Unobserved Actions of Mutual Funds

Transcription

1 Unobserved Acions o Muual Funds MARCIN KACPERCZYK CLEMENS SIALM LU ZHENG March 2005 Kacperczyk is a he Sauder School o Business; The Universiy o Briish Columbia; 2053 Main Mall; Vancouver, B.C., Canada V6T 1Z2; Phone: (604) ; [email protected]. Sialm is a he Sephen M. Ross School o Business a he Universiy o Michigan; 701 Tappan Sree; Ann Arbor, MI ; Phone: (734) ; [email protected]. Zheng is a he Sephen M. Ross School o Business a he Universiy o Michigan; 701 Tappan Sree; Ann Arbor, MI ; Phone: (734) ; [email protected]. We hank Sreedhar Bharah, M.P. Narayanan, Neja Seyhun, and seminar paricipans a he Universiy o Michigan or helpul commens and suggesions. We acknowledge inancial suppor rom Misui Lie Cener and Inquire Europe.

2 Unobserved Acions o Muual Funds ABSTRACT Muual und invesors canno observe all acions o und managers despie exensive disclosure requiremens. This paper invesigaes he eec o unobserved acions on und reurns using a new measure, he reurn gap, and asks wheher hese acions should be a maer o signiican concern or und invesors. The reurn gap is compued or each und as he dierence beween he ne reurn o a und and he gross reurn o a hypoheical buy-and-hold porolio ha invess in he previously disclosed holdings. Analyzing more han 3,000 unique U.S. equiy unds over he period , we show ha he average eec o unobserved acions or all unds is close o zero. Neverheless, we documen a subsanial heerogeneiy in he reurn gap, indicaing ha unobserved acions o some unds creae value while such acions o ohers desroy value. Moreover, we ind a srong persisence o he reurn gap up o ive years ahead or unds wih posiive and negaive iniial reurn gaps. To address he quesion o wheher unobserved acions o muual unds should be a maer o concern or und invesors, we examine he implicaions o hese acions or uure und perormance. We ind ha he reurn gap helps predic uure und perormance even aer conrolling or pas und perormance and oher und aribues. Funds wih avorable pas reurn gaps end o perorm consisenly beer beore and aer adjusing or risk- and syle-characerisics. Speciically, he decile porolio o unds wih he highes iniial reurn gap yields an average excess reurn o 1.4 percen per year relaive o he marke reurn, whereas he decile porolio wih he lowes reurn gap yields an average excess reurn o 2.6 percen per year. We conirm he relaionship beween a und s reurn gap and is subsequen perormance using panel regressions conrolling or oher und characerisics and ime ixed eecs. 2

3 I. Inroducion Muual unds have recenly received keen aenion rom invesigaors, regulaors, and he media. The alleged wrongdoings are oen rooed in conlics o ineres beween und invesors and und managemen, and ulimaely resul in invesors bearing subsanial agency coss. In he wake o he scandals, he SEC has enaced a series o reorms o proec invesors by increasing he ransparency o acions o muual unds. Despie exensive disclosure requiremens in he muual und indusry, und invesors canno observe all he acions o muual unds. This paper invesigaes he eec o unobserved acions on und reurns and asks wheher hese acions should be a maer o signiican concern or und invesors. Muual und invesors do no observe he exac iming o he purchases and he sales o securiies by muual unds and he corresponding ransacion coss. Fund invesors bear hidden coss relaed o he rading by und managers and by oher und invesors, such as commissions paid o brokers, marke impac, and sale-price arbirage losses. These various hidden coss reduce he reurn o invesors. 1 On he oher hand, und managers can use inormaional advanages and ime he purchases and he sales o individual socks opimally. Thus, inerim rades o skilled und managers can creae value or und invesors. We measure he impac o unobserved acions on invesor reurn using a new measure, he reurn gap, which is deined as he dierence beween he ne reurns o a und and he gross reurns o a hypoheical buy-and-hold porolio ha invess in he previously disclosed holdings o a muual und. The inuiion is sraighorward: The 1 Mahoney (2004) describes he various coss in more deail. 3

4 impac o unobserved acions is capured in he ne und reurns bu no in he buy-andhold gross reurns o he previously held porolio. For example, commissions paid by muual unds o heir brokers or sale-price arbirage losses do no aec direcly he gross reurns o he porolio, bu hey do aec he ne reurns o invesors, because hese coss are eecively subraced rom he asses o a und. On he oher hand, i he inerim rades o a und creae suicien value, hen we should observe ha he disclosed reurn o a und exceeds he reurn o a hypoheical porolio ha invess in he previously disclosed holdings. Thus, he reurn gap should be negaively relaed o he hidden coss o a muual und and posiively relaed o he beneis due o he inerim rades. This paper has wo main objecives. The irs objecive is o explain how unobserved acions aec und perormance. To his end, we invesigae wheher he unobserved acions are relaed o muual und characerisics, such as size, age, syle, and asse characerisics. The second objecive is o deermine wheher inormaion abou pas unobserved acions can help invesors o selec muual unds ha will perorm relaively well in he uure. I hidden coss and he inerim rading beneis are persisen phenomena, hen we should observe ha unds wih avorable reurn gaps in he pas will also end o perorm relaively well in he uure. 2 Analyzing more han 3,000 unique U.S. equiy unds over he period , we show ha he average value o he reurn gap accouns or abou 1.17 percen per year, which is very similar o he disclosed expenses o 1.19 percen per year. This indicaes ha he oal value o hidden coss and inerim rades is, on average, relaively 2 Even hough esimaing he impac o unobserved acions may serve as a helpul ool o evaluae muual unds, an alernaive and simpler way o judge any und s acions could be o merely look a is repored ne reurn. We argue ha, by benchmarking he invesor reurns agains he holding reurns, we iler ou he 4

5 small. Neverheless, we documen a subsanial cross-secional variaion in he reurn gap, indicaing ha hidden coss are more imporan or some unds while inerim rading beneis are more imporan or oher unds. Moreover, we ind a srong persisence o he reurn gap up o ive years ahead or unds wih posiive and negaive iniial reurn gaps. To address he main quesion o wheher unobserved acions o muual unds should be a maer o concern or und invesors, we examine he implicaions o hese acions or uure und perormance. We ind ha he pas reurn gap helps predic uure und perormance even aer conrolling or pas und perormance and oher und aribues. Funds wih avorable pas reurn gaps end o perorm consisenly beer beore and aer adjusing or risk- and syle-characerisics. Speciically, he decile porolio o unds wih he highes iniial reurn gap yields an average excess reurn o 1.4 percen per year relaive o he marke reurn, whereas he decile porolio o unds wih he lowes reurn gap yields an average excess reurn o 2.6 percen per year. The reurn dierence beween he wo porolios is saisically and economically signiican. This reurn dierence is no aeced signiicanly aer adjusing or common acors in sock reurns. We conirm he relaionship beween a und s reurn gap and is subsequen perormance using panel regressions conrolling or oher und characerisics and ime ixed eecs. The res o he paper proceeds as ollows. Secion II reviews he relaed lieraure. Secion III explains he use o he reurn gap in esimaing he impac o unobserved acions. Secion IV discusses he daa, while Secion V documens he empirical esimaes impac o common shocks o boh reurns and are able o obain a less noisy signal o he hidden coss and he inerim rading beneis o muual unds. 5

6 and he deerminans o he reurn gap. Secion VI invesigaes he impac o unobserved acions on uure und perormance and Secion VII concludes. II. Lieraure An exensive lieraure examines wheher muual und managers have superior invesmen abiliies. While some sudies ocus on he ne reurns o muual und invesors, oher sudies ocus on he gross reurns o he und holdings. The irs group o papers analyzes he ne reurns o muual unds. Since he seminal paper by Jensen (1968), he majoriy o sudies conclude ha muual unds, on average, underperorm passive benchmarks by an economically and saisically signiican number. Gruber (1996) inds ha beween 1985 and 1994, he average muual und underperorms passive marke indices by abou 65 basis poins per year. Carhar (1997) demonsraes very lile persisence in he muual und perormance, aer conrolling or common acors in sock reurns and expenses, concluding ha muual und managers do no have suicienly high invesmen abiliy. 3 In conras, several sudies based on he gross reurns o und porolio holdings conclude ha managers who ollow acive invesmen sraegies exhibi signiican sockpicking abiliies. Grinbla and Timan (1989, 1993) conclude ha muual und managers, in general, and managers o growh-oriened unds in paricular, have he abiliy o choose socks ha ouperorm heir benchmarks. Grinbla, Timan, and Wermers (1995) and Daniel, Grinbla, Timan, and Wermers (1997) aribue much o his perormance o 3 For evidence on und perormance, see, or example, Elon, Gruber, Das, and Hlavka (1993), Hendricks, Pael, and Zeckhauser (1993), Malkiel (1995), Brown and Goezmann (1995), Ferson and Schad (1996), Baks, Merick, and Wacher (2001), Cohen, Coval, and Pásor (2004), Lynch, Wacher, and Boudry (2004). 6

7 he characerisics o socks held by unds. Chen, Jagadeesh, and Wermers (2000) examine rades o he unds raher han he holdings and show ha he socks purchased by unds ouperorm he socks hey sell by an economically signiican margin. Kacperczyk, Sialm, and Zheng (2004) ind ha unds holding porolios concenraed in ewer indusries perorm beer, aer conrolling or dierences in risk and syle. Our paper is mos relaed o Grinbla and Timan (1989) and Wermers (2000), who compare he perormance o ne and gross muual und reurns. Grinbla and Timan (1989) quaniy his dierence and argue ha risk-adjused gross reurns o some unds are signiicanly posiive. Wermers (2000) decomposes he perormance ino sockpicking alen, syle selecion, ransacion coss, and expenses and inds ha muual unds, on average, hold socks ha ouperorm a broad marke index by 130 basis poins per year. On he oher hand, he average muual und ne reurn is 100 basis poins per year lower han he reurn o a broad marke index. He shows ha a porion o his dierence can be explained by he expenses and he rading coss. This paper diers rom he above sudies in ha we analyze he cross-secional properies o he unobserved acions o muual unds. Moreover, we delineae muual und characerisics ha aec hese unobserved acions. Finally, we invesigae wheher invesors, when choosing muual unds, could benei rom aking ino accoun hese unobserved acions. Frank, Poerba, Shackelord, and Shoven (2004) also analyze he dierence beween gross and ne reurns. They show ha copy-ca unds -- unds ha purchase he same asses as acively managed unds as soon as hese asse holdings are disclosed -- can earn reurns similar o hose o he unds hey are copying. Copyca unds do no incur he research expenses associaed wih he acively managed unds hey are 7

8 mimicking, bu hey miss he opporuniy o inves in asses ha managers ideniy as posiive reurn opporuniies beween disclosure daes. Our paper examines in more deail he dierence beween ne and gross reurns and subsequenly invesigaes wheher his dierence has any predicive power or uure abnormal perormance. Several papers have analyzed he rading coss o muual unds. Livingson and O Neal (1996) esimae average annual brokerage commissions a 28 basis poins or he period 1989 o Chalmers, Edelen, and Kadlec (1999) ind ha average annual brokerage commissions and spread coss or a sample o equiy muual unds over he period were 31 and 47 basis poins, respecively. Open-end muual unds are no raded coninuously; insead, muual unds collec he buy and sell orders a he end o he day and ransac a he ne asse value using closing prices. The closing prices migh no ully relec he mos recen available inormaion on he values o he underlying securiies. The possibiliy o sale pricing opens up he opporuniy or some invesors o perorm marke-iming arbirages. In addiion, someimes brokers permi invesors o place orders aer he close o he marke. These ransacions hur long-erm invesors in he muual und and decrease heir longerm perormance. Goezmann, Ivkovic, and Rouwenhors (2001) and Zizewiz (2003) examine such sale-price arbirage losses or inernaional muual unds. Goezmann, Ivkovic, and Rouwenhors (2001) illusrae ha muual unds are exposed o speculaive raders by showing ha a simple, day rading rule using 391 U.S. based open-end inernaional muual unds yields reurns ha ouperorm a buy-and-hold sraegy by 20 percen per year. Zizewiz (2003) esimaes ha due o such aciviy, invesors in inernaional equiy unds los on average 56 basis poins annually during he lae 1990s. 8

9 Muual und managers migh window-dress heir porolios around he disclosure daes o hide heir acual posiions, as discussed by Meier and Schaumburg (2004). Academic sudies have documened agency problems in muual und amily operaions. Nanda, Wang and Zheng (2004) show ha a spillover eec rom a sar und (sar perormance resuls in greaer cash inlow o oher unds in is amily) induce lower abiliy amilies o pursue sar creaing sraegies by increasing variaion in invesmen sraegies across unds. Gaspar, Massa, and Maos (2004) invesigae wheher muual und amilies sraegically allocae perormance across heir member unds avoring hose more likely o generae higher ee income or uure inlows. They ind evidence o a sraegic cross-und subsidizaion o 'high amily value' unds (i.e., high ees or high pas perormers) a he expense o 'low value' unds in he order o 6 o 28 basis poins o exra ne-o-syle perormance per monh. Reuer (2004) provides evidence ha allocaions o iniial public oerings avor invesors who direc brokerage business o lead underwriers. Our resuls are consisen wih such sraegic behavior o muual und amilies. III. Mehodology: Esimaing he Impac o Unobserved Acions To uncover he impac o unobserved acions on muual und reurns, we compare he repored ne reurn o an esimae o he gross reurn o he muual und holdings. The ne reurn o he muual und a ime (RF) is compued as he relaive change in he ne asse value o he muual und shares (NAV) including he oal dividend (D) and capial gains (CG) disribuions: 9

10 10 NAV NAV CG D NAV RF =. (1) On he oher hand, he gross reurn o he holdings (RH) is deined as he oal reurn o a hypoheical buy-and-hold porolio ha holds he mos recenly disclosed sock posiions: = = N i i i R w RH 1, 1, ~. (2) I a muual und discloses is holdings in he previous monh, hen he weighs o he individual asse classes depend on he number o socks held by he muual und (N) and he sock price (P): = = N i i i i i i P N P N w 1 1, 1, 1, 1, 1, ~. (3) On he oher hand, i he holding disclosure occurs more han one monh prior o a speciic monh, hen we use he mos recen holdings disclosed a ime -τ and updae he weighs assuming ha he und manager ollows a buy-and-hold sraegy: ( ) ( ) = = = + + = N i j j i i i j j i i i i R P N R P N w 1 1 1,,, 1 1,,, 1,, 1 1 ~ τ τ τ τ τ τ τ. (4) Based on he above, we deine he reurn gap, RG, as he dierence beween ne and gross reurns: RH RF RG =. (5) The reurn gap includes he ollowing componens:

11 RG = Unobserved = Inerim Acions Expenses Trades Hidden Coss = Expenses (6) The expense raio is he only componen o he reurn gap ha is observable. Expenses are subraced on a daily basis rom he ne asses o a muual und. The remaining wo componens consiue wha we deine as Unobserved Acions. One componen o he unobserved acions is he inerim rading beneis o a und (IT), which depend primarily on he proiabiliy o he inermediae rades o a und and on he cross-subsidizaion beween und amilies. Even hough we can observe he holdings o a und only a speciic poins in ime, muual unds may rade acively in beween hese disclosure daes. I hese inerim rades creae value, hen he reurn o he und RF will increase, while he reurn o he holdings RH will remain unaeced. Alernaively, muual und amilies migh improve he perormance o some speciic unds hrough cross-subsidizaion, as discussed by Gaspar, Massa, and Maos (2004). For example, und amilies regularly obain IPO allocaions, as discussed by Reuer (2004), and can subsidize speciic unds by allocaing he underpriced IPO socks o hese unds. The oher componen o he unobserved acions is he hidden coss o a und (HC), which include rading coss and commissions paid by he muual und o brokers and poenial agency coss. For example, unds ha are subjec o a higher price impac or unds ha are exposed o higher commissions will have higher hidden coss. O he hree componens only he expenses are observable. Hence, i is no possible o measure precisely he oher wo componens o he reurn gap. Since we are unable o disenangle hidden coss and inerim rading beneis, mos o our resuls 11

12 aggregae hem, analyze heir deerminans, and invesigae wheher hese unobserved componens have any predicive power or uure und perormance. IV. Daa Our sample is an updaed version o he daa used in Kacperczyk, Sialm, and Zheng (2004) and covers he ime period beween 1984 and A. Merge o CRSP and Specrum The main daa se has been creaed by merging he CRSP Survivorship Bias Free Muual Fund Daabase wih he CDA/Specrum holdings daabase and he CRSP sock price daa. The CRSP Muual Fund Daabase includes inormaion on und reurns, oal ne asses, dieren ypes o ees, invesmen objecives, and oher und characerisics. We ollow Wermers (2000) and merge he CRSP daabase wih he sockholdings daabase published by CDA Invesmens Technologies. The CDA daabase provides sockholdings o virually all U.S. muual unds, wih no minimum survival requiremen or a und o be included in he daabase. The daa are colleced boh rom repors iled by muual unds wih he SEC and rom volunary repors generaed by he unds. We link each repored sock holding o he CRSP sock daabase in order o ind is price and indusry classiicaion code. The vas majoriy o unds have holdings o companies lised on he NYSE, NASDAQ, or AMEX sock exchanges. We sar our maching process wih a sample o all muual unds in he CRSP muual und daabase. The ocus o our analysis is on domesic equiy muual unds, or which he holdings daa are he mos complee and reliable. As a resul, we eliminae 12

13 balanced, bond, money marke, and inernaional unds, as well as unds no invesed primarily in equiy securiies. Since dieren share classes have he same holdings composiion, we aggregae all he observaions peraining o dieren share classes ino one observaion. Our inal sample includes 3,008 disinc unds and 240,886 und-monh observaions. We describe in he Appendix he deailed sample selecion. B. Summary Saisics Panel A o Table I liss summary saisics o he main und aribues. Our sample includes 3,008 disinc unds and 240,886 und-monh observaions. Due o he subsanial growh in he muual und indusry over he las weny years, we have signiicanly more unds in he more recen years o our sample period. The number o unds ranges rom 226 unds (Augus 1984) o 2,212 unds (April 2002). The disribuion o he oal ne asses under managemen is skewed o he righ as he mean is considerably higher han he median. Also, he average age o a muual und in our sample is years and he age ranges beween 2 years and 80 years. The mean expense raio is 1.31 percen; however, muual unds dier signiicanly in heir expense raios. 4 Larger unds end o charge lower expenses; hus, he value-weighed expense raio equals jus 0.93 percen. Boh value- and equallyweighed expense raios increase signiicanly over our sample period. For example, he value-weighed expense raio increases rom 0.76 percen in 1984 o 0.92 percen in Mos muual unds also charge loads ranging rom 0 o 9.5 percen. The mean 4 The maximum expense raio recorded in our sample o percen per year does no appear o be a daa error. The Fronier Funds: Equiy Fund Porolio indeed charged percen in 2000, percen in 2001 and 2002, and percen in These high expense raios are conirmed using alernaive daa sources. 13

14 urnover raio is 94 percen, indicaing ha unds end o hold heir posiions, on average, or abou one year. Muual unds end o hold a relaively large number o socks. An average und holds 118 socks, bu a small number o unds hold several housand sock posiions a one poin in ime. The mean monhly ne reurn o und invesors equals 0.82 percen (9.84 percen per year), while he mean monhly gross reurn o he sock holdings equals 0.95 percen (11.4 percen per year). We will analyze he dierence beween he ne and gross reurns in more deail in he subsequen pars o he paper. Panel B repors he correlaion srucure beween he dieren und aribues. We can observe ha large unds end o be older and o charge lower expenses. I is no surprising ha he holding reurns and he repored reurns are very highly correlaed -- he correlaion coeicien beween ne and gross reurns equals C. Unavailable Holdings For our analysis, we do no have deailed daa on he holdings o non-equiy asse classes, such as preerred socks, bonds, cash, and oher asses. To miigae his problem, we ocus on domesic sock unds, primarily invesed in common socks, as described beore. We also compue in each ime period he proporion o he oal und value invesed in ive dieren classes o asses equiy, bonds, cash, preerred socks, and oher and adjus he holding reurns o relec non-equiy holdings in he und porolio. The irs daa column o Table II summarizes he mean and he sandard deviaion o he respecive weighs. On average, muual unds in our sample inves percen o 14

15 heir wealh in equiy securiies and 7.39 percen in cash or cash equivalens. On he oher hand, he percenage holdings o bonds, preerred socks, and oher asses are relaively minor. To adjus und holding reurns or he reurns on he various asse classes, we apply hree dieren mehods. The irs mehod esimaes he relevan reurns or each monh using he ollowing regression: RF = γ Equiy, + γ w Cash, Equiy, 1 w Cash, 1 + γ + γ Bonds, Oher, w w Bonds, 1 Oher, 1 + γ + ε Preerred, w Preerred, 1 + (7) In his speciicaion, he ne reurn, RF, o a muual und,, in a paricular monh,, is regressed on he lagged observed weighs, w, o he muual und in he ive dieren asse classes. This mehod allows us o impue he reurns, γ i,, on he dieren asse classes. This regression is esimaed wihou an inercep as he weighs add up o one. The second mehod uses he reurns on published indices as an adjusmen echnique. For bonds, we use he oal reurn o he Lehman Brohers Aggregae Bond Index, while or cash holdings we use he Treasury bill rae. 5 No reliable index reurns are available or preerred socks and or oher asse classes. Thus, we assume ha he reurn on preerred socks equals he reurn o he Lehman Brohers Aggregae Bond Index and he reurn on oher asses equals he Treasury bill rae. The hird mehod adjuss he reurns by esimaing abnormal reurns using various acor models, such as he CAPM model, he hree-acor model o Fama and French (1993), or he our-acor model o Carhar (1997). These models are believed o adjus appropriaely or cash holdings or oher acors capured in he various models. 15

16 Table II summarizes he reurn daa obained rom he hree mehods. Imporanly, our resuls hroughou he paper are robus o he hree dieren mehods and we usually only repor he resuls using he irs mehod. The second column o Table II summarizes he disribuion o he monhly reurns using regression (7), while he hird column summarizes he disribuion o he monhly reurns o he CRSP Toal Value-Weighed Index, he Lehman Brohers Aggregae Bond Index, and he Treasury bill rae. The correlaion beween he dierenly-measured respecive reurns is relaively high. The correlaion beween he impued equiy reurn (impued bond reurn) and he CRSP Index (Lehman Brohers Aggregae Bond Index) is percen (88.25 percen). In conras, he correlaion beween he impued reurn on cash posiions and he risk-ree rae is considerably smaller (22.17 percen). The laer migh be a resul o seasonal variaions in he cash holdings o unds or a resul o he ac ha muual unds do no inves heir cash-equivalen holdings only in shor-erm T-bills. In he subsequen ess, we will use he impued reurns on bonds, preerred socks, cash, and oher asses o adjus he equiy holding reurns. V. Esimaing he Reurn Gap This secion provides summary saisics o he invesor and holding reurns, quaniies he resuling reurn gap, and invesigaes is deerminans. 5 Daa on he Lehman Brohers Aggregae Bond Index are obained rom Daasream and he risk-ree ineres is obained rom French s websie: hp://mba.uck.darmouh.edu/pages/aculy/ken.rench. 16

17 A. Quaniicaion o he Reurn Gap To summarize he reurn daa, we compue in each monh he equally-weighed average o he repored and holding-based reurns o he muual unds in our sample. In Panel A o Table III, we repor he ime series average, wih he corresponding sandard errors in parenheses. 6 Nex, we presen wo dieren measures o he reurn gap. The irs measure is deined as a dierence beween he invesor reurns and he reurn o he equiy holdings and adjuss or he non-equiy holdings o a und using he reurns esimaed rom regression (7). 7 The second measure subracs he disclosed monhly expenses rom he irs measure o he reurn gap, and hus corresponds o he value creaed by he inerim rades ne o he hidden coss o he muual und. The average ne invesor reurn equals percen per monh or abou 12 percen per year. On he oher hand, he average reurn o a porolio, including he previously disclosed equiy posiions, is equal o percen. The dierence beween he invesor and he holding reurn (i.e., he reurn gap o he equiy porolio beore expenses) equals 9.8 basis poins per monh or 1.17 percen per year. The average expense raio equals 0.1 percen per monh or 1.19 percen per year. The reurn gap aer adjusing or disclosed expenses is insigniicanly dieren rom zero. However, we know rom previous sudies ha he rading coss o muual unds are no insigniican 8 and ha he rades o unds creae value 9. We analyze in Appendix B he beneis o 6 We obain very similar resuls i we compue he value-weighed reurn in each monh. However, expenses end o be smaller using value weighs. 7 We obain very similar resuls i we use he index reurns insead o he esimaed reurns. 8 See, or example, Livingson and O Neal (1996), Chalmers, Edelen, and Kadlec (1999), Wermers (2000) or sudies o he rading coss o muual unds. 9 See, or example, Grinbla and Timan (1989, 1993), Daniel, Grinbla, Timan, and Wermers (1997), and Chen, Jagadeesh, and Wermers (2000). 17

18 inerim rades in more deail. Thus, in he aggregae und sample he hidden coss are similar in magniude o he beneis o inerim rades. B. Risk- and Syle-Adjusing he Reurn Gap From he analysis in he previous secion we canno conclude wheher he reurn gap is correlaed wih any risk or syle acors. To shed more ligh on his issue, Panels B, C, and D o Table III summarize he abnormal reurns and he acor loadings using he one-acor CAPM (Panel B), he Fama and French (1993) hree-acor model (Panel C), and he Carhar (1997) our-acor model (Panel D). Among he hree, he Carhar (1997) is he mos comprehensive acor model and has he ollowing speciicaion: R i, R F, = α I + β i,m (R M, R F, ) + β i,smb SMB + β i,hml HML + β i,mom MOM + e i,, (8) where he dependen variable is he quarerly reurn on porolio i in quarer minus he risk-ree rae, and he independen variables are given by he reurns o he our zeroinvesmen acor porolios. The erm R M R F denoes he excess reurn o he marke porolio over he risk-ree rae; 10 SMB is he reurn dierence beween small and large capializaion socks; HML is he reurn dierence beween high and low book-o-marke socks; and MOM is he reurn dierence beween socks wih high and low pas reurns. 11 The inercep o he model, α i, is he Carhar measure o abnormal perormance. The CAPM model uses only he marke acor and he Fama and French model uses he 10 The marke reurn is calculaed as he value-weighed reurn on all NYSE, AMEX, and NASDAQ socks using he CRSP daabase. The monhly reurn o he one-monh Treasury bill rae is obained rom Ibboson Associaes. 11 The size, he value, and he momenum acor reurns were aken rom Kenneh French s Web sie hp://mba.uck.darmouh.edu/pages/aculy/ken.rench/daa_library. 18

19 irs hree acors. Table III demonsraes ha he general conclusions are no aeced i we exclude reurn componens ha are due o common acors in asse reurns. 12 C. Disribuion o he Reurn Gap Table IV summarizes he reurn gap condiional on various und characerisics. Panel A divides our sample ino acively and passively managed unds. The vas majoriy o muual unds in our sample (96.4 percen) are acively managed. Passively managed unds have a raw reurn gap ha is percen per monh lower han ha o acively managed unds. This dierence in he reurn gap can be explained primarily by dierences in disclosed expenses. Panel B separaes he unds ino hree groups according o heir objecive code in he Specrum daabase. Aggressive growh unds end o ollow he mos aggressive invesmen sraegies and inves primarily in growh companies. Growh and income unds ollow he leas aggressive sraegies and inves primarily in value companies. We ind ha he expenses and he beneis rom inerim rades are larges or aggressive growh unds and smalles or he growh and income unds. In Panel C, we spli our sample ino quiniles wih respec o he age o each und. The average age o unds in he younges quinile is 3.3 years, while he average age o he unds in he oldes quinile is 40.8 years. Our resuls indicae ha he reurn gap aer he adjusmen or expenses (column wo) is posiive or he younges unds and negaive or he older unds. This resul is consisen wih Gaspar, Massa, and Maos (2004), who 12 We ind in unrepored resuls ha he adjusmen or non-equiy holdings has a subsanially smaller impac on he reurn gap using he abnormal reurns rom he acor models, because acor models eecively conrol or cash holdings. This indicaes ha our mehod o adjusing or non-equiy posiions generaes similar resuls as he mehod using abnormal reurns adjused or common acors. 19

20 argue ha young unds are more likely o receive subsidies rom heir amilies han older unds, because he perormance-cash low sensiiviy is more pronounced or younger unds, as shown by Chevalier and Ellison (1997). Table I shows ha he TNA o a und is posiively correlaed wih und age. In Panel D o Table IV, we sor he unds according o heir lagged TNA. We observe ha he larges unds end o have he lowes reurn gaps aer adjusing or non-equiy holdings and expenses. This resul is consisen wih Berk and Green (2004), who argue abou he exisence o signiican diseconomies o scale in money managemen. In Panel E, we divide our sample ino quiniles according o und expenses. We observe ha unds wih lower average expenses have more avorable reurn gaps. As a resul, we can iner ha unobserved acions exhibi a poenially ineresing crosssecional variaion. D. Persisence o he Reurn Gap From he previous analysis one canno conclude wheher he cross-secional dierences in he reurn gap are due o persisen hidden beneis and hidden coss. To enhance our undersanding o his maer, we sudy wheher he reurn gap is a persisen phenomenon. For ha purpose, we sor all muual unds in our sample ino quiniles according o heir reurn gap over he previous year and compue he average reurn during he subsequen monh. Table V repors he resuls or he reurn gaps beore (Panel A) and aer adjusing or expenses (Panel B). The irs column o Panel A shows ha unds in he wors reurn gap quinile during he previous 12 monhs generae an average reurn 20

21 gap beore expenses o basis poins in he subsequen monh. On he oher hand, unds in he bes reurn gap quinile generae an average reurn gap beore expenses o -1.6 basis poins. The second column o Panel B shows ha he reurn gap aer adjusing or expenses is also highly persisen. Funds wih he wors reurn gap during he previous 12 monhs have an average reurn gap aer expenses o -7.0 basis poins in he ollowing monh, while unds wih he bes reurn gap have an average reurn gap o 9.0 basis poins. The uure reurn gaps o boh exreme quiniles are saisically and economically highly signiican. The hird column indicaes ha hese eecs remain even aer adjusing he reurns or he common acors speciied in Carhar (1997). These resuls show ha unds wih posiive reurn gaps end o have persisenly higher inerim rading beneis han hidden coss and conversely or unds wih negaive reurn gaps. We also rack he persisence o he reurn gap over he subsequen ive years and compue heir respecive average monhly reurn gap. Figure 1 depics he uure reurn gaps or decile porolios ormed according o he average reurn gap during he year prior o he porolio ormaion. The igure demonsraes ha he raw reurn gap is remarkably persisen over ime. Panel A adjuss he reurn gap or non-equiy holdings and Panel B or non-equiy holdings and expenses. The ranking o he decile porolios in he monh aer he ormaion period remains idenical o ha in he ormaion period. The irs decile in Panel A has an average reurn gap o 23 basis poins and he enh decile an average reurn gap o 3 basis poins. The dierence in he reurn gap beween he op and he boom deciles amouns o, approximaely, 26 basis poins per monh or o abou

22 percen per year. 13 While he lieraure on he perormance persisence o muual unds documens ha he wors unds are persisen, our resuls show ha we ind persisence in boh ails o he reurn gap disribuion. 14 The resuls indicae ha he beneis o inerim rades and he hidden coss are persisen phenomena in he muual und indusry. Panel B shows he persisence o he reurn gap aer adjusing or expenses. We ind ha hree deciles have posiive reurn gaps in he monh ollowing he ormaion period, indicaing ha hese unds end o have higher beneis o inerim rades han hidden coss. On he oher hand, or seven deciles, we conclude ha hey have higher hidden coss han inerim rading beneis. Panel C adjuss he reurn gap or expenses and or our common reurn acors ollowing Carhar (1997). Carhar shows ha perormance persisence is less signiican aer one accouns or possible momenum eecs. We ind ha he abnormal reurn gap remains persisen even aer conrolling or common acors. Thus, our resuls canno be ully explained by he dierences in sysemaic acors in he inerim rading beneis. Alhough all igures show an economically signiican persisence in he reurn gap, hey do no demonsrae wheher his persisence is saisically signiican. Table VI summarizes he Spearman rank correlaions or he en porolios and indicaes ha our persisence resuls are generally highly saisically signiican. While he lieraure generally does no ind robus persisence in muual und perormance aer conrolling or he momenum acor, we ind a relaively srong persisence in he reurn gap. One reason may be ha by measuring he invesor reurns 13 We obain very similar resuls i we compue he average reurn during he whole year ollowing he ormaion period. We repor monhly reurns o avoid overlapping observaions. 14 See Hendricks, Pael, and Zeckhauser (1993), Brown and Goezmann (1995), and Carhar (1997) or sudies on he persisence o muual unds. 22

23 relaive o he holding reurns, we iler ou he impac o common shocks o boh reurns and are able o obain a less noisy signal o he hidden coss and he inerim rading beneis o muual unds. E. Deerminans o he Reurn Gap This secion analyzes he deerminans o he reurn gap using a panel regression o he reurn gap on various und characerisics. We lag all explanaory variables by one monh, excep or expenses and urnover, which are lagged by one year due o daa availabiliy. Using he lagged explanaory variables miigaes poenial endogeneiy problems. We also ake he naural logarihms o he age and size variables, o miigae an impac o righ skewness in he disribuions o boh variables. Each regression addiionally includes ime ixed eecs. We esimae he regressions wih panel-correced sandard errors (PCSE). The PCSE speciicaion adjuss or heeroskedasiciy and auocorrelaion in und reurns (Beck and Kaz, 1995). Since mos muual unds do no exis over he whole sample period we analyze he unbalanced panel. Table VII summarizes he regression resuls. In his regression, we do no need o adjus he reurn gap or expenses, because we use he expense raio as an explanaory variable. Since we wan o analyze boh und-speciic and amily-speciic eecs, we are bound o use wo slighly dieren samples in our regressions. The irs daa column repors he resuls using our complee ime period beween 1984 and Since he managemen company o each individual muual und is only ideniied aer 1992, column wo repors he resuls using only daa beween 1993 and Thus, he number 23

24 o observaions in column wo is smaller han he number o observaions using he enire sample period. Firs, we analyze he sensiiviy o he reurn gap o a poenial impac o expenses and rading coss. We should expec ha he reurn gap decreases i a und charges higher expenses or i a und has higher rading coss, unless hese revealed and hidden coss are compensaed or wih higher inerim rading beneis. The resuls indicae a one-o-one relaionship beween he reurn gap and expenses: A one percenage poin increase in expenses decreases he reurn gap by percenage poins. Thus, he inerim rading beneis are no suicienly large or high-expense unds o ose heir higher expenses. Nex, we examine how poenial rading aciviies aec he reurn gap. On one hand, rading coss can be approximaed by he urnover o a und, he exchange on which he socks are raded, and he characerisics o he socks held. On he oher hand, hese variables migh also be relaed o he inerim rading beneis. The esimaes rom our regression exhibi no signiican relaionship beween he urnover o a und and he uure reurn gap. An insigniican coeicien esimae on urnover, however, does no necessarily imply ha he rading coss are no signiicanly relaed o urnover. I is possible ha porolio urnover has also a posiive associaion wih he inerim rading beneis. For example, exising sudies (e.g., Pásor and Sambaugh, 2002) argue ha urnover may proxy or he unobserved managerial skills. Consequenly, hese wo eecs may be oseing each oher. To deermine he exisence o a relaionship beween he exchange on which a und rades socks and he reurn gap, or each und and monh, we compue he proporion o heir mos recen posiions, raded eiher on he NYSE, NASDAQ, or 24

25 AMEX. These variables capure dierences in rading coss on he hree exchanges. We ind ha unds ha hold a larger proporion o socks raded on he NYSE and NASDAQ end o have higher reurn gaps han unds ha hold a larger proporion o AMEX socks. The relaionship is highly signiican boh saisically and economically. This resul is consisen wih he evidence ha, on average, rades on AMEX incur higher coss. To invesigae he exen o wha he reurn gap is relaed o he size o a unds holdings we compue he porolio composiion o each und. Each sock raded on he major U.S. exchanges is grouped ino respecive quiniles according o is lagged marke value. Subsequenly, using he quinile inormaion, we compue he value-weighed size score or each muual und in each period. For example, a muual und ha invess only in socks in he smalles size quinile would have a size score o 1, while a muual und ha invess only in he larges size quinile would have a size score o 5. We ind ha he reurn gap ends o be more avorable or unds ha hold small socks. This resul is consisen wih Kacperczyk, Sialm, and Zheng (2004), who demonsrae ha unds ha hold small capializaion socks end o exhibi superior perormance, presumably because inormaional asymmeries play a more signiican role or hese socks. Nex, we ind ha, over he sample period, younger unds end o have more avorable reurn gaps. However, we do no ind any saisically signiican dierence in reurn gaps beween small and large unds. Muual und amilies can eecively ranser asses rom one muual und o anoher und in heir amily. For example, Gaspar, Massa, and Maos (2004) show ha amilies allocae IPO deals o high amily value unds, which hey ideniy as young unds wih high expense raios and wih posiive recen perormance. Cross-subsidizaion 25

26 increases he reurn gap o he subsidized unds and decreases he reurn gap o he subsidizing unds. This hypohesis indicaes ha he unds, which are mos likely o receive subsidies, such as small and young unds, will end o have more avorable reurn gaps. To conrol or hese amily eecs, we include, as addiional explanaory variables, he raio beween he und and he amily expense raio, he raio beween he und and he amily TNA, and he raio o he und and he amily age. We ind ha he relaive age o a und is negaively relaed o he reurn gap and ha he relaive expenses are posiively relaed o he reurn gap. These resuls are consisen wih Gaspar, Massa, and Maos (2004), who show ha younger unds and unds wih higher expense raios in a und amily end o be cross-subsidized. We ind no evidence ha he relaive size o a und in he amily aecs is reurn gap. One speciic way o how und amilies can avor paricular unds is by allocaing underpriced IPO purchases o a group o paricular unds (Reuer, 2004; Gaspar, Massa, and Maos, 2004). Alhough we do no know which unds obain IPO allocaions direcly, we can assume ha unds ha have obained a larger proporion o IPO allocaions end o have a larger racion o recen IPO socks in heir porolios. Thereore, we compue or each und in each monh he proporion o socks ha wen public during he previous year. I und amilies allocae he IPOs consisenly o he same unds, hen we should observe ha unds, which obained pas IPO allocaions, will have more avorable reurn gaps in he uure. Table VII shows ha he weigh o recen IPOs in he und porolio has a srong predicive power or he uure reurn gap. This resul indicaes ha par o he cross-subsidizaion wihin und amilies is due o IPO allocaions. 26

27 Finally, using older holdings daa magniies he impac o inerim rades, bu should no aec he hidden coss in a paricular monh. Thus, we should expec ha he reurn gap improves when he holdings are more sale i inerim rades add value. We observe ha he reurn gap improves by 2.5 basis poins per monh or each quarer o he disclosure delay. VI. Predicabiliy o Fuure Fund Perormance In his secion we address he quesion wheher invesors should care abou unobserved acions o muual unds. We examine wheher our esimae o pas unobserved acions can help invesors o selec muual unds ha will perorm relaively well in he uure. I he reurn gap is a persisen phenomenon hen we should expec ha muual unds wih higher reurn gaps (i.e., hose wih more beneicial unobserved acions) ouperorm unds wih lower reurn gaps in he uure. A. Panel Regressions To es his hypohesis, we run panel regressions o he risk and syle-adjused perormance o muual unds on esimaes o pas value o unobserved acions, conrolling or oher und-speciic characerisics. Table VIII shows ha he reurn gap has an imporan impac on he uure und perormance, even aer conrolling or oher und characerisics, such as expenses, urnover, size, and age. Using Carhar s our-acor model, a one percen increase in he pas reurn gap increases he uure und reurn by 19 basis poins. The ac ha he gap 27

28 remains signiican, aer conrolling or expenses, indicaes ha unobserved acions, oer an addiional insigh ino he predicabiliy o uure und reurns. Previous evidence indicaes some shor-erm persisence in muual und perormance, especially or poorly perorming unds, or example, Blake, Elon, and Gruber (1993), Goezmann and Ibboson (1994), Brown and Goezmann (1995), Malkiel (1995), Elon, Gruber and Blake (1996), Gruber (1996), Carhar (1997), and Mamaysky, Spiegel, and Zhang (2005). Table IX examines he incremenal predicabiliy o he reurn gap or uure und perormance over and above pas und reurns. We ind ha pas reurns are posiively relaed o uure reurns. Also, he coeicien on he reurn gap, hough smaller in magniude han ha in he previous able, remains posiive and signiican, even aer we conrol or he lagged ne reurn o he und, which includes he hidden coss and he inerim rading beneis. Using a our-acor model, a one percen increase in he pas reurn gap increases uure und reurn by 10 basis poins. The reurn gap remains a signiican predicor o uure perormance, because i capures inormaion abou und hidden coss and inerim rading in a less noisy ashion han he ne reurns. We argue ha apar rom oher characerisics, such as expenses, urnover, TNA, and age, und invesors should also ake ino accoun he reurn gap when hey selec muual unds. B. Trading Sraegies In his secion, we examine he proiabiliy o a hypoheical rading sraegy based on he variable reurn gap, which measures he impac o unobserved acions o muual unds. Speciically, we sor all muual unds in our sample ino deciles, according 28

29 o heir average reurn gap during he previous 12 monhs. Subsequenly, we compue he average reurns in he ollowing monh by weighing all he unds in a decile equally. In Table X we repor he ne reurns or each o his decile porolio. The irs column repors excess reurns o he deciles wih respec o he marke porolio, while he remaining hree columns repor he adjused abnormal reurns according o he one-acor CAPM model, he hree-acor model o Fama and French, and he our-acor model o Carhar. Panel A sors unds according o he raw reurn gap. Funds in he irs decile have an average reurn gap o basis poins per monh during he porolio ormaion period. On he oher hand, unds in he enh decile have an average reurn gap o basis poins per monh during he ormaion period. We observe ha unds wih he mos avorable pas reurn gaps (decile en) end o perorm signiicanly beer han unds wih he leas avorable pas reurn gaps (decile one) in he subsequen monh. Invesing in he decile-en unds would have generaed an addiional excess reurn o basis poins per monh or abou our percen per year, as compared o invesing in he decile-one unds. The relaionship beween pas reurn gaps and uure perormance is almos sricly monoonic, which resuls in a very high Spearman rank correlaion coeicien o percen. 15 Our resuls are no aeced subsanially by he variaion in he risk or syle acors, as repored in he las hree columns o Table X. Ineresingly, he ideniied perormance dierence is primarily driven by he poor reurns o unds wih highly negaive reurn gaps. Wih he excepion o he Fama and 29

30 French abnormal reurn, no oher perormance measures are signiicanly posiive or he unds wih he mos avorable reurn gaps. Since we sor unds by he reurn gap beore adjusing or expenses, he reurn dierence in Panel A migh be driven by possible dierences in he und expenses. In Panel B o Table X, we sor muual unds according o he reurn gap adjused or expenses, which is equivalen o soring unds according o he value o heir unobserved acions. The resuls are no aeced subsanially when using his alernaive deiniion. This indicaes ha he proiabiliy o our rading sraegy mos likely resuls rom persisence o hidden coss or inerim rading beneis raher han rom persisence o expenses. Figure 2 presens he graphical illusraion o he resuls discussed above. VII. Conclusions In a well-uncioning inancial marke, muual und invesors are supposed o make inormaive decisions abou unds based on he inormaion disclosed by he unds o he public. I is well-known ha several und acions are no ully observed by he marke paricipans. These acions may benei or hur invesors, and hus, learning abou hese acions may help invesors o evaluae muual unds more horoughly. In his paper, we analyze he impac o hese unobserved acions on he und peormance or he U.S. equiy muual unds beween 1984 and We esimae he impac o unobserved acions by aking he dierence beween he repored ne reurns and he buy-and-hold reurns o he porolio disclosed in he mos recen pas. Much o his dierence is driven by und expenses and asse srucure, boh being disclosed o he 15 The resuls are unaeced qualiaively i we compue he average reurns over he enire year aer he porolio ormaion, as opposed o calculaing hem in he subsequen monh aer he porolio ormaion. 30

31 public. However, he residual dierence, which measures he eec o unobserved acions, presens us wih several ineresing indings. Firs, he eec o unobserved acions is persisen in he long-run. Second, unds dier subsanially wih respec o he impac o such acions. For example, in conras o old unds, young unds, on average, generae posiive reurns on heir unobserved acions. Mos imporanly, he crosssecional dierence in unobserved acions has a signiican predicive power or uure perormance, indicaing ha unds wih value-enhancing unobserved acions ouperorm unds, whose unobserved acions predominanly relec hidden coss. A hypoheical rading sraegy ha buys unds wih a posiive reurn gap and shors unds wih a negaive reurn gap would have generaed an economically large reurn on invesmen. Our paper oers several implicaions or he secor o muual unds. Firs, he exisence o sysemaic dierences in he scope o he unobserved acions among unds raises concerns or unds wih persisenly large negaive reurn gaps. This is especially imporan in ligh o he ac ha unds wih negaive acions adversely aec invesors reurn on unds. Second, muual und invesors can make beer und selecion decisions i hey ake ino accoun he unobserved acions o muual unds. We repor he laer o avoid overlapping reurn observaions. 31

32 APPENDIX A. Sample Selecion We sar our maching process wih a sample o all muual unds in he CRSP muual und daabase. This daabase liss 24,019 unds covering he period beween 1984 and The ocus o our analysis is on domesic equiy muual unds, or which he holdings daa are he mos complee and reliable. As a resul, we eliminae balanced, bond, money marke, and inernaional unds, as well as unds no invesed primarily in equiy securiies. We base our selecion crieria on he objecive codes and on he disclosed asse composiions. Firs, we selec unds wih he ollowing ICDI objecives: AG (Aggressive Growh), GI (Growh and Income), LG (Long-erm Growh), IN (Income), PM (Precious Meals), SF (Secor Funds), or UT (Uiliy Fund). I a und does no have any o he above ICDI objecives, we selec unds wih he ollowing Sraegic Insigh objecives: AGG (Aggressive Growh Funds), ENV (Environmenal Funds), FIN (Financial Secor Funds), GLD (Gold Oriened Funds), GMC (Growh MidCap Funds), GRI (Growh and Income Funds), GRO (Growh Funds), HLT (Healh Funds), ING (Income Growh Funds), NTR (Naural Resources Funds), RLE (Real Esae Funds), SCG (Small Company Growh Funds), SEC (Secor Funds), TEC (Technology Funds), or UTI (Uiliy Funds). I a und has neiher he Sraegic Insigh nor he ICDI objecive, hen we go o he Wiesenberger Fund Type Code and pick unds wih he ollowing objecives: G (Growh), G-I (Growh Income), AGG (Aggressive Growh Fund), ENR (Energy Secor), FIN (Financial Secor), GCI (Growh wih Curren Income), GPM (Gold 32

33 and Precious Meals), GRI (Growh and Income), GRO (Growh), HLT (Healh Care), MCG (Maximum Capial Gains), SCG (Small Capializaion Growh), TCH (Technology), or UTL (Uiliies). I none o hese objecives are available and he und has he CS policy (Common Socks are he mainly held securiies by he und), hen he und will be included. We exclude unds ha have he ollowing Invesmen Objecive Codes in he Specrum Daabase: Inernaional, Municipal Bonds, Bond and Preerred, and Balanced. Since he repored objecives do no always indicae wheher und porolio is balanced or no, we also exclude unds, which, on average, hold less han 80 percen or more han 105 percen in socks,. Finally, we exclude unds whose oal value o he disclosed equiy holdings is more han double he TNA o he und or whose TNA is more han double he value o he disclosed equiy holdings. This eliminaes unds which hold a large proporion o asses ha are no included in he CRSP sock price daabase, because hey are no raded on he major U.S. exchanges. Aer his screen, our sample period includes daa on 8,228 equiy muual unds. Elon, Gruber, and Blake (2001) and Evans (2004) ideniy a orm o survival bias in he CRSP muual und daabase, which resuls rom a sraegy used by und amilies o enhance heir reurn hisories. Fund amilies migh incubae several privae unds and hey will only make public he rack record o he surviving incubaed unds, while he reurns or hose unds ha are erminaed are no made public. To address his incubaion bias, we exclude he observaions where he year or he observaion is prior o he repored und saring year. We also exclude observaions where he names o he unds are missing in he CRSP daabase. Daa may be repored prior o he year o und organizaion i a und is incubaed beore i is made publicly available and hese unds 33

34 migh no repor heir names or some oher und aribues, as shown by Evans (2004). This reduces he number o unds in our daa se o 7,951. In he nex sep, we are able o mach abou 94 percen o he CRSP unds o he Specrum daabase. For 465 o he 7,951 unds we canno ind a Specrum enry. These unds end o be younger and smaller han he unds or which we ind daa in Specrum. As previously menioned by Wermers (2000), he Specrum daa se oen does no have any holdings daa available during he irs ew quarers lised in he CRSP daabase. Muual und amilies inroduced dieren share classes in he 1990s, as discussed in Nanda, Wang, and Zheng (2004). Since dieren share classes have he same holdings composiion, we aggregae all he observaions peraining o dieren share classes ino one observaion. For he qualiaive aribues o unds (e.g., name, objecives, year o originaion), we reain he observaion o he oldes und. For he oal ne asses under managemen (TNA), we sum he TNAs o he dieren share classes. Finally, or he oher quaniaive aribues o unds (e.g., reurn, expenses, loads), we ake he weighed averages o he aribues o he individual share classes, where he weighs are he lagged TNAs o he individual share classes. The aggregaion o muliple share classes reduces our sample size o 3,171 unique unds. For mos o our sample period, muual unds were required o disclose heir holdings semi-annually. A large number o unds disclose heir holdings quarerly, while a small number o unds have gaps beween holding disclosure daes o more han six monhs. To ill hese gaps, we impue he holdings o missing quarers using he mos recenly available holdings, assuming ha muual unds ollow a buy-and-hold sraegy. In our sample, 72 percen o he observaions are rom he mos recen quarer and less 34

35 han 5 percen o he holdings are more han wo quarers old. We exclude unds whose holdings are more han hree quarers old and whose oal value o he disclosed holdings accouns or less han 50 percen or more han 200 percen o he oal ne asses o he muual und. This inal selecion crierion reduces he number o muual unds used in his sudy o 3,008 unds. B. Inerim Trading Beneis An imporan porion o unobserved acions originaes due o he ac ha unds can rade beween disclosure daes. For example, he reurn on he holdings underesimaes (overesimaes) he acual gross reurn o a und i a newly acquired sock appreciaes (depreciaes) prior o he disclosure dae. We would also miss he reurns generaed by socks ha are only held or a shor ime period in beween porolio disclosure daes. The hidden beneis may also include cases where a und receives underpriced IPO allocaions, which end o appreciae signiicanly on he irs rading day. Unorunaely, we are unable o observe all hese rading beneis. We can only observe he implied rades ha ollow rom subsequen holdings disclosures. To invesigae wheher hidden rading beneis exis and o esimae a lower bound o heir value, we ollow Grinbla and Timan (1993) and compue he reurn o he disclosed rades o a muual und. The Grinbla and Timan perormance measure is deined as he dierence beween he curren reurn o a porolio ha holds he mos recenly disclosed holdings and he curren reurn o a buy-and-hold porolio ha holds he holdings disclosed τ periods ago: N i= 1 i, 1 N i= 1 i, 1, τ N ( w w~ ) GTBH = w Ri w~, τ, Ri, = Ri,. (9) i= 1 i, 1 i, 1, τ 35

36 While Grinbla and Timan (1993) use he acual lagged weighs, w i, τ, o orm he benchmark porolio, we use he buy-and-hold lagged weighs, w~ i, 1, τ, deined as in (4). Using he acual weighs requires a rading sraegy ha rebalances he benchmark porolio. In our case, we are ineresed in he conribuion o he rades relaive o a passive buy-and-hold benchmark porolio. In his respec, our perormance measure compues he conribuion o he disclosed rading ransacions during he las τ periods. For all muual unds in our daabase, we compue he GTBH measure or dieren ime gaps beween disclosure daes τ. In each monh, we compue he conribuion o he rades using he lagged TNAs o our muual unds. Figure A1 summarizes he ime series average o his measure or he muual unds in our sample. By consrucion, he GTBH measure is zero i he mos recen quarer is also he benchmark quarer (i.e., he quarer dierence is zero). We observe ha he value-weighed GTBH measure increases gradually or he irs hree quarers and decreases slighly wih a our-quarer holdings dierence or boh he equally- and he value-weighed measures. The equally-weighed measures are larger or all quarer gaps, mainly because small muual unds end o perorm beer. The disclosed rades beween wo consecuive quarers conribue 3.6 basis poins per monh, or abou 0.43 percen per year, o he oal reurn o a und. The 95 percen conidence levels or he ime series o he value-weighed GTBH perormance measures, as presened by he doed curves, indicae ha his perormance measure is signiicanly dieren rom zero. The GTBH measure equals 5.9 basis poins per monh, or abou 0.68 percen per year, i we use he disclosed rades during one year. These resuls are generally consisen wih he resuls obained by Grinbla and Timan (1993), 36

37 alhough he magniude using a buy-and-hold porolio is smaller compared o a rebalanced benchmark porolio. Nex, we apply he GTBH measure o obain a lower bound on he reurns due o inerim rading. In paricular, unds ha disclose heir holdings only semi-annually end o have higher inerim rading reurns han unds ha disclose heir holdings quarerly. To obain monhly reurns due o inerim rading wihin a quarer, we perorm an inerpolaion o values beween he nodes in Figure A1. The GTBH measure consiues a lower bound on he inerim rading reurn or wo ollowing reasons. Firs, when we compue he GTBH measure, we do no observe he proiabiliy o he rades immediaely ollowing he purchase decision. Second, i a und obains a sock a a price below he marke value, such as in an underpriced IPO allocaion, hen he GTBH measure does no capure his eec. To deermine a lower bound o he beneis rom he inerim rading, in each monh we compue he average GTBH perormance measure a he one, wo, hree, and our-quarer gap level o all unds in he sample, as shown in Figure A1. We use hese reurns o esimae he monhly reurns due o inerim rading. For example, i a und did no disclose is holdings in he las quarer, bu disclosed is holdings wo quarers ago, hen we use he average GTBH reurns wih a wo quarer lag or all unds which have his measure available in he curren monh. This mehod assumes ha he inerim rade reurn disribuion o unds ha did no disclose heir holdings las monh is idenical o he inerim rade reurn disribuion o unds ha did disclose heir holdings las monh. Based on his calculaion, we obain inerim rade beneis o 3.4 basis poins per monh. 37

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41 Zheng, Lu, 1999, Is money smar? A sudy o muual und invesors und selecion abiliy, Journal o Finance, 54, Zizewiz, Eric, 2003, Who cares abou shareholders? Arbirage-prooing muual unds, Journal o Law, Economics, and Organizaion 19 (2),

42 Figure 1 Persisence o he Reurn Gap This igure depics he average reurn gap o porolios racked over a ive-year period. The reurn gap is deined as he dierence beween he repored ne reurn and he holding reurn o he porolio disclosed in he previous period. The porolios are ormed by soring all he unds ino deciles according o heir iniial reurn gap during he previous year. Subsequenly, each porolio is racked over he nex ive-year period. In case o some unds dropping rom he porolio, he porolio weighs are adjused equally. In Panel A, we repor he oal reurn gap; in Panel B we addiionally adjus he dierence or expenses; in Panel C, he reurn is addiionally adjused or our zero-invesmen porolios marke, size, value, and momenum, as in Carhar (1997). The Figures do no show he reurn gap during he ormaion period. Panel A: Persisence in he Reurn Gap beore Adjusing or Expenses 5 Dierence in Adjused Reurns Aer Expenses (in bp per monh) Years Aer Porolio Formaion Panel B: Persisence in he Reurn Gap aer Adjusing or Expenses Dierence in Adjused Reurns Beore Expenses (in bp per monh) Years Aer Porolio Formaion 42

43 Panel C: Persisence in he Abnormal Reurn Gap Using he Carhar Four-Facor Model Dierence in Adjused 4-Facor Abnormal Reurns Beore Expenses (in bp per monh Years Aer Porolio Formaion 43

44 Figure 2 Reurns o Trading Sraegies This igure shows he average abnormal reurns during he monh ollowing he ormaion period (in basis poins). The decile porolios are ormed based on he previous one-year reurn gap beore adjusing or expenses (Panel A) and aer adjusing or expenses (Panel B), where decile one has he lowes reurn gap and decile en has he highes reurn gap. We use our measures o abnormal reurns he excess reurn in excess o he risk-ree rae; he marke-adjused abnormal reurn (CAPM); he hree-acor adjused reurn as in Fama and French (1993); he our-acor adjused reurn as in Carhar (1997). Panel A: Soring Based on he Reurn Gap beore Adjusing or Expenses Fuure Abnormal Reurn (in bp per monh Reurn Gap Porolio Three Facor Excess Reurn Four Facor CAPM Panel B: Soring Based on he Reurn Gap aer Adjusing or Expenses Fuure Abnormal Reurn (in bp per monh Reurn Gap Porolio Three Facor Excess Reurn Four Facor CAPM 44

45 Figure A1 Reurn on Trades This igure depics he mean reurn, and he 95 percen conidence inerval, on he rades or dieren quarers or he aggregae equiy muual und secor. The reurn rom rades is compued or each und in each monh as GTBH = [(w j,-1 ŵ j,-τ )R j, ], where ŵ j,-τ are he buy-and-hold weighs o he porolio ha was held a ime -τ. Reurn rom Trades (in bp per monh) Quarer Dierence 45

46 Table I Summary Saisics Panel A presens he summary saisics (mean, median, minimum, and maximum) or he sample o he acively managed equiy muual unds over he period 1984 o Panel B repors he conemporaneous correlaions beween he main variables, along wih heir saisical signiicance. Panel A: Summary Saisics Mean Median Minimum Maximum Number o disinc muual unds 3,008 Number o und-monh observaions 240,886 Number o unds per monh 1, ,212 TNA (Toal Ne Asses) (in Millions) ,526 Age Expense Raio (in Percen) Turnover Raio (in Percen) ,211 Maximum Toal Load (in Percen) Number o socks held ,596 Number o share classes Repored reurn per monh (in Percen) Holdings reurn per monh (in Percen) Panel B: Correlaion Srucure Variables TNA Age Expenses Turnover Load Socks Classes Repored Reurn TNA 1.00 Age 0.21*** 1.00 Expenses -0.13*** -0.11*** 1.00 Turnover -0.04*** -0.06*** 0.12*** 1.00 Load 0.03*** 0.19*** 0.16*** -0.03*** 1.00 Number o socks 0.12*** -0.04*** -0.20*** -0.06*** -0.10*** 1.00 Number o classes 0.09*** -0.01*** 0.10*** 0.01*** 0.25*** 0.01*** 1.00 Repored reurn *** -0.01*** -0.01*** -0.00* *** 1.00 Holdings reurn *** *** *** 0.97*** *** 1% signiicance; ** 5% signiicance; * 10% signiicance 46

47 Table II Impuing Reurns on Non-Equiy Holdings This able summarizes he disribuion o asse classes across our sample o muual unds during he period The average weigh is deermined as he ime series average o he value-weighed proporions invesed in each monh in ive basic asse classes. The reurns o he dieren asse classes are impued in each monh by running a regression o RF i, = γ Equiy, w Equiy,i,-1 + γ Cash, w Cash,i,-1 + γ Bonds, w Bonds,i,-1 + γ Pres, w Pres,i,-1 + γ Oher, w Oher,i, -1+ ε i,, where w Equiy,i,-1 are he lagged weighs invesed in Equiy by und i, and γ Equiy, are he esimaed reurns o he various asse classes. We use he esimaed reurns in each monh as he impued reurns. The corresponding index reurns are he CRSP Toal Index Reurn or equiy holdings, he risk-ree ineres rae rom French s websie or Cash, and he Lehman Brohers Aggregae Bond Index or bonds. No benchmarks were ound or preerred socks and oher. Sandard deviaions o he esimaes have been included in parenheses. Asse Class Mean and Sandard Deviaion o he Weigh (in Percen) Mean and Sandard Deviaion o Impued Reurn (in Percen per Monh) Equiy (2.99) (4.82) Bonds (1.06) (1.29) Cash (2.26) (0.98) Preerred Socks (0.31) (5.14) Oher (0.29) (1.55) *** 1% signiicance; ** 5% signiicance; * 10% signiicance Mean and Sandard Deviaion o Index Reurn (in Percen per Monh) 1.07 (4.57) 0.75 (1.35) 0.43 (0.18) Correlaion (in Percen) 97.97*** 88.25*** 23.17*** 47

48 Table III Perormance o Repored and Holding Reurns This able summarizes he means and he sandard errors (in parenheses), along wih heir saisical signiicance, or he repored (invesor) reurn, he holding reurn (beore and aer expenses), and he reurn gap over he monhly ime series o he equally-weighed porolio o all unds. The reurn gap has been deined as a dierence beween repored reurn and he holding reurn o he porolio disclosed in he previous period. Panel A repors raw reurns; Panel B, C, and D repor he one-acor, hree-acor, and our-acor adjused perormance measures and he acor loadings, respecively. Repored Reurns Holding Reurns Reurn Gap Beore Expenses Aer Expenses Beore Expenses Aer Expenses Panel A: Raw Reurns Raw Reurn 1.004*** (0.302) 1.102*** (0.303) 1.002*** (0.304) *** (0.010) (0.010) Panel B: CAPM Alpha (0.056) Marke 1.006*** (0.012) (0.055) 1.015*** (0.012) (0.044) 1.015*** (0.012) *** (0.010) *** (0.002) (0.009) *** (0.002) Panel C: Fama and French Model Alpha (0.044) Marke 0.993*** (0.011) Size 0.165*** (0.014) Value (0.016) (0.055) 1.001*** (0.011) 0.155*** (0.014) (0.017) (0.045) 1.001*** (0.011) 0.154*** (0.014) (0.017) *** (0.010) *** (0.001) 0.010*** (0.002) (0.002) (0.009) *** (0.002) 0.011*** (0.003) (0.004) Panel D: Carhar Model Alpha (0.045) (0.046) (0.047) Marke 0.993*** 1.000*** 1.000*** (0.011) (0.011) (0.011) Size 0.165*** 0.155*** 0.155*** (0.014) (0.014) (0.014) Value (0.017) (0.017) (0.017) Momenum (0.010) (0.010) (0.010) *** 1% signiicance; ** 5% signiicance; * 10% signiicance *** (0.010) *** (0.002) 0.010*** (0.003) (0.004) 0.004** (0.002) (0.010) *** (0.002) 0.010*** (0.003) 0.006* (0.004) 0.004** (0.002) 48

49 Table IV Summary Saisics on he Reurn Gap This able summarizes he means and he sandard errors (in parenheses), along wih heir saisical signiicance, or he reurn gap according o various pariions o unds over he monhly ime-series o he equally-weighed invesor and he holding reurns. The reurn gap has been deined as he dierence beween he repored reurn and he holding reurn o he porolio disclosed in he previous period. In column one we calculae he reurn gap beore adjusing or expenses; in column wo we adjus he gap or expenses, while in column hree we addiionally adjus he laer gap or our zero-invesmen porolios marke, size, value, and momenum as in Carhar (1997). Panel A sors unds wih respec o heir syle ino acively and passively-managed; Panel B sors hem wih respec o heir invesmen sraegy ino aggressive growh, growh, and growh and income; Panel C sors unds ino quiniles based on heir age; Panel D sors unds ino quiniles according o heir lagged TNA; Panel E sors unds ino quiniles wih respec o heir lagged expenses. The sample spans he period 1984 o Raw Reurn Gap Beore Expenses Raw Reurn Gap Aer Expenses Abnormal Reurn Gap Aer Expenses Using Four-Facor Model Panel A: Funds by Syle Acively Managed Funds Passively Managed Funds *** (0.010) *** (0.001) (0.010) (0.011) (0.010) (0.010) Panel B: Funds by Invesmen Sraegy Aggressive Growh *** (0.019) Growh *** (0.010) Growh and Income *** (0.010) (0.019) (0.010) (0.011) (0.017) (0.010) (0.011) Panel C: Funds by Age Younges Quinile Mean Age: 3.3 years Second Quinile Mean Age: 6.8 years Third Quinile Mean Age: 11.0 years Fourh Quinile Mean Age: 18.2 years Oldes Quinile Mean Age: 40.8 years *** (0.013) *** (0.014) *** (0.012) *** (0.011) *** (0.012) 0.049*** (0.013) (0.014) (0.012) (0.011) * (0.012) 0.043*** (0.014) (0.014) (0.012) (0.011) ** (0.012) 49

50 Table IV Summary Saisics on he Reurn Gap (Con.) Raw Reurn Gap Beore Expenses Raw Reurn Gap Aer Expenses Abnormal Reurn Gap Aer Expenses Using Four-Facor Model Panel D: Funds by Lagged TNA Smalles Quinile Mean TNA: $20M Second Quinile Mean TNA: $60M Third Quinile Mean TNA: $154M Fourh Quinile Mean TNA: $411M Larges Quinile Mean TNA: $9,996M *** (0.013) *** (0.012) *** (0.013) *** (0.012) *** (0.012) (0.013) 0.024** (0.012) (0.013) (0.012) ** (0.012) (0.013) 0.022* (0.012) (0.013) (0.013) ** (0.012) Panel E: Funds by Expenses Smalles Expenses Mean Expenses: Second Quinile Mean Expenses: Third Quinile Mean Expenses: Fourh Quinile Mean Expenses: Larges Expenses Mean Expenses: *** (0.011) *** (0.011) *** (0.011) *** (0.013) *** (0.015) (0.011) (0.012) (0.011) 0.026* (0.013) (0.015) (0.011) (0.012) (0.011) (0.013) (0.015) 50

51 Table V Persisence in he Reurn Gap This able repors he average and he sandard error (in parenheses), along wih is saisical signiicance, o he curren reurn gap or quinile porolios o he acively managed equiy muual unds sored by heir respecive lagged reurn gap. The reurn gap has been deined as a dierence beween repored reurn and he holding reurn o he porolio disclosed in he previous period. In column one, we calculae he reurn gap beore adjusing or expenses; in column wo, we adjus he gap or expenses, while in column hree we addiionally adjus he laer gap or our zero-invesmen porolios marke, size, value, and momenum as in Carhar (1997). Panel A sors unds wih respec o he reurn gap beore expenses, while Panel B adjuss he gap or expenses. The sample spans he period 1984 o Raw Reurn Gap Beore Expenses Raw Reurn Gap Aer Expenses Abnormal Reurn Gap Aer Expenses Using Four-Facor Model Panel A: Funds by Lagged Raw Reurn Gap Beore Expenses Wors Quinile Mean RG: *** (0.019) *** (0.019) Second Quinile *** *** Mean RG: (0.010) (0.010) Third Quinile *** Mean RG: (0.009) (0.009) Fourh Quinile *** Mean RG: (0.011) (0.011) Bes Quinile *** Mean RG: (0.022) (0.022) ** (0.018) *** (0.011) (0.009) (0.011) 0.062*** (0.020) Panel B: Funds by Lagged Raw Reurn Gap Aer Expenses Wors Quinile Mean RG: *** (0.018) *** (0.018) Second Quinile *** *** Mean RG: (0.011) (0.010) Third Quinile *** Mean RG: (0.008) (0.008) Fourh Quinile *** Mean RG: (0.011) (0.012) Bes Quinile *** Mean RG: (0.022) (0.022) *** (0.018) ** (0.011) (0.008) (0.012) 0.066*** (0.020) 51

52 Table VI Persisence o he Reurn Gaps: Spearman Rank Correlaions This able summarizes he Spearman rank correlaion, along wih is saisical signiicance, beween quinile porolios, sored wih respec o he reurn gap, or dieren ime horizons one, wo, hree, our, and ive years aer ormaion period. The reurn gap has been deined as a dierence beween repored reurn and he holding reurn o he porolio disclosed in he previous period. In column one we calculae he reurn gap beore adjusing or expenses; in column wo we adjus he gap or expenses, while in column hree we addiionally adjus he laer gap or our zero-invesmen porolios marke, size, value, and momenum as in Carhar (1997). One Year Aer Porolio Formaion Spearman Rank Correlaion or he Dierence Beween Invesor and Holdings Reurns (in Percen) Raw Reurn Gap Aer Expenses Raw Reurn Gap Beore Expenses Abnormal Reurn Gap Aer Expenses Using Four-Facor Model *** *** 98.79*** Two Years Aer Porolio Formaion Three Years Aer Porolio Formaion Four Years Aer Porolio Formaion Five Years Aer Porolio Formaion *** *** 85.45*** *** 96.36*** *** 98.79*** 95.15*** 91.52*** 95.15*** 75.76** *** 1% signiicance (ρ>0.794); ** 5% signiicance (ρ >0.648); * 10% signiicance (ρ>0.564) 52

53 Table VII The Reurn Gap and Fund Characerisics This able repors he coeiciens o he panel regression o he reurn gap on various und and und amily characerisics. The sample includes equiy muual unds and spans he period o The Reurn Gap is measured as a dierence beween he repored und reurn and he reurn based on he previous quarer s holdings. The independen variables include lagged und expense raios, lagged und urnover, proporion o NASDAQ socks in he porolio, proporion o AMEX sock in he porolio, he size score, he naural logarihm o lagged TNA, he naural logarihm o lagged und age, he proporion o he previous year s IPO in he porolio, he age o he repored holdings, he relaive expense raio o a und o is und amily, he relaive TNA o a und o is und amily and he relaive age o a und o is amily. The size score or a muual und is deined as a value-weighed size score o is sock holdings in each ime period, as each sock raded on he major U.S. exchanges is grouped ino respecive quiniles according o is marke value and assigned a size score o 1 (smalles marke cap) o 5 (larges marke cap). All regressions include ime dummies. Panel-correced sandard errors, along wih he saisical signiicance, have been provided in parenheses. Dependen Variable: Reurn Gap Beore Expenses (in Basis Poins Per Monh) Expenses *** (0.158) *** (0.180) Turnover (0.370) (0.380) Weigh NASDAQ (0.023) (0.024) Weigh AMEX ** (0.155) *** (0.188) Size Score (0.788) * (0.846) Log o TNA (0.252) * (0.283) Log o Age *** (0.499) (0.631) Weigh o Recen IPOs 1.628*** (0.132) 1.654*** (0.148) Holdings Age 2.375*** (0.604) 2.625*** (0.634) Expenses Relaive o Family Expenses 3.675*** (0.850) TNA Relaive o Family TNA (1.527) Age Relaive o Family Age *** (1.441) Time Fixed Eecs YES YES Number o Observaions 208, ,330 *** 1% signiicance; ** 5% signiicance; * 10% signiicance 53

54 Table VIII The Reurn Gap and Fuure Fund Perormance This able repors he coeiciens o he monhly panel regression o he general orm: PERF i, = β 0 + β 1 *RG i,-1 + β 2 *EXP i,-1 + β 3 *TU i,-1 + β 4 *LTNA i,-1 + β 5 *LAGE i,-1 + ε I,. The sample includes acively managed equiy muual unds and spans he period o (including he daa used or calculaing he abnormal reurns). PERF measures he quarerly perormance using he marke excess reurn, he one-acor abnormal reurn, he hree-acor abnormal reurn o Fama and French (1993), and he our-acor abnormal reurn o Carhar (1997), respecively. RG is deined as he dierence beween he repored und reurn and he reurn based on he previous quarer s holdings. EXP denoes expenses lagged one year; TU is he urnover lagged one year; LAGE is he naural logarihm o age lagged one quarer; and LTNA is he naural logarihm o oal ne asses lagged one quarer. All regressions include ime dummies. Panel-correced sandard errors, along wih he saisical signiicance, have been provided in parenheses. Dependen Variable: Monhly Perormance Measure (in Percen) Marke Excess Reurn One-Facor Abnormal Reurn Three-Facor Abnormal Reurn Four-Facor Abnormal Reurn Adjused Reurn Gap *** (0.0318) *** (0.0320) *** (0.0266) *** (0.0265) Expenses ** (0.3462) ** (0.3462) ** (0.3244) *** (0.3320) Turnover (0.0124) (0.0124) (0.0110) *** (0.0110) Log o TNA *** (0.0061) *** (0.0059) *** (0.0048) *** (0.0048) Log o Age (0.0138) (0.0136) *** (0.0111) (0.0111) Time Fixed Eecs YES YES YES YES Number o 180, , , ,839 Observaions *** 1% signiicance; ** 5% signiicance; * 10% signiicance 54

55 Table IX The Reurn Gap and Fuure Fund Perormance This able repors he coeiciens o he panel regression o he general orm: PERF i, = β 0 + β 1 *RG i,-1 + β 2 *EXP i,-1 + β 3 *TU i,-1 + β 4 *LTNA i,-1 + β 5 *LAGE i,-1 + ER i,-1 + ε I,. The sample includes acively managed equiy muual unds and spans he period o (including he daa used or calculaing he abnormal reurns). PERF measures he quarerly perormance using he marke excess reurn, he one-acor abnormal reurn, he hree-acor abnormal reurn o Fama and French (1993), and he our-acor abnormal reurn o Carhar (1997), respecively. RG is deined as he dierence beween he repored und reurn and he reurn based on he previous quarer s holdings. EXP denoes expenses lagged one year; TU is he urnover lagged one year; LAGE is he naural logarihm o age lagged one quarer; and LTNA is he naural logarihm o oal ne asses lagged one quarer. ER i,-1 is he lagged excess reurn over he marke. All regressions include ime dummies. Panel-correced sandard errors, along wih he saisical signiicance, have been provided in parenheses. Dependen Variable: Monhly Perormance Measure (in Percen) One-Facor Three-Facor Four-Facor Abnormal Reurn Abnormal Reurn Abnormal Reurn Adjused Reurn Gap *** ** *** (0.0317) (0.0261) (0.0262) Expenses ** *** *** (0.3557) (0.3168) (0.3271) Turnover *** (0.0122) (0.0109) (0.0109) Log o TNA *** *** (0.0058) (0.0046) (0.0047) Log o Age ** ** (0.0134) (0.0108) (0.0109) Lagged *** *** *** Excess Reurn (0.0113) (0.0090) (0.0091) Time Fixed Eecs YES YES YES Number o Observaions 168, , ,839 *** 1% signiicance; ** 5% signiicance; * 10% signiicance 55

56 Table X Trading Sraegy Based on he Reurn Gap This able repors he average perormance, along wih heir signiicance and sandard errors (in parenheses), or deciles o muual unds sored according o he previous year s reurn gap. The reurn gap is deined as he dierence beween he repored und reurn and he reurn based on he previous quarer s holdings. We use excess reurn over he marke, he one-acor alpha o Jensen (1968), he hree-acor alpha o Fama and French (1993), and he our-acor alpha o Carhar (1997) o measure und perormance. The able calculaes he perormance dierence beween he op and he boom deciles. We also repor Spearman rank correlaions o he porolio rankings and heir respecive p-values. Panel A sors unds wih respec o heir reurn gap beore adjusing or expenses, while Panel B sors unds based on he reurn gap aer adjusing or expenses. Panel A: Decile Porolios Sored by he Reurn Gap beore Adjusing or Expenses Excess Marke Reurns CAPM Alphas Fama and French Alpha Carhar Alpha Firs Decile: Mean: ** (10.10) *** (9.85) *** (6.61) *** (6.80) Second Decile Mean: ** (6.51) ** (6.55) ** (5.52) *** (5.68) Third Decile Mean: (5.49) (5.48) -9.97* (5.26) (5.35) Fourh Decile Mean: (5.66) (5.60) ** (5.37) (5.42) Fih Decile Mean: (5.80) (5.63) * (5.42) (5.51) Sixh Decile Mean: (5.55) (5.37) (5.16) (5.24) Sevenh Decile Mean: (5.62) (5.59) (5.39) (5.53) Eigh Decile Mean: (6.04) (6.10) (5.34) (5.47) Ninh Decile Mean: (7.19) (7.25) (5.55) (5.52) Tenh Decile: Mean: (14.74) 3.52 (14.40) 18.20** (8.19) 5.03 (7.51) Tenh Minus Firs Decile 33.70* (17.83) 31.22* (12.30) 38.70*** (10.50) 25.00** (10.10) Spearman Correlaion 98.79*** 89.09*** 95.15*** 86.67*** *** 1% signiicance; ** 5% signiicance; * 10% signiicance 56

57 Panel B: Decile Porolios Sored by he Reurn Gap aer Adjusing or Expenses Excess Marke Reurns CAPM Alphas Fama and French Alpha Carhar Alpha Firs Decile: Mean: ** (9.99) *** (9.70) *** (6.59) *** (6.78) Second Decile Mean: ** (6.30) ** (6.35) ** (5.48) ** (5.63) Third Decile Mean: (5.40) (5.48) -8.84* (5.13) (5.18) Fourh Decile Mean: (5.35) (5.30) *** (5.07) -9.95* (5.13) Fih Decile Mean: (5.56) (5.30) (5.13) (5.17) Sixh Decile Mean: (5.79) (5.58) -9.12* (5.38) (5.47) Sevenh Decile Mean: (5.65) (5.62) (5.37) (5.51) Eigh Decile Mean: (6.67) (6.74) (5.91) (6.05) Ninh Decile Mean: (7.51) (7.57) (5.54) (5.52) Tenh Decile: Mean: (14.93) 3.56 (14.60) 18.20** (8.18) 4.73 (7.46) Tenh Minus Firs Decile 33.24* (17.97) 30.60* (17.50) 38.00** (10.50) 24.60** (10.10) Spearman Correlaion 97.58*** 84.24*** 93.94*** *** 1% signiicance; ** 5% signiicance; * 10% signiicance 57