Day Trading International Mutual Funds: Evidence and Policy Solutions

Day Trading Inernaional Muual Funds: Evidence and Policy Soluions William N. Goezmann Zoran Ivković K. Geer Rouwenhors Yale School of Managemen Firs Draf: Ocober 2, 1999 This Version: February 20, 2000 This paper has benefied from he discussions wih Sewar Greene and he commens from paricipans a a seminar sponsored by he TIAA-CREF Insiue and Yale. We hank TrimTabs for supplying some of he daa for his sudy. 1

Absrac Daily pricing of muual funds provides liquidiy o invesors bu is subjec o valuaion errors due o he inabiliy o observe synchronous, fair securiy prices a he end of he rading day. This may hur fund invesors if speculaors sraegically seek o exploi mispricing, or if he ne flow of money ino funds is correlaed wih hese pricing errors. We show ha muual funds are exposed o speculaive raders by using a simple day rading rule ha yields large profis in a sample of 391 U.S.-based open-end inernaional muual funds. We also documen he exen o which ne fund flows may have been correlaed wih pricing errors in a sample of 116 inernaional funds. Alhough many funds have penalies for early redempion, loads ha discourage day rading, and policies o refuse business o day raders, such mechanisms are neiher perfec, nor appealing o regular cusomers. We propose a simple fair pricing mechanism ha alleviaes hese concerns by correcing ne asse values for sale prices. We argue ha fund companies and regulaors should look a alernaives ha allow funds o offer fair pricing o invesors, which in urn decreases he need o resor o monioring for day raders and expenses such as loads and redempion penalies. 2

I. Inroducion The developmen of he open-end U.S. muual fund indusry over he pas fify years has yielded enormous benefis o small invesors. The goals of he 1940 Invesmen Companies Ac have largely been achieved. Small invesors have access o hones, professional managemen a reasonable fees. Funds have a clear governance srucure, regulaed disclosure, and resricions on aciviies ha creae he poenial for conflics of ineres. Among oher feaures, he open-end muual fund srucure provides daily liquidiy o invesors, enabling hem o conver a porfolio of socks or bonds o cash hrough he re-sale of shares o he muual fund company. This liquidiy is made possible by he requiremen ha muual funds calculae heir ne asse value (NAV) daily. To do his, funds ypically use closing ransacions prices o calculae securiy values. For acive, liquid securiies whose las rade occurs near he end of he U.S. rading day his rule works well, bu he globalizaion of he muual fund indusry has made daily NAV calculaions challenging. No all markes are as liquid as he U.S. sock marke, nor do heir rading hours coincide wih hose of he markes in he U.S. In paricular, ime-zone differences creae a special dilemma for U.S. muual funds ha inves in foreign securiies. Consider a U.S. muual fund ha invess in Japanese equiies, mos of which are no cross-lised in he U.S. Suppose he fund wans o deermine he NAV in dollars (U.S.D) of is shares as of 4 PM Easern Sandard Time (EST) o sele he buy and sell orders i receives during he day. 1 Which prices should he fund use o compue he value of is Japanese holdings? One opion is o ake he Yen closing prices from he Tokyo Sock Exchange (TSE) and use he Yen/U.S.D exchange rae ha prevails a 4 PM EST o compue he dollar value of he porfolio. The TSE closes a 1 AM EST, abou nine hours before he opening New York Sock Exchange (NYSE). Therefore, his pricing rule effecively allows U.S. invesors o purchase or sell shares in he fund during NYSE rading hours a prices deermined a leas fifeen hours earlier. This leaves he funds and heir long-erm shareholders exposed o speculaive rading. For example, suppose favorable informaion abou Japanese share prices were released afer he close of he TSE bu before he NYSE close. Invesors could rade on ha informaion a sale prices by buying shares in a U.S. muual fund ha invess in Japan, in 1 Among oher reasons, 4 PM EST is desirable because i allows fund companies o ransfer invesor wealh among is funds on he same day. 3

anicipaion ha he informaion will be refleced in price adjusmens on he Tokyo exchange, and hence on he NAV of he fund shares, on he following day We are no he only researchers o poin ou he problem posed by he use of sale prices o compue NAVs. Neumark, Tinsley, and Tosini (1991) show ha he opporuniy for speculaive profis in inernaional muual funds is no so much an informaional efficiency problem as i is an insiuional efficiency problem. More recenly, Chalmers, Edelen, and Kadlec (1999), Greene and Hodges (2000), and Zizewiz (2000) invesigae he poenial profiabiliy of rading on sale prices using boh inernaional and small-cap funds. Using various performance measures, all hree papers show ha day rading in muual funds using curren informaion has he poenial o generae profis. Chalmers, Edelen, and Kadlec (1999) and Greene and Hodges (2000) also presen evidence from fund flows o sugges speculaive day rading may be a problem for some funds. Chance and Hemler (1999) demonsrae he profiabiliy of day rading in muual funds using a differen daa se daily reurns o a number of self-repored imers who eiher manage accouns or make rading recommendaions o cliens. An imporan issue in he above sudies of iming profis from day rading muual funds is he issue of decomposing sraegy profiabiliy ino gains due o sale prices and gains due o rue marke predicabiliy. Mos of Chance and Hemler s sample is comprised of managers who focus on funds raher han indices however, and a leas par of he profis due o iming in heir sample may be due o facors oher han sale prices. Our paper differs from oher work on he sale pricing problem in wo ways. Firs, we focus on economeric mehods o differeniae sale pricing profis from profis due o rue index predicabiliy. This is imporan, because he success of simple rading rules ha condiion porfolio weighs on conemporaneous informaion does no mean ha profis can be solely aribued o sale prices. Soluions o he sale pricing problem should herefore no be designed o sem legiimae profiable acive sraegies. Second, we address he fundamenal policy issue confroning muual fund managers and regulaors how can sale price rading profis be curailed wihou imposing coss on long and shor-erm invesors alike? While i is emping o regard sale pricing as simply a performance problem for fund companies or a profi opporuniy for day raders, he issues i embodies are firs and foremos hose of fairness o invesors. Regardless of wheher fund invesors on average are harmed by he use of sale pricing, or wheher he exploiaion of sale pricing by invesors is 4

inenional or no, he need for accurae daily and inra-day selemen prices will coninue o increase as web-based rading increases. Fuures exchanges and closed-end fund companies compee acively wih open-end fund companies in he marke for index producs. A quesion confroning he muual fund indusry is wheher i will remain feasible o offer producs based on periodically esimaed NAVs in a marke in which acive raders coninually seek opporuniies o arbirage sale price discrepancies. The mechanisms developed in his paper allow us o address boh issues. In our analysis, we use a daabase of daily reurns o 391 U.S.-based inernaional openend equiy funds over he period from 1990 o 1998 o examine he poenial profiabiliy of a day rading sraegy. The sraegy is a simple one i uses he S&P 500 as an indicaor of wheher o inves in he fund on any given day. We find ha day rading in he absence of loads, early redempion fees, and oher ransacions coss is highly profiable on average, and srongly ouperforms a buy-and-hold sraegy in he funds. Our resuls hus indicae ha almos all inernaional funds are vulnerable o sale pricing. Load fees or shor-erm redempion fees may aenuae he profiabiliy of his rading rule for an individual fund imer. Ye hese fees are unable o resolve he problems induced by sale prices a he fund level if he aggregae ne flows ino he fund are correlaed wih he speculaive sraegy. As long as funds charge he wrong price a he gae, i is possible for imers o benefi a he expense of he exising shareholders. We also invesigae wheher ne fund flows show iming abiliy a he individual fund level. To address his problem, we obain seveneen monhs of daily ne fund flow informaion for 116 inernaional funds from TrimTabs. Our ess sugges ha daily speculaion or invesorinduced correlaion beween ne flows and reurns has been relaively modes for he average fund. This is in par because of he low correlaion beween reurns and ne flows, bu also because ne flows are small relaive o he size of mos funds. Neverheless, we esimae he oal ransfer of wealh beween buyers and sellers of muual fund shares induced by sale prices a abou $1.5 billion during our sample period. An imporan issue is how he indusry can reduce hese pricing errors wihou inroducing oher coss and consrains on invesors. Redempion fees and loads may sem daily speculaive exploiaion, bu hey are no popular wih cusomers. The exisence of various fees, resricions, monioring of aciviy, and charges represen unwaned consrains o long-erm and shor-erm invesors alike, ye hey canno resolve he sale pricing problem imposed by 5

poenially correlaed ne flows. Thus, a mechanism ha resuls in fair pricing wihou such fricions would be desirable. We propose an economeric mehod ha can be used o adjus sale prices in such as way as o make hem orhogonal o laer daily public informaion. This mehod can be used by cusodians o check he qualiy of he daily prices from vendors and by muual fund pricing commiees o adjus daily NAV. The procedure we develop has he poenial o eliminae a leas in expecaion he speculaive gains o shor-erm rading and economic loss o shareholders ha resul from sale pricing. The adjusmen increases he volailiy of he fund very slighly, bu i leaves he mean reurn virually unchanged. The paper is organized as follows. Secion II discusses he insiuional background on NAV pricing. Secion III discusses predicabiliy and pricing errors. Secion IV illusraes a simple sale-price rading rule using a single fund as an example. Secion V provides a horough analysis of profiabiliy of he rule using 391 inernaional equiy muual funds, broken down by invesmen syle (as defined by he funds Morningsar Caegory). Secion VI evaluaes he ransacions coss associaed wih day rading and he mechanisms funds have in place o discourage speculaion on sale prices. Secion VII documens he correlaion beween daily ne fund flows and fund reurns. Secion VIII presens and ess he effecs of our correcion mehodology ha adjuss NAVs in order o preclude he profiabiliy of sraegic day rading. Secion IX addresses he issue of welfare effecs of day rading inernaional funds. The final secion concludes. II. NAV Pricing According o he Invesmen Company Ac of 1940, NAV calculaions for open-end muual funds are based on curren marke values for securiies wih respec o which marke quoaions are readily available, and on fair value as deermined in good faih by he board of direcors (Inves Company Ac, 1940, Secion 270.2a-4). Noice ha hese alernaive mehods may lead o differen values. Funds are hus no required o always use he las repored ransacion prices for he compuaion of NAVs. Fair value pricing is an alernaive, presumably o be used if he board of direcors of he fund deermines ha marke quoaions do no accuraely reflec valuerelevan informaion. In order o make such adjusmens, he boards of direcors of funds ypically have a pricing commiee o evaluae he validiy of prices and o make adjusmens in he even of a dramaic price drop. For example, Fideliy decided o use fair values o price some 6

of is Pacific Asian funds on Ocober 28, 1997, when he Hong Kong marke dropped foureen percen bu rebounded during he U.S. rading day. 2 While a fair value mechanism exiss for exraordinary evens such as he Asian currency crisis, i is an excepion raher han a regular rule. I is rarely used on days of normal marke volailiy, nor i is clear ha i could be, given he language of he Invesmen Company Ac (1940) quoed above. The cenral issue is he pracice of daily NAV pricing for open-end muual funds using informaion provided by anoher insiuion. The 1940 Invesmen Companies Ac requires muual fund companies o place heir securiies wih cusodians, who provide muual fund companies wih daily valuaion of he securiies in heir porfolios. 3 Cusodians, in urn, conrac for pricing informaion wih several firms. 4 These firms, in urn, may use sub-conracors wih experise in local markes for updaing prices. Cusodians face a number of problems beyond asynchroniciy in ime zones illiquid or non-raded asses, lags and delayed approvals for purchases or sales by inernaional invesors, dual share classes, and poor price records, o name a few. However, he paricular problems of sale pricing due o ime-zone differences has been recognized by muual fund companies for a leas five years. In Sepember of 1994, he rade periodical Pensions and Invesmens lised pricing adjused o he clien's own ime zone as an imporan challenge o cusodians (Giudice, 1994). III. Predicabiliy and Pricing Errors Reurn predicabiliy induced by sale prices is unique neiher o inernaional markes nor o muual funds. Wha is unique is ha absen special resricions muual funds offer invesors an opporuniy o rade a sale prices, while equiy markes generally do no. For example, consider he Russell 2000 index, which racks a porfolio of small socks in he U.S., many of which are raded infrequenly. Because he value of he index is calculaed using he mos recenly available ransacion prices, many of which are sale, he reurn on a porfolio of larger and more frequenly raded socks, such as he S&P 500, ends o lead he reurn on he Russell 2000 (Lo and MacKinlay (1988)). When here are common facors in securiy reurns, he compued reurn of a porfolio ha quickly reflecs he news abou hese common facors will 2 A he end of he U.S. rading day he NAV of Fideliy s Hong Kong Fund increased by 2 cens o $10.88 despie he lower close of he marke in Hong Kong (Wya, 1997). 3 Chemical Bank, Bankers Trus Company, and Sae Sree Corporaion are some of he larges cusodians serving he muual fund indusry. 7

end o predic he compued reurn on a porfolio ha is slow o incorporae his news. However, he predicabiliy of he Russell 2000 reurn caused by sale prices does no provide a profiable rading opporuniy in he componen shares, because in an efficien marke he relevan informaion will be quickly incorporaed in he price of hose securiies he nex ime hey rade. By conras, using sale prices in he compuaion of muual fund NAVs does creae he poenial for a profiable rading rule o invesors if he funds use hese NAVs o sele flows ino and ou of he fund, because his effecively allows invesors o rade a sale prices. Pricing errors affec no only hose who rade fund shares bu also he long-erm shareholders who do no rade. Invesors who do no rade are unaffeced only on he days on which here are no ne flows ino he fund, in which case any gains o purchasers of fund shares are borne by hose who sell heir shares o he fund. However, long-erm shareholders in he fund are affeced when here are ne flows. A negaive pricing error creaes a wealh ransfer from he exising o he new shareholders if here are ne inflows, and creaes a benefi o he exising shareholders in he case of ne ouflows. Fund managers care abou hese ransfers, because hey affec he performance of he fund. Consider an inernaional index fund ha aemps o replicae he performance of is benchmark index wih minimum rading coss. If he fund uses he wrong price o sele inflows and ouflows, he fund performance will deviae from he benchmark index by he amoun of he pricing error muliplied by he ne flow. If invesors sraegically ime heir inflows and ouflows because hey undersand he sign of he pricing error, or if ne flows are negaively correlaed wih he pricing errors for oher reasons, he fund will underperform is benchmark. The magniude of he pricing errors in he NAVs of inernaional muual funds induced by sale prices will depend on he amoun of value-relevan informaion ha is produced abou foreign markes while hey are closed. For example, French, Schwer, and Sambaugh (1987) show ha reurn variances in he U.S. are significanly higher during rading hours han during periods when he NYSE is closed, which is consisen wih a decline in informaion producion during imes when markes are closed. Ye, several researchers have shown ha i is possible o learn significan informaion abou he fuure reurns of inernaional markes every day hrough observaion of he reurn o he U.S. sock marke. 4 The mos commonly used services for inernaional pricing are EXTEL, Reuers, and Telekurs. 8

Hilliard (1979) applies specral analysis o he idenificaion of conemporaneous and lagged relaionships across inernaional equiy markes. While he finds no significan lagged iner-coninenal daily reurn effecs he does find srong inra-coninenal connecions. Oher researchers have found evidence ha he inernaional capial markes ransmi informaion raher efficienly around he globe. Eun and Shim (1989) sudy daily daa from a number of exchanges around he world and find ha shocks o U.S. equiy markes are ransmied o oher equiy markes, bu no vice-versa. Hamao, Masulis, and Ng (1990) use open-o-close and close-oclose daa and find ha boh volailiy and reurn innovaion spill across markes. These lagged effecs appear o be largely due o he informaional efficiency of he U.S. marke a incorporaing informaion abou shocks common o several markes. King and Wadwhani (1990) documen srong informaional spillovers beween New York, Tokyo, and London around he crash of 1987. Neumark, Tinsley, and Tosini (1991) show ha in he period following he crash of 1987 reurns of NYSE shares ha raded afer-hours in London and Tokyo correlaed o close-o-open reurns on he NYSE. Karolyi and Sulz (1996) use Japanese ADRs o explore wheher he magniude of he co-movemen of Japanese socks wih he U.S. marke can be explained via macro-economic facors. They find ha he conemporaneous movemen beween U.S. socks and Japanese socks is srong, bu no driven by macro-economic informaion. In summary, empirical work on inernaional (inra) day reurn behavior suggess ha foreign socks respond conemporaneously or wih a day lag o common news ha affec U.S. sock prices. The exen o which U.S. muual funds ha inves inernaionally incorporae he informaion ha becomes available during he U.S. rading day in heir NAV calculaions is an empirical maer. To accuraely assess he problems caused by sale pricing i is imporan o allow for he rue predicabiliy in foreign markes a would exis even if curren prices were used by fund companies for NAV calculaion. IV. A Simple Example XYZ Fund is a well-diversified global equiy fund ha invess in equiy markes around he world, including he U.S. We have chosen no o idenify i by name, alhough nohing abou is policy is unusual. A he end of 1998 he fund had over $2 billion in asses under managemen. A large componen of he shares in which he fund invess rade only in heir domesic markes 9

which eiher close before or shorly afer he sar of he U.S. rading day. The firs column of Table I summarizes he conemporaneous correlaion beween he oal fund reurn and he reurn on he S&P 500. As expeced, he XYZ Fund reurn is posiively correlaed wih he same-day S&P 500 reurn (0.26). If we spli he daily close-o-close S&P 500 reurn ino he close-o-10 AM reurn and he 10 AM-o-close reurn an ineresing paern emerges. The XYZ Fund reurn is highly correlaed wih he previous close-o-10 AM reurn on he S&P 500 (0.42), during which ime he inernaional markes are open, bu virually uncorrelaed wih he 10 AM-oclose reurn (0.03), when many foreign markes are closed. A poenial explanaion for his difference is ha during U.S. rading hours no informaion is produced ha is value-relevan for inernaional socks. However, he second column of Table I, which gives he correlaion beween he S&P 500 reurn and he nex-day fund reurn, shows ha his is clearly no he case. Firs, he correlaion beween he S&P 500 reurn and nex-day inernaional fund reurn is 0.38. This is no only higher han he same-day correlaion, bu he nex-day reurn is especially correlaed wih he curren-day 10 AM-o-close S&P 500 reurn (0.34). This is inconsisen wih he hypohesis ha no value-relevan informaion is produced during he U.S. rading day, bu consisen wih a siuaion where he fund uses sale prices o compue is NAV. Apparenly, he informaion produced during U.S. rading hours is refleced in he NAV on he nex day. Each of he inra-day hourly S&P 500 reurns is more correlaed wih he nex-day fund reurn han wih oday s fund reurn. The curren-day close 10 AM S&P 500 reurn is also posiively correlaed wih he nex-day inernaional NAV reurn (0.17), which can be expeced if he NAV calculaion is based on closing prices from Asian markes, since he laer close well before 10 AM EST. The conclusion from Table I is ha he daily NAVs values of he XYZ Fund are inefficien in ha hey do no incorporae much of he value-relevan informaion produced during U.S. rading hours. By allowing invesors o rade a hese inefficien prices he XYZ Fund opens iself up o speculaive day raders who migh aemp o ake advanage of his siuaion. A simple, ye very effecive sraegy could be based on he sign of he daily S&P 500 reurn: buy shares of he fund a he end of he days on which he S&P 500 is up and swich o cash a he end of he days on which he S&P 500 is down. A comparison beween he cumulaive buy-and-hold reurn from a dollar invesed in he XYZ Fund a he beginning of 1992 and he cumulaive reurn from swiching beween he fund and cash based on he sign of he S&P 500 reveals ha a dollar invesed in he fund in Augus of 1992 would have grown o 2.47 10

in July of 1998, while a dollar invesed he swiching rule would have grown o $5.17 (Figure 1). Moreover, a comparison of he risk of he wo sraegies shows ha he higher reurn can be achieved wih lower risk: he daily sandard deviaion of he buy-and-hold reurn is 0.605%, compared o 0.427% for he swiching sraegy. Because he swiching sraegy invess in he fund only on he days following an increase of he S&P 500, which occurs abou one-half of he ime, he variance of he sraegy reurn is abou one-half he variance of he buy-and-hold reurn, implying a raio of sandard deviaions of abou 0.7. V. Empirical Evidence V.1. Daa Descripion We obain daily oal reurns for boh acive and defunc open-end muual funds wih cerain Morningsar Caegories in he period from 01/02/1990 o 07/24/1998 from Wall Sree Web. The reurns are no adjused for sales charges (e.g., fron-end charges, deferred fees, redempion fees), bu are ne of managemen fees, adminisraive fees, 12b-1 fees, and oher coss ha are auomaically aken ou of fund asses. In order o be included ino our sample, each fund has o mee he following wo crieria: 1. Fund reurns should be available for a leas 100 days (ou of he 2165 rading daes) in he period from 01/02/1990-07/24/1998, and 2. The fund should belong o one of he following eigh Morningsar Caegories: Diversified Emerging Markes (DEM), Diversified Pacific/Asia Sock (DPA), Europe Sock (EU), Foreign Sock (FS), Japan Sock (JPN), Lain America Sock (LA), Pacific/Asia ex-japan Sock (PXJ), and World Sock (WS). The above crieria was me by 10 DEM funds, 34 DPA funds, 58 EU funds, 112 FS funds, 17 JPN funds, 31 LA funds, 65 PXJ funds, and 64 WS Funds. We use he oal reurn for he Vanguard 500 Index Fund (icker symbol VFINX) as our proxy for he S&P 500 reurn. We also uilize he daa on daily muual fund ne flows from TrimTabs for a sample of inernaional funds during he period from 02/03/1998 o 06/20/1999. In addiion o daily ne flows, his daabase conains informaion on daily NAVs and oal ne asses (TNAs). We resric ourselves o 116 funds for which a leas sixy days of flow daa are available. Aside from limied coverage, he TrimTabs daa seem o suffer from a variey of problems, including missing observaions, inerchanged digis, and wha seem o be random jumps in he posiion of he 11

decimal poin. These problems are more frequen in he ime series of ne flows han in he ime series of TNAs. For his reason, we discard he ne flow series provided by TrimTabs and insead compue ne flows on he basis of TNAs and NAVs. One paricularly imporan daa problem is ha funds seem o vary in heir reporing pracices wih respec o he TNAs some funds racked by TrimTabs seem o repor heir daily TNA before hey process he purchase and sale orders submied during he day, ha is, since he las selemen. 5 This pracice leads o inaccurae TNA figures, bu does no invalidae he daa. Raher, equipped wih he awareness of a fund s pracices, one can arrive a he exac ne fund flow using he appropriae compuaion. We will revisi his issue in Secion VII. V.2. Summary Saisics There are 391 funds in he final sample and heir performance varies widely. Panel A of Table II summarizes he daily performance of he average fund in each Morningsar Caegory. Average fund reurns are compued by consrucing an equally-weighed (EW) porfolio of he available individual funds in each caegory. The able shows ha he performance of EW porfolios reflecs he performance of global markes in he firs par of he 1990s. The S&P 500 has ouperformed all broad inernaional indices, and Europe and Lain America have fared beer han he Pacific-Asia region, in par due o he poor performance of he Japanese marke. For he purpose of his paper, he mos ineresing par of Panel A is column 5, which gives he correlaion beween he S&P 500 reurn and he nex-day reurns on EW fund porfolios. The values range from 0.12 for Lain America o 0.41 and 0.42 for he World Sock and Foreign Sock funds, respecively. The lagged cross-correlaion for Europe (0.36) is abou he same as for he Pacific Asia funds, and is slighly higher han he Japanese Funds (0.25). For comparison, he auocorrelaion of he S&P 500 is considerably smaller (0.04). Panel C of Table II gives he disribuion of performance across funds wihin each caegory. The firs wo rows peraining o each caegory show ha here is considerable variaion in average reurns and reurn volailiy. Much of he variaion may be due o he fac ha he available fund hisories differ in lengh. The hird row gives he disribuion of fund reurn auocorrelaions and he fourh row shows lagged cross-correlaion beween fund reurns and he 5 We hank John Ameriks from TIAA-CREF for drawing our aenion o his issue. I is also noed in Chalmers, Edelen, and Kadlec (1999), Edelen and Warner (1999), and Greene and Hodges (2000). 12

previous-day S&P 500 reurn. The auocorrelaion medians are highes for Diversified Emerging Markes (0.26), Pacific-ex-Japan (0.18), and, perhaps surprisingly, World Sock (0.18) funds. Posiive auocorrelaions sugges ha even he closing prices from he local exchanges are sale due o hin rading. As would be expeced, medians end o be highes for he fund caegories ha inves in more hinly raded emerging markes. Median values for Japan (0.09) and Europe (0.05) are lower, bu boh exceed he auocorrelaion of 0.04 for he S&P 500. The final row peraining o each caegory gives he disribuion of he correlaion beween he fund reurns and he previous-day S&P 500 reurns. The esimaed lagged cross-correlaions are posiive for all he 391 sample funds. For he Foreign Sock funds, he larges caegory wih 112 funds, he cross-correlaion wih he nex-day S&P 500 reurns ranges from 0.20 o 0.50. The median correlaion is above 0.30 in mos caegories, which suggess ha he resuls for he XYZ Fund repored in Secion IV are no unusual. Wih he excepion of he Lain American and Diversified Emerging Markes funds, he cross-correlaion wih he lagged S&P 500 reurns also exceeds he fund auocorrelaion by a subsanial margin. Apparenly, he informaion produced in hose local markes ha is no fully refleced in all securiy prices a he close due o hin rading is as imporan for predicing nex-day fund reurns as he informaion produced during he rading day by he U.S. marke. In conclusion, he resuls sugges ha mos sample muual funds absen resricions on rading and fees are vulnerable o sraegic day rading by marke paricipans. V.3. Inernaional Fund Reurns Condiional on U.S. Marke Movemens The posiive correlaion of inernaional fund reurns and reurns wih he prior day S&P 500 index indicaes ha he S&P 500 can serve as an informaive signal for invesing in inernaional funds. This is illusraed in Table III, which gives a breakdown of he average inernaional fund reurns by he S&P 500 reurn on he prior day. For each caegory, he EW porfolio reurns are significanly negaive on he days following a decline in he S&P 500 and significanly posiive on he days following an increase in he S&P 500. Wih he excepion of Lain American markes, which are open during much of he U.S. rading day, he difference exceeds 30 basis poins per day. I is larges for he Pacific-ex-Japan and Diversified Pacific Asia caegories (43 basis poins). Volailiy also ends o be slighly higher following a marke decline in he U.S. 13

A simple rading sraegy implied by hese condiional averages is o inves in inernaional funds a he end of he days on which he S&P 500 goes up, and avoid invesing in inernaional funds a he end of he days on which he S&P 500 declines. Shoring muual funds is generally no possible, so in carrying ou he analyses we assume ha he posiion is held in cash following down days. As shown in Table III, he U.S. marke is abou equally likely o be up or down on a given day, which implies ha he swiching sraegy would inves in inernaional funds only abou one-half of he ime. Panel A of Table IV summarizes he reurns on his sraegy applied o EW porfolios of inernaional funds by caegory. The firs hree columns show ha he sraegy reurns are posiive and highly significan for all caegories. The sraegy reurns are highes for European funds and lowes for funds ha inves in Japan. Because he sraegy only invess in he fund on abou one-half of he days, he variance of he sraegy reurns is also only abou one-half he variance of a buy-and-hold sraegy, resuling in a 30% decline of sraegy sandard deviaion relaive o he respecive caegory EW porfolio. The caegory sraegy reurns reflec, in par, he average performance of he underlying markes. For example, he las row shows ha he sraegy applied o he S&P 500 iself yields posiive average reurns of 5.3 basis poins per day, bu his is almos enirely due o he performance of he U.S. marke and no o he presence of posiive auocorrelaions. This can be seen from he nex hree columns, which compue for each caegory he sraegy reurns in excess of a buy-and-hold sraegy. In erms of average reurns, swiching beween he S&P 500 and cash does no pay, as he sraegy underperforms he buy-and-hold sraegy on average by 1.4 basis poins per day. The reason is ha, alhough he fund reurns are, on average, posiive on days following a decline in he S&P 500, any gains from exploiing he (small) posiive auocorrelaion are ouweighed by he opporuniy loss resuling from he cash posiion. By conras, he excess sraegy reurns for he inernaional funds are all significanly posiive, and vary from 5.4 basis poins (=2.62) per day for Lain America o 10.8 basis poins (=8.24) per day for he funds ha inves in Diversified Pacific Asia. Measured relaive o a buy-and-hold sraegy, hese numbers ranslae o an excess reurn of he swiching sraegy of abou 13.5 and 27 percen per annum, respecively. Excep for he Lain American EW porfolio, which rades in he same ime zone as he U.S. markes, he -saisics for he equaliy of means of he sraegy and buy-and-hold reurns exceed 5 for all fund caegories. These higher average reurns occur despie he fac ha he sraegy reurns inves in non-ineres bearing cash abou one-half of he 14

days. As shown in Table III, he average reurns of inernaional funds for he days of a decline in he U.S. marke are significanly negaive, and a posiion in cash on such days dominaes a posiion in he fund. Panel B of Table IV shows he disribuion of he sraegy reurns and he excess sraegy reurns relaive o a buy-and-hold sraegy for each caegory by fund. The raw sraegy reurns are posiive for almos all funds. Excep for a single European fund, all 391 excess sraegy reurns are also posiive. The excess sraegy reurns are he highes for he Diversified Pacific Asia funds, and he minimum -saisic for he excess sraegy reurn exceeds 4.5 in his caegory. The combinaion of a large ime zone difference and he fac ha many securiies in hese markes are hinly raded resuls in srong predicabiliy of fund reurns. 6 For oher caegories he -saisics are somewha lower, bu he median -saisic exceeds wo for every fund caegory. The conclusion from Tables II, III, and IV is ha he NAVs of mos inernaional muual funds do no efficienly reflec informaion produced during U.S. rading hours. The marke convenion of using closing prices from foreign exchanges in NAV compuaion a he end of he U.S. rading day clearly induces subsanial amoun of predicabiliy in fund reurns. VI. Transacions Coss and Barriers o Trade Wha sops speculaors from day rading on sale NAVs? Firs and foremos, fund fees. Abou 60% of he 1,796 U.S.-based inernaional equiy muual funds currenly lised in Morningsar's Principia have eiher a fron-end or a back-end load, and in mos cases he sum of he fron- and he back-end load exceeds one percen. An early redempion fee is charged by 64 funds. The quesion of ineres is wheher he profiabiliy of day rading based on he sign of he S&P 500 is limied o hose funds ha charge fees. If no-load funds are sysemaically differen from he funds ha do charge fees, perhaps by heir deliberae and successful fair pricing effors, he average sraegy reurns o no-load funds will be lower. We invesigae his possibiliy by spliing our sample of muual funds wihin each of he eigh caegories ino no-load funds (i.e., 6 Moreover, during he recen Asian crisis, holding a posiion in cash on abou one-half of he days would have furher conribued o he superioriy of he sraegy reurns over he respecive fund reurns. 15

funds ha charge neiher loads nor redempion fees) and funds ha charge loads and/or redempion fees. 7 Table V shows ha he average reurns of no-load and load funds are no saisically differen. In addiion, here are no saisically significan differences beween he corresponding average sraegy reurns. Pooling all funds, he difference beween he sraegy reurns of load and no-load funds is -0.3 basis poins per day (=-0.67). In sum, we do no find any saisical evidence o indicae ha no-load muual funds are less vulnerable o sraegic exploiaion han load funds. Besides fees, a second impedimen o aking advanage of sale NAVs is a common pracice by funds o idenify and exclude acive raders. No-load and low-load funds are especially moivaed o be vigorous in creaing and mainaining safeguards agains excessive swiching of money in and ou he fund via policies explicily designed o discourage highfrequency marke iming 8. Also, funds can rejec large purchases or revoke elecronic exchange privileges if i regards hem as disrupive o he fund s operaion or performance managemen. The grounds for such a rejecion could be eiher he iming of he invesmen or he invesor's hisory of excessive rading. In addiion, he proceeds from redempions could be mailed o invesors in he form of a check, which effecively delays he immediae availabiliy of funds. Large redempions can be delayed if hey are disrupive o he operaions of he fund, and can be me in kind, ha is, by surrendering securiies raher han cash. The array of weapons muual funds have a heir disposal hus appears capable of inroducing barriers o daily speculaion along wo primary dimensions increased cos of speculaion and decreased liquidiy of such invesmens. Muual fund supermarkes, such as Schwab's OneSource Service, provide a special challenge o no-load muual funds. These markeplaces bundle invesmens of muliple cusomers, which obscures he ideniy of poenial day raders. While funds may ask Schwab o 7 For 19 of he 391 funds we could no deermine heir load saus, which reduces he number of funds used in his calculaion o 372. 8 For example, in heir prospecuses several Vanguard funds cauion imers by highlighing he following wo senences in red: The Vanguard funds do no permi marke-iming. Do no inves in his Fund if you are a markeimer. This warning is preceded by a plain-alk descripion of harmful effecs of marke-iming sraegies. A Vanguard muual fund prospecus ypically conains he following explanaion: Some invesors ry o profi from a sraegy called marke-iming swiching money ino invesmens when hey expec prices o rise, and aking money ou when hey expec prices o fall. As money is shifed in and ou, a fund incurs expenses for buying and selling securiies. These coss are borne by all fund shareholders, including he long-erm invesors who do no generae he coss (see, e.g., Vanguard Inernaional Value Fund Prospecus (1999), p. 3). 16

monior marke iming by is cusomers, i is no clear o which exen effecive monioring indeed akes place. Schwab charges a fee in case of shor-erm redempions by is cliens, bu his fee has a sepwise srucure and is capped o a maximum. 9 This implies ha if day rading were performed on a sufficienly large scale, he round-rip coss could be driven down o several basis poins. 10 This is a poenial concern for many funds: ou of 1,796 U.S.-based inernaional muual funds currenly lised in he April 1999 Morningsar Principa, 714 funds do no charge fron-end load, back-end load, or redempion fees. To assess he poenial vulnerabiliy of such funds, we compued he average reurns o he sraegy performed on he respecive EW porfolio for each caegory under a variey of assumpions abou ransacions coss. We find ha ransacions coss are ineffecive a discouraging iming by large invesors. Depending on he caegory, fees of 30-45 basis poins per round rip are required for he average sraegy reurns o equal he reurns of he underlying EW porfolios, which is well above he roundrip ransacions coss a markeplace like Schwab would charge on a $100,000 invesmen. VII. Fund Reurns and Ne Flows Transacions coss and monioring may discourage day raders, bu neiher addresses he source of he sale pricing problem. The individual securiy values used in he NAV compuaion simply do no reflec available informaion. If ne flows are correlaed wih he pricing errors, possibly even for reasons oher han he deliberae acions of marke imers, sale prices have a diluing effec on he exising shareholder value. As poined ou in Secion V.1, he flow daa from TrimTabs daa suffer from a variey of problems, which appear o be more frequen in he ime series of ne flows han in he ime series of TNAs. We hus compued ne flows on he basis of TNAs and NAVs. A poenially imporan consideraion is ha funds seem o vary in 9 For example, Schwab's Muual Fund OneSource service, which presenly includes over 1,000 no-load muual funds, charges shor-erm redempion fees o cusomers who hold heir invesmen for 180 days or less according o he following schedule: 0.75% of principal (or $39, whichever is greaer); a maximum fee of $299 for rades placed hrough a regisered represenaive; a maximum fee of $199 for rades placed hrough auomaed channels. For funds ha do no paricipae in he service, Schwab charges heir sandard ransacions fees (in addiion o any redempion fees imposed by he fund): 0.7% of principal for ransacions from $1,000 o $14,999; 0.7% on he firs $15,000 and 0.2% on amoun over $15,000, capped a $149, for ransacions of $15,000 or more (Schwab, 1999). 10 Specifically, round-rip coss of speculaion hrough Schwab would be 20 basis poins for an invesmen of $74,500 ($99,500) ino a fund ha paricipaes in Schwab's Muual Fund OneSource service (a no-load fund ha does no charge redempion fees and is no a par of he OneSource service). Doubling he size of he invesmen o $149,000 ($199,000), of course, drives he round-rip coss o 10 basis poins, ec. 17

heir reporing pracices wih respec o he TNAs some funds migh repor heir daily TNA before hey process he purchase and sale orders submied during he day, ha is, since he las selemen. This raises he concern ha ne flows may be compued incorrecly, and may in effec be lagged by a day. Specifically, on a given dae fund i migh repor is TNA eiher before ne flows are added o i, denoed here as TNA,, or afer ne flows are added o i, denoed simply as i TNA i,. In our analyses we sudy he ne relaive flow (henceforh ne flow), denoed as flow i, ino fund i on dae. We compue he ne relaive flow as flow NewMoney, TNA, 1, where i, = TNAi, ( 1+ Ri, ) TNAi, 1 i, = i / i NewMoney is he ne dollar flow of money ino fund i on dae. Depending on he reporing pracice of fund i, oal ne asses on dae in he above formulae should be eiher aken direcly as TNA i, (if he fund repored appropriaely) or compued as he discouned value of omorrow s oal ne asses TNA, ha is, TNA 1 /( 1 R, 1). i,+1 i, + + i + The mehod of compuing oal ne asses may have considerable impac on he resuls. 11 I is herefore imporan o deermine he reporing pracices for each of he funds in our sample. To ha end, we compared for each fund he daa provided by TrimTabs, boh he repored endof-monh oal ne asses and he modified end-of-monh oal asses (compued on he basis of he assumpion ha funds repor TNA, insead), wih he end-of-monh oal ne asses repored i in he 1998 CRSP Muual Fund Daa Base. 12 For mos funds in our sample we found ha here is a very close mach beween he wo repored series; some funds exhibied a deviaion in one or wo observaions (ofen in December), ye were mached precisely in all oher monhs; only 3 funds appeared o follow he pracice of reporing TNA,. We could no classify a number of i 11 The resuls presened in Table VI, compued under he assumpion ha TrimTabs repors he rue oal ne asse values for all funds, differ from he resuls based on he assumpion ha TrimTabs repors he pre-flow oal ne asses for all funds. Differences are especially noiceable for he conemporaneous relaionship beween ne flows and reurns on he S&P 500. For example, he median conemporaneous correlaion beween ne flows and reurns on he S&P 500 increases for each of he eigh Morningsar Caegories by 0.126 or more if he pre-flow assumpion is used for all he funds. 12 Given he periods of coverage of he wo sources of daa, here were up o 11 poins for comparisons per fund. Similarly o he mehodology employed by Greene and Hodges (2000), we classified each poin as eiher posflow (indicaing he pracice of reporing TNA, ) or pre-flow (indicaing he pracice of reporing i TNA, ), depending on he magniudes of he absolue values of relaive deviaion of each TrimTabs-based oal ne asse values from he CRSP-repored oal ne asses. While for mos funds for which here were sufficienly many valid daa poins o draw meaningful inferences here was a clear majoriy paern indicaing he likely reporing pracice, a few funds feaured only a slim majoriy in favor of he pos-flow hypohesis he numbers of likely pos-flow i 18

funds because hey were added o he sample only in 1999. 13 In sum, 88 ou of 116 funds in our sample appear o be reporing he appropriae oal ne asses, 3 funds seem o be reporing TNA,, while he daa for he remaining 25 funds were eiher oo noisy o make a deerminaion i or were no available for 1998. 14 The resuls obained under he assumpion ha all 116 funds in our sample repor he appropriae TNAs and he resuls obained for he 91 funds whose likely reporing pracice we were able o idenify are very similar; for he sake of breviy, in Table VI we repor only he former. Panels A and B of Table VI summarize he correlaions of daily ne flows wih he sameday S&P 500 reurn as well as he nex-day reurns for individual funds by caegory. A posiive correlaion suggess ha ne flows anicipae fuure fund reurns. This correlaion does no speak direcly o he issue of gains and losses o he exising shareholders, because any marke iming abiliy of he ne flows will only affec he exising shareholders o he exen ha i is correlaed wih pricing errors. However, a large posiive correlaion beween he S&P 500 and ne flows would be a cause for concern o fund managers in ligh of he documened profiabiliy of he swiching sraegy. Panel A shows ha he median correlaion beween ne flows and nex-day fund reurns range from 0.029 for Diversified Emerging Markes o 0.083 for he Europe Sock funds. The median correlaion among all 116 funds in he sample is 0.027. While hese medians seem small, he spread of he correlaions is subsanial. One-quarer of all funds experience a correlaion beween ne flows and subsequen reurns ha exceeds 0.07. The boom par of Panel A gives he correlaion beween fund flows and he same day S&P 500 reurns. Abou one-half of all he funds in he sample experience on average ne inflows when he S&P 500 is up, and ouflows when he S&P 500 is down. The range of correlaions is again quie wide, which suggess ha, while he shareholder in he average fund may no be affeced by a correlaion and pre-flow observaions were very close, say 6 v. 5. Prior o adoping he compued classificaion, we looked ino he daa for each such fund and verified ha he classificaion is indeed appropriae. 13 For several funds in our sample we found sizeable deviaions (up o an order of magniude) from he oal ne asses repored by CRSP in more han one monh (in all such insances, we verified he validiy of he CRSP daa by maching i wih he daa from Morningsar Principia). 14 Greene and Hodges (2000) employ a similar mehodology, bu hey base heir classificaion on he oal ne asses compued on he basis of he N-SAR and N-30D repors ha muual funds file semi-annually o he SEC (raher han on he 1998 CRSP Muual Fund Daa Base). While we find ha he overwhelming majoriy of he funds in our sample seem o have followed he proper pracice of reporing pos-flow oal ne asses, Greene and Hodges (2000) find ha abou 2/3 of he funds from heir sample (812 funds, no resriced o inernaional sock funds) appear o have followed he pracice of reporing pre-flow oal ne asses. An unseling possibiliy, a he same ime a cavea o his mehodology, is ha some funds migh be inadverenly inconsisen in heir reporing pracices over ime. 19

beween ne flows and reurns, his is no he case for all funds. Panel B gives he disribuion of corresponding regression coefficiens of ne flows on nex-day fund reurns and same-day S&P 500 reurns. The median regression coefficiens are again close o zero, and he fracion of slope coefficiens significanly differen from zero a he 5% level is 9/116 and 4/116, respecively, which is abou wha can be expeced by chance. We also compared he no-load and load funds from he sample. Our analysis (no repored in deail for breviy) suggess ha here were no saisically significan differences wih respec o average correlaions and regressions beween he wo; ha is, fees did no o seem o have an impac on he degree o which speculaive sraegies were employed on he sample funds during he sample period. These resuls differ somewha from hose repored by Greene and Hodges (2000), who find a significan negaive impac of flows on fund reurns. We believe ha we have correcly idenified he reporing pracices of he funds in our sample and ha he discrepancy appears o be driven by he differences in classificaion. 15 In summary, he spread of he correlaions also suggess ha here have been a number of funds in which he exising shareholders have eiher benefied or have been hur a he expense of he ouside invesors. To quanify hese gains and losses we develop a more precise definiion of informaionally efficien pricing in he nex secion. VIII. Efficien NAV Pricing There are a variey of soluions o he sale pricing problem. A simple one is o impose a ransacion fee on rades of fund shares. While his may make day rading unprofiable, i is unaracive for uninformed invesors wih shorer invesmen horizons, and does no direcly address he underlying problem of inefficien pricing. The second is o change he ime of pricing of he fund shares, for example, o price European funds during he morning hours EST. This may be aracive for funds ha inves in a single (foreign) counry or ime zone, bu provides lile relief for global funds ha rade in markes locaed in many differen ime zones. The adminisraion of resuling inra-day cash posiions would also be cumbersome for fund families ha allow exchanges beween funds if hese sele a differen poins in ime. 20

The hird soluion is o improve he pricing of he fund shares by using he prices of close subsiues o he muual fund porfolio. Fuures conracs and American Deposiory Receips raded during U.S. rading hours are likely o conain value-relevan informaion and can help improve he informaional efficiency of he NAV compuaion. For example, a porfolio of Japanese socks may be priced using he informaion from he Nikkei 225 fuures conrac raded in Chicago. The inra-day reurn of a porfolio of ADRs wih a similar indusry and counry composiion as he fund porfolio may provide a good approximaion o he reurn of he muual fund shares. A final and more encompassing soluion is o use a framework o adjus he NAV and make i orhogonal (i.e. uncorrelaed) o he available informaion in he marke. This mehod is simple and inuiive. If he price of a porfolio of muual fund shares reflecs all informaion ha is value-relevan, shor-erm porfolio reurns should be approximaely unpredicable. If funds base heir NAVs on sale prices, some value-relevan informaion will be refleced in he NAV only on he nex day (or even subsequen days). Our proposed adjusmen is o ake he predicable porion of nex day s NAV and include i in oday s NAV. Consider he following regression: R, = α + β Z + ε (1) NAV i +1 i i where NAV Ri 1, + is he nex-day NAV-reurn on fund i (ha is, he percenage change of fund i s NAV) and Z is a se of curren insrumens useful in predicing he nex-day NAV-reurn. In he conex our rading rule Z would be he reurn on he S&P 500 for day. In principle, Z could be a vecor of a number of observable variables useful for predicing he nex-day NAV reurn and could include, for example, he reurn on a Nikkei fuures conrac, or he reurn on a porfolio of relevan ADRs. The predicable componen of he reurn is he fied value of he i i regression α + β Z. The correcion would ake he predicable componen of omorrow s NAVreurn and simply add i o oday s NAV: 15 Our analyses under he assumpion ha all funds in he sample repored he paper) consisen wih he findings repored by Greene and Hodges (2000). TNA, yielded resuls (no repored in i 21

NAV = NAV (1 +α + β Z ) (2) * i, i, i i This rule is quie simple o implemen by esimaing equaion (1) and using he fied values of he regression o make he adjusmen in equaion (2). In pracical applicaions i should be easy o ge accurae esimaes of b using daily daa. The consan erm is he porion of he expeced daily reurn uncorrelaed wih Z, and is subsanially more difficul o esimae. However, α i is likely o be very close o zero, and a leas an order of magniude smaller han herefore, bes ignored, which leads o he following correcion: β Z i. I is, NAV = NAV (1 + β Z ) (3) * i, i, i This correcion adjuss each daily NAV, o reflec he addiional value-relevan informaion, and will herefore have a negligible impac on he long-erm performance of he fund. This approach would be easy o implemen in pracice. The radiional NAV compued using he las observed marke prices supplied by radiional pricing services coninues o be he anchor for daily valuaion, and he correcion only requires ha Z be observed a he close of he marke. Panel A of Table VII shows he effec of using his correcion on he profiabiliy of our rading sraegy based on he sign of he S&P 500. We esimaed Equaion (1) for he EW porfolios for each caegory using he reurns on he S&P 500 as he insrumen Z. The firs wo rows for each caegory compare he disribuions of he caegory reurns based on he uncorreced and correced NAVs, respecively. The correcion slighly increases he sample sandard deviaion of he reurns, bu, as expeced, has lile or no effec on he sample average reurns. Mos imporan is he decline of he correlaion wih he lagged S&P 500 reurn, documened he fourh column, which ranges from 0.121 for Lain America o 0.424 for Foreign Sock funds for he uncorreced reurns and from 0.002 o 0.015 for he reurns based on he correced NAVs. The nex wo rows compare he sraegy reurns using he raw and he correced NAVs. As would be expeced, he NAV correcion he sraegy applied o he correced NAVs is close o zero. The correcion hus increases he efficiency of he NAV and removes he profiabiliy of rading sraegies ha exploi sale prices in he NAV calculaion. Panel B of Table VII furher 22

illusraes he effec of he correcion. For each caegory, he disribuion of EW porfolio reurns is no significanly affeced by he correcion (as noed before, here is a sligh increase in he reurn variance), while he disribuions of sraegy reurns changes dramaically from as speculaive profis are eliminaed by he correcion. IX. Wealh Transfers Our correcion mehodology also provides a useful framework o analyze he wealh ransfers ha resul from he inefficiency of he repored NAVs. The difference beween he repored and he correced NAV is an esimae of he pricing error of he fund shares ha resuls from ignoring he informaion conained in he S&P 500 reurn. I is he source of wealh ransfer beween hose who buy and sell shares during he day and he long-erm shareholders in he fund who do no rade. As poined ou in he previous secions, if here are no ne flows ino a fund, he pricing error muliplied by he gross flow is simply a wealh ransfer from hose who buy o hose who sell on a given day. The ne flow muliplied by he pricing error is an esimae of he wealh ransfer beween he long-erm shareholders in he fund who do no rade and hose who do rade. Because TrimTabs does no repor gross flows (ha is, boh inflows and ouflows), we are unable o quanify he wealh ransfers beween buyers and sellers of fund shares and we concenrae on he effec of pricing errors on he wealh of he long-erm shareholders. We consider a variey of measures o characerize he wealh effecs. The firs is he ne wealh ransfer per fund, measured over he 17 monhs ha comprise our sample. For each fund i is compued as he daily percenage pricing error muliplied by ne new money invesed in he fund. Table VIII shows ha he average daily wealh ransfer varies from -$4.62 million per day o $0.80 million per day (a negaive number indicaes a loss o he incumben shareholders who do no rade). Summed across all 116 funds and rading days in he sample, he oal ne loss o incumben shareholders is a mere -$13.85 million. This number is small compared o he esimaed 68 billion invesed in hese funds as of May of 1999, which is no surprising because he correlaion beween ne flows and nex-day reurns has been small for he vas majoriy of he funds in our sample. A low correlaion beween ne flows and reurns indicaes ha incumbens are equally likely o gain or lose on a given day. The second row of Table VIII gives he average size of he wealh ransfer by fund, compued as he absolue value of he dollar gain and loss o 23

incumben shareholders. The median fund experienced an average daily wealh ransfer beween incumbens and ousiders of $722,000, and he oal of all wealh ransfers across funds was $300.02 million during he sample period. This oal represens abou 0.44 % of he asses under managemen in hese funds. Since our sample only covers abou 20% of all inernaional funds in erms of marke capializaion, a reasonable esimae of he oal wealh ransfers boh posiive and negaive for all inernaional funds during his period is $1.5 billion. Noe ha hese esimaes exclude any wealh ransfers beween purchasers and sellers of fund shares on a given day, and are herefore a lower bound on he oal wealh effecs beween all invesors ha raded shares in inernaional muual funds during he sample period. The nex wo rows of Table VIII convey he same message using a differen measure while percenage loss per fund is fairly limied because of he low correlaion beween ne flows and nex-day fund reurns, he oal wealh ransfer amouns o abou 0.44% of he money invesed ino he funds. The remainder of Table VIII looks a he measure of mispricing resuling direcly from reurn predicabiliy, expressed as he negaive of he predicable componen of he nex-day fund reurn. The fifh and he sixh row of Table VIII look a he mispricing in he sample of 116 funds moniored by TrimTabs (Sample 1). While he fifh row suggess ha he price of muual fund shares is abou 3 basis poin oo low for he median fund, he sixh row uncovers a more compelling saisic fund reurn predicabiliy causes he median mispricing o be as large as 29 basis poins, which is a minimum a nonrivial fracion of he ypical fund s expense raio. Finally, he las wo rows replicae he mispricing analysis repored in he preceding wo rows on our sample of 391 inernaional muual funds (Sample 2) and yield qualiaively similar conclusions. I is imporan o noe ha he $1.5 billion measure is no indicaive of by how much incumben shareholders suffer a he expense of raders, since i is a measure of he absolue value of mispricing. Raher, i is measure of he unfairness of NAV pricing across inernaional fund shareholders over he period. While i may be comforing o find ha, on average, invesors were no hur oo much by he use of sale prices, his does no mean ha individual shareholders did no suffer due o he use of incorrec prices. Given ha he principal goal of he ICI was o creae a regulaory framework for he fair reamen of all shareholders, i would seem ha he reducion of his oal mispricing is a reasonable goal of he muual fund indusry as a whole. 24

X. Conclusion This paper documens evidence ha he pracice of using he final ransacions prices of foreign exchanges o compue daily NAVs by muual funds creaes predicabiliy in heir reurns. We find ha muual fund prices are no efficien wih respec o informaion ha becomes available during he U.S. rading day. Before ransacions coss, a simple rading sraegy based on his informaion in he S&P 500 can generae reurns ha ouperform a buy-and-hold sraegy in hose funds by around 20 percen per year over he period from 1990 o 1998 while incurring only 70% of he underlying funds volailiy. In ligh of hese incenives, muual funds have designed a variey of mechanisms o discourage day raders. An analysis of he paern of flows ino inernaional funds shows ha he amoun of money involved in sraegic exploiaion of hese opporuniies has been relaively modes, eiher because funds have been successful in curailing day raders, or because few invesors have been aware of hese sraegies and heir profiabiliy. Despie he fac ha long-erm shareholders have on average no seem o have been seriously affeced by day raders, a conservaive esimae of he oal of wealh ransfers among invesors semming from inefficien fund pricing is roughly $1.5 billion during he 17 monh period ending in June 1998. We propose a procedure o improve he efficiency of repored ne asse values ha is easy o implemen in pracice. This procedure requires a deparure from he indusry pracice of using las ransacions prices from foreign markes. Given he global rend owards elecronic rading and coninuous pricing, fund companies and regulaors should look a alernaives like his one ha allow funds o offer fair pricing o invesors. There is a direc radeoff beween esablishing a fair pricing rule for fund shares and he need o resor o he monioring of acive raders and he need o impose expenses such as loads and redempion penalies. 25

References Abou Muual Fund Invesing a Schwab, 1999. Available a hp://www/schwab.com. Brown, S. J., W. N. Goezmann, T. Hiraki, T. Osuki, and N. Shiraishi, 1998. The Open-End Japanese Muual Fund Puzzle. Journal of Business, forhcoming. Cai, J., K. C. Chan, and T. Yamada, 1997. The Performance of Japanese Muual Funds. Review of Financial Sudies 10(2), 237-274. Chalmers, J. M. R., R. M. Edelen, and G. Kadlec, 1999. The Wildcard Opion In Transacing Muual- Fund Shares. Working paper. Edelen, R. M. and J. Warner, 1999. Why are Muual Fund Flow and Marke Reurns Relaed? Evidence from High-frequency Daa. Working paper. Eun, C. S. and S. Shim, 1989. Inernaional Transmission of Sock Marke Movemens. Journal of Financial and Quaniaive Analysis, 24(2), 241-256. French, K., G. Schwer, and R. Sambaugh, 1987. Expeced Sock Reurns and Volailiy. Journal of Financial Economics, 19, 3-30. Giudice, J., 1994. Cusodians Meeing New Challenges: Foreign Markes Presen Problems. Pensions and Invesmens, Sepember 19, 1994, Page 19. Greene, J.T. and C. W. Hodges, 2000. The Diluion Impac of Daily Fund Flows on Open-end Muual Funds. Working paper. Hamao, Y., R. W. Masulis, and V. Ng, 1990. Correlaions in Price Changes and Volailiy across Inernaional Sock Markes. Review of Financial Sudies, 3(2), 281-307. Hilliard, J. E., 1979. The Relaion Beween Equiy Indices on World Exchanges. The Journal of Finance, 34(1), 103-114. Invesmen Company Ac, 1940. 17 C.F.R. 270 (1940). Karolyi, A. and R. Sulz, 1996. Why Do Markes Move ogeher? An Invesigaion of U.S.-Japan Sock Reurn Co-movemens. The Journal of Finance, 51(3), 951-986. King, M. A., and S. Wadwhani, 1990. Transmission of Volailiy beween Sock Markes. Review of Financial Sudies, 3(1), 5-33. Lo and MacKinlay, 1988. Sock Marke Prices Do No Follow Random Walks: Evidence from a Simple Specificaion Tes. Review of Financial Sudies, 1, 41-66. Neumark, D., P.A. Tinsley, and S. Tosini, 1991. Afer-Hours Sock Prices and Pos-Crash Hang-Overs. The Journal of Finance, 46(1), 159-178. Newey, W. and K. Wes, 1987. A Simple, Posiive Semi-Definie, Heeroskedasiciy and Auocorrelaion Consisen Covariance Marix. Economerica, 55, 703-708. Vanguard Inernaional Value Fund Prospecus, 1999. Available a hp://www.vanguard.com. Wya, E., 1997. The Marke Turmoil: The Funds; Fideliy Invokes Fine Prin And Angers Some Cusomers. The New York Times, Ocober 31, 1997, Secion D; Page 6; Column 1. Zizewiz, E., 2000. Daily muual fund ne asse value predicabiliy and he associaed rading profi opporuniy. Working paper. 26

Panel A: DEM - EW fund and sraegy wealh Panel B: DPA - EW fund and sraegy wealh log(wealh) 0.0 0.5 1.0 1.5 2.0 log(wealh) 0.0 0.5 1.0 1.5 2.0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1990 1991 1992 1993 1994 1995 1996 1997 1998 19900102 -- 19980724 Panel C: EU - EW fund and sraegy wealh 19900102 -- 19980724 Panel D: FS - EW fund and sraegy wealh log(wealh) 0.0 0.5 1.0 1.5 2.0 2.5 log(wealh) 0.0 0.5 1.0 1.5 2.0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1990 1991 1992 1993 1994 1995 1996 1997 1998 19900102 -- 19980724 Panel E: JPN - EW fund and sraegy wealh 19900102 -- 19980724 Panel F: LA - EW fund and sraegy wealh log(wealh) -0.5 0.0 0.5 1.0 1.5 log(wealh) 0.0 0.5 1.0 1.5 1990 1991 1992 1993 1994 1995 1996 1997 1998 1991 1992 1993 1994 1995 1996 1997 19900102 -- 19980724 Panel G: PXJ - EW fund and sraegy wealh 19900102 -- 19980724 Panel H: WS - EW fund and sraegy wealh log(wealh) 0.0 0.5 1.0 1.5 2.0 log(wealh) 0.0 0.5 1.0 1.5 2.0 1991 1992 1993 1994 1995 1996 1997 1998 1990 1991 1992 1993 1994 1995 1996 1997 1998 19900102 -- 19980724 19900102 -- 19980724 Figure 1: The gure displays he growh of a $1 invesmen a he beginning of he period denoed underneah each panel (assuming full reinvesmen of dividends and disribuions and ignoring axes). Panels A hrough H perain o DEM, DPA, EU, FS, JPN, LA, PXJ, and WS funds, respecively. Each panel feaures he growhofa $1invesmen ino he EW porfolio of funds (full line) and he iming sraegy performed on he EW porfolio (doed line), respecively.

Table I Daily XYZ Fund and S&P 500 Reurns This able illusraes he speculaive mechanism for XYZ fund using inra-day S&P 500 daa in he period from 08/1992 o 07/1998. The able gives he correlaion of he inernaional fund NAV reurn wih he reurn on he S&P500. Noe ha he socks in he inernaional fund rade during a period ha almos enirely precedes he opening of he U.S. marke, bu he NAV is compued only afer (he opening and) closing of he U.S. marke. Correlaion wih XYZ Reurns S&P 500 Index Reurns same day nex day Previous close Close 0.26 0.38 Previous close 10 AM 0.42 0.17 10 AM Close 0.03 0.34 10 AM 11 AM 0.05 0.18 11 AM 12 PM 0.05 0.21 12 PM 1PM 0.03 0.13 1PM 2PM 0.02 0.07 2PM 3 PM -0.07 0.10 3 PM Close 0.01 0.15 Previous Close 3 PM 0.29 0.36 10 AM 3 PM 0.03 0.33

Table II Sample Funds Some Summary Saisics The able repors summary saisics for he daily oal reurns on he funds in our sample in he period 01/02/1990-07/24/1998. The sample consiss of 391 open-end inernaional sock muual funds wih he following Morningsar Caegory: Diversified Emerging Mks (DEM), Diversified Pacific/Asia Sock (DPA), Europe Sock (EU), Foreign Sock (FS), Japan Sock (JPN), Lain America Sock (LA), Pacific/Asia ex-japan Sock (PXJ), and World Sock (WS). For comparaive purposes, he Vanguard 500 Index Fund (VAN) is presened as well. Panel A provides he basic summary saisics of ime series of daily oal reurns on equally-weighed porfolios of funds in each region/syle (consruced each day on he basis of all he funds available on ha day): arihmeic and geomeric mean, sandard deviaion, crossauocorrelaion wih oal S&P 500 reurns, and higher momens. Par B feaures he quaniles of he disribuion of oal reurns of each equally-weighed porfolio. Panel C gives he cross-secional disribuion of average fund reurns (arihmeic mean), sandard deviaion, firs-order auocorrelaion, and correlaion wih lagged S&P 500 reurns by caegory. For each fund he summary saisics are compued on he basis of daily oal fund reurns over all he days in he sample period on which he fund reurns were available. In all hree panels boh reurns and sandard deviaions are expressed in percen per day. Panel A: Basic Summary Saisics of Toal Reurns on EW Porfolios Arihmeic Geomeric Sandard Correlaion Caegory (N) Mean Mean Deviaion wih R 1 SP, Skewness Kurosis DEM (10) 0.012 0.000 0.749 0.325-1.51 12.80 DPA (34) -0.002-0.006 0.847 0.397-0.36 5.27 EU (58) 0.049 0.047 0.701 0.362-0.63 8.75 FS (112) 0.032 0.030 0.627 0.424-0.53 7.81 JPN (17) -0.013-0.019 1.096 0.252 0.01 3.19 LA (31) 0.038 0.030 1.234 0.121-1.08 14.62 PXJ (65) 0.004-0.001 0.993 0.371-0.33 12.99 WS (64) 0.041 0.039 0.550 0.409-0.78 8.63 VAN (1) 0.067 0.064 0.793 0.039-0.27 4.84 Panel B: Quaniles of Disribuions of Toal Reurns on EW Porfolios Caegory (N) Min. 1s Q. Median 3rd Q. Max. DEM (10) -7.759-0.821 0.064 0.377 4.247 DPA (34) -5.530-0.393 0.025 0.419 4.992 EU (58) -7.267-0.311 0.088 0.441 4.790 FS (112) -5.970-0.262 0.061 0.383 4.438 JPN (17) -5.451-0.574 0.000 0.535 5.588 LA (31) -13.32-0.454 0.100 0.640 9.760 PXJ (65) -8.228-0.378 0.030 0.434 8.582 WS (64) -4.877-0.220 0.064 0.361 3.885 VAN (1) -6.906-0.331 0.060 0.490 5.153

Table II Coninued Panel C: Quaniles of Cross-Secional Disribuions of Summary Saisics Caegory (N) Saisic Min. 1s Q. Median 3rd Q. Max. DEM (10) DPA (34) EU (58) FS (112) JPN (17) LA (31) PXJ (65) WS (64) VAN (1) Average Reurn -0.016-0.003 0.006 0.018 0.030 Sandard Deviaion 0.742 0.807 0.839 0.943 1.019 cor ( R i,, Ri, 1) 0.242 0.258 0.264 0.292 0.331 cor ( R i,, RSP, 1) 0.268 0.287 0.293 0.305 0.316 Average Reurn -0.300-0.120-0.037 0.002 0.022 Sandard Deviaion 0.686 0.958 1.038 1.127 1.898 cor ( R i,, Ri, 1) -0.016 0.102 0.138 0.210 0.315 cor ( R i,, RSP, 1) 0.291 0.374 0.394 0.430 0.489 Average Reurn -0.058 0.062 0.083 0.104 0.238 Sandard Deviaion 0.517 0.716 0.808 0.901 2.544 cor ( R i,, Ri, 1) -0.123 0.008 0.051 0.078 0.206 cor ( R i,, RSP, 1) 0.159 0.337 0.390 0.450 0.540 Average Reurn -0.000 0.028 0.039 0.049 0.071 Sandard Deviaion 0.458 0.672 0.718 0.771 1.167 cor ( R i,, Ri, 1) -0.226 0.054 0.086 0.136 0.248 cor ( R i,, RSP, 1) 0.199 0.352 0.381 0.406 0.499 Average Reurn -0.099-0.034-0.022-0.003 0.046 Sandard Deviaion 0.672 1.047 1.120 1.165 1.783 cor ( R i,, Ri, 1) -0.012 0.033 0.087 0.161 0.341 cor ( R i,, RSP, 1) 0.090 0.198 0.236 0.295 0.444 Average Reurn -0.149 0.005 0.026 0.038 0.093 Sandard Deviaion 1.112 1.390 1.490 1.541 2.354 cor ( R i,, Ri, 1) 0.016 0.119 0.137 0.149 0.287 cor ( R i,, RSP, 1) 0.038 0.086 0.117 0.125 0.285 Average Reurn -0.336-0.140-0.068-0.043 0.007 Sandard Deviaion 0.786 1.27 1.464 1.696 3.765 cor ( R i,, Ri, 1) 0.021 0.133 0.182 0.243 0.380 cor ( R i,, RSP, 1) 0.095 0.334 0.370 0.395 0.431 Average Reurn -0.001 0.037 0.047 0.055 0.082 Sandard Deviaion 0.401 0.597 0.666 0.763 1.051 cor ( R i,, Ri, 1) -0.040 0.110 0.181 0.218 0.285 cor R i, R ) 0.103 0.294 0.336 0.367 0.613 (, SP, 1 Average Reurn 0.0668 Sandard Deviaion 0.7932 cor ( R i,, Ri, 1) 0.0388 cor R i, R ) 0.0388 (, SP, 1

Table III Average Fund Reurns and Prior Day S&P 500 Reurns The able gives he average reurn and sandard deviaion (Sdev) of an equally-weighed porfolio of inernaional funds by Morningsar Caegory: Diversified Emerging Mks (DEM), Diversified Pacific Asia Sock (DPA), Europe Sock (EU), Foreign Sock (FS), Japan Sock (JPN), Lain America Sock (LA), Pacific ex-japan Sock (PXJ), and World Sock (WS), depending on he sign of he prior day S&P 500 reurn. For comparison he reurn on he S&P 500 iself is included (VAN). Reurns are expressed in percen per day. The -saisic (-sa) is he average reurn divided by is sandard error, and Days refers o he number of reurns used o compue he average reurns and sandard deviaions. Caegory Average Reurn Full sample Prior day S&P 500 reurn 0 Prior day S&P 500 reurn > 0 Sdev Reurn -sa Days Average Reurn Sdev Reurn -sa Days Average Reurn Sdev Reurn -sa Days DEM 0.012 0.749 0.75 2165-0.171 0.779-6.94 999 0.169 0.684 8.44 1166 DPA -0.002 0.847-0.11 2165-0.234 0.881-8.39 999 0.196 0.762 8.78 1166 EU 0.049 0.701 3.25 2165-0.137 0.723-5.99 999 0.209 0.641 11.13 1166 FS 0.032 0.627 2.37 2165-0.162 0.645-7.94 999 0.199 0.561 12.11 1166 JPN -0.013 1.096-0.55 2165-0.205 1.111-5.83 999 0.151 1.057 4.88 1166 LA 0.037 1.234 1.25 1742-0.117 1.260-2.62 797 0.168 1.196 4.32 945 PXJ 0.004 0.993 0.17 1879-0.228 1.021-6.57 866 0.201 0.924 6.92 1013 WS 0.041 0.550 8.67 2165-0.137 0.568-7.62 999 0.192 0.479 13.69 1166 VAN 0.067 0.793 3.93 2165 0.030 0.848 1.12 999 0.098 0.742 4.51 1166

Table IV Sraegy Reurns and Excess Sraegy Reurns The able repors summary of he performance of a sraegy ha selecively invess in inernaional muual funds on he days on which he prior day S& P 500 reurn is posiive and in non-ineres bearing cash on he days following he days when he S&P 500 is down. Average reurns and sandard deviaions (Sdev) are measured in percen per day. The sample consiss of 391 open-end inernaional sock muual funds wih he following Morningsar Caegory: Diversified Emerging Mks (DEM), Diversified Pacific/Asia Sock (DPA), Europe Sock (EU), Foreign Sock (FS), Japan Sock (JPN), Lain America Sock (LA), Pacific/Asia ex-japan Sock (PXJ), and World Sock (WS). For comparaive purposes, he sraegy reurns for Vanguard 500 Index Fund (VAN) are presened as well. Panel A gives sraegy reurns for he equally-weighed porfolio of funds formed by caegory, and Panel B presens he disribuion of he sraegy reurns applied o he individual funds. Excess sraegy reurns are compued as he difference beween he sraegy reurns and a buy-and-hold sraegy in he same fund. The -saisic (-sa) is he average reurn divided by is sandard error. Caegory Average Reurn Panel A: Equally-Weighed Porfolios Sraegy Reurns Sdev Reurn -sa Excess Sraegy Reurns Average Reurn Sdev Reurn -sa DEM 0.091 0.509 8.32 0.079 0.536 6.86 DPA 0.106 0.568 8.66 0.108 0.608 8.24 EU 0.112 0.482 10.87 0.065 0.496 5.91 FS 0.107 0.423 11.77 0.075 0.445 7.84 JPN 0.082 0.779 4.87 0.095 0.761 5.78 LA 0.091 0.885 4.29 0.054 0.854 2.62 PXJ 0.109 0.686 6.87 0.105 0.702 6.49 WS 0.103 0.364 13.17 0.063 0.392 7.48 VAN 0.053 0.547 4.51-0.014 0.576-1.12

Table IV Coninued Panel B: Individual Funds Caegory (N) Saisic Min. 1s Q. Median 3rd Q. Max. Average Sraegy Reurns 0.081 0.087 0.095 0.100 0.104 DEM (10) Average Excess Sraegy Reurns 0.066 0.080 0.081 0.097 0.115 -sa 4.497 5.132 5.672 5.897 6.617 Average Sraegy Reurns 0.055 0.088 0.098 0.117 0.148 DPA (34) Average Excess Sraegy Reurns 0.088 0.117 0.146 0.208 0.394 -sa 4.504 5.088 5.958 6.986 8.413 Average Sraegy Reurns 0.057 0.134 0.148 0.195 0.275 EU (58) Average Excess Sraegy Reurns -0.013 0.055 0.064 0.078 0.324 -sa -0.201 2.337 3.294 4.364 6.289 Average Sraegy Reurns 0.072 0.105 0.115 0.120 0.142 FS (112) Average Excess Sraegy Reurns 0.039 0.065 0.074 0.082 0.120 -sa 2.865 5.229 5.728 6.490 8.229 Average Sraegy Reurns 0.037 0.064 0.089 0.105 0.182 JPN (17) Average Excess Sraegy Reurns 0.062 0.080 0.107 0.122 0.280 -sa 2.919 3.633 4.268 5.021 5.447 Average Sraegy Reurns 0.071 0.099 0.107 0.123 0.182 LA (31) Average Excess Sraegy Reurns 0.040 0.068 0.073 0.113 0.229 -sa 0.828 1.904 2.153 2.685 4.025 Average Sraegy Reurns -0.003 0.067 0.104 0.127 0.197 PXJ (65) Average Excess Sraegy Reurns 0.532 0.889 1.040 1.206 2.646 -sa 1.656 3.633 4.268 5.021 5.447 Average Sraegy Reurns 0.035 0.098 0.105 0.115 0.204 WS (64) Average Excess Sraegy Reurns 0.012 0.051 0.059 0.071 0.158 -sa 1.466 4.379 4.950 6.108 11.480 Average Sraegy Reurns 0.053 VAN (1) Average Excess Sraegy Reurns -0.014 -sa -1.159

Table V Cross-Secional Comparison of Load and No-Load Funds The able documens a comparison of cross-secional means of average reurns for inernaional funds ha charge neiher loads nor redempion fees (No-Load) and funds ha charge loads and/or redempion fees (Load) from he following Morningsar Caegories: Diversified Emerging Mks (DEM), Diversified Pacific/Asia Sock (DPA), Europe Sock (EU), Foreign Sock (FS), Japan Sock (JPN), Lain America Sock (LA), Pacific/Asia ex-japan Sock (PXJ), and World Sock (WS). Panel A feaures fund reurns and Panel B feaures sraegy reurns. The firs column of each panel feaures he cross-secional mean of average oal fund reurns for no-load funds; he second column of each panel feaures he cross-secional mean of average oal fund reurns for load funds. The hird column of each panel feaures he -saisic (-sa) for a wosample -es comparison of means of average reurns for no-load and load funds. Throughou he able reurns are expressed in percen per day. Caegory (N) No. Panel A: Fund Reurns Panel B: Sraegy Reurns No-Load/Load No-Load Load -sa No-Load Load -sa DEM (9) 6/3 0.006 0.011-0.43 0.096 0.093 0.41 DPA (33) 7/26-0.105-0.068-0.84 0.089 0.106 0.10 EU (56) 16/40 0.082 0.087-0.30 0.145 0.167-1.66 FS (105) 64/41 0.041 0.038 1.35 0.113 0.111 0.96 JPN (17) 8/9-0.017-0.027 0.59 0.109 0.080 1.41 LA (29) 6/23 0.024 0.027-0.17 0.117 0.109 0.96 PXJ (62) 14/48-0.081-0.102 0.89 0.092 0.095-0.24 WS (61) 15/46 0.046 0.046-0.02 0.102 0.107-0.97 Pooled (372) 136/236 0.021 0.004 2.01 0.111 0.114-0.67

Table VI Relaionship beween Fund Flows and Reurns Panel A documens for each of he eigh lised Morningsar Caegories (characerized by a subsanial porion of inernaional equiies in he porfolio) he cross-secional disribuion of correlaions (1) beween relaive ne flows ino funds and nex-day fund reurns and (2) relaive ne flows ino funds and conemporaneous reurns on he S&P 500. These correlaions are compued for 116 U.S.-based inernaional funds for which he daa on daily NAVs and TNAs were obained from TrimTabs. Flow is compued as flow i, = NewMoneyi, / TNAi, 1, where NewMoney TNA 1+ R TNA denoes he ne new money inflow ino fund i on dae. i, = i, ( i, 1) i, 1 Panel A: Cross-Secional Disribuion of Correlaions by Caegory Caegory (N) Quaniles of cor flow i, R ) (, i, + 1 Min. 1s Q. Median 3rd Q. Max. DEM (11) -0.134-0.038-0.029 0.029 0.064 DPA (4) 0.020 NA 0.031 NA 0.123 EU (4) 0.066 NA 0.083 NA 0.087 FS (46) -0.045 0.000 0.026 0.063 0.136 JPN (2) -0.053 NA NA NA 0.026 LA (5) -0.078-0.054-0.051 0.025 0.085 PXJ (11) -0.014 0.006 0.042 0.071 0.216 WS (33) -0.148 0.016 0.036 0.097 0.179 Pooled (116) -0.148-0.000 0.027 0.069 0.216 Quaniles of cor flow i, R ) (, SP, Min. 1s Q. Median 3rd Q. Max. DEM (11) -0.096-0.061-0.027 0.022 0.179 DPA (4) 0.013 NA 0.031 NA 0.076 EU (4) -0.023 NA 0.028 NA 0.045 FS (46) -0.162-0.032 0.006 0.035 0.157 JPN (2) -0.077 NA NA NA -0.032 LA (5) -0.006 0.003 0.012 0.070 0.088 PXJ (11) -0.085-0.021 0.023 0.090 0.174 WS (33) -0.154-0.043 0.008 0.046 0.199 Pooled (116) -0.162-0.032 0.009 0.044 0.199

Table VI Coninued Relaionship beween Fund Flows and Reurns Panel B documens for each of he lised Morningsar Caegories he cross-secional disribuion of regression coefficiens in he OLS regressions of (1) relaive ne flows ino funds on nex-day fund reurns (denoed as β 1 ) and of (2) relaive ne flows ino funds on conemporaneous reurns on he S&P 500 (denoed as β SP ). In addiion o he quaniles of each disribuion of regression coefficiens, he able also documens for each Morningsar Caegory he number of funds for which he posiive -saisics on he bea coefficien exceed sandard significance levels (denoed as > 1. 96). The -saisics were compued using he Newey-Wes (1987) correcion for heeroskedasiciy and auocorrelaion up o five lags. The regressions are compued for he same funds as in Panel A. Panel B: Cross-Secional Disribuion of Regressions Beas by Caegory Caegory (N) Quaniles of β 1 Min. 1s Q. Median 3rd Q. Max. > 1. 96 DEM (11) -0.312-0.085-0.042 0.035 0.085 0 DPA (4) 0.005 NA 0.021 NA 0.026 1 EU (4) 0.013 NA 0.028 NA 0.044 1 FS (46) -0.047 0.000 0.021 0.055 0.327 0 JPN (2) -0.009 NA NA NA 0.022 0 LA (5) -0.133-0.086-0.062 0.028 0.036 0 PXJ (11) -0.032 0.003 0.029 0.082 0.174 1 WS (33) -0.823 0.015 0.051 0.116 0.530 6 Pooled (116) -0.823-0.000 0.025 0.062 0.530 9 Quaniles of β SP Min. 1s Q. Median 3rd Q. Max. > 1. 96 DEM (11) -0.081-0.045-0.012 0.018 0.081 1 DPA (4) 0.019 NA 0.057 NA 0.558 0 EU (4) -0.098 NA 0.085 NA 0.136 0 FS (46) -0.627-0.025 0.004 0.028 0.355 0 JPN (2) -0.335 NA NA NA -0.046 0 LA (5) -0.006 0.002 0.028 0.148 0.287 0 PXJ (11) -0.224-0.034 0.016 0. 118 0.473 2 WS (33) -0.662-0.018 0.001 0.028 0.084 1 Pooled (116) -0.662-0.026 0.005 0.035 0.558 4

Table VII A Comparison of Correced and Uncorreced Fund Reurns The able repors summary saisics for he correced daily oal reurns on he funds in our sample in he period 01/02/1990-07/24/1998. The sample consiss of 391 open-end inernaional sock muual funds wih he following Morningsar Caegory: Diversified Emerging Mks (DEM), Diversified Pacific/Asia Sock (DPA), Europe Sock (EU), Foreign Sock (FS), Japan Sock (JPN), Lain America Sock (LA), Pacific/Asia ex-japan Sock (PXJ), and World Sock (WS). The able displays for each caegory he oal reurn disribuion of he equally weighed (EW) porfolio of all funds belonging o he caegory, correced EW porfolio reurns (see Secion VI), he sraegy based on EW porfolio reurns (see Secion III), and he sraegy based on he correced EW porfolio reurns. Panel A provides he basic summary saisics of ime series of daily oal reurns: arihmeic and geomeric mean, sandard deviaion, cross-auocorrelaion wih oal S&P 500 reurns, and higher momens. Par B feaures he quaniles of he disribuion of oal reurns. In boh panels reurns and sandard deviaion are expressed in percen per day. Caegory N) DEM (10) DPA (34) EU (58) FS (112) JPN (17) LA (31) PXJ (65) WS (64) Panel A: Basic Summary Saisics of Toal Reurns on EW Porfolios Porfolio Arihmeic Mean Geomeric Mean Sandard Deviaion Correlaion wih R 1 SP, Skewness Kurosis EW funds 0.012 0.000 0.749 0.325-1.51 12.80 Correced EW funds 0.013 0.009 0.851 0.011-1.37 13.29 EW sraegy 0.091 0.090 0.509 0.234-0.06 16.20 Correced EW 0.009 0.007 0.581 0.022-0.22 15.74 EW funds -0.002-0.006 0.847 0.397-0.36 5.27 Correced EW funds -0.002-0.006 0.892 0.015-0.25 4.55 EW sraegy 0.106 0.104 0.568 0.279 1.47 11.02 Correced EW -0.008-0.010 0.608 0.019 0.56 8.94 EW funds 0.049 0.047 0.701 0.362-0.63 8.75 Correced EW funds 0.050 0.047 0.767 0.013-0.47 8.40 EW sraegy 0.112 0.111 0.482 0.297 1.11 11.84 Correced EW 0.026 0.025 0.526 0.061 0.72 14.13 EW funds 0.032 0.030 0.627 0.424-0.53 7.81 Correced EW funds 0.033 0.030 0.706 0.014-0.45 8.01 EW sraegy 0.107 0.106 0.423 0.339 1.55 13.73 Correced EW 0.017 0.016 0.478 0.058 0.95 15.82 EW funds -0.013-0.019 1.096 0.252 0.01 3.19 Correced EW funds -0.013-0.019 1.125 0.009 0.01 3.19 EW sraegy 0.082 0.079 0.779 0.167 0.92 9.02 Correced EW -0.012-0.015 0.799 0.012 0.67 9.46 EW funds 0.038 0.030 1.234 0.121-1.08 14.62 Correced EW funds 0.038 0.030 1.296 0.002-1.01 15.56 EW sraegy 0.091 0.087 0.885 0.123-0.16 20.47 Correced EW 0.041 0.037 0.913 0.049-0.16 19.93 EW funds 0.004-0.001 0.993 0.371-0.33 12.99 Correced EW funds 0.004-0.002 1.033 0.005-0.13 11.09 EW sraegy 0.109 0.106 0.686 0.252 1.25 21.09 Correced EW -0.016-0.019 0.722 0.012 0.04 16.06 EW funds 0.041 0.039 0.550 0.409-0.78 8.63 Correced EW funds 0.041 0.038 0.672 0.012-0.64 8.29 EW sraegy 0.103 0.103 0.364 0.357 1.27 13.22 Correced EW 0.027 0.026 0.447 0.072 0.67 13.90

Table VII Panel B: Quaniles of Disribuions of Toal Reurns on EW Porfolios Caegory (N) Porfolio Min. 1s Q. Median 3rd Q. Max. DEM (10) DPA (34) EU (58) FS (112) JPN (17) LA (31) PXJ (65) WS (64) EW funds -7.759-0.821 0.064 0.377 4.247 Correced EW funds -9.451-0.339 0.058 0.452 4.630 EW sraegy -4.341 0.000 0.000 0.216 4.247 Correced EW sraegy -5.039-0.025 0.000 0.072 4.630 EW funds -5.530-0.393 0.025 0.419 4.992 Correced EW funds -5.476-0.469 0.014 0.462 5.092 EW sraegy -3.084 0.000 0.000 0.210 4.992 Correced EW sraegy -3.754-0.077 0.000 0.031 4.086 EW funds -7.267-0.311 0.088 0.441 4.790 Correced EW funds -7.683-0.334 0.073 0.474 5.771 EW sraegy -2.759 0.000 0.000 0.257 4.790 Correced EW sraegy -3.450 0.000 0.000 0.106 5.771 EW funds -5.970-0.262 0.061 0.383 4.438 Correced EW funds -6.411-0.315 0.045 0.416 5.461 EW sraegy -2.186 0.000 0.000 0.216 4.438 Correced EW sraegy -2.964-0.013 0.000 0.072 5.461 EW funds -5.451-0.574 0.000 0.535 5.588 Correced EW funds -5.912-0.586-0.007 0.577 6.174 EW sraegy -3.888 0.000 0.000 0.183 5.588 Correced EW sraegy -4.351-0.106 0.000 0.039 6.174 EW funds -13.324-0.454 0.100 0.640 9.760 Correced EW funds -14.360-0.490 0.080 0.685 10.040 EW sraegy -7.441 0.000 0.000 0.224 9.760 Correced EW sraegy -7.415 0.001 0.000 0.146 10.040 EW funds -8.228-0.378 0.030 0.434 8.582 Correced EW funds -7.268-0.444 0.009 0.523 10.000 EW sraegy -4.781 0.000 0.000 0.213 7.740 Correced EW sraegy -5.382-0.098 0.000 0.008 6.195 EW funds -4.877-0.220 0.064 0.361 3.885 Correced EW funds -6.133-0.283 0.063 0.401 4.744 EW sraegy -2.060 0.000 0.000 0.221 3.885 Correced EW sraegy -2.695 0.000 0.000 0.105 4.744

Table VIII The Wealh Impac of Sale Pricing This able documens several measures of he impac of sale pricing on muual fund shareholders. Panel A documens quaniles of he cross-secional disribuion of ime-series averages for he 116 inernaional open-end muual funds for which he daily NAV and TNA daa were obained from TrimTabs (Sample 1), I liss (1) daily dollar loss per fund, (2) wealh ransferred per fund, (3) percenage loss per fund, (4) percenage wealh ransferred per fund, (5) pricing error, and (6) absolue mispricing. The six measures are compued for each fund as he ime-series average of he following quaniies: * NAV (1) i, NAV i, NewMoneyi, = βirsp, NewMoneyi,, NAV i, * NAV (2) i, NAV i, NewMoneyi, = βirsp, NewMoneyi, NAV i, * NAVi, NAVi, (3) flowi, = βirsp, flowi,, NAV i, * NAVi, NAVi, (4) flowi, = βirsp, flowi, NAV i, * NAVi, NAVi, (5) = βirsp,, and NAV i,, * NAVi, NAVi, (6) = βirsp,, NAVi, where flow and new money for fund i on dae are compued as flowi, = NewMoneyi, / TNAi, 1and NewMoney i, = TNAi, ( 1+ Ri, 1) TNAi, 1, respecively. Panel B repors he laer wo pricing error measures for he oher sample of 391 inernaional open-end muual funds used in his sudy (Sample 2). Daily Average Min. 1s Q. Median 3rd Q. Max. Panel A: Sample 1 Dollar Loss per Fund ($MM) -4.620-0.086-0.002 0.025 0.796 Wealh Transferred per Fund ($MM) 0.006 0.251 0.722 1.810 31.200 Percenage Loss per Fund (%) -0.745-0.048 0.009 0.025 0.481 Percenage Wealh Transferred per Fund (%) 0.011 0.204 0.438 1.094 5.212 Pricing Error (%) -0.043-0.030-0.026-0.020-0.011 Absolue Mispricing (%) 0.118 0.211 0.278 0.320 0.458 Panel B: Sample 2 Pricing Error (%) -0.074-0.029-0.024-0.020-0.005 Absolue Mispricing (%) 0.042 0.170 0.219 0.248 0.634,