The Economics of the Mutual Fund Trading Scandal

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Economics of the Mutual Fund Trading Scandal Patrick E. McCabe 2009-06 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

∗ The Economics of the Mutual Fund Trading Scandal PatrickMcCabe BoardofGovernorsoftheFederalReserveSystem December9,2008 Abstract I examine the economic incentives behind the mutual fund trading scandal, which made headlines in late 2003 with news that several asset management companies had arranged to allow abusive—and, in some cases, illegal—trades in their mutualfunds. Mostofthegainsfromthesetradeswenttothetraderswhopursued market-timingandlate-tradingstrategies. Thecostswerelargelybornebybuy-andholdinvestors,and,eventually,bythemanagementcompaniesthemselves. A puzzle emerges when one examines the scandal from the perspective of those management companies. In the short run, they collected additional fee revenuefromarrangementsallowingabusivetrades. Whenthosedealswererevealed, investors redeemed shares en masse and revenues plummeted; management companies clearly made poor decisions, ex post. However, my analysis indicates that those arrangements were also uneconomic, ex ante, because—even if the managementcompanieshadexpectednevertobecaught—estimatedrevenuefromthedeals fellwellshortofthepresentvalueofexpectedlostrevenuesduetopoorperformance inabusedfunds. Why some of the mutual fund industry’s largest firms chose to collude with abusivetradersremainssomethingofamystery. Iexploreseveralpossibleexplanations, including owner-manager conflicts of interest within management companies (betweentheirshareholdersandtheexecutiveswhobenefittedfromshort-termasset growth), but none fully resolves the puzzle. Management companies’ decisions to allowabusesthatharmedthemselvesaswellasmutualfundshareholdersconveya broaderlesson,thatshareholders,customers,andfiduciaryclientsbecautiousabout relyingtooheavilyonfirms’ownself-interesttogoverntheirbehavior. ∗TheopinionsexpressedaremineanddonotnecessarilyreflectthoseoftheFederalReserveBoardorits staff. IamparticularlyindebtedtoDavidChofordedicated,exceptionalresearchassistanceandcountless discussionsabouttheeconomicsandtheodditiesofthemutualfundscandal.Thispaperalsohasbenefitted fromhelpfulcommentsandsuggestionsfromSeanCollins,JoshuaGallin,MichaelPalumbo,andBrianReid, andseminarparticipantsattheFederalReserveBoard. 1

1 Introduction Thescandalthatrockedthemutualfundindustrybeginninginlate2003centeredonabusivetradesthatreapedoutsizedreturnsforselectedinvestors,particularlyhedgefunds, at the expense of buy-and-hold mutual fund shareholders. In a September 3, 2003 complaint, New York State Attorney General Eliot Spitzer alleged that several mutual fund firmshadarrangementsallowingtradesthatviolatedtermsintheirfunds’prospectuses, fiduciary duties, and securities laws. Subsequent investigations showed that at least twenty mutual fund management companies, including some of the industry’s largest firms,hadstruckdealspermittingimpropertrading. One common explanation for this behavior is that management companies had put self-interest ahead of fiduciary responsibilities to shareholders, since the deals that allowed abusive trades boosted revenues. In contrast, I find that, in facilitating trades thatcutintotheirmutualfunds’performance,managementcompaniesactedagainsttheir owninterests—eveniftheyhadthoughtthattheywouldneverbecaught. This conclusion arises from an exploration of the economics of the mutual fund trading scandal from the perspective of the management companies. I compare the expected present value of the revenues and costs associated with deals allowing abusive trades. Costs included the expected consequences of getting caught in violating fiduciaryduties—officialpenalties,civillitigationoutlays,andthelossoffuturefeerevenues because investors would likely respond by redeeming shares—weighted by the likelihood of getting caught. But management companies incurred other costs that would have arisen even if the breach of fiduciary duties had never been detected, because, as I show, the trading abuses substantially impaired mutual fund returns. Subpar performancewoulddiminishexpectedfuturefeerevenuesthatarebasedonassetsundermanagementbecauselowerreturnswouldslowassetgrowththroughcapitalgainsandalso reduceprojectednetinflowsfrominvestors. I find that, in expected present-value terms, the performance-related costs of the tradingabuses—coststhatmanagementcompanieswouldhaveincurredevenifthewrongdoing had never been revealed—easily outweighed the revenues that these companies garnered by allowing abuses. Moreover, professional asset managers should have foreseentheserevenuesandcostswhentheystruckdealstoallowtradingabuses. Thus,even if management companies had never expected to be caught, they made self-destructive decisionsinallowingimpropertradingtohurtperformance. Ofcourse,theadditionalexpectedcostsofgettingcaughtshouldhavemadetheexantedecisioneveneasier: Workingwithabusivetraderswouldnotpay. Myfindingsnotwithstanding,stateofficialsandtheSEChaveallegedthatatleast twentyfirms,includingsomeoftheindustry’slargestassetmanagers,electedtocollude 2

with abusive traders and share in the short-term gains they generated. That decision proved disastrous to many of those firms. Exactly why they made this choice remains something of a puzzle. Previous research has focused on fiduciary conflicts of interest betweenmutualfundinvestorsandassetmanagementfirms, butbyshowingthatthese firmsactedagainsttheirowninterests, myresultsindicatethatsuchconflictsalonecannotexplainthescandal. Agencyconflictswithinassetmanagementfirms—betweentheir owners and managers—may have been part of the problem, although that explanation falls short in some respects, as some principals with substantial ownership interests in their firms chose to allow and facilitate trading abuses that harmed their own interests. Myopiaorimpatiencemighthaveplayedarole,asthecostsofthetradingarrangements were incurred with some delay compared with the revenues they generated, but only very high discount rates would have rationalized collusion. It is worth noting that the decisionsatissuewerenotmerelytheactionsofrogueemployees;officialcomplaintsand settlement documents indicate that senior executives at almost every firm (and board chairs, chief executive officers, or presidents at most) approved of deals with abusive traders, and in many cases, mutual fund executives aggressively sought such arrangements. My results argue for a reinterpretation of the lessons of the mutual fund scandal; thiswasnotasimpleinstanceofself-interesttrumpingfiduciaryduty. Shareholders,customers,andfiduciaryclientsshouldbecautiousaboutrelyingtooheavilyonfirms’own self-interest to govern their behavior—for example, by assuming that firms will not engageinmalfeasanceiftheexpectedpresentvalueofpenaltiesoutweighsanyimmediate benefit. One salient (and ironic) example of the consequences of overconfidence in privateself-interestisthemutualfundscandalitself. AccordingtoaU.S.GeneralAccountabilityOffice(GAO)reportthatexaminedwhytheSecuritiesandExchangeCommission (SEC)hadnotaggressivelyexaminedmutualfundcompaniesfortradingabusespriorto theNewYorkAttorneyGeneral’scomplaint: Prior to September 2003, SEC did not examine for market timing abuses becauseagencystaffviewedmarkettimingasarelativelylow-riskareaandbelieved that companies had financial incentives to establish effective controls, thatis,bymaximizingfundreturnsinordertosellfundshares(U.S.GovernmentAccountabilityOffice,2005). MyanalysisindicatesthattheSECwascorrectaboutthoseincentivesbutnotabouttheir effectsonbehavior. 3

2 Backgroundandliterature: Markettimingandlatetrading An investor who purchases mutual fund shares for less than their fair value (a “timer”) gains the difference between the actual value and the price paid.1 Because mutual fund sharesareclaimsonacommonpoolofassets,thetimer’sgainisjustatransferofwealth from other mutual fund shareholders. By creating new shares in the common pool and sellingthemforlessthantheirproportionalworth,themanagementcompanydilutesthe valueofexistingshares.2 The potential for dilution of mutual fund shareholders’ wealth has been understood at least since the 1930s, although dilution vulnerabilities and the mechanisms for exploitingthemhavechangedovertime. TheInvestmentCompanyActof1940included provisions intended to curb rampant exploitation—especially by brokers who sold mutual fund shares—of discrepancies between share prices and values that arose because mutualfundnetassetvalues(NAVs)weretypicallysetbasedonthepreviousday’sclosing prices (U.S. Securities and Exchange Commission, 1940; United States v. National Association of Securities Dealers, Inc. et al., 1975). In 1968, the SEC adopted rule 22c-1, whichmandated“forwardpricing,”thatis,fundshadtoexecutetransactionsatthenext net asset value calculated after the order was received, to eliminate investors’ ability to transactatstalepricesthatdeviatedfromcurrentmarketvalues(Barbash,1997). Yet,evenwithforwardpricing,mutualfundNAVscanbestaleiftheyarebasedon market prices of securities that have not recently traded. World equity funds are particularlyvulnerablewhentheyvalueforeignstocksattheirmostrecentoverseas-exchange market-close prices, which can be more than 12 hours old by 4 p.m. Eastern time when mostU.S.mutualfundscomputetheirNAVs. Butpricesforothertypesoffunds,suchas thosethatinvestindomesticsmall-capstocksorbondsthattradeinfrequently,canalsobe stalewhenthemostrecenttransactionsasofmarketclosedonotincorporateup-to-date information. Transactions in mutual fund shares to exploit these stale and predictable pricescametobeknownas“markettiming.”3 1This description of the dilutive effects of mispricing mutual fund shares is very brief. For a more detailedanalysisoftheproblemseeChalmersetal.(2001),whoexploredmutualfunddilutioninthecontext of the broader problem of intermediaries that set prices without full information or strong incentives to maintainpricesatfairvalues;Zitzewitz(2003),whoestimateddilutionacrossabroadrangeofassetclasses, analyzed the efficacy of proposed remedies, and first suggested that owner-manager conflicts of interest withinmanagementcompaniesmightbepartoftheproblem; andKadlec(2004), whobrieflyoutlinedthe causes of mutual funds’ structural vulnerability to dilutive trading (NAV predictability and low or zero transactionscosts)andsomepossibleremedies. 2Atimerwhosellsmutualfundsharesformorethantheirfairvaluealsobenefits,byavoidingaloss, andwiththerighthedgingstrategy,shecancollectacashgainequaltothepricediscrepancy.However,the timercanonlyexploitoverpricedsharesifsheownsthesharesinitially,asmutualfundsharesthemselves cannotbesoldshort. 3MarkettiminginthiscontextreferstoexploitingmutualfundNAVsthatdonotreflectcurrentmarket valuesandshouldbedistinguishedfromthebroaderuseofthetermtoindicatebuyingandsellingofassets basedonpredictionsoffuturepricemovements. 4

Investment management firms have recognized that dilutive trades are possible even with forward pricing at least since 1980, when the Putnam Funds sought and received from the SEC assurance that it would not take action against Putnam for using a “fair value determination” to value foreign stocks if “some extraordinary event” occurred between the daily closing of a foreign stock exchange and 4 p.m. Eastern time (Ropes & Gray, 1980; U.S. Securities and Exchange Commission, 1981). This would, according to Putnam, “avoid the abuses which forward pricing, as set forth in Rule 22c-1, was intended to limit.” SEC letters to the Investment Company Institute in 1999 and 2001wentastepfurtherinurgingfundstofairvaluesecuritiestoeliminatestalepricing andprotectlong-termfundinvestorsfromdilution(Scheidt,1999,2001). By2000,many mutualfunds—includingthoseinfamiliesthatwerelatercaughtupinthescandal—had includedprospectuslanguageindicatingthattheyprohibitedmarkettiming. As early as 1995, however, several mutual fund management companies began colluding with market timers to permit extensive dilutive trades, often as part of quidpro-quo arrangements. For example, asset management firm ABC might stipulate that a hedge fund seeking market-timing access to the ABC international equity fund must maintain a stable investment (“sticky assets”) in one of the ABC bond funds. The sticky assets would generate a steady stream of management fee revenue for ABC, and the hedgefundwouldobtainanagreed-upon“timingcapacity,”thatis,amaximumvolume of market-timing transactions for a specified time period. Timing capacity was often a multiple of the sticky assets; multiples of five and ten were common. To improve the profitability of market timing in their mutual funds, some management companies also disclosed non-public portfolio composition data and waived redemption fees—which were designed in part to prevent market timing—for selected customers (see, for example,U.S.SecuritiesandExchangeCommission(2003a,2004a,b,c);AttorneyGeneralofthe StateofNewYork(2004a,2005a,b)). Worseyet,ahandfulofportfoliomanagersandmutualfundexecutivesabusively traded their own mutual funds (Massachusetts Securities Division, 2003; U.S. SecuritiesandExchangeCommission,2003c;Tufano,2005;U.S.SecuritiesandExchangeCommission, 2004c). And some mutual fund firms (and several brokers and transactionsprocessing firms) facilitated “late trading,” that is, transactions in mutual fund shares at previously-determined NAVs (see, for example, Attorney General of the State of New York(2005a);U.S.SecuritiesandExchangeCommission(2007b)). Latetrading,likemarket timing, seeks to exploit stale prices and dilutes buy-and-hold investors’ wealth, but latetradingalsoviolatesrule22c-1,andisthusillegal. Well before the scandal broke, researchers began documenting evidence of widespreadmarkettiming,particularlyamongworldequityfunds. Bhargavaetal.(1998)describedtheprofitabilityofsimplemarket-timingstrategiesininternationalequityfunds, 5

and Chalmers et al. (2001) documented exploitable opportunities in small-cap domestic equityfundsaswell. Boudoukhetal.(2002)provideddetailedstrategiesformarkettimingseveralspecificinternationalequityfundsandnoted: “Currently,weknowofatleast 16 hedge fund companies covering 30 specific funds whose stated strategy is ‘mutual fund timing.’” Although Goetzmann et al. (2001) also documented stale prices in world equity funds, they found that market-timing flows were causing only minor dilution of returns. In contrast, Greene and Hodges (2002) found evidence of substantial dilution in international equity funds, particularly in those with high flow volatility. Zitzewitz (2003)providedestimatesofdilutionacrossabroaderrangeoffunds, includingdomestic mid- and small-cap equity funds and precious metals funds, as well as world equity funds. Hearguedthatmanagementcompanies’sluggishresponsetoaproblemascostly and prevalent as abusive trading reflected an owner-manager conflict of interests between the companies and mutual fund shareholders. Moreover, foreshadowing the thesis of this paper, Zitzewitz provided a back-of-the-envelope calculation to suggest that managementcompaniesmightbeactingagainsttheirowninterestsinallowingabusive trades. Evenso,theextentofmanagementcompanies’collusionwithabusivetraderswas apparentlywell-concealedbeforeSeptember3,2003. Onthatday,theNewYorkAttorney Generalissuedacomplaintagainstahedgefund,CanaryCapitalPartners,whichhadarrangementspermittingextensivemarkettimingandlatetradingatseveralmutualfunds. Thescandalbroadenedinthefollowingmonthsandeventuallyensnared21mutualfund firms,whichtogethermanaged22percentofindustryassetsinlate2003. The scandal revelations prompted a flurry of research. Several papers surveyed the wrongdoing and offered explanations and remedies. Mahoney (2004), assuming that management companies had acted in their own interests in colluding with abusive traders, attributed the wrongdoing to “basic conflicts of interest between mutual fund investors and the companies and individuals that organize, sell and provide services to mutualfunds.” Kadlec(2004)providedabriefoverviewofthevulnerabilitiesofmutual funds to market timing and a simple framework for addressing them. Greene and Ciccotello (2004) showed that the dilution losses of buy-and-hold investors depend on the cash management policies of portfolio managers, and Zitzewitz (2006) estimated the dilutive impact of late trading, which was not addressed in the academic literature before thescandalbroke. Qian(2006)examinedtherelationshipbetweenwrongdoingandfund family attributes, such as governance, and found that families for which net flows were lesssensitivetopastperformanceweremorelikelytohavebeentaintedbythescandal.4 That conclusion is relevant to my analysis, as it suggests that ex ante costs of colluding mighthavebeenlowerforfamiliesthatchosetodoso. Nonetheless,Ifindthatevenfor 4Notably,Qian’sfocusisongovernanceofmutualfundsratherthanmanagementcompanies. 6

thetaintedfundfamiliesthemselves,thatchoicewasaverypoorone. Otherresearchhasfocusedonthepenaltiesthatmarketsandgovernmentofficials imposed on mutual fund firms that were caught allowing abusive trading. Houge and Wellman (2005) found that in the three days following news of wrongdoing by a managementcompany,itsstockprice(orthatofitsparentfirm)droppedonaveragebymore than five percent, and that, relative to their untainted competitors, tainted firms’ assets under management had fallen by 13 percent in the first six months following the scandal revelations. Choi and Kahan (2006) showed that stiffer official penalties and more press coverage were associated with larger net redemptions from tainted mutual fund families,andthatwithinayearofthescandalrevelations,netredemptionsfromtainted families had reached 19 percent of pre-scandal assets. According to Schwarz and Potter (2006), net outflows continued well into the second year after the scandal broke. Zitzewitz(2007b)foundthattheNewYorkAttorneyGeneral’sinvolvementinsettlementnegotiationsraisedtheratioofpenaltiestodilutiondamagebyroughlythree-tofour-fold. 3 Data I employed annual, monthly, and daily data from the Center for Research in Securities Prices U.S. mutual fund database (CRSP) to compute monthly fund flows, returns, and distributions from 1991 to 2007. To compute net new cash flow, that is, flows net of reinvesteddistributions,IalsouseddatafromtheInvestmentCompanyInstituteonthe fractions of distributions reinvested by mutual fund investment objective. I obtained daily mutual fund assets information from TrimTabs and share-price and distribution data from CRSP and Yahoo! Finance to compute estimates of the dilution due to trading abuses. Data for calculations of management companies’ weighted average costs of capitalcamefromCompustatandCRSP. 4 Identifyingmutualfundsthatweresubjecttotradingabuses To identify the mutual funds that were subject to arrangements allowing market timing andlatetradingabuses,Iusedfourtypesofsources. Thefirstwaspublishedlistsoffirms that were tainted by the scandal, such as The Wall Street Journal’s “Mutual Fund Scandal Scorecard,” whichtrackedmutualfundcomplexes, investmentadvisers, brokers, hedge funds, and others who allegedly benefitted from trading abuses. Houge and Wellman (2005),Qian(2006),andZitzewitz(2007b)alsoprovidelistsofthefirmsthatwerecaught upinthescandal. Thesecond,mostimportantresourcewasstateandSECfilings,includingcomplaints,cease-and-desistorders,assurancesofdiscontinuance,proposedplansof distribution, and other documents. These filings were essential in identifying the individual mutual funds that were subject to arrangements allowing abusive trades. A 7

thirdresourcewasprospectusupdatesandpublishedsummariesofinternalreviewsregardingabusivetradingthatwereprovidedbythemutualfundmanagementcompanies themselves. Finally, I used press reports to identify an additional handful of funds not mentioned in official documents and to pin down the timing of the revelations about wrongdoingatdifferentfundfamilies. 4.1 “Abused”and“tainted”mutualfunds. I label a mutual fund “abused” if, according to the sources listed above, its management company entered into an arrangement allowing the fund to be market timed or late traded or if the fund was abused by principals or employees at its management company.5 Abused funds include those that were subject to abusive trades as part of quid-pro-quo arrangements that required investors to park “sticky assets” within the fund family—for example, at another mutual fund or a hedge fund. However, I do not labelafundabusedifitreceivedstickyassetsorwasontheothersideofmarket-timing exchanges (that is, held temporarily between timing “investments”), but was not itself markettimedorlatetraded. Idefineas“tainted”anymutualfundthat,accordingtomysources,wasnotitself abusedbutwasoperatedbyamutualfundfamilythatmanagedatleastoneabusedfund. Taintedfamiliesarethosethatoperatedabusedandtaintedmutualfunds. Hence,tainted fundsandabusedfundsaretwomutuallyexclusivesetswhoseunionisallmutualfunds operatedbytaintedmutualfundfamilies.6 Table 1 lists tainted mutual fund families, their assets under management at the endofAugust2003(attheeveofthescandal),thedateswhentheywerepubliclyimplicatedforwrongdoing,thenumberofabusedmutualfundstheyoperated,andtheassets under management in those funds.7 In total, tainted families managed over $1 trillion in assets in long-term mutual funds—22 percent of the industry’s assets under management in long-term mutual funds at that time.8 Combined, they managed 145 abused 5AtPutnam,portfoliomanagersextensivelymarkettimedtheirownmutualfundsandotherfundsin thecomplex. TheirtimingactivitywaswidespreadandaffectedabouttwodozendifferentPutnammutual funds,buttrading(andtheresultingdilution,asestimatedinPutnam’sdistributionplan)washeavilyconcentratedin10fundsandwasrelativelysmallintheothers.Ihavelabeledas“abused”onlythose10funds (Tufano,2005). 6Thispaperaddressesabusesrelatedtomarkettimingandlatetrading,soIdonotconsideramutual fund family to be “tainted” based on allegations about other types of questionable behavior (for example, managementcompanieshavingundisclosed“shelf-space”arrangementswithbrokerswhosoldfund shares). 7Oneadditionalmutualfundfamily,Ameriprise(whichwaspreviouslyownedbyAmericanExpress, andwhosemutualfundshavecarriedthebrands“AXP”and“Riversource”)wasimplicatedforallowing market-timingtrades. Ameriprisefundsarenotincludedinmyanalysis,however,becauseIcouldfindno informationaboutwhichmutualfundsthemanagementcompanyallowedtobeabused(U.S.Securitiesand ExchangeCommission,2005a). 8ThisfigureisbasedonInvestmentCompanyInstitutedatathatshowthatthemutualfundindustry 8

funds with $277 billion in assets—6 percent of the industry total. These funds spanned a broad range of investment objectives, including 81 domestic equity funds, 38 world equityfunds,3hybridfunds,14taxablebondfunds,and9municipalbondfunds. 4.2 Officialpenalties The New York Attorney General’s complaint in September 2003 not only signaled a sweepinginvestigationofmutualfundmanagementfirms,broker-dealers,abusivetraders, intermediaries,andothersbyhisoffice,butalsopromptedinquiriesbytheSECandstates attorneys general from Massachusetts to Colorado. These official actions resulted in a slew of penalties assessed against management companies that were found to have facilitatedandprofitedfromtradingabuses,aswellasfinesformanycompanyexecutives andemployees. Table 2 lists these penalties. They included $2.3 billion in civil penalties and disgorgement levied by the SEC and state officials against mutual fund management companies and their parent firms (columns 1 and 2). An additional $47 million in penalties was self-imposed by four fund families that initiated their own shareholder restitution programs (column 3).9 Several top executives—management company chairmen, chief executive officers, and presidents—paid a total of about $220 million in disgorgement and civil penalties (columns 4 and 5). Aggregate penalties for other less-senior employeeswerelessthan$5million(columns6and7). Finally,NewYorkAttorneyGeneralEliot Spitzernegotiatedverylargemanagementfeereductionsaspartofhissettlementswith severalmutualfundcompanies. HeexplainedhisrationaletoTheWallStreetJournal: ... [I]nacontextwhereacompanyhasviolateditsfiduciarydutiesandfailed toprotectshareholdersbyacquiescingtofeeshigherthanamarketpermits,a rollbackshouldbeanappropriatepartoftheremediesimposedonacompany (Solomon,2003). The New York Attorney General’s settlements mandated that the fee reductions occur over five years. Cumulative fee reductions for all tainted firms totalled $1.1 billion (column8). Aggregatepenalties,includingcivilpenalties,disgorgement,restitution,andfee reductions,sumto$3.7billion(column9). managed$4.8trillioninassetsinlong-termmutualfundsattheendofAugust2003. Theassetsoffundsin theCRSPdatabasetotaled$4.3trillionattheeveofthescandal,sotaintedfamiliesmanaged24percentof industryassetstrackedbyCRSP. 9I include restitution payments because management companies typically made them in advance of officialcomplaintsandsettlements,andinsomecases,disgorgementamountswerereducedbytheamounts oftherestitutionthathadpreviouslybeenpaid. 9

5 Lossestobuy-and-holdinvestorsinabusedfunds 5.1 Previousestimatesoflosses Previousstudiesofthecostsofmarkettimingandlatetradingforbuy-and-holdinvestors fall into two categories. First, in papers mostly completed before the scandal broke, researchersestimateddilutionduetotradingabuseswithoutanyspecificknowledgeofthe fundsthatwereharmedbytrading-abusearrangements. Thesepapersidentifiedinvestmentobjectivesinwhichdilutionwasmostproblematic,andtypicallyarguedforpolicy changes—by mutual fund management companies and regulators—that would reduce or eliminate dilution due to market timing. A second group of papers, written after the scandalfirstmadeheadlinesinSeptember2003,focusedmorespecificallyontaintedmutualfundfamiliesandeitherestimateddilutioninthosefamiliesorcomparedthereturns oftheirmutualfundstothoseofuntaintedfundstoascertainthecoststoinvestorsofthe abusive-tradingarrangements. As shown in table 3, papers written before September 2003 employed measures ofdilutiontoestimatelossestobuy-and-holdinvestors. GreeneandHodges(2002)used daily data on fund flows and returns and estimated that dilution in world equity funds with above-median flow volatility averaged 0.94 percentage point of assets per year in the period from February 1998 to March 2001. Their estimates of dilution in other investment objectives were small. Zitzewitz (2003) used futures data to identify timing opportunitiesmorepreciselyandfoundsubstantialdilutioninworldequityfunds,with the worst problems in regionally-focused (Pacific, Japan, and European) equity funds, whereannualdilutionaveraged1.60percentagepointsfrom1998to2001. Generalinternationalequityandprecious-metalsfundsalsosufferedsubstantialdilution. Zitzewitz’s (2006) estimates of dilution due to late trading were considerably smaller than those he computed for market timing, although the late-trading losses are averaged over much broadercategoriesoffunds. Afterthescandalbroke,researchersturnedtheirattentiontothetaintedfundfamilies. Basedonmutualfunds’shareturnoverrates,Zitzewitz(2007b)foundaveragedilutionofaboutone-halfpercentagepointperyearfrom2000to2003amongall(bothabused and tainted) international equity funds in tainted families—with predicted dilution exceeding three percentage points in a couple of complexes. Other researchers examined differencesinfundreturnstoestimatelossestoinvestors. HougeandWellman(2005)estimatedthatsimpleaveragereturnsfrom2000to2003forfundsatscandal-taintedcomplexeswere0.15percentagepointperyearbelowthoseoffundsatnon-taintedfamilies, but they also did not distinguish funds that were subject to abusive trading and those that were not, and their calculation does not control for the investment objectives and risks of the funds offered at different complexes. Schwarz and Potter (2006) estimated 10

that the risk-adjusted returns of domestic equity funds at tainted complexes lagged those oftheirpeersbyanaverageof0.83percentagepointfrom2000to2003. Again,theircalculationdidnotdifferentiatemutualfundsthatweresubjecttodilutivetradesandthose that were not. Qian (2006) sought to distinguish tainted and abused mutual funds and estimated that abused funds suffered performance penalties of roughly two percentage pointsfromJanuary2001throughAugust2003. 5.2 Newestimatesoflosses Because the effects of abusive trading on mutual fund performance are central to the thesis of this paper, and since estimates of these effects in previous research have been motivated by questions different from those addressed here, I computed new estimates of the performance losses among abused funds. I used a two-stage approach: First, I computed the risk-adjusted relative performance for every mutual fund in my sample, using methods discussed below; and second, I tested whether the adjusted returns of abused and tainted funds were significantly different from those of other funds in the yearsbeforeandafterthescandalbroke. 5.2.1 Stage1: Estimatingeachfund’sannualrisk-adjustedrelativeperformance. The mutual funds that were abused in the trading-abuse scandal covered the full range of investment objectives and included domestic equity, world equity, taxable bond, municipal bond, and hybrid funds. However, standard measures of risk-adjusted mutual fund performance, such as that employed by Carhart (1997), are generally applicable only to U.S. equity funds and would only be useful for a subset of abused funds. To makeindustry-widecomparisons,Iusedthreemeasuresofrisk-adjustedrelativeperformancethatareapplicableacrossalltypesofmutualfunds. Myprimarymethodemploysasset-weightedmeanreturnsfordifferentcategories ofmutualfundsasriskfactors; thatis, itcontrolsforthedegreeofcategory-specificrisk (as well as broader market risks) that each fund exhibits. I computed two additional measuresofrisk-adjustedreturnstoshowthatmyestimatesofthelossesduetotrading abuses are robust to different methods of adjusting returns for risk. One is just the differencebetweenafund’sreturnandtheaveragereturnofallotherfundsinitscategory. Theothermethodusesasetofstandardmarket-riskfactors. 1. Relative return. A simple, if primitive, measure of risk-adjusted returns is a fund’s return less the average return of funds sharing its investment objective. I define a mutual fund’s “category return” as the asset-weighted mean return of all funds that share its S&P investment objective,10 and its “relative return” as its total return less its 10IusedtheStandard&Poor’sdetailedobjectivestoidentifyeachmutualfund’sinvestmentcategory. 11

categoryreturn. 2. Alphasbasedoncategory-returnriskfactors. Asecondmethodadjustsrelative return for risk by employing three risk factors for each fund: The fund’s own category excess return, the asset-weighted mean excess returns of all funds sharing its broader asset class, and the asset-weighted mean excess return of all mutual funds.11 A mutual fund’sloadingontothecategory-returnriskfactorisameasureofitssensitivitytotherisk commontoallfundsthatshareitsspecificinvestmentobjectives,whileloadingontothe returns of its broader asset class picks up exposure to risks from related fund categories due, for example, to a management strategy that encompasses multiple objectives or to misclassification by S&P. And loading onto the returns of all funds indicates a fund’s exposure to general market risk, controlling for its comovement with its narrower asset classes. Iestimatedrisk-adjustedreturn,α ,inthefollowingregression: i r = α +βCr Ci +βBr Bi +βMrM+ε . (1) it i i t i t i t it Here, r isfund i’sexcessreturn(returnlessthemeanmoneymarketfundyield) it in month t, r Ci is the asset-weighted excess mean return for i’s category, r Bi is the ext t cess mean return of fund i’s broader asset class, and rM is the excess mean return of all t long-term mutual funds. (Relative return is α estimated in equation (1) subject to the i constraintsthat βC = 1and βB = βM = 0.) i i i 3. Alphas based on market risk factors. I also computed risk-adjusted performanceusingacommonsetofmore-standardriskfactors,namely: (1)theS&P500index return, (2)theRussell2000indexreturnlesstheS&P500indexreturn(asizepremium), (3) the Nasdaq index return less the S&P 500 index return (a technology premium), (4) the MSCI excluding-US value-weighted index return, (5) changes in constant-maturity off-the-run10-yearTreasurybondyields,and(6)changesinspreadson10-yearBBBcorporatebondsoverTreasuries(acreditspread). Ingeneral,thecategory-returnriskfactorsexplainslightlymoreofthevariancein mutualfundreturnsoverthesampleperiodsIstudied. Forexample,themedianadjusted R2fromthecategory-returnrisk-factorregressionsdescribedbyequation(1)forthethree years ending August 2003 is 0.92, while that for the standard risk-factor regressions is 0.87. For the three years following the scandal revelations, the median adjusted R2s are 0.92and0.88respectively. Gross and net returns. Because mutual fund investors earn returns net of fees, S&Pclassifieslong-termmutualfundsinto155objectives(93ofthemaretax-exemptcategories). Imerged categorieswithlessthan10funds(e.g.,S&Pmaintainsseparatecategoriesforshort-term,intermediate-term, andgeneralMarylandmunicipalbondfunds,butIcombinedthethree)andfinishedwith102categories. 11Broader asset classes are domestic equity, world equity, hybrid, taxable bond, and tax-exempt bond funds.“Excess”returnsinagivenmontharereturnslesstheindustry-averagemoney-marketfundyieldfor themonth(notannualized). 12

rather than gross returns, fund performance is usually reported net of fees, and most research focuses on net returns. However, the effects of trading abuses on performance should be seen most clearly in gross returns, because variation in net returns would reflect not only the effects of trading abuses but also any differences in fee structures.12 Hence,Iusedgrossreturnsinmybaselinecalculationsofrisk-adjustedperformance,but Ialsoreportresultsusingnetreturns. Sampleperiods. Toestimatethelossestotheshareholdersofabusedandtainted mutual funds, I initially examined the performance of these funds in the three years before the scandal broke (September 2000 through August 2003) and in the three years afterward (January 2004 through December 2006) relative to that of untainted mutual funds. While there is evidence that some abusive-trading arrangements were in effect wellbeforeSeptember2000,Ididnotfind(asdiscussedbelow)statisticalevidenceofan aggregateperformancelossamongabusedfundspriorto2000. 5.2.2 Stage 2: Estimating the effects of trading abuses on risk-adjusted annual performance. To capture the performance effect of the trading abuses, I estimated a cross-sectional regression of each fund’s alpha (from stage 1) on two dummies—one for abused funds and a second for tainted funds. I also included the natural log of each fund’s assets undermanagementintheregression,becauseotherresearchershavepredictedorfound thatrisk-adjustedexcessreturns,timing-relateddilution,andthelikelihoodofcollusion withabusivetradersvariedwithfundsize.13 α = c +γ AbusedFund +γ TaintedFund +ξ(ln(assets ))+η (2) i 0 1 i 2 i i i Here,AbusedFund isequaltooneifandonlyiffundi isanabusedfund,TaintedFund i i isequaltooneifandonlyiffundiisataintedfund,andassets isthemeanassetsoffund i iovertheperiodinquestion. Estimated losses for buy-and-hold investors. My results are shown in table 4, which reports regression coefficients γ ,γ , and ξ obtained using five different perfor- 1 2 mance measures and two different sample periods: the three years before and the three years after the mutual fund trading scandal broke. Columns 1, 2, and 3 show results 12Onecomplication,however,isthatgrossreturndataisgenerallynotobserveddirectly,andcanonly becalculatedasthesumofnetreturnsandtheexpenseratio. Butassessedexpensesmaynotbereported accurately,ifdatavendorsmissfeewaiversthatreduceassessedfeesfromlevelspublishedinprospectuses (forexample,Christoffersen(2001)foundthatfeewaiverswerecommonamongmoneymarketfunds). So, grossreturnsdatamaybelessaccuratethannetreturnsdata. 13For example, Berk and Green (2004) developed a model that predicts that larger funds earn smaller excessreturns. Qian(2006)foundthatlargermutualfundsweremorelikelytobeinvolvedinthescandal. Ontheotherhand, Zitzewitz(2007b)foundthatdilutionduetoabusivetradingwasnegativelycorrelated withfundsize. 13

for the three performance measures discussed above: relative returns, alphas based on category-return risk factors, and alphas based on six market-risk factors. A fourth measureusesthecategory-returnriskfactorsbutincludesNasdaqexcessreturnsasanadditionalfactortocontrolforthepossibilitythatsomemutualfundshadloadedheavilyon technology-stock risks. Finally, column 5 shows estimated coefficients based on alphas computedusingnetreturns,ratherthangrossreturns,andcategory-returnriskfactors. The results reported in panel A of the table indicate that estimated performance lossesforabusedfundsinthethreeyearspriortoSeptember2003arestatisticallysignificantandenormous. Therelativereturnsofabusedfundswere,onaverage,4.9percentagepointslowerthanthoseoftheiruntaintedcounterpartseachyear. Moresophisticated controlsforriskresultinsomewhatlowerestimatedperformancepenalties,intherange of3.6to4.4percentagepointsperyear,buttheseeffectsarestillverylarge—muchlarger thanestimatesfrompreviousresearch. Coststobuy-and-holdinvestorsinabusedfundsimpliedbythesefiguresarestunning. Thesmallestoftheperformancepenaltiesshownonthetable(3.6percentagepoints peryear)representslossesofapproximately$10.4billionperyear,giventhatthetotalassets under management in abused funds over the three years before the scandal broke averaged $321 billion, and assuming, conservatively, that 90 percent of the dilution was sufferedbyshareholderswhowerenotabusingthefunds.14 Inaddition,taintedfundssustainedstatisticallysignificanthitstoperformancein the three years prior to the scandal revelations, with risk adjusted returns of 60 to 90 basis points below those of their untainted peers. The relatively poor returns of tainted funds probably reflect several factors that weighed on performance. First, the costs of rapidexchangesofabusivetraders’moneyamongfundsatataintedfamilyaffectednot onlyabusedfundsbutalsofundsontheothersideoftheseexchanges. Second, because some tainted mutual fund families earned reputations for being “timer friendly”—that is, broadly accessible to market timers—dilution and the other costs of trading abuses werenotnecessarilyconfinedtothefundsIhaveidentifiedasabused(see,forexample, U.S. Securities and Exchange Commission 2004b; Attorney General of the State of New York2003). Third,thelegaldocumentsandothersourcesIhaveusedtoidentifyabused mutual funds likely missed some mutual funds that were subject to abusive arrangements, so the poor performance of tainted funds may, in part, reflect a misclassification 14Thereislittledirectevidenceaboutabusivetraders’shareofassetsundermanagementinabusedmutual funds, but it probably averaged well under 10 percent in most fund complexes. Official documents indicatethatthepeaklevelsofmarkettimers’assetsinabusedfundsinallbutonefundfamilywerebelow 10percentofthosefunds’assets.Abusivetraders’dilutionlosseslikelywouldhavebeensmallerthantheir shareofassets, however, asmarkettimerswerelesslikelytobeholdingsharesondayswhensubstantial dilutionoccurred.Forexample,abusivetradersprobablyheldmorethan1percentofassetsinJanus’abused fundsatonepoint,butestimateddilutionsufferedbyabusivetradersatJanuswasonly0.08percentoftotal dilution(James,2007). 14

ofabusedfundsastaintedfunds. Risk-adjusted relative returns for the three years after the scandal broke are reported in panel B of table 4. The performance of abused funds was, by most measures I employed to adjust for risk, statistically indistinguishable from that of untainted funds. Other funds at tainted families—the “tainted” mutual funds—outperformed their peers by 20 to 30 basis points by most risk-adjustment measures, although the performance advantage disappeared when I used alphas based on category-return risk factors and Nasdaqreturns. Figure 1 shows smoothed histograms of relative returns and estimated alphas in the three years before and the three years after the scandal broke. For the three years priortoSeptember2003,thedistributionsofperformancemeasuresforabusedfunds(the thick,redcurves)lienoticeablytotheleftofthethoseforallfunds(thethinblackcurves) andfortaintedfunds(thebluecurves). Clearly,theestimateddifferencesbetweenabused and other mutual funds are not just due to a few outliers. In the three years after the scandal, despite some statistically significant differences reported in table 4 for tainted andabusedfunds,theirhistogramslineupfairlycloselywiththoseforallfunds. Year-by-year estimates of performance losses. To pin down the timing of the performancelossesinabusedfundsmoreprecisely,Iestimatedeachmutualfund’sriskadjustedrelativeperformanceonanannualbasisusingarolling36-monthregressionof thefund’smonthlyreturnsonthethreeriskfactors: r = α I0+α I +βCr Ci +βBr Bi +βMrM+ε . (3) it 0i t i t i t i t i t it This is similar to equation (1), but in equation (3), I estimated two different intercepts: one for the first 24 months of the rolling sample period (α ), and the alpha of interest 0i (α ) forthelast12monthsofthesampleperiod. Thatis, I0 isanindicatorvariableequal i t to 1 for the first 24 months of each rolling sample period (and zero otherwise), and I is t equal to one only for the last 12 months of the sample period (and zero otherwise). To maintaincomparableannualsampleperiodswhileexaminingtheeffectsofascandalthat wasrevealedtothepublicinearlySeptember2003,myrollingregressionsendinAugust ofeachyear. Figure 2 shows the annual relative returns of abused and tainted funds in the upperleftandlowerleftpanels,respectively. Bythemetricofrelativereturns—whichdo not control for within-category variation in risk—abused funds outperformed their peers from 1998 to 2000, underperformed in the three years prior to the scandal revelations, andrecordedmixedperformanceafter2003. Amongtaintedfunds,relativereturnswere substantiallylessvolatile,buttheywerebetterthanaveragein1998and2000andworse thanaveragein2001. Risk-adjusted excess returns provide a somewhat cleaner picture of the relative 15

performanceofabusedandtaintedfunds. Abusedfunds’alphasbasedonthecategoryreturn risk factors, which are plotted in the upper right panel of figure 2.A, are significantly better than those of their peers in 1996 and 2000, but a period of substantial underperformance begins in 2001 and lasts through 2004. Thereafter, alphas are roughly zero. Alphas for tainted funds, shown in the lower right panel, are for the most part statisticallyindistinguishablefromzero. Othermeasuresofrisk-adjustedperformanceareshowninfigure2.B.Theleftpanelsdepictalphascomputedusingthesixmarket-riskfactors,whicharequitevolatile,and therightpanelsshowalphasbasedoncategory-returnandNasdaqriskfactors. Allfour measuresofadjustedreturnsindicateabnormallypoorperformancefortheperiodfrom 2001 through 2004 (although by one measure—relative returns—performance was not significantly below average in 2003). On the other hand, abused funds experienced relatively good performance in a couple of years, notably 1996 and 2000. Among tainted funds, no particular pattern emerges. For example, three of the measures show statistically significant underperformance in one of the years between 2001 and 2003, but the badyearisdifferentforeachmeasure. Comparisonwithpreviousstudies. Theestimatedperformancepenaltyforabused fundsinthethreeyearspriortothescandalrevelationsissubstantiallylargerthanwhat previous studies have found. For example, performance losses of 3.6 percentage points per year far exceed pre-scandal estimates of dilution losses for even the most-abused investment objectives (such as Asian equity funds). This is not surprising, for several reasons. First, losses at abused funds are likely to be have been larger than those at other funds that shared the same investment objective, but dilution studies done before the scandal broke pooled funds that were traded abusively and those that were not. Thus, thesestudieslikelyunderstateddilutionatabusedfunds.15 Second, dilution only accounted for a portion of the losses at abused funds, so thehittoperformancesufferedbythesefundsprobablyexceededdilutionconsiderably. Other costs were largely deadweight losses: They cut into the returns of mutual funds withoutgeneratinganygainsfortimers. Thesecostsincludedtheportfolio-assettrading costs and administrative costs due to the heavy inflows and outflows associated with abusive trading. These massive inflows and outflows also reportedly forced portfolio managers to hold sub-optimal asset allocations (for example, large cash positions) that could be a drag on performance. These problems compounded one another: Managers whoheldlargecashpositionssometimesmadesignificantassetpurchasesatmonth-end to show that they were fully invested. And large cash flows were also an enormous 15Some researchers examined variation within categories to pinpoint dilution at the most vulnerable funds. GreeneandHodges(2002),forexample,foundthatamongfundssharinganinvestmentobjective, thosewiththemostdailyflowvolatilitysufferedthemostdilution. 16

distraction for portfolio managers. For example, a Seligman portfolio manager wrote in a2001emailmessagetothefirm’schiefinvestmentofficer: ... By my reckoning, we’ve had 14 round trips of massive flows in and outmeaning28tradingdaysIhaveeitherbeenscramblingtogetinvestedor raisingliquidity. Therewereonly49tradingsessionsoverthisperiod,sothis ishowI’vespentabout60%ofmytime. Giventhatwecannotemployfuturesandoursystemsfornotifyingmeof activitydonotallowmetogetinvestedonatimelybasis,theexecutioncosts are huge to our existing shareholders (Attorney General of the State of New York,2006,Exhibit2). ThechiefcomplianceofficeratInvescocomplainedinamemotothefirm’spresidentand CEO: Inshort,markettimerscananddointerferewithaportfoliomanager’sdecisionmaking process. Virtually every portfolio manager at INVESCO would concedethatheorshehashadtomanageFundsdifferentlytoaccommodatemarkettimers. Certainly, theamountoftimespentmanagingvolatilecashflows could be better spent picking securities and developing long-term strategies (AttorneyGeneraloftheStateofNewYork,2003,ExhibitA). Evenwithoutabusivetrading,mutualfundportfoliotradingcosts,whichinclude brokerage costs, spread costs, and the price impacts of large trades, can be quite large. Using data from 1984 to 1991, Chalmers et al. (1999) found that reported brokerage fees plusestimatedspreadcostsexceeded1.37percentofassetsperyearforfundsinthe90th percentile, compared to just 0.70 percent per year for the median fund. Their estimates likely understated trading costs, however, because they excluded the price impacts of trades, missed the costs of some trades, and used reported brokerage fees, which probably understate actual fees (Cassidy, 2004). Even so, Cassidy reported brokerage fees as highas8percentofassetsperyearinsomeextremecases. Itisplausiblethatsomeofthe highesttradingcostswerethosebornebyfundsthatsawheavyabusive-tradingflows. Edelen (1999) showed that “liquidity-motivated trading,” that is, portfolio-asset trades that are prompted by net flows to and from mutual funds, on average cost equity mutual funds 1.4 percentage points of risk-adjusted performance per year in the late1980s—presumablywellbeforethemassiveflowsassociatedwithmarkettimingbecame a problem. Moreover, he found that an annual rate of liquidity-motivated trading equal to a fund’s assets cost it, on average, 1.5 to 2 percentage points of return per year. Liquidity-motivated trading was probably a major drag on performance at many abused mutual funds; Zitzewitz (2007b) reported that international equity fund share 17

turnover exceeded 100 percent of assets at most tainted mutual fund families in the period from 2000 to 2003, and share turnover was reportedly many multiples of assets in some abused mutual funds. For example, Invesco’s own chief compliance officer computed share turnover rates of 6,000 percent at one of the family’s abused funds (which wasmarketedtounsuspectingchildren!) andmorethan22,000percentatanother. Worse yet, the timing of cash flows from abusive traders made their impact especially deleterious. The senior portfolio manager at Invesco complained at one point, ”I had to buy intoastrongrallyyesterday,andIknowI’mnegativecashthismorningbecauseofthese bastards and I have to sell into a weak market” (Attorney General of the State of New York,2003). Losses not captured in my estimates. The loss estimates presented here may be biaseddownwardbecausetheyarebasedonacomparisonofthereturnsofabusedfunds and those of their untainted competitors. Underlying this comparison is the assumption that trading abuses did not reduce returns at mutual funds in untainted families. But even for managementcompanies that aggressively worked to prevent abusivetrading in their funds, market timing was often difficult to detect and stamp out, so abuses may have been more widespread among funds than was reflected in official complaints and settlements, news reports, and fund disclosures. To the extent that untainted funds sufferedlossesfromtradingabuses,myestimatesoftheeffectsoftheseabusesonperformancewouldbetoosmall.16 6 Comparingtherevenuesandcostsofabusive-tradingarrangements My primary finding in this paper is that mutual fund management companies made pooreconomicdecisionsinstrikingdealsthatallowedabusivetradingoftheirfunds. To makemyargumentaspreciseaspossible,Ianalyzedthedecisionwhetherornottoenter into arrangements to allow market timing (or late trading) as of three years before each mutualfundfamily’sarrangementsbecamepublic. Forexample,forthefirmsthatwere namedintheNewYorkAttorneyGeneral’sfirstSeptember2003complaint,theanalysis was done from the perspective of the end of August 2000; for firms whose wrongdoing wasdetectedlater,theperspectivewasadjustedaccordingly. Because the revenues and losses from facilitating abusive trading cannot be esti- 16Myestimatesdonotincludetwoadditionalformsoflossesthatmighthavebeenimportanttobuy-andholdinvestors.First,Idonotconsidercapital-gainstaxliabilitiesgeneratedbyheavyportfolioassettrading. Chalmersetal.(1999)estimatedthatsuchtaxliabilities—atleastoverthesampleperiodtheyanalyzed— weresmallrelativetothetypicalmutualfund’sexpenseratioandtradingcosts.Still,suchcostsmighthave beenmoresubstantialinfundswithhighpastreturns,particularlyforinvestorswhoplannedtoholdfund sharesforlongperiodsintaxableaccounts,andwhoexpectedtowaitmanyyearsbeforerealizingcapital gains.Second,Ididnotattempttocomputetheopportunitycostsoflossesthaterodeinvestors’capital:Lost returnsdepriveinvestorsoffuturecapitalgains(losses)whenfuturereturnsarepositive(negative). 18

mated with any precision for most individual management companies, I measured the aggregaterevenuesandcostsofthisbehaviorforalltaintedfundfamilies. Whilemyanalysis does not address some of the margins on which this decision might be made (for example, allowing timing only in certain types of funds), the finding that average costs of trading arrangements so outweighed the average revenues suggests that a marginal analysiswouldbeevenmoreunfavorabletothesedeals.17 Therevenuesthatmutualfundmanagementcompaniesreapedfromabusivetrading arrangements were mostly increased management fees, including those assessed on “sticky assets” and on traders’ investments in the funds they were abusing, although that money often stayed in the funds only for brief intervals. In addition, fund portfolio managers and senior executives at some companies profited directly from abusive tradingoftheirownfunds. Totheextentthattheseindividualskepttheirtradinggains, management companies did not benefit directly. Nonetheless, the trading gains representedadditionalcompensationforcompanypersonnel,andIincludeestimatesofthese individuals’gainsfromtradingabusesinmytallyofcompanyrevenues.18 By facilitating trading abuses, a management company incurred two types of expected future costs: those that would accrue regardless of whether the arrangements were detected and those that would be incurred only if the firm were caught. Even if deals to allow abusive trading were never discovered, the depressing effect of the trades onperformancewouldbeexpectedtocutintoassetsundermanagementandreducefee revenue. Once arrangements were revealed, a management company would anticipate incurringthreetypesofadditionalcosts: officialpenalities,includingfinesanddisgorgement; civil litigation costs; and a damaged fiduciary reputation that would result in net outflowsfromthecompany’sfunds. Discountingrevenuesandcosts. Boththerevenuesandthecostsofadecisionto allowandfacilitatetradingabuseswouldaccrueovertime,soacomparisonofrevenues and costs requires an appropriate discount rate. For each tainted mutual fund manage- 17Thereisreasontobelievethatthemarginalcostsofallowingabusivetradesincrease,andthemarginal revenues decrease, with the magnitude of trading allowed. Mutual fund investors respond non-linearly to past returns, suggesting that the flow penalty for abuse-related performance losses may increase more than proportionally with those losses. Moreover, small amounts of timing would be difficult to detect in performanceorothermeasures,butlarger-scaleabuseswouldeventuallybeobservableinincreasedshare turnover statistics and ultimately, despite the considerable noisiness of returns, in reduced performance. Hence, the chance that a mutual fund company would eventually be caught by prosecutors or identified byresearchersorindustrymonitorsas“timerfriendly”likelyincreasesnonlinearlyinthemagnitudeofthe abuses.Andastheaftermathofthescandalindicates,theresultingdamagetoanassetmanager’sreputation fromsuchrevelationswouldbeextremelycostly. Moreover,dilutiongainstotradersdiminishasabusive tradingflowsbecomealargerfractionofamutualfund’stotalassetsundermanagement(inthelimit,ifan investoraccountsforallofafund’sassets,shecannotreapanygainsfromabusivetrading). 18Forexample,evenafterseniorexecutivesatPutnambecameawarethatportfoliomanagersweremarkettimingtheirownfunds,themanagerswereallowedtocontinuetheirabusivetrading—whilemanaging thefunds—andtoretaintheirtiminggains(MassachusettsSecuritiesDivision,2003;U.S.SecuritiesandExchangeCommission,2003c). 19

ment firm (or its parent) with publicly traded debt or equity, I computed a weightedaveragecostofcapital(WACC)equaltotheweightedmeanofthetax-adjustedyieldon publicly traded debt and an expected return on equity based on the market beta of the firm’s stock. The debt and equity components are each weighted by their market value. Since I focused on investment management companies’ decision whether or not to collude with abusive traders as of the end of August 2000—three years before the scandal broke—all of the WACC computations are based on yields and betas measured in 2000, although using data for 2000 through 2002 has no material effect on the average. The WACCs I computed for tainted mutual fund firms ranged from 9.0 percent to 15.2 percent per year. The mean WACC of the tainted firms in 2000, weighted by their mutual fundassetsundermanagement,was11.6percentperyear. Revenues,costs,andprofits. Myanalysiscomparestherevenuesobtainedthrough arrangements with abusive traders and revenues foregone because of future reductions in assets under management, rather than reviewing the arrangements’ profitability, per se. Sincethebenefitstomutualfundcompaniesthatcolludedwithabusivetraderscame mostly in the form of asset management fees assessed on “sticky assets” as well as on short-lived“investments”inabusedfunds,thecomparisonsdrawnherearereasonable.19 7 Managementcompanyrevenuefromabusive-tradingarrangements Mutual fund firms that sought to benefit from trading abuses had no reason to tally up those gains, and there are no comprehensive data on their revenues. To fill this gap, I used three methods to derive very rough estimates of scandal-related revenue. Where precision in estimating revenues was particularly difficult to obtain, I attempted to err on the side of overstating them in order to make a convincing case that revenues from tradingarrangementsfellfarshortofthecostsofabusivetrading. Broadly speaking, I computed revenues by multiplying an estimate of management companies’ share of the profits from abusive trading by the total gains from such trading. Thiscanbedoneinoneoftwoways,beginningwitheithershareholders’losses duetothetradingoranestimateoftheaggregategainsfromsuchtrades: 19Severalaspectsofthescandalcomplicatematterssomewhat,butprobablydonotaffectthemainpoints ofthispaper. First,totheextentthatcompanyinsidersgaineddirectlyfrommarkettiming,theirearnings couldbeseenas“pure”profit,althoughsuchtradingrepresentedonlyatinyshare(lessthan2percent)of estimated aggregate management company revenues from abusive-trading arrangements. Second, to the extentthatquid-pro-quoarrangementsrequiredabusivetraderstoparkassetsinhedgefunds,ratherthan mutualfunds,operatingmarginsmayhavebeenhigheronsomeoftheassetsgarneredfromabusivetrading than for the assets lost due to poor performance. On the other hand, official penalties, which eventually amountedtoaverysubstantialcosttothefirmsthatwerecaught,camestraightoutofthebottomline,so directcomparisonsofthesecoststoothercostsandrevenuesunderstatetheimportanceofthepenalties. 20

ManagementCompanyRevenuefromCollusionwithAbusiveTraders = Totallossestomutualfundshareholders ×(1−deadweightlossshare) ×managementcompanies’shareofgains (4) = Totalgainsfromabusivetrades ×managementcompanies’shareofgains. (5) 7.1 Managementcompanies’shareofabusive-tradinggains Legal documents arising from the scandal provide some evidence about management companies’ share of the gains from trading abuses, net of deadweight losses. Complaints,settlements,anddistributionplansoftenreportthegainstobothabusivetraders andmanagementcompaniesfromspecificarrangements; thefigureslistedintable5are drawnfromthesereports. Thedataarelimitedinscopeanddonotrepresentacomprehensiveaccountingoftheshareofabusive-tradinggainscollectedbyanyofthemanagement companies listed, so shares for individual firms should only be viewed as suggestive. Takentogether,however,theyarequiteinformative. Whilemanagementcompanies obtainedaslittleas2percentandasmuchas43percentoftheprofitsfromabusivetrading,mostmanagementcompaniesearnedrelativelysmallshares—under10percent—of thegainsfromabusivetrading.20 Even these figures probably exaggerate management companies’ typical share of abusive trading gains, because the records documenting quid-pro-quo deals probably captured the most favorable distributions for mutual fund firms. Many tainted fund familiestoleratedtradingabusesbytimerswhodidnothavespecialarrangements, and 20Thetwooutliersontable5—thesharesforBancofAmericaandWaddellReed—areprobablynotrepresentative,butfordifferentreasons. The43percentshareforBancofAmericareflectsthefactthatitwas collecting revenue for much more than facilitating trading abuses in its own mutual funds (the Nations Funds).Thefirm’sassetmanagementaffiliate,BancofAmericaCapitalManagement,onlyreceived2.2percentoftherevenuesfromthedealsthatallowedabusivetradinginitsfundsandthatwerememorialized inofficialdocuments. Butotheraffiliates,includingBancofAmericaSecurities(BAS),profitedmorehandsomely. BAS helped Canary Capital Partners, a hedge fund that engaged in widespread trading abuses, set up in Canary’s offices a trading platform that used Banc of America’s proprietary trading network and enabled Canary to market time and late trade funds in a broad array of mutual fund families. BAS also earnedfeesforcreatinghedgesthatallowedabusivetraderstomarkettimeothermutualfundsmoreprofitably. Indeed, thedistributiontoinjuredpartiesofpenaltiesanddisgorgementpaidbyBancofAmerica indicatedthatitsownmutualfundinvestorssufferedonly6percentofthetotalestimateddamagesfromits arrangementswithabusivetraders(seeU.S.SecuritiesandExchangeCommission,2005b,2007a).Theshare forWaddell&Reed,at31percent,representsestimatedgainsandfeesfromarrangementswithjustthree markettimers,oneofwhomlostover$6millionbytradingWaddell&Reedfunds. Thiscompany’sshare oftherevenuefromarrangementswiththeothertwotraderswasastill-high19percent(U.S.Securitiesand ExchangeCommission,2006a). 21

management companieslikely obtainedsmaller shares oftheir gains. Moreover, traders who had struck agreements with tainted families frequently overstepped the bounds of those arrangements—far exceeding agreed-upon “timing capacity,” for example—so stated terms of the deals may overstate the portion of the gains going to management companies. Ontheotherhand,themanagementcompanyexecutivesandportfoliomanagers who market timed their own mutual funds reaped considerably larger shares—usually all—oftheabusive-tradingprofits. Altogether,theseinsiderscollectedapproximately$11 million in net gains from abusive trading over several years. As noted above, I assume thatmanagementcompaniesreapedallthegainsfromsuchinternalabuse. Table 5 indicates that management companies’ share of the gains from abusive trading averaged 12.0 percent. Adjusting this figure for the portion of dilution due to internalmarkettiming—whichisnotreflectedinthedataonthetable—bringstheshare up to 12.4 percent. Applying a range of different weights to these family-level observations, including assets in abused funds, total dilution estimates from Zitzewitz (2007b), and total penalties, results in share estimates ranging from 8.6 percent to 16.6 percent. Below,Iusedthehighestfigureinthatrange. 7.2 Revenuesestimatedfromtotalshareholderlosses Insection5.2.2,Iestimatedthatmutualfundshareholders’lossesduetoabusivetrading arrangements totaled $10.4 billion per year. This money would have been split among abusivetraders,managementcompanies,anda“deadweightloss”thatwasabsorbedin fundadministrativecosts,portfoliotradingcosts,andtheopportunitycostsofmanaging flowsduetoabusivetradesandholdingsuboptimalassetallocations. Although the deadweight losses associated with abusive trading—as discussed above—were probably substantial, I have little direct evidence on their magnitude. By assuming that deadweight loss was zero, however, I can derive an upper bound for management companies’ revenues from collusion with abusive traders, conditional on the share of abusive-trading profits derived above. Using equation (4), I multiply shareholderlossesof$10.4billionperyearby16.6percentandobtainanestimateof$1.7billion peryear. 7.3 Revenuesestimatedfromabusive-tradinggainsanddilution A more direct approach to assessing the revenues from abusive-trading arrangements begins with estimates of the wealth transferred from buy-and-hold investors to abusive traders. AsdescribedinsectionsA.1andA.2oftheAppendix,abusivetraders’gainsand buy-and-hold investors’ dilution losses (one component of their total losses) are roughly 22

equivalentunderarangeofcircumstances—forexample,whentimersholdmutualfund sharesforjustonedayatatime, orwhentimersholdmutualfundsharesforlongerperiods but fully hedge those positions (and fund portfolio managers invest timers’ flows immediately). This suggests that off-the-shelf methods of measuring dilution might be modifiedtoestimateabusivetraders’gains. Bymultiplyingthesegainsbymanagement companies’shareoftheprofits, onecanapproximatetheadditionalrevenuethecompaniescollectedbycolludingwithtimers. To estimate abusive traders’ gains in abused funds, I used a modified version of a method employed by Greene and Hodges (2002) to estimate dilution.21 Consider a mutual fund with assets A t−1 on day t−1. Suppose that, on day t, the fund adjusts its NAV by fraction r to reflect returns to its portfolio, but fails to incorporate a second t component of return, π , which investors can either predict or observe. For example, π t t might be post-Nikkei-close appreciation of Japanese stocks that is not incorporated in a fund’s NAV. Define π such that, had the fund incorporated this component of return t in computing its NAV, total return to mutual fund shares on day t would have been (1+r t )(1+π t ). Let r t+1 be the return recorded (in terms of change to NAV) on the followingday. Supposethatabusivetraderspurchase g t A t−1 worthofsharesonday t toexploit thefund’spricingerror(presumably, when π > 0, g > 0, andviceversa). Atthesame t t time, buy-and-hold investors, whose trades the portfolio manager anticipates, purchase φ A worth of shares. Then, in year T, abusive traders gains, G , are, for each mutual t t T fund:22 (cid:18) (cid:19)(cid:18) (cid:19) G T ≈ t∈T ∑ ,gt ≥0 A t−1 g t r t+1 + t∈T ∑ ,gt <0 A t−1 g t 1+ r t+ r t 1 +1 1+ 1+r g t t +φ t (6) Inestimatingequation(6),Iassumethatφ t A t−1 istheexpectedcomponentofdailyflow, conditionaloninformationavailableondayt−1,andthatabusivetraders’flow, g t A t−1 , is the surprise component. Under the null hypothesis that there are no abusive-trading gains, flow surprises, g t , are uncorrelated with next-day returns, r t+1 , and estimated gainsarezero. Butwheninflowsanticipatepositivereturnsandoutflowsanticipateprice declines—becausetradersareexploitingstaleNAVsbymarkettimingorlatetradingmu- 21Because it is based on the correlation between mutual fund flow and next-day changes in NAV, the methodthatGreeneandHodges(2002)usetocomputedilutionhasbeencalled“next-day-NAV”method. Researchers,aswellasconsultantsdetermininghowtodistribute“FairFunds”(penaltiesanddisgorgement collectedfromtaintedmanagementcompanies)toshareholderswhosufferedlosses, havealsousedthree othermethodstoestimatedilution: Onebasedoncorrelationsofflowsandpredictedmutualfundpricing errors,onebasedonabusivetraders’holding-periodprofits,andonethatexplicitlytakesintoaccounthow portfoliomanagershandlecashfromabusivetraders(Zitzewitz,2003,2007b;GreeneandCiccotello,2004). I discuss these methods, and my reasons for using an approach similar to the next-day-NAV method, in sectionsA.1andA.2oftheAppendix. 22Equation(6)isderivedinsectionA.3oftheAppendix. 23

tualfundshares—estimatedabusive-tradinggainswillbepositive. I estimate (6) using daily assets data from TrimTabs and returns data from CRSP, TrimTabs, and Yahoo! Finance.23 The TrimTabs data, described extensively by Greene andHodges(2002)andZitzewitz(2003),includedailyobservationsonassetsundermanagement and NAVs for 84 of the 145 abused mutual funds that I have identified. To compute daily returns, I adjusted changes in NAVs as appropriate using data on splits and distributions from CRSP and Yahoo! Finance. Net new cash flows are flows net of reinvested distributions, which I estimated using monthly data from the Investment CompanyInstituteonthereinvestmentratesfordistributionsmadebydifferenttypesof mutualfunds. Since TrimTabs data covered only 84 of the abused funds, I applied the assetweighted average rates of abusive-trading gains for each investment objective in the TrimTabssampletoaggregateassetsundermanagementforallabusedfundssharingthe same investment objective. Summing over all objectives, estimated gains from market timingandlatetradingamongabusedfundsamountedto$2.68billioninthethreeyears beforethescandalbroke(fromSeptember2000toAugust2003), anaverageof$894million per year. Multiplied by management companies’ 16.6 percent share of the revenue, thisimpliesthatthesefirmsreceived$148millionperyear. Therearesomedrawbackstousingthismeasureofabusive-tradinggainsasabasisforestimatingrevenue. Calculationsusingequation(6)areimprecise,inpartbecause thedailyflowsforeachfundarenotoriouslynoisy(GreeneandHodges,2002;Zitzewitz, 2003; see also section A.4 of the Appendix), but also because this method does not precisely distinguish abusive-trading flows and other types of flow.24 Moreover, trading gains measured in this manner may substantially overstate timers’ actual gains because equation (6) captures the potential gains from sales of shares at above their true value (when g < 0and π < 0)aswellasthemorestraightforwardlossesduetotimers’purt t chases of mutual fund shares at below their fair value. As discussed in section A.3.2 of theAppendix,suchtimedredemptionsdocauselossesforothershareholders,butunless timers employ hedging strategies, their redemptions do not reap cash gains—they only avoid losses. Hence, if abusive traders time their redemptions but do not hedge their mutualfundpositions,estimatesofrevenuesbasedon(6)willbebiasedupward. Zitzewitz(2007b)dilutionestimates. Zitzewitz’sestimatesofdilutionatscandal- 23SectionA.4oftheAppendixdiscussessomeofthechallengesposedinusingthesedailydatatoestimate abusivetraders’gains,aswellassomeoftheassumptionsandfiltersIemployedinprocessingthedata. 24The“predicted-NAV”methodofestimatingdilutionaimstoidentifyabusive-tradingflowsmoreprecisely by using the signals—such as changes in index futures prices—that market timers and late traders employedtotriggerdilutivetrades. Thechoicebetweenthenext-day-NAVandpredicted-NAVmethodsis probablynotimportantformypurposes,however,asZitzewitz(2007b)employsbothmethodstocalculate dilutionformutualfundsintaintedfamiliesandobtainsverysimilarestimatesusingeitherapproach. See sectionA.1oftheAppendix. 24

tainted fund families offer a useful check on my estimates of abusive-trading gains. To besure,hisobjectivesandmeasuresaredifferentfrommine: Heestimateddilutionforall abused and tainted world equity funds and small- and mid-cap equity funds at scandaltaintedmutualfundfamilies,whileIexaminedgainstoabusivetradersfromtimingtrades involving only abused mutual funds, which included bond and hybrid funds as well as equity funds. Zitzewitz employed the predicted-NAV method to compute dilution, whereasIusednext-day-NAVs, andthereareminordifferencesinourcoverageoffund familiesandtimeperiods. Nonetheless,myestimatesofabusive-tradinggainsarequiteclosetothedilution estimates that Zitzewitz reported. As indicated above, I estimated that abusive traders’ gainsfromtimingmutualfundsfromSeptember2000throughAugust2003amountedto $2.68 billion, while Zitzewitz reported dilution of $2.56 billion for January 2000 to June 2003atthe20mutualfundcomplexesIanalyzed.25 7.4 Revenuesestimatedfromofficialpenalties Official penalties imposed on management companies provide some additional clues about the magnitude of the revenues from arrangements that allowed trading abuses. The penalties (excluding fee reductions negotiated by the New York Attorney General) appear, in practice, to have been an upper-bound for prosecutors’ and regulators’ estimatesofthedilutiondamagedonetomutualfundshareholders. Furthermore,SECrules indicate that disgorgement—a portion of the total penalites—should itself be a direct measureoftheill-gottengainsofmanagementcompanies. 7.4.1 Totalpenalties In assessing the penalties imposed on mutual fund management companies and their employees,stateofficialsandtheSECappeartohavejointlyaimedfortotalsthatapproximatedorexceededthetotaldilution-relateddamagestomutualfundshareholders.26 The primaryevidenceforthiscomesfromdistributionplanswhichallocatethepenaltiespaid by tainted mutual fund management companies to shareholders based on damages— primarilydilutionlosses—theyincurred. Fornineofthetencompaniesforwhichdistribution plans are available, plan authors indicated that shareholders would receive pay- 25Zitzewitzreportedatotalof$2.58billionindilutiondamages,butthefigureincludedestimateddilution of$20millionintheAmeriprise(or”AXP”)funds,whichIdidnotanalyze(seenote7).Hedidnotprovide dilutionestimatesforSeligmanorWachovia’sEvergreenfunds. AnSECsettlementwithWachoviaandan AttorneyGeneralofNewYorkcomplaintagainstSeligmanindicatethatdilutionatthesefamilies’mutual fundstotaledroughly$110million.Withtheseadjustments,Zitzewitz’sfiguressuggestthattotaldilutionat the20mutualfundfamiliesIanalyzedwouldbe$2.67billion. 26Negotiatedfeereductionswereamajorexceptiontothisrule.TheNewYorkAttorneyGeneralmadeit clearthatthefeereductionswereessentiallyrebatesfor“excessive”feeschargedbyfirmsthathadviolated fiduciaryduties,ratherthanameasureofthedamagescausedbyabusivetrading. 25

mentsthatexceededestimateddamage(andfortheremainingfirm,Columbia,estimated damage was approximately equal to the penalty payments plus interest). Among the seven distribution plans that quantified damages to shareholders, aggregate penalties exceededtotalestimateddamagetoshareholdersby52percent.27 Moreover,damageestimatesusuallyincludedcoststoshareholdersthatcouldnot have been gains for abusive traders or management companies. Five of the distributionplansthatquantifieddamagesincludedestimatesofsomedeadweightlossesdueto abusivetrading,suchasthetransactionsoradministrativecostscausedbyheavytiming flowsandthemassiveredemptionsthatfollowedthescandalrevelations. On the other hand, Zitzewitz (2007b) suggested caution in interpreting penalties asupperboundsfordilutiondamage. Hereportedthattheratioofpenaltiestodilution rangedfrom0.1to10, sopenaltiesdonotnecessarilycorrelatestronglywith, andsometimesfellfarshortof,totaldilutionintaintedmutualfundfamilies. Zitzewitzarguesthat thewiderangeinthisratioreflected,inpart,theNewYorkAttorneyGeneral’stendency tonegotiateparticularlylargesettlements. Therangemayalsoreflectheterogeneityinthe scope of damages examined by the SEC and state officials; in some cases, they focused narrowly on damage from abusive-trading arrangements and in others they estimated damageduetoalldilutivetradesinafamily’sfunds,regardlessofthemanagementcompany’s culpability in allowing those trades to occur. Zitzewitz’s estimate encompasses dilutioninall(abusedandtainted)equityfunds. 7.4.2 Baselineestimatesofrevenuesfromcollusionwithabusivetraders: Maximum ofpenaltiespaidandestimateddilution Onewaytoexploittheinformationinthepenaltiesassessmentswhileincorporatingthe caveats suggested by Zitzewitz is to use, for each management company, the maximum of the penalties it paid (shown in column 10 of table 2) and an independent estimate of abusive traders’ gains in its mutual funds. My estimates of those gains are incomplete anddonotincludefiguresformanyofthetaintedfirms, butZitzewitz(2007b)provides dilutionestimatesformutualfundsatalmosteverytaintedfamily,asshownincolumn13 oftable2. Moreover,asindicatedinsection7.3,myestimatesofabusivetraders’gainsare quite similar to Zitzewitz’s dilution estimates. So, one practical approach to estimating the total gains from abusive trades is to use the maximum, for each management com- 27Fortheotherthreefirms,distributionplansmerelystatedqualitativelythatfundstobedistributedexceededestimateddamage. Onereasonthatpenaltiesmayhavesystematicallyexceededshareholderdamages was the New York Attorney General’s claim that management companies had committed fraud in makingarrangementstofacilitateabusivetradingandthuswerenotentitledtokeepadvisoryfeescollected whiletheabusewasoccurring. Thisargumentappearstohavemotivatedlanguageinmanydistribution plans that stipulated that “Fair Funds” be distributed first to compensate mutual fund shareholders for lossesduetoabusivetrading,andthen—iffundsremained—torebateshareholdersforaportionofthefees thatthey(throughtheirfunds)hadpaidtomanagementcompaniesthatwereallowingtradingabuses. 26

pany, of the penalties it paid and Zitzewitz’s estimates of dilution in its funds. Column 14showsthesemaxima,whichtotal$3.55billion. Usingthisfiguretoestimateanannualrevenuestreamrequiressomeknowledge of the timing of the malfeasance for which firms paid penalties, but that is rarely clear insettlementdocuments. Somemanagementcompaniesevidentlyhadinitiatedarrangementstoallowtradingabusesbefore2000,withseveralagreementsbeginningasearlyas 1998 and at least one firm’s arrangements dating back to 1995. Nonetheless, I assumed that the penalties were for malfeasance lasting just three years.28 Annual gains to abusive traders reflected in the penalties and dilution estimates would therefore be $1.18 billion. Applying a management-company share of revenues of 16.6 percent, I obtained arevenueestimateof$196millionperyear,whichIusedasmybaselinefigureformanagementcompanies’annualrevenuesfromcollusiveagreementswithabusivetraders. 7.4.3 Disgorgement AccordingtotheSECRulesofPractice(2003b),“thepurposeoftheCommission’sadministrative disgorgement remedy is to deprive violators of ill-gotten gains and thus serve as a deterrent to violations, rather than to compensate injured investors.”29 Taken literally, this implies that disgorgement totals (plus fund restitution payments) should be a measure of management company revenues from collusive arrangements. Table 2 summarizes disgorgement and restitution amounts: $1.35 billion in disgorgement paid by management companies (column 2); $151 million and $3 million in disgorgement paid by senior executives and employees, respectively (columns 5 and 7); and $47 million in restitution payments (column 3).30 As shown in column 11 , the twenty tainted mutual fund firms and their executives and employees paid a total of $1.6 billion in disgorgement and restitution. Dividing that figure over three years yields a revenue estimate of $528millionperyear.31 This estimate likely substantially overstates the revenues of mutual fund managementcompanies. Settlementdocumentsaregenerallysilentonthederivationofdisgorgementamounts,andmakenoclaimsthatthesefiguresrepresentill-gottengains,per se. Ontheotherhand,asdiscussedabove,thetotalpenaltiesimposedgenerallyexceeded 28This likely biases upward the annual revenue estimates, but the assumption is consistent with my findingthatshareholderlosseswereconcentratedinthethreeyearspriortothebreakingofthescandaland withmybiastowardoverstatingrevenues. 29TheRulesgoontocitetheSenateReportaccompanyingtheSecuritiesLawEnforcementRemediesand PennyStockReformActof1990:“disgorgementforcesadefendanttogiveuptheamountbywhichhewas unjustlyenriched”(U.S.Senate,1989). 30Seenote9. 31SeligmanhasnotyetsettledwithanystateagencyortheSEC,sothecompanyhasnotpaidanydisgorgement. Iimputeddisgorgementof$36millionforSeligmanbasedonestimateddilutionof$80million inSeligmanfunds(AttorneyGeneraloftheStateofNewYork,2006)andtheratioofotherfirms’aggregate disgorgementpenalties(column11oftable2)tothemaximumoftotalpenaltiesanddilution(column14). 27

estimated total dilution profits shared by abusive traders and management companies. Although management companies probably collected less than 20 percent of that total, as indicated in table 5, disgorgement represented 60 percent of total penalties imposed. Nonetheless,Iusedthisdisgorgement-basedfigureof$528millionperyearasahighestimatefortherevenuesthatmanagementcompaniesobtainedthroughtheiragreements withabusivetraders. 8 Thecostsofabusive-tradingarrangements A mutual fund management company that sought revenues by allowing and abetting tradingabusesfacedcoststhatwouldbeincurredwithsomeuncertaintyanddelaycompared with the realization of revenues. Most obvious, in retrospect, were the disastrous consequences of getting caught, and with the benefit of hindsight, one can catalogue thesecosts: Thebrand-destroyingheadlinesofSeptember2003,thewaveofmutualfund share redemptions that followed the scandal news, the enormous official penalties that were imposedby prosecutorsand regulators, and the private civillitigation that continues to this day. But a second form of costs—those arising from impaired performance of mutual funds that were subject to abusive arrangements—would have been borne by mutual fund families even if those arrangements had never been revealed. Had mutualfundmanagementcompaniesfullytakenintoconsiderationthesecosts,whichcould have been foreseen long before public officials learned about the trading abuses, there mightneverhavebeenamutualfundscandal. 8.1 Costsarisingfromimpairedperformance Any reduction in a mutual fund’s performance will cut into expected future assets undermanagement,andhenceintothefeerevenuethatisproportionaltomanagedassets, throughtwochannels. First,sincemutualfundshareholdersautomaticallyreinvestmost of their capital gains, poor returns will diminish future assets directly. Second, because mutual fund shareholders make purchase decisions based on past returns, poor performancealsoweighsonfutureassetsbydepressingnetinflows. Ibeginwithananalysisoftheexpectedlossesthroughthesetwochannelsfroma strategyoffacilitatingmarkettimingforthreeyears,beginningroughly(formosttainted mutual fund families) in September 2000 and ending in August 2003. This corresponds approximately to what actually happened; dilution due to abusive trading appears to have risen dramatically around 2000 and diminished considerably after the New York AttorneyGeneral’sinitialcomplaint(seefigure2andZitzewitz,2007a). Consideramutualfundthatinperiod t−1hasassets A t−1 ,earnsareturnnetoffeesr t inperiod t,and attracts net inflow, f , expressed as a fraction of previous-period assets. If the fund imt 28

mediately distributes capital gains to investors, who automatically reinvest fraction θ , t fundassetsgrowto A t = A t−1 (1+θ t r t + f t ) bytheendofperiod t.32 Ifthefundallows abusivetradingthatreducesreturnsby ∆randcausesalossofnetflows ∆f ,assetsgrow t onlyto A t L = A t−1 (cid:0) 1+θ t (r t −∆r)+ f t −∆f t (cid:1) . (7) Therefore, a fund that allows trading abuses from period T to T will “lose” managed 0 assets ∆A = A −AL T0,T T T T ∏ = A (1+θ r + f ) T0 t t t t=T0 +1 T (cid:16) (cid:17) −A ∏ 1+θ (r −∆r)+ f −∆f . (8) T0 t t t t t=T0 +1 Expectedrevenuelossesinperiod T arethepredictedchangeinassetsfromequation(8) multipliedbythefund’sexpenseratio,netofany12b-1fee(sincesuchfeesaretypically passedontothird-partydistributors). Applyingadiscountfactor,δ,thediscountedvalue ofexpectedrevenuelossesfromperiod-T perspectiveis: 0 T E (∆R ) = ∑ δt−T0 x ∆A . (9) T0 T0,T t T0,T t=T0 +1 I estimated the expected revenue losses using asset-weighted aggregate data for abused funds for the period from three years before the scandal revelations to three years after. x istheasset-weightedmeanexpenseratio(netof12b-1fees),and A isthetotalassets t T0 ofabusedfundsthreeyearsbeforewrongdoingwasfirstreported(about$490billion).33 The reinvestment rate for distributions, θ , varies by fund type, but the asset-weighted t average among abused funds was about 85 percent. The performance effect of the trading abuses, ∆r, is as estimated above; to maintain a conservative stance on the costs of 32Inreality,capitalgainsaredistributedandreinvestedwithsometimesconsiderabledelaysthatwould be difficult to model, but I assumed that gains were distributed immediately. Also, while θt effectively should be larger when rt is negative than when it is positive (losses are not distributed), I assumed an extremevalueofθt =1forcapitallosses. Bothassumptionscausesomedownwardbiastomyestimatesof thecostsofimpairedperformancebyunderstatingbaselinemutualfundgrowth. 33Totalassetsofabusedfundsfellsharplyovertheperiodfrom2000to2006—moresharplythanwouldbe predictedbytheasset-evolutionequation(7),whichdoesnotcaptureallchangesinassets(forexample,fund closures). Whileitisarguablewhetherornotsuch“lost”assetsshouldbeincludedinanexanteanalysis ofdecisionsmadein2000,doingsowouldclearlyraiseestimatesoflosses. Hence,inestimatingequations (8)and(9),Iusedassetsobservedeachmonth,ratherthanusinginitialassetsandtheasset-evolutionpath suggestedby(7).Thatis,Icomputedassetlosseseachmonthusingobservedassetsundermanagementatthe beginningofthemonth,andcumulatedtheselosses(whichincludetheopportunitycostofforegonecapital appreciationonassetslostinpreviousmonths),ratherthanusingequation(7)topredictassets. 29

the trading arrangements, I used the smallest value of alpha shown on table 4 (an annual logarithmic return of -0.036, converted to monthly return). The observed monthly asset-weightedmeanreturnofabusedfunds,whichincludestheperformanceimpactof abusive trading, is r −∆r, so r itself is estimated. The discount factor, δ, is based on t t anannualWACCof11.6percent. Finally,Ihadtoestimatetheeffectoftheperformance lossesonnetflow, ∆f ,asdescribedbelow. t 8.1.1 Theeffectofperformancelossesonexpectednetinflows. Theliteraturethatexplorestherelationshipbetweenmutualfundflowsandperformance isextensiveandpredatesthemutualfundscandalbyseveraldecades(see, forexample, WhartonSchool,UniversityofPennsylvania(1962),Friendetal.(1970),Smith(1978),Ippolito(1992),ChevalierandEllison(1997),SirriandTufano(1998),DelGuercioandTkac (2002)). This research indicates that flows vary nonlinearly with past returns measured overarangeoffrequencies. Forexample,investorsrespondindependentlytoreturnsin recent months and to returns measured over the previous several years, and flows are especially sensitive to the returns of funds at the top of the performance distribution. Because my objective is to estimate the effects of individual abused mutual funds’ poor relativeperformanceontheirsubsequentcashflows,Ialsodistinguishedbetweenfunds’ relative returns, which were depressed by trading abuse, and category returns, which I assumedwerenot.34 Toestimatetheeffectsofreducedperformanceonexpectedfuturerevenues,Iemployedanempiricalmodelofmutualfundflowasafunctionofcurrentandpastreturns: (cid:16) (cid:17) f = ∑ πpr p +πpHr pH +πpLr pL+γpc p +γpHc pH +γpLc pL it it it it it it it p∈P +b +m +ΓX i t it 35 35 + ∑ βScandalDScandal + ∑ βAbusedDAbused+ε . (10) s ist s ist it s=−12 s=−12 The unit of observation is the mutual fund share class i in month t, and the dependent variable in the regression, f , is 100 times the log of one plus cash flow over lagged it p p assets. The model includes relative returns, r , and category returns, c , measured over it it 34Market timing was not confined to abused funds at scandal-tainted complexes, and the pre-scandal literaturethatexaminedthedilutiveeffectsofmarkettimingbyinvestmentobjectiveshowedthatcategory returnswereaffectedbymarkettiming.Hence,poorcategoryperformancelikelyaffectedflowstobroadinvestmentobjectivesthatwereheavilytraded,suchasJapan-equityfunds.However,instudyingthedecision bysomemutualfundfamiliestoaccommodateabusivetraders,myfocuswasontherelativeperformance penaltythatthesefundssufferedandhowitaffectedfuturerevenues. Tothatend,Ianalyzedonlytheeffectsofabuseonrelativeperformanceandothermeasuresofrisk-adjustedreturnsthatcontrolforcategory performance. 30

different intervals, p, in the set P, which includes the current month, each of the three previous months, the past year, and the past three years.35 To capture the nonlinear responsetoperformance,Iseparatelyincludedforeachperformanceperiodandtypeof return (relative and category) a fund’s returns conditional on those returns being in the topandbottomquintiles.36 Thatis: (cid:40) p p r ifr isinthetopquintileamongmutualfundsini’scategory. r pH = it it it 0 otherwise. (cid:40) p p r ifr isinthebottomquintileamongmutualfundsini’scategory. r pL = it it it 0 otherwise. (cid:40) p p c ifc isinthetopquintileamongallmutualfundcategories. c pH = it it it 0 otherwise. (cid:40) p p c ifc isinthebottomquintileamongallmutualfundcategories. c pL = it it it 0 otherwise. Theregressorsb andm areshare-classandmonthlytimefixedeffects,respectively. The i t vector X is a set of controls, including the logarithm of the assets in each share class, it its expense ratio excluding 12b-1 fees, its 12b-1 fee (if any), and a dummy variable for load funds. Finally, DScandal and DAbused are dummy variables used to control for the ist ist large net redemptions of scandal-tainted families’ mutual fund shares after the scandal revelations. Thesearediscussedinmoredetailinsection8.2.1. I estimated equation (10) using monthly CRSP data from January 1993 to May 2007. Results are reported in table 6. Estimated linear coefficients on relative and category returns (columns 2 and 5) are positive and significant over every performance interval in the model. There is also evidence of nonlinear responses to performance, but the patterns are not uniform. At short horizons, responses to relative performance among the bottom fifth of funds (column 1) are significantly smaller than responses to relativeperformanceintherestofthedistribution. Investorsareespeciallyresponsiveto relative returns among the best performers over one- and three-year horizons (column 3). Responses to lowest-quintile category returns (column 4) are muted compared with responsestoreturnsinthemiddleandupperpartsofthedistribution. The model indicates that single month’s poor performance has repercussions for 35Returnsoveroverlappingintervalsarenetofoneanother. Thatis,annualreturnsarereturnsoverthe previous12monthslessreturnsoverthepastthreemonths. Andreturnsoverthepreviousthreeyearsare netofreturnsintheprevious12months.Allreturnsareexpressedinlogarithmicterms. 36Other forms of nonlinearity, such as separate intercepts for top- and bottom-quintile returns, and a combinationofseparateslopesandintercepts,yieldedsimilarresults;thedifferenceswerenotimportantfor myconclusions. 31

net flows to the fund for three years. Consider a change in returns, ∆r , in month t, t definedas: (cid:40) ∆r iffundisfacilitatingtradingabusesinmontht ∆r = t 0 otherwise. If we denote the estimated coefficient on relative return s months ago πt−s, previousyear returns π(t−4,t−5,...,t−12), andthe past three-years’ returns π(t−13,t−14,...,t−36), changes inflow, ∆f,resultingfrom ∆r are:37 t ∆f = ∆r ×πt−1 ∆f = ∆r ×π (t−13,t−14,...,t−36) t+1 t t+13 t ∆f t+2 = ∆r t ×πt−2 ∆f t+14 = ∆r t ×π (t−13,t−14,...,t−36) ∆f t+3 = ∆r t ×πt−3 ∆f = ∆r ×π (t−4,t−5,...,t−12) t+4 t . . . . . . ∆f t+12 = ∆r t ×π (t−4,t−5,...,t−12) ∆f t+36 = ∆r t ×π (t−13,t−14,...,t−36) . If the poor performance persists another month, ∆r t+1 will affect flows in months t+2 through t+37, and so forth. Hence, the cumulative effect of past changes in returns on flowinmonthtis:38 3 12 ∆f t = ∑ ∆r t−s ×πt−s+ ∑ ∆r t−s ×π (t−4,t−5,...,t−12) s=1 s=4 36 + ∑ ∆r t−s ×π (t−13,t−14,...,t−36) . (11) s=13 I plugged this estimated change in net flow into equations (8) and (9) to estimate lost fee revenue. Again, I assumed an annual performance loss ( ∆r) of 3.6 percent, the lowestestimateamongtherisk-adjustedfiguresfromtable4.39 37I compute baseline estimates of flow effects using the linear relative-return coefficients, πp. Since abused funds were disproportionately likely to fall in the lowest-performing quintiles in their categories, Ialsoestimatedfloweffectsusingtherelative-returncoefficientsthatwouldapplytobottom-quintilefunds, thatis,πp+πpL.Thesecoefficientsyieldperformance-relatedrevenuelossesthatare4to6percentsmaller thanthebaselineestimates.Seesection9.2.3. 38Thisomitsanycontemporaneouseffectofperformanceonflows(∆ftisnotincludedinthesummation). Returnsandflowsinagivenmontharelikelysimultaneouslydetermined,andparticularlyinthepresence ofheavymarkettimingflows,theestimatedcoefficientoncurrent-monthreturnsreflectsmorethanjustthe responseofinvestorstopastperformance. Ofcourse, thatresponseismostlikelypositive, sosettingthe coefficienttozeroforthepurposeofestimatingcostsalmostcertainlyunderstatesthem. 39Moreprecisely,thelossisalogarithmicannualizedreturnof-0.036,convertedtomonthlyreturn. The returnsusedinestimatingequation(10)arerelativereturns,whichweresubstantiallylarger—at4.8percent peryear—thanthisestimatedalpha. Whileitwouldbepreferabletoestimateequation(10)usingreturns thathavebeenfullyadjustedforriskinthemannerdescribedinsection5.2,therangeofpast-performance 32

Thelastingeffectofperformancelossesimpliedby(10)isstriking. Onceincurred, poor returns can be expected to weigh on net flows for several years (three years, in the model I estimate, although the literature features models with even longer lasting effects). But the effects on revenue last even longer than the impact on flow, because a dollar of lost assets is, all else equal, lost forever. Of course, a management company could take other actions—advertising or (perhaps) hiring talented portfolio managers, for example—to boost flows and bring assets back, but such actions could have been takenevenifperformancehadneversuffered.40 8.1.2 Comparingrevenuesfromabusive-tradingarrangementstoperformance-related losses. Table7listscumulativerevenuesandcostsforacoupleoftrading-abusescenarios. Panel Areportstheconsequencesofadecisiontofacilitatetheabusesforexactlythreeyears— a choice akin to those made by management companies three years before the scandal revelations finally made the arrangements untenable. Estimated revenues, discussed in section 7, are shown in columns 1 and 2. According to my baseline revenue estimate, management companies would collect $196 million per year for each of the three years and—inthisscenario—nothingthereafter. Revenuescumulatetoabout$600million(and apresentvalueof$500million)fortimehorizonsofthreeormoreyears. Column2shows cumulative fees based on the high-revenue estimate (based on disgorgement amounts), whichhaveapresentvalueof$1.3billionfortimehorizonsofthreeyearsormore. Theperformance-relatedlosses, whichappearincolumn3, accrueslowlyatfirst; theirpersistence,nottheirshort-runmagnitudes,makesthemimportant. Afteroneyear of trading abuses, expected revenue losses due to impaired performance would have cumulated to only about $80 million. After two years, the expected total would have been $0.3 billion, and after three, $0.7 billion. In this scenario, the trading abuses end (by assumption) after the third year, but the losses would continue to grow. By the end of the sixth year, flow would no longer be impaired by poor past performance, but a permanently lower asset base would continue to generated diminished fee revenue. By the tenth year, total expected revenue losses would add up to $5 billion, with a present value of $2.7 billon.41 The expected present value of these costs over an infinite horizon intervalscapturedinthemodelmakesthisinfeasible. 40Moreover, advertising and performance interact positively: Fund families advertise their bestperformingfunds, notlosers(SirriandTufano,1998). So, advertisingwouldpresumablybelesseffective inattractingflowstoafundthathadsufferedpoorperformanceduetotradingabusesthaninboostingthe flowsofanuntainted,better-performingfund. 41Inordertoprojectcostsbeyondthesampleperiod,whichextendsapproximatelythreeyearsafterthe scandalrevelationsformostfirms,Ihadtomakeassumptionsaboutexpectednetreturnsandflowsinthe absenceoftradingabuses.TheresultsIreporthereimbedthemostconservativeassumptions—namely,that ratesofreturnandflowwouldbeequaltothosethatwouldhaveoccurredintheperiodfromroughlythree 33

wouldhavebeen$5billion. The top panel of figure 3 plots the same results: The thick solid (green) line represents the present value of baseline revenues as a function of time horizon, and the thick dotted (green) line traces the high-revenue estimate. The thick dashed (black) line shows performance-related costs. Perhaps a very myopic management-company executive might view collusion with abusive traders as attractive, as estimated revenues ($196millionor$528million)garneredinthefirstyearwouldeasilyexceedtheexpected performance-related loss of $80 million. But as poor performance continued and investors’responsescumulated,collusioneventuallywouldhavebeguntolookfarlessenticing. Dependingontheestimatedrevenuestream,afterthreetofiveyears,discounted cumulatived costs already would have exceeded discounted cumulative revenues. The present value of infinite-horizon costs ($4.7 billion) would exceed the present value of baselinerevenues($0.5billion)bynearlyanorderofmagnitude,andwouldexceedeven the high estimate of revenues ($1.3 billion) by a factor of three. Even without consideration of the consequences of getting caught, which include both official and market penalties (discussed below, and shown in columns 4, 5, and 6 of table 7), the deals with abusivetradersshouldhavebeenveryunattractive. And what if management companies had expected that their abusive-trading arrangements would remain confidential? If so, as shown in panel B of table 7 (and plotted in the lower panel of figure 3), they might have anticipated accommodating market timersindefinitelyandcollectingannualrevenuesof$196million(or$528million),with apresentvalueof$1.8billion($4.8billion). However,thepresentvalueofperformancerelatedcostswouldhaveexceeded$8billion. Collusionwithabusivetradersisapuzzle; this analysis indicates that if management companies had acted in their own interests, thetrading-abusescandalwouldneverhavehappened. 8.1.3 Performance-relatedrevenuelossesandagencyconflictsbetweenmanagement companiesandmutualfundinvestors My results do not imply that the possibility of performance-related asset losses can resolve all agency conflicts between mutual fund investors and management companies. The abusive trading arrangements were uneconomical in part because the companies claimed only a small share of the investors’ lost wealth. The estimated gains to abusive traders were a small portion of the damage they did to fund returns, and management companiescollectedsmallsharesofthegainsfromabusivetrading. yearsbeforethescandalrevelationstoaboutthreeyearsafterwards,hadtherebeennotradingabuses.Even adjusting for the effects of the abuses, however, returns and net flows over this period were quite paltry. HadIbasedexpectedreturnsandflowsonalongerhistory—say,tenyearsofdata—expectedassetgrowth wouldhavebeenmuchmoresolid,sothecostsofpoorperformance,whicharecomputedasafractionof assets,wouldhavebeenconsiderablylargerindollarterms. 34

However,ifmanagementcompanieshadbeenabletoclaimalargershareofmutual fund shareholders’ losses, the companies’ financial incentives might have been different. Consider an extreme counterfactual example: Had a management company just secretly skimmed 1 percent of its mutual funds’ assets each year, revenues would have exceeded the performance-related costs, as estimated in this paper, by almost an order of magnitude. Figure 4 shows the discounted cumulative revenues and costs from such ahypotheticalscenario,undertheassumptionthattheasset-skimmingwentundetected forever. Thus, leaving ethical and legal considerations aside, if a management company couldskiminvestors’wealthsecretly,itwouldhaveafinancialincentivetodoso,despite theeffectsonfundperformanceandexpectedfutureinflows. 8.2 Thecostsofgettingcaught 8.2.1 Reputation-relatedoutflowsfollowingthescandalrevelations Management companies’ arrangements with abusive traders, which should have been unattractiveevenifthecollusionhadbeenundetectable,begantolookquiteuglyindeed in September 2003 as the deals made regular headlines. The news prompted a swift, sharp reaction from investors who held shares in tainted mutual fund families. Heavy redemptions—above and beyond the response to impaired performance—began immediately and continued for several years. To estimate the magnitude of the shareholder reaction,anditseffectonmutualfundrevenues,Iincludedinequation(10)twosetseach of48monthlydummyvariables,indexedbys ∈ [−12,35],whichatdatettakethevalues: (cid:40) 1 iistaintedorabusedands = t−V DScandal = i ist 0 otherwise (cid:40) 1 iisabusedands = t−V DAbused = i ist 0 otherwise. Here,V isthescandal-revelationdatefori’sfamily. Inmontht,thedummyvariableD i ist is zero unless month t is exactly s months after the initial revelations that i’s family had madearrangementswithabusivetraders.42 Estimated coefficients βScandal and βAbused are plotted in figure 5, along with 95s s percentconfidenceintervals. Inthe12monthspriortothescandalrevelations,netflows to tainted mutual funds (shown in the top panel of the figure) were not statistically distinguishable from those to their peers. However, news that a family had struck deals to allowabusivetradesinsomeofitsmutualfundspromptedanimmediatedeclineinnet flowstoitsother(tainted)mutualfunds. Controllingforotherdeterminantsofnetflows, 42In this framework, estimated coefficients βScandal measure abnormal net flows to tainted funds, and s βScandal+βAbusedmeasurethetotalabnormaleffectonabusedfunds. s s 35

onemonthafterthenews,theflowstotaintedfundswere1.1percentagepointsofassets less than flows to their untainted rivals. While net flows rose to more typical magnitudesovertheremainderoftheyear,onthewholetheyremainedabnormallylowforthe threeyearsfollowingthescandal. Althoughindividualmonthlydummycoefficientsfor taintedfundsarenotallsignificantlylessthanzero,annualizednetflowforthesefunds averaged a statistically significant 2.5 percentage points below normal even in the third year—months24through35—followingthescandalrevelation. The abused mutual funds fared much worse. The lower panel plots the additional impact of news that a particular fund was itself abused through arrangements with timers: Net flows were a further 1.7 percentage points below average in the first monthafterthescandalrevelations,andremainedsignificantlybeloweventhoseoftheir tainted peers in every month for three years following the news. Annualized net flows toabusedfundsinthethirdyearfollowingthescandalnewswere10.4percentagepoints belowthosetotaintedfundsand12.6percentagepointsbelowthosetountaintedmutual funds.43 Figure 6 plots the cumulative effects of the scandal revelations on net flows. I cumulateflowsfrom12monthspriortothescandalrevelationstohighlightanyabnormal flowspriortothenewsofillicitbehavior. Amongtaintedfunds,controllingforpastperformance and other correlates of flow, there is little evidence of abnormal flow prior to the scandal news. But by the end of the third year after that news broke, reputationrelatedoutflowshadreducednetassetsundermanagementintaintedfundsby8percent onaveragecomparedwithassetsinfundsatnon-taintedfamilies. As shown by the red line in figure 6, abused funds attracted abnormally low net flows in the year prior to the scandal news, but once the scandal broke, outflows accelerateddramatically. Abnormalflowscumulatedfromoneyearbeforethescandalbroke totheendofthethirdyearafterwardsaveraged39percentofassetsundermanagement. Abnormallylowflowafterthescandalbrokecutassetsundermanagementbyacumulative37percent. Tocomputetherevenuelossesduetothereputation-relatedoutflows,Iaddedthe predicted impact on net flows, estimated in equation (10), to ∆f in equation (8), and t recalculated equation (9).44 Results are shown in column 4 of the top panel of table 7 and plotted as the very thick (red) line in the top panel of figure 3. Outflows prompted by the scandal revelations cost management companies an estimated $2.3 billion in rev- 43Becauseallfloweffectsareestimatedinlogarithmicterms,thereputation-relatedoutflowsforabused fundsarecomputedmultiplicatively,basedonthe2.5percentage-pointlossfortaintedfundsandtheadditional10.4percentage-pointlossforabusedfunds:12.6percent=1−(1−0.104)(1−0.025). 44Becausenetflowstoabusedfundswereapproximately0.3percentagepointsbelowaverageevenin theyearbeforethescandalnews,Isubtracttheaverageabnormalnetflowoverthe12monthspriortothe scandalfromeachestimateddummycoefficient,βAbused,toobtaintheestimatedscandal-newseffectforeach s month. 36

enues in the first three years after the scandal broke (that is, through year six after the initialdecisiontocolludewithmarkettimers). Toestimatethecostofreputation-related outflowsbeyondthesampleperiod, Iassumedthatoutflowfouryearsafterthescandal revelationsishalftheaveragethatprevailedinthethirdyear,thatoutflowfiveyearsafterwardisone-quarterthatofthethirdyear,andsoforth(thatis,thatoutflowsafterthree yearshaveahalf-lifeofoneyear).45 Usingthisapproach,Iestimatedthatthereactionof shareholders to the scandal will cost management companies $8.6 billion over the first sevenyearsfollowingthescandalnews—afigurefarinexcessoftherevenuesthatabusive trading generated for management companies, and substantially greater than even the performance-related losses. The discounted present value of the lost revenue due to reputation-relatedoutflowsoveraninfinitehorizonwouldbenearly$10billion. 8.2.2 Officialpenalties Asdiscussedinsection4.2,managementcompanies’arrangementswithabusivetraders ultimately prompted a slew of official investigations by several state prosecutors, the SEC, and other government agencies. The civil penalties, disgorgement, and mandated feereductionsthatfollowedaresummarizedintable2. AsZitzewitz(2007b)pointsout, thenetcostofagovernment-imposedfeereductionforaprofit-maximizingfirmmaybe considerably smaller than the nominal amount of the cut; at the margin, profits should beunaffectedbychangesinfees. Thus,penaltiesexcludingthe$1.1billioninmandated fee reductions (column 8) are probably most relevant to an analysis of the costs of the abusive-tradingdeals. Also,forthepurposesoftallyingupthecostsoftradingarrangements for management companies, I subtracted off the $5 million in penalties levied on non-executiveemployees(columns6and7). Idoincludepenaltiespaidbyseniorexecutives,however.46 Adjustedpenalties,shownincolumn12,sumto$2.6billion. Penalties and fee reductions are also summarized in columns 5 and 6 of table 7 andplottedintheupperpaneloffigure3. Whilethepresentvalueofthepenaltiesalone surpassedthatoftheestimatedrevenuesgeneratedbytheabusive-tradingarrangements, themarketpenalties—revenueslostbecauseofpoorperformanceandreputation-related netredemptions—dwarfedtheofficialpenalties. 45Alsoseenote41. 46Astheprimarydecisionmakers—andsometimesthelargestshareholders—intheirfirms,theseprincipalsmadedecisionsthatsimultaneouslyaffectedtheirindividualfortunesandthoseoftheirfirms, and ananalysisoftheirdecisionstoprofitfromtradingabuseprobablycannotcleanlysegregateexpectedrevenuesandcostsforindividualsandfirms. Asdiscussedabove,Iincludeincompany-revenueestimatesthe gainsthatmanagementcompanyexecutivesandemployeesobtainedbyabusingtheirownmutualfunds. In consideringcosts,however,Ionlyincludethepenaltiesassessedagainstindividualswhoweretheprimary decisionmakersattheirfirms:chairmen,chiefexecutiveofficers,andpresidents. 37

8.2.3 Privatecivillitigation Mutual fund management companies that colluded with market timers have faced private lawsuits, in addition to official and market penalties. As of this writing, 17 mutual fund firms were embroiled in private litigation, and none has yet settled with plaintiffs (Isbister,2008). Settlementamountsunderdiscussionareconfidential,soIcannotinclude thosecostsinmyestimates. 9 Whydidtheydoit? Themanagementcompaniesthatstruckdealstobenefitfromabusivetradesintheirmutualfundsmadewhatturnedouttobeverypoordecisions. Thecostsofgettingcaught— officialpenalties(withorwithoutthemandatedfeereductions)andreducedfeerevenue due to reputation-related redemptions—exceeded my high estimate of revenues from these deals by nearly an order of magnitude (compare columns 4 through 6 in table 7 with column 2). But if these had been the only possible costs of the abusive-trading arrangements, such deals still might have made sense ex ante if management companies hadeitherplacedverylowoddsondetectionorunderestimateditsconsequences. What they expected is a matter of conjecture, although there is some evidence that management company insiders were well aware of the potential fallout from getting caught. OneSeligmanemployeewarned,ina2002memotothecompanypresident: Iwritethismemotobringtoyourattentionanescalatingproblemthatthreatenstheperformanceofourfunds,andthereforeourlivelihood. Itisthepractice of NAV arbitrage by professional traders (usually hedge funds), which loots percentage points in total return from the funds these traders utilize. Thepracticethreatensthefutureoffundcompaniesthatdon’tunderstandits effect on their long-term returns. In addition, it is a ticking time bomb for the entire mutual fund industry, set to go off the day the press realizes that fundcompaniesroutinelysellthereturnsearnedbytheshareholdersoftheir fundstoshort-termtraders(AttorneyGeneraloftheStateofNewYork,2006, Exhibit1). But as the memo suggests, and this paper confirms, the “ticking time bomb” of possibledetectionwasnottheonlydeleteriousconsequenceofabusive-tradingarrangements. Theharmfuleffectsoftradingabusesonmutual-fundperformanceandtheresulting costs to management companies would have been incurred without any revelations in the press. In light of these costs, deals with abusive traders did not make economic sense for management companies, even if they had correctly assumed that they would neverbecaught. Addingthepotentialcostsofdetectiontotheperformance-relatedlosses 38

makesthedecisiontocolludewithabusivetraderslookquitepuzzlingindeed. Whydid managementcompaniesdoit? 9.1 Anagencyproblem—withinmanagementcompanies Managementcompaniesthemselvesdidnotchoosetocolludewithabusivetraders;some principals and employees of those companies did. Management company executives whostrucksuchdealshurttheirfirmsandtheownersofthosefirms. Yet, evidencepresented in official complaints, cease-and-desist orders, and similar documents indicates that in justifying arrangements with abusive traders, executives typically argued that tradingarrangementswouldboostassetsundermanagementandfeeincome—andthey were right, but only in the short run. To the extent that managerial contracts rewarded executives for short-run asset growth, their decisions would have been less mysterious. That is, a classic agency problem arising from the different objectives of the owners and managers of asset management firms might have been partly to blame for the mutual fundscandal. Interestingly, in the wake of the scandal, this form of agency conflict has drawn relatively little attention from policy makers and researchers, who have mostly focused onthefiduciaryconflictsofinterestbetweenmutualfundshareholdersandmanagement companies,ratherthantheowner-managerconflictsbetweenmanagementcompanyshareholdersandthemanagersofthosefirms.47 Becausetheregulatoryoversightofmanagement companies centers on their fiduciary responsibilities to mutual fund investors, the policy response to the scandal naturally addressed the breach of fiduciary duty evident inthetrading-abusearrangements. Forexample,afterthescandalerupted,theSECproposed rules to increase the fraction of independent members on the boards of mutual funds (not on those of management companies) and require that board chairs be independent (U.S. Securities and Exchange Commission, 2006b).48 Academic studies of the role of governance and incentives in the mutual fund scandal have generally focused on governance of mutual funds, rather than that of management companies (Mahoney, 2004; Tkac, 2004; Qian, 2006).49 A notable exception is Zitzewitz (2003), who—writing beforethescandalbroke—arguedthat“fundmanagementcompanieshaveasubstantial interestinreducingdilution,”largelybecauseoftheresponseoffutureflowstothepoor performance of abused funds. Observing rampant dilution problems in mutual funds, 47Thedistinctionisimportantbutcanbelostintheambiguityof“shareholder”inthiscontext. Amanagementcompanymustservetheinterestsoftwotypesofshareholders: investorsinthethemutualfunds thatthecompanyoperatesandtheownersofthemanagementcompanyitself. Igenerallyrefertoconflicts betweenmutualfundinvestorsandmanagementcompaniesasexternalorfiduciaryconflicts,andconflicts betweenmanagementcompanies’ownersandexecutivesasinternalorowner-managerconflicts. 48TheproposedruleswererejectedtwicebytheU.S.CourtofAppealsandhavenotbeenadopted. 49Qian,forexample,studiesgovernancebylookingatthecompositionofmutualfundboardsbutnotthe boardsofthemanagementcompanies. 39

Zitzewitzconcludedthat“thereisanotherlayerofagencyproblemsinsidemanagement companies.” To be sure, the fiduciary conflicts between mutual fund shareholders and management companies are important; their regulation is the objective of many of the provisionsoftheInvestmentCompanyActof1940. Moreover,asdiscussedinsection8.1.3, the primary channel by which these conflicts are governed in the marketplace, through theeffectsofperformanceonassetsundermanagement,isinsufficienttodiscouragemutual fund managers from simply expropriating assets from investors—hence the importanceofregulation. Butthispaper’sresultsindicatethattheincentivesshouldhavebeen strong enough to prevent management companies from expropriating investors’ wealth indirectly by arranging deals with abusive traders. Thus, the fiduciary conflict between mutualfundshareholdersandmanagementcompaniesshouldnothavebeenaproblem when the latter were offered small shares of the gains from dilutive trades. The ownermanager conflict between management company shareholders and executives, however, appearstohaveplayedacrucialroleinthemutualfundscandal. Owner-managerconflictsaremoredifficulttosquarewithsomeofthebehaviorin the scandal, however. For example, several principals who owned substantial shares of their asset management firms, including PBHG, RS Investments, Seligman, and Strong, nonetheless chose to accommodate abusive traders, and even to market time their own funds.50 And several of the management companies were affiliates of much larger financial corporations, which presumably would have understood the conflicts facing asset managers and prevented them from risking a parent firm’s fiduciary reputation by buildingassetsthroughdealswithabusivetraders. 9.2 Otherexplanations? Below, I consider some alternative explanations for my empirical findings and for managementcompanies’decisionstocolludewithabusivetraders. 9.2.1 Theactionsofrogueemployees? An alternative explanation for the scandal might be that the trading arrangements were the unauthorized work of a few rogue employees who sought strictly personal gain. However,collusionwashardlytheworkofisolatedlow-levelemployeesactinginsecret: 50Thegainsfromone’sownmarkettimingfarexceededtherevenuesobtainedbyaccommodatingothers’ tradingabuses,sothefactthatRichardStrongandGaryPilgrimbenefitteddirectlyfromthetradingabuses mayhelpexplainwhy theychosetoallowthem. Evenso, itishardto imaginethatthe$1.6millionthat Stronghimselfnettedthroughhistimingactivitycouldpossiblyhaveoutweighedtherisktothevalueof his85percentstakeinStrongFinancialCorporation(AttorneyGeneraloftheStateofNewYork,2004b;U.S. SecuritiesandExchangeCommission,2004c). 40

Evidence presented in official documents indicates that at 15 of the 20 tainted firms, decisionstofacilitateabusivetradingweremadeorapprovedbytopexecutives(chairmen, chief executive officers, and presidents), and senior executives were culpable at most of the other firms. Top executives at half of the tainted firms paid substantial penalties for their parts in the scandal (see table 2). Executives chose to accommodate market timers inmostcasesdespitewarningsfromportfoliomanagers,complianceofficers,andothers thattheabusivetradingwashurtingfundperformanceand,ultimately,themanagement company. 9.2.2 Endogeneityofperformanceandabusive-tradingarrangements Another possible interpretation of the link between abusive-trading arrangements and the poor performance of abused mutual funds is that lousy returns led to bad decisions. Ifso,attributingtheabnormalreturnsofmutualfundstotradingabusewouldbewrong. Instead, it might be the case that executives at mutual fund families with unattractive funds inked arrangements with abusive traders because those executives thought they hadlittletolose. The timing of the abusive-trading arrangements, estimated dilution, and the deteriorationofperformanceamongabusedmutualfundssuggestsotherwise: Tradingarrangementstypicallyprecededpoorreturns. Mostofthemutualfundfamiliesthatstruck deals with abusive traders first did so in early 2000 or before, when they were still, on average,outperformingtheirpeers(seefigure2).51 Moreover,dilution—whichisunambiguouslycausedbyabusivetradingandwhich contributedto poor performance—increasedsubstantiallyatthe sametimethat abusive trading by arrangement, as recorded in official documents, was ramping up. Part of the storybehindthesurgeinmarkettimingactivityaround2000mayhavebeenthedissemination of information about the profitability of market timing. For example, Zitzewitz (2003)arguesthatthecirculationofseveralacademicpapersin1999and2000thathighlightedthepotentialprofitabilityofmarkettimingpromptedanincreaseindilution. My estimates of dilution in abused funds—computed independently of relative returns and unambiguouslyrelatedtoabusivetrading—doubledbetween1999to2000andthendoubledagainin2001. 51Tobesure, therewereinstancesinwhichdecliningmanagedassetspromptedcollusionwithmarket timers. OnenoteworthycasewasFredAlger, whichhadofficesintheWorldTradeCenterandtragically lostmanyemployeesintheSeptember2001terroristattacks. Concernsaboutthefirm’sabilitytocontinue operations(notpoorperformance)apparentlypromptedshareholderredemptionsofitsmutualfunds. AlthoughAlgerManagementalreadyhadarrangementswithselectedmarkettimersbeforeSeptember2001, thedeclineinassetsafterthetragedyconvincedseniorexecutivestocourtmarkettimersmoreaggressively (U.S.SecuritiesandExchangeCommission,2007b). 41

9.2.3 Smallerlossesforpoorperformers? A related possibility is that I have overstated the effects of poor performance on flow by using estimated coefficients, πp, from equation (10) that apply to the middle of the returns distribution. However, abused funds were disproportionately likely to fall in the lowest-performing quintiles in their categories, and as shown in column 1 of table 6, the flow response to relative returns in the bottom quintile was on average smaller than the response to relative returns in the middle quintiles (column 2). Performancerelated losses computed from estimated coefficients that would apply to low-quintile funds (πp +πpL, the sum of columns 1 and 2) are indeed smaller, but only by 4 to 6 percent—not nearly enough for a management company with poorly performing funds tojustifycollusionwithabusivetraders. Itappearsthatthemanagersofeventhepoorestperformingmutualfundshadalottoloseinmakingarrangementswithabusivetraders. 9.2.4 Wereinvestorsattaintedfamilieslessresponsivetopastperformance? Qian (2006) argued that the investors who held mutual funds at tainted families were less sensitive to past performance and so provided less effective monitoring and disincentives for arrangements with abusive traders. However, when I estimated equation (10) using only data for tainted mutual fund families through August 2000, I found that the estimated flow sensitivity to relative returns was larger for these funds than for the full sample. Thus, the expected performance losses for the tainted families should have providedstrongincentivesagainstarrangementswithabusivetraders. 9.2.5 Highdiscountrates? Onepossibleexplanationformanagementcompanies’behavioristhattheysimplyfailed to recognize the long-term consequences of impaired performance on their own future revenues. While internal communications show that managers and executives at most tainted families were well aware that trading abuses cut into returns, I am not aware of anythatanalyzedthemagnitudeofpotentiallossesinassetsundermanagementdueto poorreturns. Evidence from the literature on the economics of crime indicates that violent offenders tend to have high subjective discount rates (see, for example, Lee and McCrary, 2005). The applicability of this finding to white-collar crime and financial malfeasance is not clear, but with sufficiently high discount rates, the more immediate benefits of arrangementswithabusivetraderswouldoutweightheexpectedcosts,whichareincurred with some delay. For example, discount rates exceeding 36 percent at an annual rate would rationalize management companies’ decisions to accommodate abusive traders permanently,undertheassumptionsthattheabusive-tradingarrangementswouldnever 42

berevealedandthatfundcompaniescollectedhigh-estimaterevenues($528millionannually) from the arrangements. Even higher discount rates would be needed to rationalizeshorter-durationarrangements; three-yeardealswouldhavemadesenseonlyfor discountratesexceeding42percent(andazeroexanteprobabilityofgettingcaught). 10 Conclusion Conflictsofinterestbetweenassetmanagementfirmsandbuy-and-holdmutualfundinvestorsseldomhavebeenasapparentasinthemutualfundscandalthatmadeheadlines inlate2003. Theassetmanagementfirmsthatsoughttoshareinthegainsfromabusive trading breached their fiduciary duties to mutual fund shareholders and, in the aggregate, cost them billions of dollars. Prosecutors were quick to frame the scandal as the outcome of such conflicts; a State of New York assurance of discontinuance provided a typicaldescriptionoftheproblem: By placing their own interest in generating compensation from short-term or excessive trading above the interests of long-term shareholders to whom this trading posed a risk of harm, and by failing to disclose these arrangementsandtradingandtheconflictsofinteresttheycreated,[themanagement company]engagedinfraudulentconduct...(AttorneyGeneraloftheStateof NewYork,2005b). Regulatorsrespondedwithreformproposalsintendedtoreinforcemutualfundinvestors’ interestsvis-a-visthoseofmanagementcompanies. Thescandalalsohaspromptedacademic research on the link between mutual fund governance and abusive-trading arrangements. Thispapershows,however,thatthefiduciaryconflictsbetweenmutualfundshareholdersandthefirmsthatmanagetheirfundswereunlikelytohavebeentheonlyexplanation for the mutual fund scandal. A particularly salient aspect of this scandal is that asset management companies struck deals that harmed mutual fund investors and the managementcompaniesthemselves. Evenifthecompanieshadcorrectlyassumedthattheir transgressionswouldneverbedetected,theymadedecisionsthatwerenotintheirown long-term interests. Why they did so remains something of a puzzle. Agency conflicts within the management companies—between their owners and executives—may have playedanimportantrole; executivesmayhavecutdealsthatfurtheredtheirownshortterm interests to the detriment of their firms. Some executives may have been simply unaware of the full costs of abusive trading to their firms, or they may have discounted tooheavilythelong-termcostsoftheabuse. My results suggest a new interpretation of the lessons of the mutual fund scandal, as this was not a simple example of profitability outweighing fiduciary duties. The 43

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Table 1. Tainted mutual fund families. (1) (2) (3) (4) Assets under Assets under Date Number of management in management publicly abused abused funds Fund Complex (billions of dollars)* implicated funds (billions of dollars)* Alliance 51.8 Sep 2003 10 22.2 Bank One ‐ One Group 40.6 Sep 2003 3 2.2 Banc of America ‐ Nations 30.3 Sep 2003 13 12.0 Columbia ‐ Fleet ‐ Liberty 49.1 Jan 2004 18 22.1 Deutsche ‐ Scudder ‐ Kemper 61.0 Jan 2004 22 12.7 Federated 47.8 Oct 2003 8 17.3 Franklin Templeton 124.4 Feb 2004 4 30.5 Fred Alger 3.1 Oct 2003 4 1.8 Fremont 2.9 Nov 2003 2 1.5 Invesco/AIM 76.1 Nov 2003 7 13.1 Janus 98.3 Sep 2003 7 24.8 Massachusetts Financial Services 73.1 Dec 2003 9 44.4 Pilgrim Baxter (PBHG) 6.4 Nov 2003 5 2.7 PIMCO 132.3 Feb 2004 6 18.5 Putnam 143.6 Oct 2003 10 37.5 RS Investments 4.1 Mar 2004 1 1.5 Seligman 9.1 Jan 2004 7 6.6 Strong 24.8 Sep 2003 5 3.1 Wachovia ‐ Evergreen 46.2 Aug 2004 3 1.7 Waddell & Reed 19.4 Jul 2006 1 0.8 Industry Totals 1044.3 145 277.0 * Assets under management as of August 30, 2003. Data for long‐term mutual funds only (money market funds are excluded).

Table 2. Official penalties and mandated fee reductions (millions of dollars) (1) (2) (3) (4) (5) (6) (7) (8) (9) Other State‐ Management Management Executive employee Other mandated company civil company Fund civil Executive civil employee fee Total Fund Complex penalties disgorgement restitution penalties disgorgement penalties disgorgement reductions penalties Alliance 100 150 0 0.7 0.0 0.2 0.0 350 601 Bank One ‐ One Group 40 10 0 0.1 0.0 0.0 0.0 40 90 Banc of America ‐ Nations 125 250 0 0.0 0.0 0.2 0.0 160 535 Columbia ‐ Fleet ‐ Liberty 70 70 0 0.0 0.0 0.3 0.0 0 140 Deutsche ‐ Scudder ‐ Kemper 26 103 0 0.0 0.0 0.1 0.1 86 215 Federated 45 27 8 0.0 0.0 0.0 0.0 20 100 Franklin Templeton 25 30 0 0.0 0.0 0.0 0.0 0 55 Fred Alger 10 30 0 0.0 0.0 0.4 0.0 5 45 Fremont 2 2 0 0.1 0.0 0.0 1.0 0 5 Invesco/AIM 142 235 0 0.6 0.0 0.4 0.0 75 453 Janus 51 50 32 0.0 0.0 0.0 0.0 125 258 Massachusetts Financial Services 50 175 0 0.5 0.1 0.0 0.0 125 351 Pilgrim Baxter (PBHG) 50 40 0 40.0 120.0 0.0 0.0 10 260 PIMCO 58 8 2 0.5 0.3 0.0 0.0 0 69 Putnam 100 54 0 0.0 0.0 0.8 0.7 0 155 RS Investments 14 12 0 0.3 0.0 0.0 0.0 5 30 Seligman 0 0 6 0.0 0.0 0.0 0.0 0 6 Strong 40 40 0 30.0 30.0 0.4 0.4 35 176 Wachovia ‐ Evergreen 4 29 0 0.2 0.0 0.0 0.0 0 33 Waddell & Reed 12 40 0 0.0 0.0 0.0 0.0 25 77 Industry Totals 963 1,354 47 72.9 150.5 2.7 2.2 1,061 3,654

Table 2 (continued). Official penalties and mandated fee reductions (millions of dollars) (9) (10) (11) (12) (13) (14) Penalties excluding Penalties excluding Total fee reductions and Estimated fee reductions disgorgement and employee fines dilution Maximum of Total (column 9 less restitution (columns (column 10 less (Zitzewitz, penalties and Fund Complex penalties column 8) 2, 3, 5, 7) columns 6 & 7) 2007b) dilution* Alliance 601 251 150 251 64 251 Bank One ‐ One Group 90 50 10 50 20 50 Banc of America ‐ Nations 535 375 250 375 117 375 Columbia ‐ Fleet ‐ Liberty 140 140 70 140 89 140 Deutsche ‐ Scudder ‐ Kemper 215 129 103 129 268 268 Federated 100 80 35 80 96 96 Franklin Templeton 55 55 30 55 479 479 Fred Alger 45 40 30 40 43 43 Fremont 5 5 3 4 19 19 Invesco/AIM 453 378 235 377 378 378 Janus 258 133 82 133 255 255 Massachusetts Financial Services 351 226 175 226 35 226 Pilgrim Baxter (PBHG) 260 250 160 250 282 282 PIMCO 69 69 10 69 41 69 Putnam 155 155 54 154 246 246 RS Investments 30 25 12 25 70 70 Seligman 6 6 6 6 none 80 Strong 176 141 70 140 14 141 Wachovia ‐ Evergreen 33 33 29 33 none 33 Waddell & Reed 77 52 40 52 45 52 Industry Totals 3654 2593 1554 2588 2561 3553 *Maximum of columns 10 and 13. Figure for Seligman comes from NYAG complaint.

Table 3. Some estimates of losses to buy‐and‐hold investors Losses Losses Type/Study Group of interest Period (percent, estimated annual rate) Pre‐scandal studies 1. Greene & World equity funds with 1998‐2000 Dilution 0.94 Hodges highest flow activity (2002) 2. Zitzewitz Regionally focused world 1998‐2001 Dilution 1.60 (2003) equity funds General international funds 1998‐2001 Dilution 0.81 Precious‐metal funds 1998‐2001 Dilution 1.17 3. Zitzewitz International equity 1998‐2000 Dilution due to 0.06 (2006)* late trading Domestic equity 1998‐2000 Dilution due to 0.02 late trading Post‐scandal studies 4. Zitzewitz Scandal‐tainted families 2000‐2003 Dilution 0.49 (2007b) (international equity) 5. Houge & Scandal‐tainted families 2001‐2003 Raw returns 0.15 Wellman (only equity funds affected) (2005) 6. Schwartz & Scandal‐tainted families 2000‐2003 Risk‐adjusted 0.83 Potter (2006) (domestic equity) returns 7. Qian (2006) Scandal‐tainted funds 2000‐2003 Risk‐adjusted 0.34 returns Abused funds 2000‐2003 Risk‐adjusted 1.95 returns 8. This study Abused funds 2000‐2003 Risk‐adjusted 3.62 (all types) relative returns *Written after mutual fund scandal broke, but similar to pre‐scandal papers in that dilution was estimated by investment objective rather than by whether a fund had been identified as having allowing late trading.

Table 4. Abnormal performance of scandal‐tainted and abused mutual funds (1) (2) (3) (4) (5) Alpha based Alpha based Alpha based Alpha based on on category‐ on market risk on category category Relative performance factors performance performance, Dependent variable return risk factors (incl. Nasdaq) plus Nasdaq using net returns Panel A. September 2000 to August 2003 (three years before the scandal broke) Constant (c ) 0.90 0.64 2.73 0.57 0.30 0 (7.74) (7.26) (31.09) (6.62) (3.47) Abused (γ ) ‐4.86 ‐3.69 ‐4.37 ‐3.62 ‐3.62 1 (‐6.57) (‐6.83) (‐8.05) (‐6.89) (‐6.77) Tainted (γ ) ‐0.83 ‐0.62 ‐0.89 ‐0.60 ‐0.63 2 (‐3.33) (‐3.35) (‐4.71) (‐3.37) (‐3.44) Log of assets x 10‐5 (ξ) 2.24 1.81 1.14 2.02 4.04 (0.88) (1.06) (0.68) (1.19) (2.22) R‐squared 0.013 0.013 0.019 0.013 0.013 Number of obs. 5040 5040 5040 5040 5040 Panel B. January 2004 to December 2006 (three years after the scandal broke) Constant (c ) ‐0.57 ‐0.69 2.29 ‐0.52 ‐0.99 0 (‐12.95) (‐15.13) (42.11) (‐11.98) (‐21.43) Abused (γ ) 0.05 ‐0.57 ‐0.02 ‐0.18 ‐0.49 1 (0.17) (‐2.03) (‐0.07) (‐0.72) (‐1.76) Tainted (γ ) 0.18 0.28 ‐0.12 0.22 0.27 2 (2.05) (3.03) (‐1.04) (2.56) (2.91) Log of assets x 10‐5 (ξ) 2.94 3.68 2.57 2.71 5.26 (4.32) (5.30) (3.80) (4.82) (6.06) R‐squared 0.003 0.006 0.001 0.003 0.009 Number of obs. 4984 4986 4986 4986 4986 Notes. Unit of observation for each regression is a mutual fund. Dependent variable units are 100 times logarithm of annual returns. Figures in parentheses are t‐statistics based on robust standard errors. See text for discussion of risk factors used to derive each dependent variable.

Table 5. Mutual fund companiesʹ share of abusive‐trading revenues from selected arrangements (1) (2) (3) Net gains Fees earned by Management of market management company timers company share Fund Complex ($ millions) ($ millions) (percent) Alliance 64.0 4.8 7.0 Banc of America ‐ Nations* 16.7 12.5 42.8 Columbia ‐ Fleet ‐ Liberty 30.4 0.5 1.6 Deutsche ‐ Scudder ‐ Kemper 32.7 1.3 3.7 Federated 4.4 0.4 8.8 Janus 15.7 0.8 5.0 Pilgrim Baxter (PBHG) 9.0 0.7 7.1 Wachovia ‐ Evergreen 0.4 0.0 6.2 Waddell & Reed 8.2 3.6 30.8 Industry Totals 181.4 24.6 12.0 Adjusted for internal trading abuse 12.4 Weighted by: Assets in abused funds 8.6 Total dilution 10.2 Total penalties 16.6 * Management company fees include revenues of affiliates, such as Banc of America Securities. The share of revenues captured by the management company itself (Banc of America Capital Management) was 2.2 percent.

Table 6. Flow response to relative and category returns Relative returns Category returns (1) (2) (3) (4) (5) (6) bottom‐ top‐ bottom‐ top‐ quintile mid‐ quintile quintile mid‐ quintile increment distribution increment increment distribution increment current month ‐3.06 11.46 1.62 ‐6.77 14.80 0.22 (‐2.67) (12.49) (1.30) (‐10.25) (23.71) (0.35) monthly, 1 lag ‐2.70 12.26 2.19 ‐2.39 9.78 1.37 (‐2.44) (13.74) (1.85) (‐3.80) (16.91) (2.36) monthly, 2 lags ‐1.02 10.09 ‐0.96 ‐4.16 8.95 ‐0.08 (‐0.93) (11.75) (‐0.79) (‐6.81) (16.36) (‐0.14) monthly, 3 lags ‐1.54 10.54 0.14 ‐1.20 5.58 2.54 (‐1.55) (13.35) (0.12) (‐1.95) (10.67) (4.49) annual ‐0.11 6.05 2.27 ‐1.99 5.17 ‐0.79 (‐0.29) (20.80) (5.00) (‐6.42) (23.43) (‐4.51) 3‐year ‐0.29 3.32 0.90 ‐0.41 0.88 0.49 (‐1.12) (16.35) (3.18) (‐2.13) (6.22) (4.39) Number of observations 918,407 Adjusted R2 0.180 Notes. Dependent variable is 100*ln(1+flow/lagged assets). t‐statistics in parentheses are based on robust standard errors for data clustered by mutual fund. Regression includes time and share‐class fixed effects.

Table 7. Revenues and costs of cheating (billions of dollars) Revenues Costs (1) (2) (3) (4) (5) (6) Time Based on Based on Performance‐ Reputation‐ Mandated Horizon penalties and disgorge‐ related related Official fee (years) dilution ment losses outflows penalties reductions Panel A. Trading abuses allowed for three years and are then detected Cumulative revenues and costs (not discounted) 1 0.2 0.5 0.1 0.0 0.0 0.0 2 0.4 1.1 0.3 0.0 0.0 0.0 3 0.6 1.6 0.7 0.0 0.0 0.0 6 0.6 1.6 2.6 2.3 2.6 0.5 10 0.6 1.6 5.0 8.6 2.6 1.1 Discounted present value* 1 0.2 0.5 0.1 0.0 0.0 0.0 2 0.4 0.9 0.3 0.0 0.0 0.0 3 0.5 1.3 0.6 0.0 0.0 0.0 6 0.5 1.3 1.7 1.3 1.8 0.3 10 0.5 1.3 2.7 4.0 1.8 0.6 ∞ 0.5 1.3 4.7 9.9 1.8 0.6 Panel B. Trading abuses allowed forever and are never detected Cumulative revenues and costs (not discounted) 1 0.2 0.5 0.1 0.0 0.0 0.0 2 0.4 1.1 0.3 0.0 0.0 0.0 3 0.6 1.6 0.7 0.0 0.0 0.0 6 1.2 3.2 3.3 0.0 0.0 0.0 10 2.0 5.3 8.5 0.0 0.0 0.0 Discounted present value* 1 0.2 0.5 0.1 0.0 0.0 0.0 2 0.4 0.9 0.3 0.0 0.0 0.0 3 0.5 1.3 0.6 0.0 0.0 0.0 6 0.9 2.3 2.1 0.0 0.0 0.0 10 1.2 3.2 4.3 0.0 0.0 0.0 ∞ 1.8 4.8 8.3 0.0 0.0 0.0 Notes. Based on a 3.6 percentage‐point reduction in relative return due to trading abuses. *As of the beginning of the period in which trading abuses are allowed, using a weighted average cost of capital of 11.6 percent.

Figure 1. Distributions of Risk−Adjusted Excess Returns S e p t e m b e r 2 0 0 0 − A u g u s t 2 0 0 3 January 2004 − December 2006 A. Relative returns Frequency Frequency Frequency Frequency 1000 50 250 1000 50 250 All (left axis) 800 Tainted (far−right axis) 40 200 800 40 200 Abused (near−right axis) 600 30 150 600 30 150 400 20 100 400 20 100 200 10 50 200 10 50 0 0 0 0 −25 −20 −15 −10 −5 0 5 10 15 20 25 −25 −20 −15 −10 −5 0 5 10 15 20 25 Annual risk−adjusted excess return (percent) Annual risk−adjusted excess return (percent) B. Alphas based on category−performance risk factors Frequency Frequency Frequency Frequency 1000 50 250 1000 50 250 800 40 200 800 40 200 600 30 150 600 30 150 400 20 100 400 20 100 200 10 50 200 10 50 0 0 0 0 −25 −20 −15 −10 −5 0 5 10 15 20 25 −25 −20 −15 −10 −5 0 5 10 15 20 25 Annual risk−adjusted excess return (percent) Annual risk−adjusted excess return (percent) C. Alphas based on market risk factors Frequency Frequency Frequency Frequency 1000 50 250 1000 50 250 800 40 200 800 40 200 600 30 150 600 30 150 400 20 100 400 20 100 200 10 50 200 10 50 0 0 0 0 −25 −20 −15 −10 −5 0 5 10 15 20 25 −25 −20 −15 −10 −5 0 5 10 15 20 25 Annual risk−adjusted excess return (percent) Annual risk−adjusted excess return (percent) D. Alphas based on category−performance and Nasdaq risk factors Frequency Frequency Frequency Frequency 1000 50 250 1000 50 250 800 40 200 800 40 200 600 30 150 600 30 150 400 20 100 400 20 100 200 10 50 200 10 50 0 0 0 0 −25 −20 −15 −10 −5 0 5 10 15 20 25 −25 −20 −15 −10 −5 0 5 10 15 20 25 Annual risk−adjusted excess return (percent) Annual risk−adjusted excess return (percent)

Figure 2.A. Relative Performance of Abused and Tainted Mutual Funds Deviations from Industry Averages Abused funds: Relative returns Percentage points, Abused funds: Alphas based on Percentage points, annual rates category−performance risk factors annual rates 10 10 7 7 6 6 8 8 5 5 6 Upper bound of 95−percent 6 4 4 confidence interval 4 4 3 3 2 2 2 2 1 1 0 0 0 0 −1 −1 −2 −2 −2 −2 −4 Parameter estimate −4 −3 −3 Lower bound of 95−percent −6 confidence interval −6 −4 −4 −5 −5 −8 −8 −6 −6 −10 −10 −7 −7 1996 1998 2000 2002 2004 2006 1996 1998 2000 2002 2004 2006 Years ending August Years ending August Tainted funds: Relative returns Percentage points, Tainted funds: Alphas based on Percentage points, annual rates category−performance risk factors annual rates 10 10 7 7 6 6 8 8 5 5 6 6 4 4 4 4 3 3 2 2 2 2 1 1 0 0 0 0 −1 −1 −2 −2 −2 −2 −4 −4 −3 −3 −6 −6 −4 −4 −5 −5 −8 −8 −6 −6 −10 −10 −7 −7 1996 1998 2000 2002 2004 2006 1996 1998 2000 2002 2004 2006 Years ending August Years ending August Note. All estimates control for mutual fund assets under management.

Figure 2.B. Relative Performance of Abused and Tainted Mutual Funds Deviations from Industry Averages Abused funds: Alphas based on Percentage points, Abused funds: Alphas based on Percentage points, market−risk factors annual rates category−performance and Nasdaq risk factors annual rates 8 8 6 6 5 5 6 Upper bound of 95−percent 6 confidence interval 4 4 4 4 3 3 2 2 2 2 1 1 0 0 0 0 −1 −1 −2 −2 −2 −2 −4 Parameter estimate −4 −3 −3 Lower bound of 95−percent −4 −4 −6 confidence interval −6 −5 −5 −8 −8 −6 −6 1996 1998 2000 2002 2004 2006 1996 1998 2000 2002 2004 2006 Years ending August Years ending August Tainted funds: Alphas based on Percentage points, Tainted funds: Alphas based on Percentage points, market−risk factors annual rates category−performance and Nasdaq risk factors annual rates 8 8 6 6 5 5 6 6 4 4 4 4 3 3 2 2 2 2 1 1 0 0 0 0 −1 −1 −2 −2 −2 −2 −4 −4 −3 −3 −4 −4 −6 −6 −5 −5 −8 −8 −6 −6 1996 1998 2000 2002 2004 2006 1996 1998 2000 2002 2004 2006 Years ending August Years ending August Note. All estimates control for mutual fund assets under management.

Figure 3. Discounted Cumulative Revenues and Costs Trading arrangements last three years Billions of dollars 1100 1100 Revenues Based on disgorgement Based on penalties and dilution 88 88 Costs Reputation−related outflows Performance−related losses Official penalties 66 Mandated fee reductions 66 44 44 22 22 00 00 −−22 −−22 00 55 1100 1155 2200 2255 Time horizon (years) Trading arrangements permanent (never detected) Billions of dollars 1100 1100 Revenues Based on disgorgement Based on penalties and dilution 88 88 Costs Performance−related losses 66 66 44 44 22 22 00 00 −−22 −−22 00 55 1100 1155 2200 2255 Time horizon (years)

Figure 4. Discounted Cumulative Revenues and Costs Skim 1 percent of assets annually (forever) Billions of dollars 2200 2200 1188 1188 1166 1166 1144 1144 1122 1122 1100 1100 "Revenues" from skimming 88 88 Costs: Performance−related losses 66 66 44 44 22 22 00 00 −−22 −−22 00 55 1100 1155 2200 2255 Time horizon (years)

Figure 5. Abnormal Flows to Scandal−Tainted Mutual Fund Families Abnormal flows to tainted mutual funds Percent of assets 1.5 1.5 Monthly 1.0 Upper bound of 95−percent 1.0 confidence interval 0.5 0.5 0.0 0.0 −0.5 −0.5 −1.0 −1.0 Lower bound of 95−percent Estimated abnormal flow −1.5 confidence interval −1.5 −2.0 −2.0 −2.5 −2.5 −3.0 −3.0 −12 −9 −6 −3 0 3 6 9 12 15 18 21 24 27 30 33 36 Months relative to initial revelation of scandal Additional abnormal flows to abused funds Percent of assets 1.5 1.5 Monthly 1.0 1.0 0.5 0.5 0.0 0.0 −0.5 −0.5 −1.0 −1.0 −1.5 −1.5 −2.0 −2.0 −2.5 −2.5 −3.0 −3.0 −12 −9 −6 −3 0 3 6 9 12 15 18 21 24 27 30 33 36 Months relative to initial revelation of scandal

Figure 6. Cumulative Abnormal Flows to Scandal−Tainted Mutual Fund Families Cumulative abnormal flows Percent of assets 5 5 Monthly 0 0 −5 −5 Tainted mutual funds −10 −10 −15 −15 −20 Abused mutual funds −20 −25 −25 −30 −30 −35 −35 −40 −40 −45 −45 −12 −9 −6 −3 0 3 6 9 12 15 18 21 24 27 30 33 36 Months relative to initial revelation of scandal

Appendix: Estimatingabusive-tradinggainsanddilution A.1 Methodsofestimatingdilution As Greene and Ciccotello (2004) and Zitzewitz (2007b) have outlined, researchers—and consultants working on mutual fund litigation—have employed three basic approaches toestimatingdilutionfromtradingabuse. Thefirstmightbecalledthe“flow-correlation” approach, as it is based on correlations between daily net flows and either predicted pricing errors (the “predicted-NAV” method) or realized next-day returns (the “nextday-NAV”method).52 Thesecond(“profits”or“consulting”)approachlooksatholdingperiodgainsforabusivetraders. Thethird(“cash-model”)approach,proposedbyGreene and Ciccotello, combines the other two but also explicitly takes into account how portfolio managers handle cash from abusive traders, since realized dilution may depend importantlyonthesecash-managementpolicies. Earlyestimatesofdilutioncausedbytradingabusesemployedtheflow-correlation approaches.53 Goetzmann et al. (2001) used the predicted-NAV method with pricing errors modelled using same-day S&P 500 index returns. Zitzewitz (2003, 2007b) used a similar strategy, but added several other predictors of pricing errors, including Nikkei futures,returnsonspecialityindexes,andcategory-averageNAVchangesforsometypes offunds. GreeneandHodges(2002)introducedthenext-day-NAVapproachinestimatingdilutioninworldequityfunds. ThisistheapproachIusedtoderive(6),asdescribed insectionA.3below. The predicted-NAV and next-day-NAV methods are especially useful in estimating dilution with fund-level net-flows data but without information about individual abusive traders’ transactions. Each method has its benefits. The predicted-NAV approach aims to pinpoint abusive-trading flows by using the signals—such as changes in index futures prices—that market timers and late traders employed to trigger dilutive trades. This gives it a precision advantage over the next-day method, which infers the trading signals from noisier next-day-NAV changes. On the other hand, the nextday-NAV method is simpleto employ, requires no modeling assumptions about pricing errors, and provides a more direct measure of realized gains from abusive trades and dilution to buy-and-hold investors’ wealth. Also, the next-day-NAV method—unlike the predicted-NAV approach—will capture dilution from trading opportunities that timers 52Greene and Ciccotello labelled these the “one-day” methods, while Zitzewitz called them the “academic”methods. 53Muchearlier,Lyon(1984),whodocumentedevidencethatmarkettimerswereexploitingstalepricesin moneymarketfunds,alsoestimateddilutionbyexaminingthecorrelationofnetflowsandestimatedpricing errors.Thepricingerrorsheestimated,however,werepersistentdiscrepanciesbetweenmoneymarketfund yieldsandyieldsonothermoneymarketinstruments,ratherthantheone-daypricingerrorsthathavebeen theprimaryproblemamonglong-termmutualfunds. A-1

observe but an econometrician does not. For example, some management companies provided detailed non-public information about their mutual funds’ portfolio holdings to market timers, so they could identify profitable trading opportunities even more preciselythanindexfuturesmightindicate. In any case, the choice between the next-day-NAV and predicted-NAV methods is probably not important for my purposes. Zitzewitz (2007b) employed both methods to calculate dilution for mutual funds in tainted families and obtained very similar estimatesfromeachmethod. The second major approach to estimating dilution—the “profits” or “consulting” method—isbasedontheholding-periodgainsofabusivetraders. Abusivetraders’gains are equal (or approximately equal) to buy-and-hold investors’ dilution losses in several circumstances: (1)iftimersholdmutualfundsharesforonlyonedayatatime,andthus do not market-time their redemptions; (2) if portfolio managers hold flows from timers in cash and timers do not hedge their positions or market-time their redemptions; and (3)ifportfoliomanagersfullyinvestflowsfromtimersinregularportfolioassetsassoon aspossible,andthetimersfullyhedgetheirpositions. Theprofitsmethodcapitalizeson thecloserelationshipbetweentimers’profitsandotherinvestors’dilutionlosses. Greene and Ciccotello (2004) developed a third approach to estimating dilution, which they dubbed the “cash-model” method, that allows for a more flexible set of portfolio-management policies on investing abusive traders’ inflows. For example, this methodcouldbeusedtomeasuredilutionaccuratelyifaportfoliomanagerinvestednew cash flows into portfolio assets gradually over several days. When detailed data on the net flows and cash-management practices of individual mutual funds are available, the cash-model approach should generally provide the most accurate estimates of dilution. But when high-frequency data on mutual funds’ cash holdings cannot be obtained, researchersandconsultantsareleftwithachoicebetweentheflow-correlationandprofits methods. The profits approach has both advantages and disadvantages in comparison to the flow-correlation method. Consider the three scenarios listed above in which gains are roughly equal to dilution. In the first—when traders hold mutual fund shares for just one day at a time—both methods should accurately measure dilution to incumbent investorsaswellastimers’gains. Inthesecondscenario,however,theprofitsmethodis amoreaccuratemeasureofdilution,becausetheflow-correlationmethodonlypicksup thatportionofthetimer’sgain(andincumbentinvestors’losses)thatoccursonthefirst dayofthetimer’sinvestment. Butinthisscenario,thetimers’netgainonhismutualfund sharesovertheentireholdingperiodis,dollarfordollar,alosstoincumbentinvestors.54 54Sincethefundholdsthetimer’sinflowincash,anyreturnheearnsonhisshareswhileinvestedinthe fund—abstractingfromreturnsoncash—comesstraightoutofthepocketsofotherinvestors. A-2

Inthethirdscenario,theflow-correlationmethodisthesuperiormeasureofboth dilution and abusive traders’ gains, because this method captures just the dilution and gainsthatoccurwhenthetimerpurchasesandredeemsmutualfundshares. Theprofits method,incontrast,alsopicksupholding-periodgainsthatoccurbetweenthetimedpurchase and the (possibly timed) redemption. If the fund portfolio manager has invested thetimer’sinitialflow,theseholding-periodgainsdonotdiluteincumbentinvestors’returns, and the holding-period gains do not contribute to the timer’s net profits (because he has hedged his position). Furthermore, in the same scenario, the flow-correlation method captures the net gain from timed redemptions, which do cause dilution, but the profitsmethodmissesthistypeofprofitanddilution.55 The profits method has a couple of additional drawbacks relative to the flowcorrelation method. The profits method requires detailed data on all abusive traders’ transactions, and estimates of dilution (or abusive traders’ gains) will be biased downwardtotheextentthatsuchtraderscannotbeidentified. Also,asZitzewitz(2007b)points out,theprofitsmethodissensitivetoswingsinmarketreturns;forexample,poormarket returnswilldepresstimers’“profits”and,therefore,estimateddilution. Theseproblems donotaffectdilutionorgainscomputedusingflow-correlationmethod. Moreover,Zitzewitz finds that, in practice, cash holdings among international equity funds varied little withfundshareturnoverintheperiodfrom2000to2003. Thisresultsuggeststhatportfolio managers did invest abusive traders’ inflows promptly and weakens the argument forusingtheprofitsmethod(oreventhecash-modelapproach).56 The tradeoffs in using the different methods are apparent in the plans for distributing the penalties and disgorgement that were collected by government agencies from tainted management companies. Because these plans aim to allocate money to the mutualfundshareholderswhowereharmedbyabusivetradesinproportiontothelosses they suffered, the plans require detailed fund-level estimates of dilution. Every method discussed here has been used in at least one distribution plan, and several plans employed more than one method to accommodate varying circumstances among abused funds(suchasdifferencesinportfoliomanagers’cash-managementpolicies). 55Redemptions are timed to occur when the mutual fund’s NAV fails to incorporate an observable or predictablenegativecomponentofreturn(intermsofthemodeldescribedinsectionA.3,whenπt <0).The profitsmethodonlyrecordsgainsonthetimer’smutualfundposition,butthetimer’sclosingofthisposition justavoidsaloss. Thegainoccurswhenthetraderclosesthehedge,whichisashortpositioninaportfolio thatreplicatesthemutualfund’sportfolio.Seenote58. 56Ontheotherhand,evidence(suchasthatpresentedinsomedistributionplans)thatportfoliomanagers inspecificmutualfundsorfundfamiliesdidnotinvesttimers’inflowswouldstrengthentheargumentfor usingtheprofitsorcash-modelmethod,atleastforthosefundsorfamilies. A-3

A.2 Estimatingabusivetraders’gains As described above, abusive traders’ gains are equal (or approximately equal) to buyand-hold investors’ dilution losses in several types of scenarios. In the circumstances inwhichdilutiondeviatessignificantlyfromabusivetraders’gains,thedifferencesarise either from market fluctuations over timers’ holding periods (which can generate gains foratimerwithoutcausingdilutionofothershareholders’wealth)orfromdilutiondue totimedredemptions,whichcancauselossesforothershareholderswithoutgenerating gainsfortimers. The close relationship between dilution and abusive traders’ gains suggests that the best methods for measuring dilution and gains should be similar. Indeed, for my purposes, and given the constraints on available data, the flow-correlation methods are best-suited to capturing those gains. Flow-correlation methods will not capture capital gains or losses that abusive traders experience when holding mutual fund shares for longer than one day without hedges, but such profits were not central to the mutual fund scandal. And flow-correlation methods may overstate trader gains due to timed redemptions, but that would be consistent with the general bias in this paper toward overstatingrevenues.57 Inderivingmybaselineestimatesofrevenuesfromabusivetrading,Isidestepped (tosomeextent)theproblemofchoosingthe“right”methodofcomputinggainsbyusing a hybrid approach. As described in section 7.4.2, I assumed that the gains from trading abusesineachmanagementcompany’sfundswerethemaximumofthepenaltiesitpaid and Zitzewitz’s (2007b) estimate of total dilution in its mutual funds. Penalties paid were, as noted in section 7.4.1, generally larger than dilution estimated in distribution plans using the method or methods that plan authors deemed most appropriate. And Zitzewitz’s dilution estimates are very close to the estimates of abusive traders’ gains thatIcomputedusingtheflow-correlationmethod(seesection7.3andsectionA.3ofthis appendix). 57Theprofitsmethodmightseemtobethemostappropriateapproachforcomputingabusivetraders’ gains. Andwhenabusivetradersholdontomutualfundsharesformorethanonedayatatimewithout hedgingtheirpositions,theprofitsmethodhasanadvantageovertheflow-correlationmethodinthatonly theformerpicksupholding-periodgainsandlossesontopofanydilutiongainatpurchase. Asoutlined above,however,therearesomeimportantdrawbackstotheprofitsmethodformeasuringdilution. Anadditionalproblemarisesinestimatingtheabusivetraders’gains, becausetheprofitsmethodcapturesonly thereturnsrealizedfrompurchasesandsalesofmutualfundsharesandnotanyprofitsfromotherinvestments made as part of a timing strategy. In particular, the profits method would not pick up gains from hedging positions designed to offset the market risk of a long position in mutual fund shares and to set uparbitrage-profitopportunitiesfortimedredemptions(seealsosectionA.3.2). Finally,itisworthnoting thattheinnovationsinthecash-modelapproach,whilewell-suitedformeasuringdilution,arenotaimedat measuringabusivetraders’gains. A-4

A.3 Derivationofequation(6) Consider a mutual fund with assets A t−1 on day t−1. Let shares outstanding be A t−1 , sotheprice(NAV)pershareis1. Onday t,incomputingitsnewNAV,thefundrecords a return on portfolio assets r , but fails to incorporate a second component of return, π , t t which investors can either predict or observe. For example, π might be post-Nikkeit closeappreciationofJapanesestocksthatisnotincorporatedinafund’sNAV.Defineπ t suchthat,hadthefundincorporatedthiscomponentofreturnincomputingNAV,gross returntomutualfundsharesondaytwouldhavebeen(1+r )(1+π ). t t Insuchacircumstance,somedilutionmayoccurifthefundhasnetflowsonday t,evenwithoutabusivetradesdesignedtoexploitthefund’spricingerror. Inthecourse of normal operations, the fund receives flow F t = f t A t−1 , creates new shares f 1 tA + t r − t 1, and recordsassetsundermanagementattheendofdaytof A t−1 (1+r t )+ f t A t−1 . On the following day, t+1, the fund’s portfolio earns an additional return, (cid:101) t+1 , which is unpredictable and uncorrelated with the previous day’s flow. In addition, the fund “catches up” with market developments on the previous day and marks up the portfolio assets it held before day-t flow by π . For simplicity, suppose that there is no t additional predictable but unrecorded return (π t+1 = 0) and the fund attracts no net new cash flow. At the end of day t+1, assets under management are A t−1 (1+r t )(1+ π t )(1+(cid:101) t+1 )+ f t A t−1 (1+(cid:101) t+1 ). Dilution has occurred because the flow f t A t−1 arrived afterreturns (1+r )(1+π ) wererealizedonday t,butthepricingofsharespurchased t t withthisflowonlyreflectedappreciation(1+r ). t Attheendofdayt+1,withthenumberofsharesunchangedfromdayt: NAV = Assets t+1 = A t−1 (1+r t )(1+π t )(1+(cid:101) t+1 )+ f t A t−1 (1+(cid:101) t+1 ) t+1 Shares t+1 A t−1 + f 1 tA + t r − t 1 (cid:18) (cid:19) π f = 1+π t − 1+r t + t f (1+r t )(1+(cid:101) t+1 ). t t Since NAV = 1+r ,thegrossreturnondayt+1is: t t (cid:18) (cid:19) π f 1+r t+1 = 1+π t − 1+r t + t f (1+(cid:101) t+1 ). (A-1) t t Withoutdilution,thefundwouldrecordgrossreturnsof(1+π t )(1+(cid:101) t+1 )ondayt+1. Letd t+1 bedilutiontoreturnsrealizedondayt+1,thatis: 1+r t+1 = (1+π t )(1+(cid:101) t+1 )−d t+1 . (A-2) π f d t+1 = 1+r t + t f (1+(cid:101) t+1 ). (A-3) t t A-5

Thedelayedcomponentofday-treturn,π ,isnotdirectlyobservable;substitutionyields: t f (r −(cid:101) ) d t+1 = t t+ 1 1 +r t+1 . (A-4) t Dilutioncanbeeitherpositiveornegativeandcanbecausedbyeithernetinflowsornet redemptions; equation (A-4) measures dilution to returns in any scenario. For example, whenafundreceivespositivenetflowsondaytandrecordsr t+1 < (cid:101) t+1 onthefollowing day, dilution is negative because the new shares earn a smaller return on day t+1 than thatearnedbythefund’sportfolioassets(so, incumbentshareholdershaveearnedmore thanthefund’sportfolio). Ontheotherhand,whenr t+1 < (cid:101) t+1 ,outflowscausepositive dilution (more descriptively, a concentration of losses) among shareholders who do not redeem. Equation (A-4) might be useful in estimating dilution, even though the unpredictable component of return, (cid:101) t+1 , is not observable, if one assumes that E(f t (cid:101) t+1 ) = 0. If so, then summing d t+1 = f 1 t + rt+ rt 1 over a period of interest would give an unbiased estimate of dilution (to returns) over that period. However, for a growing (shrinking) fund withpositive(negative)averagereturnsovertheestimationperiod,theexpectedproduct of net flow and next-day return may positive even in the absence of any pricing inefficiencies (that is, even if π = 0,∀t). So, estimates of dilution using this summation may t bebiased. One means of correcting for this problem is to split flow into two components, f t = φ t +g t , where φ t ≡ E t−1 (f t ). The expected component of flow, φ t , might be interpreted as flow from buy-and-hold investors, while g might be timer flow. One might t also argue that the predictable component of return, φ , could be invested by the portt foliomanagerinadvanceofanyunpricedappreciationofassets, π . Thiseliminatesthe t possibility of dilution due to buy-and-hold investors’ transactions and simplifies interpretation without affecting the basic results, so I use this assumption in my calculations here. Asbefore,considerafundwithinitialassets A t−1 ondayt−1,sharesoutstanding A t−1 ,andanNAVof1. Ondayt,thefundrecordsareturnonportfolioassetsr t ,butfails toincorporateasecondcomponentofreturn, π t . Flowonday t is F t = (φ t +g t )A t−1 ,as outlinedabove. Theportfoliomanagerinvests φ t A t−1 , butnot g t A t−1 , inadvanceofthe realizationofreturnπ . Neithercomponentofflowisinvestedbeforereturnr isrealized. t t At the end of day t, the fund records an NAV of (1+r t ), assets of A t−1 (1+r t )+ A t−1 (φ t + g t ), and shares A t−1 + At− ( 1 1 ( + φ r t + t ) gt ) . On day t+1, with additional return (cid:101) t+1 butnonetflow,recordedassetsare A t−1 ((1+r t +φ t )(1+π t )+g t )(1+(cid:101) t+1 ). Thefund A-6

recordsaday-t+1grossreturnof: (cid:18) (cid:19) NAV π g 1+r t+1 = NAV t+1 = 1+π t − 1+r + t φ t +g (1+(cid:101) t+1 ) t t t t = (1+π t )(1+(cid:101) t+1 )−d t+1 . Dilutiontoreturnsis: (cid:18) (cid:19) g π d t+1 = 1+r + t φ t +g (1+(cid:101) t+1 ) t t t (cid:18) (cid:19) r −(cid:101) = g t+1 t+1 . (A-5) t 1+r +φ t t Dilution in dollar terms, D t+1 , is equal to the dilution to returns, d t+1 , times “diluted assets,” that is, the assets of buy-and-hold investors who do not trade on day t. But the measure of diluted assets depends on whether the dilution is caused by inflows or outflows. A.3.1 Dilutionandmarket-timinggainsduetotiminginflows When market timers purchase mutual fund shares (in advance of expected π > 0), dit luted assets are those held by investors net of the timers’ purchases on day t, that is, A t−1 (1+r t +φ t ),so: (cid:18) (cid:19) r −(cid:101) D t in + f 1 low = d t+1 A t−1 (1+r t +φ t ) = g t 1 t+ + 1 r + t+ φ 1 A t−1 (1+r t +φ t ) t t = A t−1 g t (r t+1 −(cid:101) t+1 ). (A-6) Equation (A-6) also records the timer’s gain from dilution. She purchases A t−1 g t worth of mutual fund shares on day t. Absent any pricing error, with π = 0, the onet day return she earns on day t+1 is A t−1 g t (cid:101) t+1 , but a consequence of the fund’s lagged recognition of π t (cid:54)= 0 is that r t+1 (cid:54)= (cid:101) t+1 . Her timing gain from trades made on day t, inflow G ,istheadditionalreturngivenby(A-6): t G t inflow = A t−1 g t (r t+1 −(cid:101) t+1 ) = D t in + f 1 low . (A-7) To estimate timer gains due to inflows, we can sum equation (A-7) over an interval of interest (such as a calendar year) for days on which g t ≥ 0. Assets, A t−1 , and returns, r t+1 ,canbeobserveddirectly. Toobtainthesurprisecomponentofdailyflow,g t ,Isimply assumedthatafund’sexpectedflowinagivenyearwasitsmeandailyflowforthatyear, as estimates of timer gains were not sensitive to the methods used to compute expected flow. Finally,although(cid:101) t+1 isnotobserved,g t and(cid:101) t+1 areuncorrelatedandE(g t ) = 0,so A-7

E(g t (cid:101) t+1 ) = 0. Aslongas E(A t−1 g t (cid:101) t+1 |g t ≥ 0) ≈ 0alsoholds,timergainsfrominflows inperiod T canbeestimatedby: G t in ∈ f T low ≈ ∑ A t−1 g t r t+1 . (A-8) t∈T,gt ≥0 A.3.2 Dilutionandmarket-timinggainsduetotimingoutflows Market timers may also sell mutual fund shares in advance of expected π < 0. Here, t g < 0,anddilutedassetsarethoseheldbyinvestorsafterthetimers’salesondayt,that t is, A t−1 (1+r t +φ t +g t ),so: (cid:18) (cid:19) r −(cid:101) D t o + ut 1 flow = d t+1 A t−1 (1+r t +φ t +g t ) = g t 1 t+ + 1 r + t+ φ 1 A t−1 (1+r t +φ t +g t ) t t (cid:18) (cid:19) g = A t−1 g t (r t+1 −(cid:101) t+1 ) 1+ 1+r t +φ . (A-9) t t While equation (A-9) captures losses for buy-and-hold investors, it does not exactly measure the timer’s gains. The timer sells At−1 (−gt ) shares at a price of 1+r per 1+rt t share. Ifthemutualfund’sNAVhadreflectedallavailableinformationattimet,theprice wouldhavebeen(1+r t )(1+π t ),andshewouldhavehavereceived A t−1 (−g t )(1+π t ) forhershares. Her gain, A t−1 g t π t (which is positive for g t < 0 and π t < 0), is actually a loss avoided; sheobtainsnocashflowfromthetimedredemptionitself. However,thetimer can use a hedging strategy to obtain the equivalent cash gain.58 Although π is not obt served,wecansubstituteusing: (cid:18) (cid:19)(cid:18) (cid:19) r −(cid:101) g π = t+1 t+1 1+ t . t 1+(cid:101) t+1 1+r t +φ t 58Thatstrategywouldbeginondayt withherinitialmarket-timingpurchaseofSmutualfundshares. 0 ShewouldsimultaneouslysellshortaportfolioofassetsthatreplicatesSsharesworthofthemutualfund’s portfolioassets. Sinceshebuysthemutualfundsharesforlessthantheirvalue,thecashsheobtainsfrom theshortsaleexceedsthecostofthesharesshepurchases;thedifferenceishergain,whichisapproximately G inflow , as defined in equation (A-8). (If she were able to exactly anticipate the return on day t +1, she t0 0 wouldsellshortjustenoughoftheportfoliotomatchherlongpositioninthemutualfundondayt +1, 0 Ginflow andhernetgainondayt wouldbe t0 ). When,ondayt,sheobservesapredictablenegativereturn 0 1+(cid:101)t0+1 thatisnotreflectedinNAV,shesellsherfundsharesatapricethatexceedstheirfairvalue,simultaneously outflow closestheshortpositionatitsfairvalue,andpocketsthedifference,G . t Markettimersapparentlyemployedsuchschemestoexploitmutualfundpricinginefficiencies; several officialdocumentsrefertotheuseofreplicatingportfolios. Indeed,BancofAmericaSecurities’derivatives deskapparentlystructuredsuchportfoliosspecificallyforhedgefundsthatwereengagedinabusivetrading (U.S.SecuritiesandExchangeCommission,2005b). A-8

Andthetimer’savoidedlosses(orgains,ifshehasemployedthehedgingstrategy)are: (cid:18) (cid:19)(cid:18) (cid:19) r −(cid:101) g G t outflow = A t−1 g t t 1 +1 +(cid:101) t+ t+ 1 1 1+ 1+r t t +φ t . outflow D = t+1 . (A-10) 1+(cid:101) t+1 Sincethetimer’sflow,g ,shouldbeuncorrelatedwiththeunpredictablecomponentofthe t (cid:110) (cid:16) (cid:17)(cid:16) (cid:17)(cid:12) (cid:111) followingday’sreturn,(cid:101) t+1 ,IassumethatE A t−1 g t 1+ (cid:101)t (cid:101) + t 1 +1 1+ 1+r g t t +φt (cid:12) (cid:12) g t < 0 ≈ 0. Ifso,thenwecansum(A-10)overdaysonwhichg < 0toestimatemarket-timinggains t (orlossesavoided)duetooutflowsinaninterval T: (cid:18) (cid:19)(cid:18) (cid:19) G t o ∈ u T tflow ≈ t∈T ∑ ,gt <0 A t−1 g t 1+ r t+ (cid:101) 1 t+1 1+ 1+r g t t +φ t . (A-11) Onecomplicationinestimating(A-11)isthatwedonotobserve(cid:101) t+1 . Since r t+1 = (cid:101) t+1 +π t +π t (cid:101) t+1 −d t+1 ≈ (cid:101) t+1 +π t −d t+1 , and π t will be negative for outflow dilution, r t+1 < (cid:101) t+1 . Replacing (cid:101) t+1 with r t+1 in (A-11)wouldthusbiasourestimateoftimergainsupward,butthiswouldbeconsistent withthegeneralbiasinthispapertowardoverstatingrevenues. Hence, (cid:18) (cid:19)(cid:18) (cid:19) G t o ∈ u T tflow ≈ t∈T ∑ ,gt <0 A t−1 g t 1+ r t+ r t 1 +1 1+ 1+r g t t +φ t . (A-12) A.3.3 Abusive-tradinggainsanddilutionlosses Bycombining(A-8)and(A-12),weobtaintheformulaforabusive-tradinggainsinequation(6): G = G inflow+G outflow t∈T t∈T t∈T (cid:18) (cid:19)(cid:18) (cid:19) ≈ t∈T ∑ ,gt ≥0 A t−1 g t r t+1 + t∈T ∑ ,gt <0 A t−1 g t 1+ r t+ r t 1 +1 1+ 1+r g t t +φ t (A-13) Equation (A-13) is valid only if abusive traders use hedging strategies, as discussed in note 58; otherwise, abusive-trading gains are only those measured by the first term (the sum for days on which g ≥ 0). Under the assumption that timers do employ hedging strategies, the dilution caused by abusive trading is almost identical to the gains it gen- A-9

erates: (cid:18) (cid:19) D t∈T ≈ ∑ A t−1 g t r t+1 + ∑ A t−1 g t r t+1 1+ 1+r g t +φ (A-14) t∈T,gt ≥0 t∈T,gt <0 t t A.4 Dailydatausedtocomputedilution As described in section 7.3, I used a combination of data sources to estimate daily flows and dilution in abused mutual funds, including: TrimTabs daily assets data; CRSP, Yahoo! Finance,andTrimTabsprice(NAV)data; distributionsdatafromCRSPandYahoo! Finance;andInvestmentCompanyInstitutedataonreinvestmentrates. Thedailyassets dataarenotoriouslynoisyandsubjecttoatimingproblemoftheirown: Dailyassetsare almostalwaysreportedona“preflow”basis—thatis,assetsfordaytareusuallyrecorded beforeanyday-tnetpurchasesofsharesareaddedin. Theproblemisdocumentedindetail in Greene and Hodges (2002) and Zitzewitz (2003). Following Zitzewitz, I assumed thatallassetswerereportedona“preflow”basisexceptthoseforselectedfamilies(RightimeandRydex,forexample)thatspecificallycateredtohigh-frequencytraders. (Tothe extent that I have incorrectly reassigned the timing of assets observations, my estimates ofdilutionwouldbebiasedupward.) TrimTabsandotherdailydatarequireextensivecleaningtobeusefulinresearch. Someoftheproblemsarereparable. Forexample,reportedassetsonsomedaysarezero but can be inferred because TrimTabs also reports daily net flow, and all observations for July 2002 were reported with a one-day lag. Other problems are less tractable, so I employed a variety of filters. For each mutual fund share class (ticker), I dropped daily observationsforwhich: changesinassets,shares,orNAVexceededfivestandarddeviationsofthatticker’smeanchange(inagivenyear)forthatparticularvariable;changesin assets, shares, or NAV exceeded 10 percent; “flip-flop” observations in which a variable hadopposite-signchangesofmorethan2.5standarddeviationseachontwoconsecutive days;and“flip-flop”observationsinwhichavariablehadopposite-signchangesofmore than5percenteachontwoconsecutivedays. Ialsodroppedfromtheanalysistickersfor which more than 3 percent of the daily flow estimates exceeded (in absolute value) 5 percent of assets and tickers for which more than 1 percent of the daily flow estimates exceeded(inabsolutevalue)10percentofassets. Finally, in estimatinggains to abusive tradersusing equation (A-13), I foundnegative values for a few investment objectives in some years. While negative gains and dilution are certainly plausible, I dropped the negative observations in aggregating the dilutionfigures. Again,thiswillcontributetoanupwardbiasinmyestimates,consistent withageneralbiastowardoverstatingrevenues. A-10