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Benot Mandelbrot Rsum

1987-2010 YaleUniversity,professorofmathematicalsciences(nowemeritus) 2004 PublishesThe (Mis)Behavior of Markets: a Fractal View of Risk, Ruin and Reward 2003 JapanPrizeforScienceandTechnology 1993 WolfFoundationPrizeforPhysics 1986 FranklinMedalforSignalandEminentServiceinScience 1985 BarnardMedalforMeritoriousServicetoScience 1982 PublishesThe Fractal Geometry of Nature1958-1975 IBMResearchCenter,NewYork,researchstaffmember1957-1958 UniversitLilleandcolePolytechnique,Paris,lecturer 1952 FacultdesSciences,Paris,PhD,mathematicalsciences1949-1957 CentreNationaldelaRechercheScientique,Par is,seniorresearcher 1948 CaliforniaInstituteofTechnology,MSc,aeronautics

Source:MichaelMarsland/YaleUniversity

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the markit magazine Autumn 2010


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Q: Professor Mandelbrot, your book, The (Mis)Behavior

of Markets offered a wonderful critique of how tradi-

tional nance theory has failed over the years, and

more or less predicted back in 2004 that we would

face another nancial crisis like the one we have just

suffered. Do you feel vindicated?

A: Ofcourse,butthedelayhasbeencostly.Iamamath-ematician,andnotaneconomist.Itrytogostepbystep.Idontwanttoexplainwhatmaynotbetrue,whichisveryoftenthecase.Allofmyideasgobacktothe1960s.Idevelopedadescriptionofthenancialmarketsandwaitedfortheworldtoreact.Itsbeen40years.Theworldhasreactedtoitinthesenseithasboughtmanycopies

ofmybooks,butithasignoredtheeconomicschapters.IdontthinkIneedtosayItoldyouso.Itisveryineffective.Whenpeopledontwanttolisten,theydontlisten.

Q: One of your main themes is that risk is underestimated

by many in the nancial world. Why do you think they

keep missing this essential truth?

A: Peoplethinkthatriskmeansthatifyouinvest$10,youmaygetback$11ifyourelucky,perhaps$10.30,butsomewherecloseto$10.Infact,ifyoulookattheactualdataoftrading,notforeveryprice,butfortheimportantpricesonthemarket,largepricechangesareobservedoftenenoughtomatteralot.Suchlargeswingsmeanthe

The ractalso lie

Professor Benot Mandelbrot appliedmathematical theories to describe thebehaviour o markets. Sadly, he diedin October. The Markit Magazine is

ortunate to have had the chance toask him about his perspective on risk intodays fnancial system

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Autumn 2010 the markit magazine


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gamedenitelychanges.Thenancialtheorythatwasdevelopedin1900saysthatbigchangesdonothappen.Thattheory,whichisstil ltaughtinbusinessschools,isnotcorrect.Itdoesnotdescribethebehaviourofmarkets.

Q: One of your key insights is that turbulence in nan-

cial markets is similar to turbulence in wind tunnels

and raging rivers. Obviously they dont have the same

underlying causes but exhibit the same patterns,

you believe. What is the implication of this theory for

people who work in the nancial sector?

A: Theimplicationistobeverycarefulattakingbigrisks.Butdetailsremaintobeworkedout.Donttakeasbigariskaspossibleintheexpectationyouwillbeluckyandearnbigrewards.

Q: Your book, The Fractal Geometry of Nature, has

become a classic of chaos theory. Weather is one

area where it comes into play. But the fact is we

cant predict weather accurately yet. All we can do

is observe it once it happens. Some specialists say

the same thing about nancial markets. Do you agree

with that?

A: Thebookwasntspeakingaboutweatheroranythingspecic.Itmerelytellsustheworldisverycomplicated.Youknow,thissciencedevelopedinthesimplestpartsof

theworldandwaswidelyaccepted.Butnowkeypeoplehavebecomeveryarrogantinthinkingthattheyknowhowmarketsbehaveandtheyactuallydonotknow.Therearemanystatementsaboutnancebywell-knownscholars

thatIdontthinkcouldbejustiedonthebasisoftheevidence.

Q: You came up with your theory of how market prices

work by studying the cotton market over a hundred

years. How did you happen to choose this area for

study, which yielded such an important conclusion

that prices in nancial markets arent really random

even though they seem to be?

A: Itwasjustaluckyaccident.WhenIstartedmyworkoncotton,Iwouldntsayitwassexy,thatsnottherightterm,butpeopledontexpectamathematiciantowriteaboutcotton.CottonhasbeenacommodityforaverylongtimeanddataaboutcottonsaleshavebeengatheredinCairooverthisperiod.TherewasanoldEnglishmaninCairowhowasverybrilliant,andhehadverylittletodosohestudiedscienceasanavocation.SothereisagreatdealofdataaboutcottonandIwasluckyenoughtohearaboutit.Cottonisamongthemostvariableinpriceofallthecommodities,Wheatspriceislessvariablethancottonsis,butcottoniseasiertostudy.Sotherewasallthisdatainoneplace,itwasnotexpensiveformetoaccesstheinformationandIcoulddowhatIwantedwithit.

The implication is to be very careul at taking big risks. But detailsremain to be worked out. Dont take as big a risk as possible in theexpectation you will be lucky and earn big rewards.

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Q: Yes, and in the process you found out something

extremely interesting about nancial markets. That

cotton prices were not distributed over a bell curve,

as modern nancial theory believes prices for various

assets are distributed. You found the distribution wasnot normal but was better described by the theories of

French mathematician Paul Pierre Lvy. What was the

signicance of that?

A: Itshowsthatlargepricemovementshappenonlyrarely,butoftenenoughtomatteragreatdeal.Inmybook,Iamcarefultoshowexamplesofwhatdatathatareruledbyabellcurvereallylooklike.Theynevergoupenormously,theynevergodownenormously.Thebellcurvebecameverywellknownaround1800thanksto(GermanscientistCarlFriedrich)Gauss,averygreatman,whowasstudyingsimplephenomenainastronomy.Whenhegotaverylargevariationinhisdata,hethoughtitwasanerrorofmeasurement.Thingsdidntgoupanddownverymuch.Itwasamistake.Butinphenomenalikeprices,thatsnotso.Everysooften,notsorarely,priceschangedramati-cally,andtodaypricesmovemuchmorequicklyandthesechangesaremuchmoreimportant.Butithasalwaysbeenlikethat.TherearestoriesintheMerchant of VenicebyShakespeare,andevenmucholderbooksthanthat,whichtalkedabouttheexistenceofacategoryofpeople,bankers,whoknewverywellfromexperiencethatshipssometimeswentsafelyonalongtripandsometimes

didnt.Andwhentheydidntreturn,itwasabiglosstotheirbusiness.Asinglelosscouldverywellsinkabigcompany.Thatwaswellknownhundredsofyearsagoanditwasntamatterofamathematicaldispute.

Q: This leads to the problem you describe of what

happens when there is not a bell curve distribution of

prices. You get so-called fat tails, which are extreme

variations from normal distributions. The Black-

Scholes model of options pricing, on the other hand,

is based on a normal distribution using a bell curve.

What does your theory tell you about large swings in

prices?

A: Youbuysomethingforacertainpriceandndthataminutelateritsworthonehalfofwhatyoupaidforit.Nooneexpectedthingstochangethatmuch.Givenwhatthemarketknowsaboutaparticularcommodity,itdoesntexpectthatsogreatachangeinpricecouldhappen.

Q: Is that what leads to nancial market bubbles?

A: Itsalittlesubtlerthanthat.Thatisreallytherststepinmytheoryofbubbles.Buttherearesuddenchangesofprices.Ifyoucallthembubblesyouarealreadyjudgingthem;youaresayingtheyarebad,theyaresomethingundesirable.Theyarenotundesirable.Theyarethere,andifonedoesnottakeaccountofthepossibilityofaprice

It shows that large price movements happen only rarely, but otenenough to matter a great deal.

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goingupverysuddenly,orgoingdownverysuddenly,onetakesariskthatishigherthananyonewants.

Q: This leads into your criticism of the famous EfcientMarkets Theory, which is still popular in the nancial

markets and used to structure many types of invest-

ments. It maintains that there arent any bubbles. You

say this theory died under the weight of real data. Why

doesnt this theory work dont you believe that the

market knows all the information that it is possible to

know?

A: No,alltheinformationaboutamarketisneverknown.Ihaventworkedinthesecuritiesbusinessbutintheworldofcommodities.Evenstill,Iknowthatintherealmofsecurities,therearemanycompaniesthatbeginwithalargedegreeofoptimism,buttheythenhitasuddendowndraftthattheydidntallowforandtheyvanish.Ithappensallthetime.

Q: In place of the old theories about nancial markets

and price swings, you have come up with your own

parameters. Tell us how those work.

A: Therstoftwoparametersisinspiredbytheworkof(ItalianeconomistVilfredo)Pareto,whostudiedthedistri-butionofincomes,notofpricechanges.Paretoobserved

thatifyoulookedatthedistributionofincomeintheking-domsofGermanywherehewasgettinghisdata,asmallgroupofthewealthiest,justafewpercent,hadmostof

thetotalincome.Ifyoutookalargenumberofpeopletherewouldbeanincreasingchanceofndingsomerichpeople.Sothequestionis:howmanyrichpeoplewouldyound?Forthattherewasamathematicaldistributiontheorythatwasthefavouredideaallthewaybacktothe1800s.Bythetimethe1900scamearound,itwasverywellknown,butitwascompletelywrong.Infact,therealitywasthattherichestpeopleweremuchricherthantheywouldbeifincomewasruledbyanormaldistribution.ButifyouusethedistributionofincomesthatwasdiscoveredbyParetojustbefore1900,youndthatittsverywell.Itprovidedanuncannyapproximationoftheorderofmagni-tudeoftherichestpersoninacountryoraprofession.Theotherkeyparametergovernsthedistributionintime.Ifyouspeakofindividualincomes,likeParetodid,youndtimeisnotinvolved.Butwewanttofollowthevariationofapriceintimeandoftenitisverystrong.ParetosworkhadledtotheideathatpricesfollowedwhatwascalledBrownianmotion,anideawhichwasproposedin1900by(FrenchmathematicianLouisJean-Baptiste)Bachelier.UntilIdidmywork,peoplehadassumedpricesfollowedthisBrownianmotion,meaningtheywereverysimpleandthisisthesourceofthenotionthatpricesmovedupanddownonlyalittleandwerenotveryrisky.

Pareto observed that i you looked at the distribution o income in thekingdoms o Germany where he was getting his data, a small groupo the wealthiest, just a ew per cent, had most o the total income.

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Q: Do you think the nancial markets still underestimate

risk?

A: Ithinkso.WhenIcameupwithmyworkinthe1960s,nooneexpectedtherealworldtobesocomplicated.Ihadstudentswhoatrstfollowedme,evenwhenIfoundithardtofollowmyself,butthentheypreferredtogobacktotheteachingsofBachelierin1900,basedonthenormaldistributionofprices.(HeisreferringmainlytoEugeneFama,oneofMandelbrotsstudents,whoasananceprofessorattheUniversityofChicagoBoothSchoolofBusinessbecametheauthorofthemodernEfcientMarketsTheorythatMandelbrotnowviewsasinvalid).Theybelievedthatallinformationiswellknown,thatthingsareveryeasytohandle,and,ofcourse,thatwasamistake.Atthattime,Itriedtorepeatmyargumentsandtoldthemthisisgoingtoleadtotroubleverysoon.OfcourseIwaslaughedat,butIdidnotjustgositinacornerunhappy.Ididworkonthingsotherthanprices.IfeltthattheevidencewassoclearthatpriceswouldcomebacktotheforefrontwhetherIspentmylifeworkingonthistopicornot.Infact,Ispentaverysmallpartofmylifeworkingonprices,buttheworldhasntchanged.

Q: One of the crowning achievements of your career was

to coin the now famous term fractals and make them

immensely popular with your computer-generated

depictions known as the Mandelbrot Set. You applied

fractals to such things as the shoreline of Britain, but

say they also apply to nancial markets. Do you still

feel fractals have a useful role in looking at the nan-cial world?

A: Ithinkthathasbeenthethingtolookatforthelast50years.Therearenotmanyotherpossibilities.EverythingthecurrenttheoryofnancialmarketsusesisessentiallyBacheliersideaonthenormaldistributionofprices.OrBachelierwithsomelittlemodications.Thenthereismyalternativetheory,whichisthatpricesarenotnormallydistributed.

Q: But you make clear that you cant use fractals to

predict prices, that you cant make a million dollars

in the stock market using the Mandelbrot theory. So

practically speaking, whats the advantage of them?

A: Theadvantageperhapsistoreduceyourprobabi lityofbeingruinednanciallybecauseyouhavemisjudgedrisk.Forexample,youcanusefractalstocomparetwoport-folioswithdifferentgoalsandbyusingfractalsyoucanchooseaportfolioforadifferentlevelofrisk.Mytheoryislessdefectivethanpopularmarkettheoryandmayhelptheworldavoidormitigatetheagoniesthatwearenowexperiencing.

I had students who at frst ollowed me, even when I ound it hard toollow mysel, but then they preerred to go back to the teachings oBachelier in 1900, based on the normal distribution o prices.

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