t udy can bemade." Nor is it a coincidencethat Keynes's Treatise on Probabil-ity also appeared in 1921 and is,in essence, an attack upon thewhole idea that mathematics candefine the future with any degreeof certainty. Keynes even takesup arms against Gauss's worshipof the concept of the mean. Later,writing in the shadow of theGreat Depression, Keynes de-scribed decision making underuncertainty in these words:

[Most of our decisions! to dosomething positive . . . canonly be taken as a result ofanimal spirits . . . and not asthe outcome of a weighted av-

erage of quantitative benefitsmultiplied by quantitativeprobabilities.Seen from this perspective,

what are we to think about theelegant structure of capital ideasthat recently inspired me: mean-variance, CAPM, and the effi-cient markets hypothesis (EMH)?Although I have not heard any-one refer to this body of theory asclassical, its balance, cohesion,clarity, and consistency provideall the necessary hallmarks ofclassical forms. Today, the classi-cal capital ideas are suspected ofsuffering from kurtosis, skew-ness, and other less farruliar ma-lignancies. They are under attackfrom nonlinear hypotheses, over-whelmed by fears of discontinui-ties rather than pricing volatilitiesand factors, and frequently madeirrelevant by exotic new financialinstruments that come in unfa-miliar shapes and hedge unfamil-iar risks. As the mathematics thatdefine these risks grows increas-ingly complex, the dimensions,contours, and limits of risk arebecoming correspondingly ob-scure.

These developments do notmean that the classical conceptsof finance were in some sense"wrong." The argument runs theother way. The effort to abandonthe beautiful and coherent logicof the classical ideas reflects, noton the ideas, but on the changingenvironment in which we live.

The philosophical roots ofmean-variance, CAPM, andEMH, I would argue, stemmedfrom the optimism of the earlypostwar years—the 1950s and1960s. That was a time when peo-ple believed that men andwomen of good will could re-make the awful w^orld of the1930s into a new world: well be-haved, functioning within clearlyrecognized standard deviations,and with generally accepted

10 Financial Anaiysts Joumal / January-Febaiary 1995

means to which matters wouldinexorably regress. I use finance-speak here, but I refer to thecontours of life in its broadestsense. In such a world, financialmarkets are always orderly andrisk is recognizable, measurable,manageable, and containable. Insuch a world, in short, you havesome sense of where the shockswill be coming from.

The reluctant acceptance of theclassical ideas by practitioners af-ter the turbulence of 1973 and1974 reflected a search for orderat a terrifying moment whenOPEC had taken pains to remindus that we were verging onchaos. In the wake of stunninglosses of wealth, nominal as wellas real, risk control became an

explicit goal for the first time inmany years—an occasion forwhich the new theories of port-folio management and marketbehavior were made to order.

But time has proven once againthat the world does not come inneat and familiar packages. In aworld that is changing faster thanany of us can understand, riskseems less amenable to measure-ment than most investors hadcome to believe. The result is thattried-and-true methods of riskmanagement are on the defen-sive, even though risk aversion isas intense as ever—perhaps moreintense than ever. An explosivedemand for novel forms of con-taining risk is developing, someof which, I fear, may in the end

make markets more risky ratherthan less.

All of these developmentsshould come as no surprise.Throughout history, the percep-tion of risk has reflected the tem-per of the times in each society.From the superstitions of the an-cients to the strict regulations ofthe early Christian church, fromthe rational views of the Renais-sance and the Enlightenmentto the upheavals provoked byWorld War I and the Great De-pression, and from the classicalconcepts of modern portfolio the-ory to the dark and hidden forcesdriving us today, perceptions ofrisk are the most powerful symp-toms of what a society is allabout.

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