Journalof Economic Perspectives—Volume 17,Number 4—Fall 2003—Pages 191– 202

Anomalies TheLawofO nePriceinFinancialMarkets

Owen A.Lamont and RichardH. Thaler

Economicscan bedistinguished from other social sciences by the belief that most(all?) behavior can beexplained by assuming that rationalagents withstable, well-deŽned preferencesinteract in markets that (eventually)clear. An empirical resultqualiŽ es as an anomaly ifit is difŽ cult to rationalize or if implausible assumptions arenecessary to explain it within the paradigm. Suggestionsfor future topics should besent toRichard Thaler,c/ o Journalof Economic Perspectives, Grad- uateSchool of Business, Universityof Chicago, Chicago, IL60637,or ^[email protected] &.

Introduction

It isgood fora scientiŽc enterprise,as wellas fora society,to have well- establishedlaws. Physics has excellentlaws, such as thelaw of gravity. What does economicshave? The Ž rstlaw of economicsis clearlythe law of supply and demand, and aŽnelaw it is. Wewould nominate as thesecond law“ thelaw of one price,” hereaftersimply the Law. TheLaw states that identicalgoods must have identical prices.For example, an ounce ofgold should have thesame price (expressed in U.S. dollars)in London as itdoes inZurich, otherwisegold would  owfrom one cityto theother. Economic theory teaches us toexpect the Law to hold exactlyin competitivemarkets with no transactions costs and no barriersto trade, but in practice,details about marketinstitutions are important in determining whether violationsof the Law can occur. y Owen A.Lamontis Visiting Professor of Finance at Yale School ofManagement, New Haven,Connecticut. Richard H. Thaleris Robert P. GwinnProfessor of Behavioral Science andEconomics, Graduate School of Business, University of Chicago, Chicago, Illinois. 192Journal of Economic Perspectives

Considerthe case ofaspirin. Suppose, forthe sake of argument, that Bayer aspirinand storebrand aspirinare identical products, but that Bayercosts twiceas much because someconsumers believe(falsely, in this example)that Bayeris better.Would weexpectmarkets to eradicate this pricedifference? Since the Bayer brand name istrademarked, it is not (legally)possible to go into the business of buyingthe store brand aspirinand repackagingit in Bayerbottles. This inabilityto transformthe store brand intoBayer prevents one method arbitrageurs might use todrive the two prices to equality.Another possibility for arbitrageurs would be to tryto sell the more expensive Bayer aspirin short today, bettingthat theprice discrepancy willnarrow once thebuyers of Bayer “cometo their senses. ” Short sellingworks like this: an arbitrageurwould borrow some bottles from a cooperative owner,sell the bottles today and promisethe owner to replacethe borrowed bottles withequivalent Bayer bottles in the future. Notice that twoproblems impede this strategy.First, there is no practicalway to sell a consumerproduct short, and second, thereis no wayto predictwhen consumers willsee the error in theirways. Theseproblems create limits to the forces of arbitrage, and inmost consumer goods markets,the Law may be violated quite dramatically. 1 Theaspirin example illustrates the essential ingredients to violations of the law ofone price. First, some agents have tobelieve falsely that thereare real differences betweentwo identical goods, and second, therehave tobe some impediments to preventrational arbitrageurs from restoring the equality of prices that rationality predicts.Can theseconditions hold in Ž nancial markets,where transactions costs aresmall, short sellingis permitted and competitionis Ž erce? Traditionally,economists thought that theLaw could beapplied almost exactly in Ž nancial marketsbecause oftheworkings of arbitrage. Arbitrage, de Ž ned as the simultaneousbuying and sellingof the same security for two different prices, is perhaps themost crucial concept ofmodern Ž nance. Theabsence ofarbitrage opportunitiesis the basis ofalmost all modern Ž nancial theory,including option pricingand corporatecapital structure. In capitalmarkets, the Law says that identicalsecurities (that is, securitieswith identical state-speci Ž cpayoffs) must have identicalprices; otherwise, smart investors could makeunlimited pro Ž ts by buying thecheap oneand sellingthe expensive one. It does not requirethat allinvestors berational or sophisticated, onlythat enough investors(dollar weighted) are able torecognize arbitrage opportunities. According to the standard assumptions, the Lawshould hold in Ž nancial marketsbecause ifsome investors mistakenly think that odd-numberedshares ofsome stock arebetter than even-numberedshares, rationalarbitrageurs will prevent these investors from driving up theprice of odd-numberedshares (unlikethe aspirin market discussed above). Moreover, unlikeinternational trade where it may take some time to move gold physically fromLondon toZurich, onewould expect the Law to hold not onlyin the long run, but almostinstantaneously, sinceone can quicklybuy and sellsecurities.

1 SeeRussell and Thaler(1985) fora discussionof whenmarkets eliminate the effects ofirrationality. Owen A.Lamontand Richard H. Thaler193

Unlikegovernment-enforced laws prohibiting litter on thesidewalk, the Law does not requirehired law enforcement agents any morethan oneneed enforce a lawprohibiting the littering of $100 bills. Rather, theLaw is enforced by arbitra- geursas abyproduct offollowing their sel Ž sh proŽ tmotives,that is, pickingup the $100bills. In this sense, thelaw of one price, while not quiteas automatic as thelaw ofgravity, seems like a lawthat should neverbe broken in awell-functioningcapital market.For this reason, theoristshave used itas an uncontroversialminimal condition, astartingpoint that leadsto other implications. Upon theLaw, they have builtthe mighty edi Ž ce of modern Ž nancial theory,including the Modigliani- Millercapital structure propositions, theBlack-Scholes option pricingformula and thearbitrage pricing theory. But it turns out that theapplication ofthe Law in Ž nancial marketsis not as uncontroversialas was originallythought. Overthe past decadeor so, numerous violationshave beendetected. We surveysome of themore interestingones hereand then considerthe implications for how weshould think about Ž nancial markets.

Closed-EndCountry Funds

Closed-end funds area specialsort of mutual fund that areinteresting from theperspective of the law of oneprice. Traditional mutual funds stand readyto buy and sellshares toinvestors at theunderlying value of theassets theyown (thenet asset value,or NAV). In contrast, closed-endfunds issueshares inthe fund that tradein markets. (See the Anomalies article on this topicby Lee, Shleifer and Thaler,1990, for details.) The relationship between closed-end fund pricesand net asset valuescan varyacross funds and across timeswith both discounts and premia ofgreater than 30percent commonly observed. Whileclosed-end fund discounts and premiumsappear tobe a violationof the lawof one price, they might not beconsideredpure examples, since the two assets (theunderlying securities owned by thefund and thefund itself)are not precisely identical.One differenceis that theportfolio manager of the fund chargesa feefor his servicesand incurs otherexpenses, and thus thecash  ows goingto the holders ofthe fund aredifferent from the cash  ows goingto theholders of the underlying assets. This could, inprinciple, justify moderate discounts. Evenpremia could be rationalif the closed-end fund managerhad superiorstock picking ability, though inpractice, there is little relation between discounts/ premiaand futureasset returns.Nevertheless, these rational justi Ž cations fordiscounts and premiacan at bestjustify small deviations between price of thefund ’sshares and thevalue of the assets thefund owns. Thelate 1980s saw aproliferationof a specialtype of closed-end fund called country funds, which tradeon U.S. exchanges, but hold equitiesin a speci Ž c foreigncountry (Klibanoff,Lamont and Wizman, 1998).These country funds often had much largerdeviations between price and valuethan those observedin the domesticfunds, and thedeviations were much toolarge to be consistent withany 194Journal of Economic Perspectives

rationalstory. An extremeexample is the Taiwan Fund tradingon theNew York StockExchange. Duringearly 1987 (shortly after its start), ithad a205percent premium,meaning that theprice was morethan threetimes the asset value (thepremium stayed above 100 percent for ten weeks and above50 percent for 30weeks). This mispricingcan persistdue to legal barriers preventing U.S. inves- torsfrom freely buying Taiwanese stocks. Still,the question remains why U.S. investorswere willing to pay adollarto buy lessthan 33cents worthof assets. Anotherextreme example is the behavior of the Germany Fund when the BerlinWall fell in late 1989. At the beginning of 1989, the Germany Fund had a smalldiscount ofabout 9percent.As politicaldevelopments in 1989made the fall ofthe Communist regime and theeventual reuni Ž cation ofGermany more likely, Germanstocks wentup. Thevalue of the Germany Fund, tradedon theNew York StockExchange, wentup evenmore, and bySeptember 1989, the fund had a premiuminstead ofa discount. ByJanuary 1990,the premium was 100percent. Afterthat, theeuphoria in theUnited States wore off, theprice of Germany Fund shares felland thepremium returned to about zeroin April1990. This exampleis evenmore of a puzzlesince U.S. investorswere free to invest directly in Germany. (A similar “bubble” occurredin the Spain Fund at about thesame time.) One explanation, which wediscuss furtherbelow, is short-sale constraints. Someevi- denceindicates it was dif Ž cultfor arbitrageurs to short theGermany and Spain Funds.

American Depositary Receipts: Coming to America

Anothersituation involvinginternational equity markets is the pricing of AmericanDepositary Receipts, or ADRs. ADRsare shares ofspeci Ž cforeignsecu- ritiesheld in trustby U.S. Ž nancial institutions. Claimsto theseshares tradein U.S. markets,such as theNew York Stock Exchange, and arecreated to make it easier forU.S. investorsto own shares inforeign companies. Likeclosed-end funds, ADRs can have pricesdifferent from the value of the underlying assets, although inmost cases, theydo not have signi Ž cant deviations,since arbitrage is possible. For example,if an ADRwereselling at apremiumto the underlying security, a Ž nancial intermediarycould buy shares oftheoriginal stock inthe home market and create newADRs, makingan instant pro Ž t. Occasionally, however,price discrepancies do existin this market.A particu- larlyremarkable example is Infosys, an Indian informationtechnologies company tradingin Bombay, and the Ž rstIndian company toliston an Americanexchange (Nasdaq). As ofMarch 7, 2000,Infosys had experienceda hugeincrease in value, and itsADR was tradingat $335,up from$17, the (split-adjusted) priceat which it had beenintroduced to the U.S. marketjust ayearearlier. However, as withthe GermanyFund in1989,the enthusiasm ofAmerican investors appeared to be much greaterthan that oflocal investors. The ADR was tradingat a136percent premium tothe Bombay shares. Anomalies:The Law of One Pricein Financial Markets 195

In this case, of Ž cialbarriers prevented Americans from buying the shares tradingin Bombay, and so therewas no wayfor American arbitrageurs to create newADRs and thus instantly pro Ž tfromthis relativevaluation. Whileit certainly appears that Americaninvestors were acting irrationally in buying Infosys, this is hard toprove.In segmentedmarkets, it can berationalfor the same asset tohave differentprices in differentmarkets, re  ectingdifferences in supply and demand. In thecase ofInfosys, theinterpretation would be that Americaninvestors value Infosys because itsreturns are uncorrelated with other assets heldby Americans, so Infosys offersvaluable diversi Ž cation. Indian investors,on theother hand, correctly placea lowervalue on Infosys sinceit confers no diversi Ž cation beneŽ t to them. It isdubious, however,that such an argumentcan everjustify as largea discrep- ancy as was seenhere. And sincethe deviation has now (summer2003) fallen to 41percent,or about athirdof what itwas at thepeak, onewould also have toargue that thehedging premium is highly volatile.

Twin Shares: Can the Stock Market Multiply by 1.5?

Athirdsituation frominternational equity markets is Siamese Twins. Siamese Twins, as discussed inRosenthal and Young (1990)and Frootand Dabora (1999), are Ž rmsthat forhistorical reasons have twotypes of shares with Ž xedclaims on the cash  ows and assets ofthe Ž rm.An exampleis RoyalDutch/ Shell,which has both RoyalDutch shares (tradedin Amsterdam)and Shell(traded in London). Thereis only one Ž rm,the Royal Dutch/ ShellGroup, but based on the1907 merger agreement,all cash  ows aresplit so that RoyalDutch shares receive60 percent and Shellshares receive40 percent.Given this setup, theratio of the market value of the RoyalDutch tothe market value of Shell should be1.5. However,this ratiohas variedconsiderably from its theoretical value, from 30 percent too low in 1981to morethan 15percent too high in1996. After trading at apremiumof greaterthan 10percent for most the decade of the 1990s, Royal Dutch shares arenow trading at roughlypar withthe Shell shares (seeFigure 1). Thesubstantial deviationsthat have beenobserved are somewhat surprising sinceboth RoyalDutch and Shelltrade in highly liquid and open marketsin Europeand, additionally,have ADRstrading in the United States. Thus, topro Ž t fromthe mispricing, a U.S. investordoesn ’tevenneed to trade in international markets.All that isnecessaryis to short theoverpriced shares, buy theunderpriced shares and hold forever.Still, forever is alongtime, and, inthenear term, the price disparitycan widen,producing lossesto this strategy.(More on this below.) Evenif there are not enough arbitrageurstaking the strategy of buying the cheap versionand shortingthe dear one, thereis an evensimpler strategy that one mightthink would be enough tokeep the prices lined up. Why don ’t investors simplybuy whicheverversion of thestock ischeaper?Why, duringthe 1990s, when RoyalDutch was sellingfor a premiumover Shell, did U.S. mutualfunds own billionsof dollars of RoyalDutch? One partialanswer to this questionis that Royal 196Journal of Economic Perspectives

Figure 1 Pricingof Royal DutchRelative to Shell (deviationfrom parity )

20%

15%

10% n o i t a

i 5% v e D 0%

25%

210% 0 0 0 1 1 1 2 2 3 3 3 4 4 5 5 5 6 6 7 7 7 8 8 8 9 9 0 0 1 1 1 2 2 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 -0 -0 -0 -0 -0 -0 -0 n y t r l c y p b l v r p n n v r g n n t r g c y t r g n n v r g a a c a Ju e a e e Ju o p e a u o p u a u c a u e a c a u a u o p u J M O M D M S F N A S J J N A A J J O M A D M O M A J J N A A

Dutch was, untilrecently, a memberof the S&P 500index. This fact meantthat indexfunds trackingthe S&P 500index were forced to buy themore expensive versionof the stock, and evenactive large cap U.S. mutualfund managerswhose performancewas comparedto the S&P 500index might be inclinedto own Royal Dutch ratherthan ischeaper identical twin. One bitof evidence for this factor beingimportant is that on July10, 2002,S&P announced itwas droppingall foreign stocks, includingRoyal Dutch, fromthe index. The premium had been6 percent theprevious day, but fellto 1 percenton theannouncement. Although the premiumhad been  uctuating around zeroin the previous year, the fact that it dropped sharply on theannouncement adds support tothe index inclusion hy- pothesis.2 Still,whatever the reason, this exampleis ablatant violationof the Law, and onethat issurprising since there are no impedimentsto short sellingor other restrictionson theactions ofarbitrageurs.

Dual Share Classes

Anotherway in which companies can sometimeshave twodifferent types of shares ofstock intheir company iswhen theyhave twoclasses ofstock withdifferent votingrights. Usually these two classes tradeat about thesame price, except at times when thereis somebattle for corporate control, inwhich case votingstock ismore

2 It isa well-knownpuzzle that whenthe S&P500adds astockto its index,the priceof this stockjumps. This isapuzzlebecause S&P doesnot claimthat the additionhas informationcontent; additionsusually occurbecause other stocks have beendropped (often becauseof mergers), and stocksare selected mostlyon the basisof sizeand industry. SeeShleifer (1986), whoargues that the effect showsthat the demandcurve for stocks is downward sloping. Owen A.Lamontand Richard H. Thaler197

Figure 2 Premiumof Molex common over Molex Class A, 1990– 2002 0.6

3/22/00 0.5 Peak

0.4

0.3

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11/30/99 0.1 Added to S&P 500

0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 1 1 2 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 ------l l l l l l l l l l l l l n n n n n n n n n n n n u u u u u u u u u u u u u a a a a a a a a a a a a J J J J J J J J J J J J J J J J J J J J J J J J J 20.1 valuable.An examplewith evidence of Law violations is the case ofMolex, a manufacturing company. Molexhas twoclasses ofstock with claims to identical dividendsand cash  ows, but differentvoting rights. In August 1999,the voting stock was tradingat a15percent premium. At the time, 15 percent was seenas inexplicablyhigh (thepremium had tendedto range between zero to ten percent inpreviousyears), and aMolexof Ž cial said, “Ican seeno rationalreason forsuch abigdiscrepancy ” (Rublin,1999). Then inNovember 1999, S&P announced itwas adding Molexto theS&P 500index. S&P chose toinclude the common stock (with votingrights), but not theclass Anonvoting shares intheindex. On theannounce- ment,the premium rose from 12 percent to 24 percent and subsequentlyrose as high as 49percentin March 2000(see Figure 2). Whateverthe value of the voting rightsin Molex, it is hard tosee why these rights would become more valuable because the Ž rmwas includedin the S&P 500. 3

Corporate Spinoffs: Canthe Stock Market Multiply by 1.5?(Part II)

Asituation wherethe relationship between the price of twostocks isbounded bysome common ratiocan arisein the case ofa corporatespinoff. One example occurredin 1999 when aSiliconValley technology company called3Com felt that

3 In an evenmore bizarre Law violation involving voting rights inMay 2001,McData had shareswith superiorvoting rights trading at a22percent discount. 198Journal of Economic Perspectives

thestock marketwas not givingtheir shares properrespect, in spite of the fact that 3Comowned the Palm division, maker of the hot newhandheld computers.3Com decidedto spin offits Palm division, presumably to “unleash” itstrue value. Notice that this action inand ofitselfis suspicious froma Lawabiding perspective —if the same cash  ows always have thesame price, why should bundling orunbundling securitieschange value? Toinitiatethis divorce,3Com adopted atwo-stepprocess. The Ž rststep was an “equitycarve-out, ” inwhich 3Comsold asmallportion of the value of Palm in an initialpublic offering (IPO). Speci Ž cally,4 percentof the shares ofPalmwere sold intheIPO and another 1percentwas sold toaconsortiumof institutionalinvestors. Thesecond step, calledthe “spinoff,” wouldtake place in about sixmonths. Atthis point, theremaining 95 percent of the shares wouldbe distributed to 3Com shareholders. When thespinoff tookplace, each 3Comshareholder would receive 1.5shares ofPalm. In this case, theLaw requires that investorsobey an inequality, namely,that once Palmshares starttrading, shares of3Commust sellfor at aprice equalor greater than 1.5times the price of Palm. On theday beforethe IPO, 3Comwas sellingfor $104. The Palm shares were sold tothe public at $38a share, but endedthe day sellingfor $95 (after trading as high as $165!).During this sameday, thestock priceof 3Com actually fell 21percentduring the day to$82.To seehow ludicrousthis priceis, considerthe so-called “stub value” of3Com, which isthe implied value of 3Com ’s non-Palm assets and businesses. To computethe stub value,one just has tomultiply the Palm share priceby 1.5 to get $145 and then subtract this fromthe value of 3Com, obtainingthe novel result of a negative$63 per share (using theprecise ratio of 1.525).Indeed, themarket was valuingthe remaining (pro Ž table)3Com business at minus $22billion. To add insultto injury, 3Comhad about $10a share incash! Investorswere willing to pay over$2.5 billion dollars (based onthenumber of Palm shares issued)to buy expensiveshares ofPalm rather than buy thecheap Palm shares embeddedin 3Com and get3Com thrown in. This exampleis even more puzzling than that ofclosed-end funds ortwin stocks, becausethere is acleartermination date. Topro Ž tfromthe mispricing, an arbitrageurwould need only to buy oneshare of3Com, short 1.5shares ofPalm and waitsix months orso. In essence,the arbitrageur would be buying a security worthat worstworth zero for 2$63and wouldnot needto waitvery long to realize the proŽ ts. Thespinoff did depend on afavorableIRS ruling,but this appeared highlylikely. Figure 3 shows theactual timepattern of the stub valueof 3Com,that is, itsnon-Palm assets. As can beseen, thestub returnedto a morerational level afterseveral months. This mispricingwas not inan obscurecorner of capital markets, but rather tookplace in a widelypublicized initial public offering that attractedfrenzied attention. Thenature of the mispricing was so simplethat eventhe dimmest of marketparticipants was ableto grasp it.On theday afterthe issue, themispricing was widelydiscussed, includingin twoarticles in the WallStreet Journal , one in the New York Times ,and iteven made USAToday! Anomalies:The Law of One Pricein Financial Markets 199

Figure 3 3Com/PalmStub, 3/ 2/00 –9/18/00 30 7/27: Distribution 20 3/20: 3Com announced distribution to occur by September, earlier than planned 10 e

r 0 a h s

210 r

e 5/8: IRS approval announced,

p 220

s Palm shares to be distributed 7/27 r a

l 230 l 3/16: Options start o

D 240 trading on subsidiary 250 260 270 2 9 6 3 0 6 3 0 7 4 1 8 5 1 8 5 2 9 6 3 0 7 3 0 7 4 1 7 4 / / 1 2 3 / 1 2 2 / 1 1 2 / / 1 2 2 / 1 2 2 / 1 1 2 3 / 1 3 3 / / / 4 / / / 5 / / / 6 6 / / / 7 / / / 8 / / / / 9 / 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 8 9

Why wouldanyone everbuy oneshare ofPalmfor $95 instead ofbuying one share of3Com(embedding 1.5 shares ofPalm) for $82? One super Ž ciallyappeal- ingexplanation for the mispricing is when onlya smallportion of the subsidiary Ž rmis sold inan equitycarve-out, thedemand forthese shares outstripssupply. Once 3Comsells the remaining 95 percent of Palm, this argumentgoes, supply of Palmstock willrise and thus theprice will fall. While this argumentmust betrue at somelevel, it is inconsistent withmarket ef Ž ciency,with rationality and with the Law. What preventedarbitrageurs from enforcing the Law in this case?The primary problemwas theinability of investors to sell Palm short. Tobe able to sellshort a stock, onemust borrowit, and this borrowingis typically done through Ž nancial institutions, such as mutualfunds, trusts orasset managerswho lendtheir securi- ties.In thecase ofPalm, retailinvestors rather than institutionsheld most of the shares, thus makingPalm hard toborrow. At one point, 148percent of the  oating shares had beenborrowed. 4 ThePalm/ 3Comepisode is not unique. Lamont and Thaler(2003) provide otherexamples during the 1998 –2000stock marketbubble. These mispricings ofteninvolved technology and Internetstocks, withthe more exciting Internet stock beingoverpriced and themore traditional stock underpriced.A somewhat olderexample comes from the 1920s. In 1923,a young man named Benjamin Graham, laterto coauthor aclassic bookon securityanalysis, was managing money. Graham noticedthat although DuPont owneda substantial numberof GM shares,

4 Arelationin Ž nancecalled put-call parity isanotherapplication of the Law, and it says oneshould not beable to construct asecurityusing options that has the samepayoff as Palmbut a differentprice. Lamontand Thaler(2003) lookat optionsprices on Palm. While this isnot the placeto provide details, wefound massive violations of put-call parity dueto the dif Ž culty ofshorting Palm. Given time, the shortingmarket can continueto expand the sharesavailable to sell, but this processis far from instantaneous. 200Journal of Economic Perspectives

Du Pont’smarketcapitalization was about thesame as thevalue of itsstake in GM. DuPont had astub valueof about zero,despite the fact that DuPont was oneof America’sleadingindustrial Ž rmswith other hugely valuable assets. Graham bought DuPont, shortedGM and pro Ž tedwhen DuPont subsequentlyrose (Lowe, 1994). AstheBenjamin Graham episodeshows, despiteenormous changes incapital marketsand informationtechnology, it is not clearthat Ž nancial marketshave gottenmore Law abiding since 1923. The tech stock mania periodof 1998 –2000 suppliesmany oftheexamples discussed here.In this period,companies largeand smallappeared to be  agrantlymispriced, where “mispriced” has aclearand provablemeaning. The weight of the evidence is overwhelming.Beyond a reason- abledoubt, U.S. equitymarkets are violating the Law.

Long-Term Capitalin aShort-Term World

What preventsarbitrageurs from enforcing the Law? In thecase ofPalm and 3Com,short-sale constraints limitedthe amount ofmoneythat could bemade and theamount ofprice pressure arbitrageurs could bringto bear. In someof the examplesof closed-end country funds, limitson foreigninvestments prevented somekinds ofattractive trades. Butthese cases arespecial. For many ofthe exampleswe have discussed, marketswere free and open, and sellingshort was not particularlycostly. So, whyaren ’tthearbs doingtheir job? Theanswer is that violationsof theLaw do not generallycreate arbitrage opportunities (meaning sure proŽ ts withno risk),they just creategood but riskybets. Therisks to arbitrageursare particularly large in situations withouta speci Ž ed terminaldate. One riskis that aftertaking a position, thevaluation disparitywidens, causing thenet wealth of the arbitrageurs to fall.De Long, Shleifer,Summers and Waldmann (1990)dub this risk “noisetrader risk. ” Theidea is whatever the irrationalopinion was that caused noisetraders to getexcited (or depressed) about somesecurity and createa mispricing,it could getworse before it gets better! In extremecases, this wideningspread can cause thearbitrageur to approach bank- ruptcy, as his networth becomes negative and heno longerhas thecollateral to hold his positions. Aprominentexample is Long-Term Capital Management (LTCM),which had several “convergencetrades ” inplace during the summer of 1998.These are bets that mispricingswould narrow. Most ofLTCM ’sbetsinvolved mispricedbonds and derivativesecurities, but LTCMhad equitypositions as well, includingsome of the examples discussed here.For example, LTCM had a $2.3billion pairs trade on RoyalDutch/ Shell(Spiro and Laderman, 1998).When spreads widenedin 1998, diverging instead ofconverging,LTCM entered Ž nancial distress.LTCM attempted to raise new money, but found no takers,despite the fact that theconvergence strategy had presumablybecome more attractiveas thevalue disparityincreased. LTCM was forcedto enter into an agreementwith its creditors, leadingto an eventualliquidation of its positions. This scenariohad been Owen A.Lamontand Richard H. Thaler201

anticipatedone year earlier by Shleifer and Vishny (1997)in theirarticle on limits toarbitrage. They discussed thepossibility that arbitrageopportunities may fail to beeliminated, and mispricingsmay widen, if arbitrageurs are driven out ofbusiness (orexperience withdrawals by scared investors)by adverse market movements (see also Edwards, 1999).

Commentary

Thelaw of one price is thebasic buildingblock of most of Ž nancial economic theorizing.The logic of why it should hold issimple:if the same asset issellingfor twodifferent prices simultaneously, then arbitrageurswill step in, correctthe situation and makethemselves a tidypro Ž tat thesame time. The concept isso basic that SteveRoss (1987)has writtenthat “tomake a parrotinto a learned Ž nancial economist,he only needs to learn the single word ‘arbitrage.’” Astheexamples we have discussed illustrate,it may be necessaryto teach theparrot at leasta fewnew words: “limits” and “risk” immediatelycome to mind and, forthe very talented parrot, perhaps “short-saleconstraints. ” Cynical Ž nancial economists, and parrotswith only one-word vocabularies, may complainthat wehave merelypicked out aseriesof peculiar examples. Surely, they wouldclaim, the Law holds forthe vast majorityof securities. For example, most ADRsare not mispricedrelative to the underlying security because arbitrageis mechanicallypossible. While this claimis correct (true riskless arbitrage opportu- nitiesare both rareand  eeting),it isnot clearhow usefulit is. Thereason isthat formost securities that themarket needs to price, there are not good substitutes. Thereare no closesubstitutes for GE orfor the whole stock market,so arbitrage cannot berelied upon toset their prices correctly. What can welearnfrom these special cases about thebig picture question: areasset marketssending the “right” signals?What economistsshould really careabout iswhether Ž nancial marketsare sending approximatelycorrect signals tomarket participan ts inorder to direct capital toits most productive uses. Our viewis that thesespecial cases areinteresti ngbecause theyshould be situations inwhich itis particular lyeasy for the market to getthings right.To priceRoyal Dutch correctlyversusShell requires investors merely to multiplyby 1.5. Thesame is true for Palm and 3Com. If themarket is  unking these no-brainers, what elseis itgetting wrong? Duringthe Nasdaq bubbleof the late 1990s, approximately $7 trillion of wealthwas createdand then destroyed.Was this arationalprocess offorecasting thefuture cash  ows ofnew technology or an investingfrenzy based on mob psychology?No one knows theanswer to this question, but thefact that some investorswere willing to pay moreto have oneshare ofPalm than 1.5imbedded shares ofPalm tells us that thefrenzy hypothesis isnot altogetherimplausible. y Theauthors thank Ken Frootfor supplying some ofthe data used to make Figure 1. 202Journal of Economic Perspectives

References

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