The (Bad?) Timing of Mutual Fund Investors. Oded Braverman,* Shmuel Kandel,** and Avi Wohl*** First version: February 2005 This version: August 2005

Transcription

1 Th (Bad? Timing of Mutual Fund Invstos by Odd Bavman,* Shmul Kandl,** and Avi Wohl*** Fist vsion: Fbuay 2005 This vsion: August 2005 W thank Invstmnt Comany Institut (ICI fo oviding us th mutual fund data and Yakov Amihud, Azi Bn Rfal, Fank DJong, Ilya Dichv and aticiants of th CEPR symosium at Gzns 2005 fo hlful commnts. Kandl and Wohl thank th Isal Institut of Businss Rsach at Tl Aviv Univsity fo atial financial suot. * Doctoal Pogam, Th on Rcanati Gaduat School of Businss Administation, Tl Aviv Univsity ** Th on Rcanati Gaduat School of Businss Administation, Tl Aviv Univsity, Whaton School, Univsity of Pnnsylvania, and CEPR *** Th on Rcanati Gaduat School of Businss Administation, Tl Aviv Univsity 1

2 Th (Bad? Timing of Mutual Fund Invstos Abstact This a ovids a nw look at th timing of mutual fund invstos. W -xamin th lationshi btwn invstos' agggat nt flows into and out of th funds and th tuns of th funds in subsunt iods. Th ngativ lationshi that w find (using monthly data of agggat US uity mutual funds in th yas and a statistical tst basd on bootstaing of tuns causs mutual fund invstos, as a gou, to aliz a low long-tm accumulatd tun than th long-tm accumulatd tun on a "buy and hold" osition in ths funds. Th "bad" fomanc of mutual fund invstos can b xlaind ith by "bhavioal xlanations" such as invsto sntimnt o by "ational makt xlanations" that a basd on tim-vaying isk miums. W snt a siml ovlaing-gnation modl which dicts a ngativ lationshi btwn flows and subsunt tuns. It is assumd that flows into and out of funds a not latd to infomation about futu cash flows (dividnds, but a causd by changs in oth factos affcting th dmand fo stocks. nc, a ositiv (ngativ nt flow in a givn month imlis a ositiv (ngativ ic chang in th sam month, but also low (high xctd futu tuns. W show that in ach month th chang in th xctd futu tuns may b lativly small (lativ to th tun vaianc, but th accumulatd ffct of ths changs may b significant. This sult may xlain why vious studis, using monthly data of flows and tuns in ith siml gssion modls o VAR, could not hav significantly dtctd th monthly chang in th xctd futu tuns vn in a 15-ya saml. 2

3 Intoduction Can flows into and out of uity mutual funds dict stock tuns? Sval studis in th last dcad hav invstigatd th lationshi btwn agggat monthly mutual funds flows and stock tuns, concluding that th is no ffct of laggd flows on futu tuns 1. In this a w ovid a nw look at this issu and agu that th is a ngativ lationshi btwn nt flows into uity funds and th long-un tuns following thm. Unlik th lack of vidnc fo th laggd flows-lad tuns lationshi, sachs hav documntd a significant ositiv contmoanous lationshi btwn monthly fund flows and th uity tuns in thos months. 2 This contmoanous lation is consistnt with two main hyothss. Th fist is th infomation hyothsis: Good (bad nws gading th uity makt lads both to ositiv (ngativ tuns and to flows into (out of uity funds. This hyothsis imlis no lationshi btwn laggd flows and futu tuns. Th scond hyothsis is th shot-tm ic ssu hyothsis: If dmand fo uity is not fully lastic, a lag flow into (out of uity funds will ush scuity ics u (down, and this will b vsd in th following iods, namly laggd ositiv flows should dict ngativ tuns and vic-vsa. As no miical vidnc has bn found of th ngativ laggd flows-futu tuns lationshi, Wath 995 and Fant 999 jct th ic ssu hyothsis. 1 S, fo xaml, Wath 995, Edwads and Zhang 998 and Fant Wath 995 is th fist aticl to documnt a stong ositiv lationshi btwn unxctd monthly flows and concunt monthly stock tuns. This finding was lat confimd by many oth studis (.g. Santini and Ab 998, Mosbach and Najand 999 and Fant 999. Fant 999 lats th finding only to xchangs in and out of th domstic uity funds. Edln and Wan (2001 find simila sults using daily flow data, and also conclud that agggat flows follow makt tuns with a on-day lag. Gotzmann and Massa (2003 confim ths sults, documnting a stong colation btwn nt daily cash flows to indx funds and contmoanous uity tuns. 3

4 In this a w suggst a thid xlanation gading th contmoanous lationshi btwn flows and tuns, which has oth dictions fo th lationshi btwn laggd flows and lad tuns. W hyothsiz a long-tm ic ssu that is associatd with a tim-vaying man-vting ocss of uity miums. To fomally div and illustat this hyothsis, w mloy a siml ovlaing-gnation modl. Th modl's basic assumtions a simila to thos in D ong, Shlif, Summs and Waldman 990, haft DSSW, namly, two saat gous of invstos who diff in thi dmand fo th isky asst (uity. In ou modl, th fist gou is always in th uity makt whil th scond gou may nt and lav th uity makt fo lativly long iods. Unlik DSSW, w do not mak bhavioal assumtions such as misction. Th modl imlis a contmoanous ositiv lationshi btwn flows of th scond gou and th makt ic of th isky asst. Mo imotantly, th uity isk mium xctd fo futu iods is ngativly latd to th snc of th scond gou's invstos in th uity makt. In oth wods, whn th invstos of th scond gou nt th makt, th uity ic incass but th is also a long-tm (but man vting ffct of a dclin of th ic of isk and th invstos of th scond gou an a low uity mium whn thy hold th uity. Th uity ic dcass and th uity mium incass whn ths invstos lav th makt. W aly th dictions of ou siml modl to mutual fund invstos. Ths dictions a simila in siit to thos mad by Bkat, avy, and umsdain (2002 with sct to flows into mging makts. Thy agu that unxctd flows to mging makts a associatd with ic incass that a not tmoay and not vsd (as dictd by th "u ic ssu hyothsis" and that this mannt chang is th sult of an additional isk shaing and a ducd cost of 4

5 caital ("th mannt chang in th cost of caital hyothsis". In ou modl (and hyothss th ffct is not mannt, but it is slowly man vting and may xist fo a vy long tim. As w show in th modl's xamls, th chang in th cost of uity may b small lativ to th actual chang in ic. In ou miical study w us monthly data of flows and asst valus of agggat US uity mutual funds in th yas Du to a significant chang in th fund oulation includd in th data bas in 1991, w study saatly two sub-iods: , and As th modl imlis, w fist inf a significant ositiv contmoanous lationshi btwn th funds' monthly flows and tuns. W thn tst and significantly jct th null hyothsis that futu tuns a not latd to laggd flows, favoing th hyothsis that th lationshi is ngativ. Th fomal statistical tsts a basd on bootstaing of accumulatd monthly tuns. It is shown that this sult holds vn whn w contol fo th sistnc of th flows and th contmoanous lation btwn flows and tuns. W also dictly tst and inf that th ngativ lationshi is du to tim-vaying uity miums and not th iskf ats. This ngativ lationshi causs mutual fund invstos, as a gou, to aliz a low long-tm accumulatd tun than th long-tm accumulatd tun on a "buy and hold" osition in ths funds. Th "bad" fomanc of mutual funds invstos, documntd in this a, can b xlaind ith by "ational makt xlanations" that a basd on ational tim-vaying isk miums o "bhavioal xlanations" such as invsto sntimnt. Assuming invstos a ational and makts a fficint, ou sults can b xlaind by uilibium modls with htognous agnts having htognous constaints, incom o fncs [s Cambll (2000]. owv, assuming that individual 5

6 invstos ty to tim th makts by channling thi mony in and out of mutual funds, ou sults indicat that thy a bad foms. Th bad fomanc of mutual fund invstos is calld in a concunt a by amont and Fazzini (2005 th dumb mony ffct. Whil thi focus is not on th timing of mutual fund invstos but on invstos ability to allocat mony acoss mutual funds, thy find that ov th long un invstos an low tuns as a sult of thi allocation acoss funds. Ou sults also shd nw light on th fomanc of individuals vs. institutions otd in cnt studis. Th miical vidnc on this issu is mixd. Sval studis xamin th fomanc of individuals basd on uniu datasts of bokag houss. Odan 999 and Bab and Odan (2000 find that individuals buying otfolios und-fom thi slling otfolios ov th following two yas. Th sults of Coval, ishlif and Shumway (2002 suggst, howv, that skillful individual invstos xloit makt infficincis to an abnomal ofits, abov and byond any ofits availabl fom wll-known statgis. Sval oth aticls us mo comhnsiv datasts of individual tading. Ginblatt and Klohaju (2000 us a datast that consists of otfolio holdings fo all Finnish invstos. Thy documnt that individual invstos fom ooly whil institutions aticulaly foigns fom wll. Bab,, iu and Odan (2005 us a comlt tading histoy of all invstos in Taiwan. Thy documnt that, du to tading, th agggat otfolio of individuals suffs an annual fomanc nalty of 3.8% whil institutions njoy an annual fomanc boost of 1.5%. Kanil, Saa and Titman (2004 us classification cod of NYSE to idntify individuals tansactions. Thy documnt that stocks that individuals buy xhibit ositiv xcss tuns in th following month. San (2005 mloys data on institutional holdings, insid 6

7 tansactions and tading volum fo all NYSE and NASDAQ-NM stocks, and concluds that institutions gain lss than individuals. Ou study contibuts to undstanding th lativ fomanc of individuals and institutions by mhasizing that th fomanc of institutional invstos is affctd by th invstos flows into and out of th funds as wll as managmnt skills (if any. Whn analyzing th fomanc of institutional invstos such as mutual funds on has to consid th two ffcts and thi mutual lations 3. W us ou mthodology to -xamin Dichv s (2004 sults which indicat a ngativ lationshi btwn laggd flows and futu tuns fo th uity makt as a whol. W find such a significant ngativ lationshi only in th sub-iod , but th lation is not significant onc th flows into and out of uity funds a xcludd. Finally, w aly ou statistical tsts to anoth catgoy of funds, bonds and mony makt funds, and find a simila ngativ lation btwn futu tuns and laggd flows into and out of ths funds. In od to asss th conomic significanc of ou sults, w calculat th avag valu wightd tuns of uity fund invstos (wights accoding to total uity funds NAV at th bginning of ach month and th intnal at of tun (IRR basd on th monthly flows into and out of ths funds, and coma thm to th aithmtic and gomtic mans of th tuns. This comaison is simila to that in Dichv (2004 fo th whol uity makt in th USA. ik Dichv, w find that th monthly valu wightd avag tuns of invstos in uity funds a considably low than th aithmtic avag monthly tuns. In al tms: 0.45% and 0.37% vs. 0.72% and 0.75% fo th two sub-iods, sctivly. Th IRR is 3 Rgading individual funds, Wms (2003 viws th litatu and ovids nw vidnc on th lation btwn flows, manag bhavio and fomanc sistnc. 7

8 also low than th gomtic man monthly tun by 0.1% and 0.21%, in al tms, fo th two sub-iods, sctivly. Th sults a simila in nominal tms. Th a is oganizd as follows. Sction 1 intoducs ou siml ovlaing-gnations modl and divs its hyothss. Sction 2 dscibs th data and summay statistics. In sction 3 w snt th main sults of th miical study. Sction 4 concluds th a. 1. Th Modl Th modl is a siml ovlaing-gnations modl with two-iod-livd agnts and two financial assts. Th fist asst is a isklss asst which ays an intst aymnt at th nd of ach iod. Th xists a fctly lastic suly of this asst at th ic of 1. Th scond asst is isky and th a X outstanding shas of this asst. An own of shas may gt a dividnd at th nd of ach iod. Th dividnd s ossibl valus a 0 and 1 sha with ual obabilitis. Th dividnds a idntically and indndntly distibutd acoss iods. As in DSSW 990, th modl assums two gous of invstos who diff in thi total dmand fo th isky asst (uity. Th is no consumtion in th fist iod, no labo suly dcision, and no bust. Th only dcision an agnt maks is choosing a otfolio whn young. Th young agnts aiv at th financial makt with thi ndowmnts at disct oints of tim (t=1,2,3,., and buy financial assts fom th old agnts. Th old agnts sll th financial assts, and thn consum and di. Th numb of young agnts who aiv at th makt at tim t is a andom vaiabl. Dnot this vaiabl by N t, and assum that it has two ossibl valus, ith a low valu o a high valu. N t dnds on N t-1 : N t = N t-1 with obability. On way to intt this assumtion is that th xist two gous of invstos: 8

9 on gou of invstos ( G1 is always snt in th stock makt and a scond gou ( G2 is snt only at of th tim. Evy agnt has utility only fom th total walth at th nd of th iod, W. W assum an xonntial utility function: U(W= - -W wh is a cofficint of isk avsion. Th uilibium At th bginning of ach iod, ach stock may b valuatd as a combination of two comonnts: A th dividnd aymnt at th nd of th iod B th following dividnds (aft th nd of th iod Two obsvations a usful in calculating uilibium ics: 1. Bcaus dividnd aymnts a indndnt acoss tim, th ic of comonnt B is indndnt of th dividnd aid at th nd of th vious iod. 2. Bcaus of th invstos xonntial utility function and th indndnc of futu ayoffs of comonnts A and B, th makt valus of A and B can b calculatd saatly. Both of thm dnd on th only tim-vaying stat vaiabl N t (th numb of young agnts at th bginning of th iod. 3. nc, th ic of th stock is simly th sum of th two valus of A and B. As N t can gt on of two valus, and, th ic of th stock can also gt on of two valus, P o P, sctivly. 9

10 Using mma A1 (in th Andix, th uilibium ics P and P a shown to b th solution of th following st of uations: P P 1 = 1 1 = 1 X N X N P P P P ( P P X N ( P P X N ( P P X N ( P P X N / / (2 A numical xaml Vaiabl Notation Valu in Examl Numb of shas X 3,000 Cofficint of isk avsion 1 Numb of young agnts whn low 2000 Numb of young agnts whn high 3000 Pobability of sistnc of numb of agnts 0.99 Risklss at % of P. In this xaml P = 4.58 and P = Th diffnc btwn th ics is Th xctd dividnd yild is 0.5 *1 0.5 * 0 = ic 0.5. ic Thfo, in th stat th xctd dividnd yild is 0.5/4.58 = 10.92% and in th stat it is 9.20%. Th xctd tun du to caital gain in th stat is 0.01*(5.43/ = 0.19% and in th stat it is -0.16%. Ovall th xctd tun in th stat is high by oughly 2% than th avag tun in th stat 1.10% vs. 9.04%. 10

11 Th actual at of tun fo ach iod dnds on th stat (ic at th bginning of th iod, th actual dividnd, and th actual stat (caital gain of th following iod. nc, fo ach stat ( o, th a fou ossibl valus fo th at of tun. Fo xaml, th tun in th stat if th dividnd is 1 and th is no ic chang is 1/ 5.43 = 18.4%, and th tun in th stat if th dividnd is 0 and th is a ic incas is 5.43 / = 18.6%. Th tabl blow snts th distibution of tuns fo ach stat: Stat Stat Rtun obability Rtun obability 40.4% % % % % % % % Avag 11.1% Avag 9.0% STD 9.6% STD 11.1% Not that it not asy to dtct ic lvl changs by looking only at th tuns. Also not that th diffncs in avag tuns a lativly small lativ to tun vaiancs. Modl s miical dictions fo G2 s invstos 1. Th is a ositiv lationshi btwn nt flows into and out of th uity makt (of G2 s invstos and contmoanous tuns. 2. Th is a ngativ lationshi btwn nt flows into and out of th uity makt (of G2 s invstos and subsunt tuns. 11

12 3. Valu wightd xctd tun on uity (hld by G2 s invstos< xctd uity tun Th modl s dictions fo G1 s invstos a th mio imags of thos fo G2 s invstos. In addition, th modl imlis that th uity isk mium is ositiv in vy iod. In ou miical study that follows, w idntify th flows of G2 s invstos with th nt flows into and out of uity mutual funds. 2. Data 2.1 Data soucs Agggat uity fund data fo th months 1984:01 though 2003:12 w obtaind fom th Invstmnt Comany Institut (ICI. Similaly to Fant 999, w focus on US domstic uity funds, agggating th flows and makt valus of th following catgois: Gowth, Aggssiv Gowth, Gowth and Incom, Incom Euity and Scto 4. W did not includ th Intnational Euity and Global Euity catgois. Similaly to Wath 995, w calculat th monthly nt flow as agggatd nw sals lus xchangs in minus dmtions and xchangs out. Th nominal monthly tun of th uity funds is calculatd as: R t = NAV 0.5 Nt _ Flow NAV t 0.5 Nt _ Flow t1 t t 1 (2.1 wh NAV snts th total valu of th uity funds at th nd of th month and Nt_Flow snts th nt flow within a givn month. This calculation imlicitly assums that half of th otd monthly flow occus at th bginning of th month and half of th flow occus at th nd of th month. 4 Fant 999 dos not includ th Scto catgoy in his study. Wath 995 also includs intnational and global uity catgois. 12

13 In Januay 1991, TIAA-CREF funds w addd to th oulation of funds covd by ICI. W thfo consid in ou miical study two sub-iods: Januay 1984 to Dcmb 1990, and Januay 1991 to Dcmb Th total valu of th uity makt was obtaind fom th Cnt fo Rsach in Scuity Pics (CRSP as th total valu of NYSE, AMEX and NASDAQ stocks. CPI data (All Uban Consums and 30-day t-bill tuns a also obtaind fom CRSP. 2.2 Summay statistics Tabl 1 snts summay statistics of th vaious vaiabls. Figu 1 dicts two sis of accumulatd tuns: uity mutual fund tuns vs. th whol US uity makt tuns (including invstd dividnds, th stating oint in 1984:01 nomalizd to 100. It can b sn that th tuns a highly colatd th colation cofficint btwn th two sis is Fo th full saml, th avag makt monthly tun is 1.066% and xcds th avag mutual funds tun which is 0.984%. Th diffnc btwn thm is conomically significant (sums to aound 1% annually and it is statistically significant (-valu of t-tst small than 0.001, but th standad dviation of th funds tun is slightly small than th standad dviation of th makt tun: 4.35% vs. 4.58%. Aft contolling fo ths diffncs in th standad dviations by foming a otfolio of th uity makt and invstmnt in shot t-bills, th funds undfom this otfolio by 0.6% oughly annually and th diffnc is significant. 5 Januay 1991 is xcludd fo th colation calculation. Fo th calculation of accumulatd tuns, th monthly tun fo th whol US makt in Januay 1991 is also usd fo th uity funds. 13

14 Figu 2 dicts nt flows into th uity funds (in Januay 1984 al tms. It can b sn that ov tim th is a tnd of nt flow incas and also an incas in th vaiability of th nt flows. Th 2002 flows a xamls of both high ositiv and ngativ nt flows. A sult of th incas in th nt flows ov tim is an incas in th atio of th valu of uity funds to th valu of th whol US uity makt (haft dnotd by FR Funds Ratio. FR incasd fom aound 4% in 1984 to aound 22% at th nd of Th monthly avag nt inflow ov th iod was mo than $6.5B, lading to an annual gowth of 21.1% of th nt asst valu of th uity funds lativ to an 11% annual gowth of th total uity makt valu. Figu 3 dicts th valus of th uity funds, th whol US uity makt, and th sulting FR. 4. Emiical Rsults Ou modl s fist diction is about th contmoanous ositiv lationshi btwn monthly flows into and out of uity funds and th funds tuns. As discussd in th Intoduction, this lationshi is wll documntd in th litatu. W also find a significant ositiv colation btwn nt flows and th contmoanous tuns. Fo th fist sub-iod , th colation cofficint is 0.67, fo tuns and flows ith in nominal o al tms. Whn flows a nomalizd (th flow is dividd by makt valu of uity, th cofficint is Fo th scond sub-iod , th colation cofficint is 0.46 fo tuns and flows in both nominal and al tms, and 0.49 whn flows a nomalizd. In all cass th -valu is small than Th colation matix of th tuns, flows and thi laggd valus is sntd in Tabl 2. 14

15 Ou modl maks th simlifying assumtion that nt flows a slowly man vting. In th modl, this assumtion imlis that, ov tim, th is a ositiv lationshi btwn contmoanous xctd flows and xctd tuns. As documntd in th litatu (s, fo xaml, Wath 995 and Fant 999, nt flows a sistnt in th shot un. Thfo, on should not xct to find in th data a ositiv contmoanous lationshi btwn xctd flows and xctd tuns. owv, th dictd contmoanous ositiv lationshi btwn unxctd flows and unxctd tuns is indndnt of ou simlifying assumtions. To stimat xctd and unxctd flows, w consid th following vaiabls in a gssion modl: F t /M t-1 = th atio (in cntag tms btwn th nt flow into and out of uity funds in month t and th vious month s total valu of th uity makt, and A t /M t = th atio (in cntag tms btwn th nd-of-month total valu of th uity funds and th nd-of-month total valu of th uity makt. Th stimatd gssion lation is (t-statistics in anthss: Ft M t1 Ft = M t At M.88 1 t1 ε t R 2 = 0.42 W thn gss th monthly al tuns on th xctd and unxctd flows. Th stimatd lation is (t-statistics in anthss: R t = EXPECTED _ FOW UNEXPECTED_ FOW ε (2.40 ( R 2 = 0.42 t 15

16 Th sults a consistnt with thos of Wath 995 that th souc of th contmoanous lationshi btwn flows and tuns is th colation btwn unxctd flows and unxctd tuns. Ou scond diction is gading a ngativ lationshi btwn monthly flows and subsunt tuns. In sction 1 w not that, vn in ou simlifying modl, th dcas (incas in th uity mium following a flow into (out of uity funds sms to b small lativ to th standad dviation of th tuns. nc, a vy long saml might b ndd to dtct a ngativ lationshi in a siml gssion modl. Indd, lik vious studis, w too do not find th colation btwn monthly tuns and laggd flows to b significantly ngativ. But, if th ffct xists, and is sistnt, w may dtct it using long tm tuns and non-lina tchnius. W mloy a bootstaing tchniu to tst th lation btwn laggd flows and futu tuns. In all th tsts that follow, th null hyothsis is that th is no such lationshi, and und th altnativ hyothsis (as divd fom ou siml modl th lationshi is ngativ. In ou fist tst, dnotd by TEST-1, w simly intt th null hyothsis as a hyothsis of statistical indndnc btwn flows and tuns. This indndnc is consistnt with th no ic ssu hyothsis, nith a shottm ic ssu no a long-tm ic ssu. A simulation is un wh th flows into and out of uity funds a ual to th alizd al flows, but in ach ound of th simulation th al monthly tuns a shuffld ov th iod. W thn aly th simulatd (o shuffld tuns, togth with th al flows, to calculat th simulatd valu of th funds at th nd of th iod ( tminal funds valu. W at this ocdu 10,000 tims. Und th indndnc hyothsis, 16

17 on should xct that th actual tminal funds valu would not b significantly diffnt fom th simulatd avag tminal funds valu. Und a ic ssu hyothsis, wh th is a ngativ lationshi btwn laggd flows and futu tuns, th actual total tminal funds valu should b significantly small than th simulatd avag. Tabl 3 snts th sults of all simulation tsts. Th sults of TEST-1 indicat that, fo ach sub-iod, th actual tminal valu is indd at th lft tail of th simulatd distibution: only 10.53% and 5.66% of th simulatd valus a low than th actual valus in th fist and scond sub-iods, sctivly. Th distibutions of th sults a sntd in Figu 4-A and Figu 4-B. Taking th two figus togth, and aoximating th simulatd distibutions with nomal distibutions, th null hyothsis of indndnc is jctd at th 5% significanc lvl. Th sults (not sntd a simila whn flows and tuns a xssd in nominal tms and whn w assum a zo valu fo th stating valu of th funds in ach sub iod. In th scond tst, TEST-2, w chck whth th sult of th fist tst, namly th lativly low actual tminal funds valu, is solly th outcom of th contmoanous ic imact of th unxctd flows into and out of uity funds (as w and oths hav documntd. To do so, w fist stimat th xctd tun conditiond on th unxctd contmoanous flow. A simulation is thn un wh, lik th simulation of th fist tst, th flows into and out of uity funds a ual to th alizd al flows, but in ach ound of th simulation th unxctd (sidual tuns of th gssion a shuffld ov th iod. W thn aly th alizd al flows and thi contmoanous xctd al tuns togth with th simulatd (o shuffld unxctd tuns to calculat th tminal funds valu. Again, und th null hyothsis th actual tminal funds 17

18 valu should not b significantly diffnt fom th simulatd avag tminal funds valu, and und th altnativ hyothsis th actual total tminal funds valu should b significantly small than th simulatd avag. Similaly to th sults of th fist tst, fo ach sub-iod th actual tminal funds valu is at th lft nd of th simulatd distibution: Only 3.0% and 7.8% of th simulatd valus a low than th actual valus in th fist and scond subiods, sctivly. Taking th two figus togth, and aoximating th simulatd distibutions with nomal distibutions, th null hyothsis of indndnc is jctd at th 5% significanc lvl. again th sults (not sntd a obust to xssing th flows and tuns in nominal tms instad of al tms. TEST-3 is simila to TEST-1, but th hyothsis focuss dictly on th uity isk mium: th null hyothsis is that th uity mium is indndnt of ast flows, whil this lationshi is ngativ in th altnativ hyothsis. In ach ound of th simulation th uity miums a shuffld ov th iod. 16.2% and 5.5% of th simulatd valus a low than th actual valus in th fist and scond subiods, sctivly. Th null is jctd at th 5% significanc lvl (in a on-sidd tst; in a two-sidd tst, th -valu is 6.8%. Basd on th th tsts, w inf that th is a ngativ lationshi btwn laggd flows and futu tuns. Moov, th uity isk mium is tim-vaying and is ngativly latd to laggd flows. In od to dmonstat th conomic significanc of th infd ngativ lationshi, w coma th Valu wightd avag tun to th aithmtic man tun in ach sub-iod. Th valus sntd in Tabl 4 indicat that in both subiods th Valu wightd avag tun is low than th aithmtic man tun. Fo th monthly al tuns: 0.45% vs. 0.72% and 0.36% vs. 0.75%, fo th two sub- 18

19 iods, sctivly. Simila diffncs hold fo th nominal tuns. Anoth way to asss th conomic significanc of th sults is to coma th IRR (calculatd using th flows to th gomtic man tun. In ou saml th is a uniu IRR fo ach sub iod, and it is indd low than th gomtic man (fo monthly al tuns 0.53% vs. 0.63% and 0.46% vs. 0.67%. Ou sults a simila in siit to thos of Dichv (2004 gading th ngativ lationshi btwn tun and nt flows into and out of th whol uity makt in th iod W aly ou mthodology to oduc Dichv s sults fo ou saml iod 6. Ou TEST-4 is simila to TEST-1, but with flows into and out of th whol uity makt lacing th flows of th uity funds and tuns of th makt lacing th uity funds tuns. Fo th fist sub-iod, 68.8% of th simulatd tminal valus a small than th actual tminal valu. Fo th scond sub-iod, only 1.3% of th simulatd tminal valus a small than th actual tminal valu. Basd on ths sults th null hyothsis of indndnc can not b jctd at th 5% significanc lvl fo th whol uity makt and fo th two sub-iods. Nxt, w chck whth Dichv s (2004 and th abov sults gading th whol uity makt (scially fo th scond sub-iod can b xlaind by flows into and out of uity funds 7. In TEST-5 w licat TEST-4 but with th uity makt nt flows lacd by uity s non-funds nt flows, calculatd as uity s non-funds nt flows = uity makt nt flows uity funds nt flows. As can b sn in Tabl 3, th sults a not significant at th 5% significanc lvl. nc, w inf that th ngativ lationshi btwn laggd flows and futu uity 6 Dichv (2004 holds th tuns constant and shuffls nomalizd flows. 7 Th colation of th monthly flows into th uity funds to th stimatd monthly flows to th whol US makt stimatd as in Dichv 2004 a aound 0.25, in ach sub-iod. 19

20 tuns, if it xists in th whol US uity makt, is mostly linkd to nt flows into and out of uity funds. Is th oo timing of mutual fund invstos uniu to uity funds? TEST-6 xamins th hyothsizd ngativ lationshi btwn laggd al flows to bonds and mony makt funds and th al tuns following thm. TEST-7 xamins this lation fo flows to all uity, bonds, and mony makt funds. Not suisingly, w find that th sults a vy simila to thos latd to uity funds only. Namly, onc th tuns a shuffld ov th iod, th tminal funds valu is significantly high than th actual tminal valu. 4. Conclusions This a ovids a nw look at th fomanc of mutual fund invstos. W -xamin th lationshi btwn invstos' agggat nt flows into and out of th funds and th tuns of th funds in subsunt iods and find this lationshi to b significantly ngativ. This ngativ lationshi causs mutual fund invstos, as a gou, to aliz a low long-tm accumulatd tun than th long-tm accumulatd tun on a "buy and hold" osition in ths funds. Th "bad" fomanc of mutual fund invstos can b xlaind ith by "ational makt xlanations" that a basd on ational tim-vaying isk miums o "bhavioal xlanations" such as invsto sntimnt. Assuming invstos a ational and makts a fficint, ou sults can b xlaind by uilibium modls with htognous agnts having htognous constaints, incom o fncs. owv, assuming that individual invstos ty to tim th makts by channling thi mony in and out of mutual funds, ou sults indicat that thy a bad foms. 20

21 Rfncs Bab, Bad, Yi-Tsung, Yu-Jan iu, and Tanc Odan, 2005 Who loss fom tad? Evidnc fom Taiwan, Woking Pa, SSRN # Bab, Bad, and Tanc Odan, 2000, Tading is hazadous to you walth: Th common stock invstmnt fomanc of individual invstos, Jounal of Financ, 55(3, Bkat, Gt, Cambll R. avy, and R.. umsdain, 2002, Th dynamics of mging makt uity flows, Jounal of Intnational Mony and Financ, 21(3, Cambll, John Y., 2000, Asst icing at th millnnium, Jounal of Financ, 55(4, Coval, Joshua D., David. ishlif, and Tyl Shumway, 2002, Can individual invstos bat th makt?, Woking Pa, SSRN # D ong, Badfod J., Andi Shlif, awnc. Summs, and Robt J. Waldmann, 1990, Nois tad isk in financial makts, Jounal of Political Economy, 98(4, Dichv, Ilia D., 2004, What a stock invstos' actual histoical tuns?, Woking Pa, Univsity of Michigan. Edln, Rog M., and Jold B. Wan, 2001, Agggat ic ffcts of institutional tading: A study of mutual fund flow and makt tuns, Jounal of Financial Economics, 59, Edwads, Fanklin R., and Xin Zhang, 1998, Mutual funds and stock and bond makt stability, Jounal of Financial Svics Rsach, 13(3,

22 Fant,. Fanklin, 1999, Invstmnt bhavio of mutual fund shaholds: Th vidnc fom agggat fund flows, Jounal of Financial Makts, 2, Gotzmann, William N., and Massimo Massa, 2003, Indx funds and stock makt gowth, Jounal of Businss, 76, Ginblatt, Mak, and Matti Klohaju, 2000, Th invstmnt bhavio and fomanc of vaious invsto-tys: A study of Finland s uniu data st, Jounal of Financial Economics, 55, Kanil, Ron, Gidon Saa, and Shidan Titman, 2004, Individual invsto sntimnt and stock tuns, Woking Pa, SSRN # amont, Own, and Anda Fazzini, 2005, Dumb mony: Mutual fund flows and th coss sction of stock tuns, Woking Pa, Yal Intnational Cnt fo Financ. Mosbach, Michal, and Mohammad Najand, 1999, A th stuctual changs in mutual funds invsting diving th U.S. stock makt to its cunt lvls?, Th Jounal of Financial Rsach, 22(3, Odan, Tanc, 1999, Do invstos tad too much?, Amican Economic Rviw, 89, Dcmb 1999, San, Ganit, 2005, Who gains mo by tading: Individuals o institutions?, Woking Pa, SSRN # Santini, Donald., and Jack W. Ab, 1998, Dtminants of nt nw mony flows to th uity mutual fund industy, Jounal of Economics and Businss, 50, Wath, Vincnt A., 1995, Agggat mutual fund flows and scuity tuns. Jounal of Financial Economics, 39, Wms, Russ, 2003, Is mony ally smat? Nw vidnc on th lation btwn mutual fund flows, manag bhavio, and fomanc sistnc, Woking Pa, Univsity of Mayland. 22

23 Tabl 1 Saml Summay Statistics Vaiabl Dscition N Man Std Dv Minimum Maximum N Man Std Dv Minimum Maximum ntflow Nt flow in nominal dollas to uity funds ($Billions assts End of iod nt assts of uity funds ($Billions ,779 1, ,944 makt Total nominal valu of th uity makt, as comutd by th CRSP: NYSE AMEX NASDAQ ($Billions 83 2, ,613 3, ,463 4,410 3,339 18,349 tun Monthly agggatd uity fund nominal tun (in % tun Monthly agggatd uity fund al tun (in % mt Monthly uity makt nominal tun (in % nflow Nomalizd flow (in % = 100*ntflow / makt f Fund atio- Total valu of uity funds as cnt of total uity makt Tabl 1 snts dscitions and saml summay statistics fo vaiabls of flows, asst valus and tuns. Th saml includs two subiods: and , wh th fist month of ach sub-iod is xcludd. Fund flows and nt asst valus w obtaind fom th Invstmnt Comany Institut and includ domstic uity funds of th following catgois: Gowth, Aggssiv Gowth, Gowth and Incom, Incom Euity and Scto. Th calculation of th nominal monthly tun on th uity funds is sntd in uation (2.1. Th total valu of th uity makt was obtaind fom th Cnt fo Rsach in Scuity Pics (CRSP as th total valu of NYSE, AMEX and NASDAQ stocks. Ral valus a calculatd using CPI data (All Uban Consums. 23

24 Tabl 2 Colation Matix nflow lag (nflow tun lag (tun nflow (< (< lag (nflow ( ( (< tun (0.247 lag (tun 1 Tabl 2 snts th colation matix of two vaiabls, nflow and tun, and thi laggd valus fo th full saml iod , S Tabl 1 fo th dscition of th vaiabls. 24

25 Tabl 3 Simulation Rsults Summay TEST-1 Euity funds Shuffld: Ral tuns TEST-2 Euity funds Shuffld: Unxctd funds tuns TEST-3 Euity funds, Shuffld: Euity miums TEST-4 Whol US Euity makt Shuffld: Ral tuns TEST-5 Euity makt "non-uity funds" flows Shuffld: Ral tuns TEST-6 Bond and mony makt funds Shuffld: Ral tuns TEST- 7 Bond, mony makt and uity funds Shuffld: Ral tuns Dc 2003 al tms $ Billions Actual tminal funds valu 291 3,167 Avag simulation sult 311 3,914 Standad dviation % of sults low than actual 10.53% 5.66% Actual tminal funds valu 291 3,167 Avag simulation sult 311 3,641 Standad dviation % of sults low than actual 3.0% 7.8% Actual tminal funds valu 291 3,167 Avag simulation sult 306 3,900 Standad dviation % of sults low than actual 16.2% 5.50% Actual tminal makt valu 4,104 14,582 Avag simulation sult 3,981 15,403 Standad dviation % of sults low than actual 68.76% 1.33% Actual tminal makt valu 3,805 11,148 Avag simulation sult 3,655 11,166 Standad dviation % of sults low than 71.20% 43.47% actual Actual tminal funds valu 1,088 3,293 Avag simulation sult 1,110 3,397 Standad dviation % of sults low than 1.16% 0.50% actual Actual tminal funds valu 1,378 6,460 Avag simulation sult 1,416 7,112 Standad dviation % of sults low than 7.95% 4.60% actual Tabl 3 snts th simulation sults fo svn tsts. In ach ound of th simulation a tminal valu was calculatd using th initial al nt asst valu, al flows, and shuffld monthly al tuns o unxctd tuns. Fo ach tst, th fist column dscibs th ty of funds o makt tstd and th shuffling mthod. 25

26 Tabl 4 Slctd Statistics fo Monthly Fund Rtuns iod Ral monthly tuns: Avag Valu wightd avag Gomtic man IRR Nominal monthly tuns: Avag Valu wightd avag Gomtic man IRR 0.72% 0.45% 0.63% 0.53% 1.05% 0.77% 0.96% 0.86% 0.75% 0.36% 0.67% 0.46% 0.95% 0.52% 0.87% 0.65% Tabl 4 snts slctd statistics gading th monthly tuns in th two subiods. All figus w calculatd using th agggatd uity funds data fom ICI. Avag tuns snt siml aithmtic mans of th monthly tuns. Valu wightd avag tuns w wightd using th uity fund assts. Th gomtic man snts th avag comoundd monthly tun, assuming a "buy and hold" invstmnt. Th IRR was calculatd using al nt flows and th initial and tminal nt asst valus (a uniu IRR xists fo ach sub-iod. 26

27 1200% Figu 1 Accumulatd Rtuns: Euity Funds and th Total Makt Accumulativ total tun fom Jan % 800% 600% 400% 200% 0% Makt accumulatd total tuns Funds accumulatd total tuns Jan-84 Jan-85 Jan-86 Jan-87 Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Figu 1 dmonstats th undfomanc of agggat uity funds otfolio lativ to th fomanc of th makt otfolio ov tim. Euity funds monthly tuns w calculatd using nt agggat flows and balanc fom th ICI datast, assuming nt flows fom funds occu half at th bginning of th month and half at th nd of th month. Makt tuns w basd on th CRSP total tun. Du to tchnical changs in th ICI databas fom 12/90 to 1/91, with th inclusion of additional funds in th databas, w could not calculat th Jan 91 uity funds tun, so usd th makt tun fo this scific month. 27

28 Figu 2 Nt Flows to Euity Funds 40 Ral nt flows Dc 2003 tms ($B Jan-84 Jan-85 Jan-86 Jan-87 Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan Figu 2 dicts nt flows (nw sals lus "xchangs in" minus dmtions and "xchangs out", in Januay 1984 al dolla tms into th uity funds though tim. Du to tchnical changs in th ICI databas fom 12/90 to 1/91, with th inclusion of additional funds in th databas, th saml is saatd into two sub-iods: until Dc 90 and fom Jan

29 Figu 3 Valus of Euity Makts and Euity Funds 6,000 25% 5,000 Funds valu indx Total CRSP valu Indx 20% 4,000 3,000 2,000 1,000 - Jan-84 Jan-85 Jan-86 Jan-87 Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 INDEX (Jan 84=100 Ratio of uity funds to total uity makt 15% 10% % of total uity makt 5% 0% Figu 3 dicts th incas in th valu of th uity makt, th uity funds (both in al dolla tms, indxd to 100 in Jan 1984, and in th FR (th atio of th valu of uity funds to all uity makt valu. An annual al gowth of 21.1% in th uity fund agggatd total assts, lativ to a modst 11% annual gowth in th total uity makt valu lad to an incas in FR fom aound 4% in 1984 to aound 22% at th nd of

30 Figu 4-A simulation Dc 1990 uity funds ttoal assts ($B Dc 2003 Tms Figu 4-A gahically snts th distibution of th 10,000 simulation sults fo Bootstaing Tst 1 (s Tabl 3. Th d dottd lin snts th actual valu at th nd of th iod. 30

31 Figu 4-B Dc 2003 uity funds total assts ($B Dc 2003 Tms 7,000 6,500 6,000 5,500 5,000 4,500 4,000 3,500 3,000 2, simulation Figu 4-B gahically snts th distibution of th 10,000 simulation sults fo Bootstaing Tst 1 (s Tabl 3. Th d dottd lin snts th actual valu at th nd of th iod. 31

32 Andix mma A1 Th a N invstos. Invsto s i initial walth is W i. utility is basd on W, th total walth at th nd of iod U(W= - -W. Th isklss intst at is. A isky asst ays o with obabilitis and -, sctivly. Th dmandd uantity of ach of th agnts, d i, of th isky asst conditional on its ic,, is: d ln( 1 = ( and th ic of th isky asst is = { ( X N ( X N }/ Poof: Buying d units of th isky asst imly two ossibl walth lvls at th nd of th iod: [W i ( d ] o [W i ( d ] Th xctd utility is : EU = [ Wi ( d ] [ Wi ( d ] Diving by d yilds 32

33 33 } ] [ ] [ - { ]d [- - ]d [- - 1 ( Wi Euating to 0 to find th maximum yilds: d d ( ( ] [ ] [ = Aft aanging w gt 1 ] [ ] [ d d = = d ( 1 = d ( 1 = d 1 ln{ ( } and ( 1 ln( d = At th uilibium ic X= Nd Thfo X N = ( 1 ln( Aft aanging w gt N X ( 1 ln( 1 ( = N X ( 1 =

34 34 N X ( } - { - - = } {- - ( ( N X N X = and }/ { N X ( N X ( = Q.E.D