New Evidence on Mutual Fund Performance: A Comparison of Alternative Bootstrap Methods. David Blake* Tristan Caulfield** Christos Ioannidis*** and


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1 New Evidence on Muual Fund Performance: A Comparion of Alernaive Boorap Mehod David Blake* Trian Caulfield** Chrio Ioannidi*** and Ian Tonk**** June 2014 Abrac Thi paper compare he wo boorap mehod of Koowki e al. (2006) and Fama and French (2010) uing a new daae on equiy muual fund in he UK. We find ha: he average equiy muual fund manager i unable o deliver ouperformance from ock elecion or marke iming, once allowance i made for fund manager fee and for a e of common rik facor ha are known o influence reurn; 95% of fund manager on he bai of he fir boorap and almo all fund manager on he bai of he econd boorap fail o ouperform he zerokill diribuion ne of fee; and boh boorap how ha here are a mall group of ar fund manager who are able o generae uperior performance (in exce of operaing and rading co), bu hey exrac he whole of hi uperior performance for hemelve via heir fee, leaving nohing for inveor. Keyword: muual fund, uni ru, open ended invemen companie, performance meauremen, facor benchmark model, boorap mehod, ochaic dominance JEL: C15, C58, G11, G23 * Penion Iniue, Ca Buine School, Ciy Univeriy London; ** Univeriy College London; ***Deparmen of Economic, Univeriy of Bah; **** School of Managemen, Univeriy of Bah The daae ued in hi paper wa conruced while Ian Tonk wa an ESRC Buine Fellow a he UK Financial Service Auhoriy in 2009 (RES ), and he i graeful o he FSA Economic of Regulaion Uni for hoing hi vii. 1
2 1. Inroducion Evidence colleced over an exended period on he performance of (openended) muual fund in he US (Jenen, 1968; Malkiel, 1995; Wermer e al., 2010) and uni ru and openended invemen companie (OEIC) 1 in he UK (Blake and Timmermann, 1998; Lunde e al., 1999) ha found ha on average a fund manager canno ouperform he marke benchmark and ha any ouperformance i more likely o be due o luck raher han kill. More recenly, Koowki e al. (2006, hereafer KTWW) repored ha he ime erie reurn of individual muual fund ypically exhibi nonnormal diribuion. 2 They argued ha hi finding ha imporan implicaion for he luck veru kill debae and ha here wa a need o reexamine he aiical ignificance of muual fund manager performance uing boorap echnique. They applied a boorap mehodology (Efron and Tibhirani (1993), Polii and Romano (1994)) ha creae a ample of monhly peudo exce reurn by randomly reampling reidual from a facor benchmark model and impoing a null of zero abnormal performance. Following he boorap exercie, KTWW deermine how many fund from a large group one would expec o oberve having large alpha by luck and how many are acually oberved. Uing daa on 1,788 US muual fund over he period January 1975 December 2002, hey how ha, by luck alone, 9 fund would be expec o achieve an annual alpha of 10% over a fiveyear period. In fac, 29 fund achieve hi hurdle: hi i ufficien, aiically, o provide overwhelming evidence ha ome fund manager have uperior alen in picking ock. Overall, our reul provide compelling evidence ha, ne of all expene and co (excep load charge and axe), he uperior alpha of ar muual fund manager urvive and are no an arifac of luck (p. 2553). Applying he ame boorap mehod o 935 UK equiy uni ru and OEIC beween April 1975 December 2002, Cuhberon e al. (2008) find imilar evidence of ignifican ock picking abiliy among a mall number of opperforming fund 1 Thee are, repecively, he UK and EU erm for openended muual fund. There are difference, however, he principal one being ha uni ru have dual pricing (a bid and an offer price), while OEIC have ingle pricing. 2 KTWW (p.2559) pu hi down o he poibiliie ha (1) he reidual of fund reurn are no drawn from a mulivariae normal diribuion, (2) correlaion in hee reidual are nonzero, (3) fund have differen rik level, and (4) parameer eimaion error reul in he andard criical value of he normal diribuion being inappropriae in he cro ecion. 2
3 manager. Blake e al. (2013) how ha fund manager performance improve if he degree of decenralizaion in he form of increaing pecializaion i increaed. However, hee reul have been challenged by Fama and French (2010, hereafer FF) who ugge an alernaive boorap mehod which preerve any correlaed movemen in he volailiie of he explanaory facor in he benchmark model and he reidual. They calculae he Jenen alpha for each fund, and hen compue peudo reurn by deducing he Jenen alpha from he acual reurn o obain benchmarkadjued (zeroalpha) reurn, hereby mainaining he croecional relaionhip beween he facor and reidual volailiie (i.e., beween he explained and unexplained componen of reurn). Their ample coni of 5,238 US muual fund over he period January 1984 Sepember 2006, and following heir boorap calculaion, hey conclude ha here i lile evidence of muual fund manager kill. There are hree difference beween he KTWW and FF udie. Fir, while boh udie ue daa for US domeic equiy muual fund, KTWW ue daa from , wherea he daae in FF i from Second, he udie ue differen fund incluion crieria: KTWW reric heir ample o fund ha have a minimum of 60 monhly obervaion, wherea FF reric heir o fund ha have a minimum of 8 monhly obervaion Third, wih repec o he boorap mehod ued, he former imulae fund reurn and facor reurn independenly of each oher, wherea he laer imulae hee reurn joinly. I i imporan herefore o idenify wheher he differen reul from he wo udie are due o he differen ime period analyzed, differen incluion crieria or he differen boorap mehod ued. We will ue a daae of UK domeic equiy muual fund reurn from January 1998 Sepember 2008 o ae he performance of muual fund manager. We will alo compare he wo differen boorap mehod uing he ame ample of fund over he ame ime period and wih he ame fund incluion crierion. I i well known ha he Jenen alpha meaure of performance i biaed in he preence of fund manager marke iming kill (Treynor and Mazuy, 1966; Meron and Henrikon, 1981). Grinbla and Timan (1994) have uggeed a oal performance meaure which i he um of he Jenen alpha and marke iming coefficien in an exended facor benchmark model. Allowing for marke iming exacerbae he nonnormaliy of andard ignificance e and an addiional 3
4 conribuion of hi paper i o ae he ignificance of he oal performance meaure in he KTWW and FF boorapped diribuion. The rucure of he paper i a follow. Secion 2 review he approach o meauring muual fund performance and how how hi approach ha recenly been augmened hrough he ue of boorap. Secion 3 dicue he daae we will be uing. The reul are preened in Secion 4, while Secion 5 conclude. 2. Meauring muual fund performance 2.1 Meauring performance uing facor benchmark model Building on Jenen original approach, we ue a fourfacor benchmark model o ae he performance or exce reurn over he rikle rae ( Ri rf ) of he manager of muual fund i obained in period : + R rf R rf SMB HML MOM (2.1) i i i m i i i i where he four common facor are he exce reurn on he marke index ( R rf ), he reurn on a ize facor, SMB, and a bookomarke facor m HML (FamaFrench, 1993), and he reurn on a momenum facor, MOM (Carhar, 1997). The genuine kill of he fund manager, conrolling for hee common rik facor, i meaured by alpha (α i ) which i alo known a he eleciviy kill. 3 Under he null hypohei of no abnormal performance (i.e., no eleciviy kill), he ˆi coefficien hould be equal o zero. For each fund, we could e he ignificance of each ˆi a a meaure of ha fund abnormal performance relaive o i andard error. We migh alo e he ignificance of he average value of he alpha acro he N fund in he ample (Malkiel, 1995). Alernaively, we could follow Blake and Timmermann (1998) (and alo Fama and French, 2010, Table II) and regre an equalweighed (or a valueweighed) porfolio p of he exce reurn ( R rf ) on he N fund on he four facor in (2.1) and e he ignificance of he p eimaed ˆ p in hi regreion. The original Jenen approach made no allowance for he marke iming abiliie of fund manager when fund manager ake an aggreive poiion in a bull 3 Feron and Schad (1996) ugge a condiional verion of hi fourfacor benchmark model ha conrol for imevarying facor loading. However Koowki e al. (2006) repor ha he reul from eimaing he condiional and uncondiional model are very imilar, and in he remainder of hi paper we follow hem and only conider he uncondiional verion of (2.1). 4
5 marke (by holding highbea ock) and a defenive poiion in a bear marke (by holding low bea ock). Treynor and Mazuy (1966) eed for marke iming by adding a quadraic erm in he marke exce reurn in he benchmark model o capure he curvaure in he fund manager performance a he marke rie and fall. To e joinly for eleciviy and marke iming kill, we eimae a fivefacor benchmark model: + 2 R rf R rf SMB HML MOM R rf (2.2) i i i m i i i i m i Marke iming abiliy i meaured by he ign and ignificance of ˆi. To capure boh eleciviy and iming kill imulaneouly, we ue he TreynorMazuy oal performance meaure (TM i ) derived in Grinbla and Timan (1994): i i i m TM Var R rf (2.3) who how ha he ignificance of TM i can be aeed wih repec o i andard error defined in Grinbla and Timan (1994, Appendix B, p. 441). 2.2 Meauring performance uing boorap mehod On accoun of nonnormaliie in reurn, boorap mehod can be applied o boh of he facor benchmark model (2.1) and (2.2) o ae performance. To apply he KTWW boorap in (2.1), we fir obain OLSeimaed alpha, facor loading and reidual uing a ime erie of monhly exce reurn for fund i in equaion (2.1). We hen conruc a ample of peudo exce reurn by randomly reampling reidual wih replacemen from { ˆ i, Ti 0,..., Ti 1} and impoe he null of zero abnormal performance ( i 0 ): b ( ) ˆ ˆ ˆ + ˆ b R rf R rf SMB HML MOM ˆ (2.4) i i m i i i i where b i he b h boorap and ˆb i i a drawing from{ ˆ i, Ti 0,..., Ti 1}. By conrucion, hi peudo exce reurn erie ha zero alpha. For boorap b = 1, we regre he peudo exce reurn on he facor: b ( R rf ) R rf SMB HML + MOM (2.5) i i i m i i i i and ave he eimaed alpha. We repea for each fund, i = 1,, N, o arrive a he fir b draw from he croecion of boorapped alpha { i, i 1,..., N; b 1} and he correponding aiic { ( b ), i 1,..., N; b 1}. We hen repea for all boorap i 5
6 ieraion b = 1,, 10,000. Noe ha he common rik facor are no reampled in he KTWW boorap: heir hiorical ordering i no varied acro imulaion run. We now have he croecional diribuion of alpha from all he boorap b imulaion { i, i 1,..., N; b 1,...,10,000} ha reul from he ampling variaion under he null ha he rue alpha i zero. The boorapped alpha can be ranked from malle o large o produce he luck (i.e., pure chance or zerokill) cumulaive diribuion funcion (CDF) of he alpha. We have a imilar croecional diribuion of boorapped aiic { ( b ), i 1,..., N; b 1,...,10,000} which can be compared wih he diribuion of acual i { ( ˆ ), i 1,..., N} value once boh e of aiic have been reordered from malle o large. We follow KTWW who prefer o work wih he aiic raher han he alpha, ince he ue of he aiic conrol for difference in rikaking acro fund (p. 2555). 4 FF employ an alernaive boorap mehod. They calculae alpha for each fund uing he ime erie regreion (2.1) a in KTWW. Bu FF do no reample he reidual of each individual fund a in KTWW, raher hey reample wih replacemen over he full cro ecion of reurn, hereby producing a common ime ordering acro all fund in each boorap. In our udy, we reample from all 129 monhly obervaion in he daae and we impoe he null hypohei a in FF by ubracing he eimae of alpha from each reampled monh reurn. 5 For each fund and each boorap, we regre he peudo exce reurn on he facor: b ( R ) ˆ i rf i i i Rm rf i SMB i HML + imom i i (2.6) b and ave he eimaed boorapped alpha { i, i 1,..., N; b 1,...,10,000} and  aiic { ( b ), i 1,..., N; b 1,...,10,000}. We hen rank he alpha and aiic i from lowe o highe o form he wo luck diribuion under he null hypohei. 4 KTWW (p. 2559) noe ha he aiic alo provide a correcion for puriou oulier by dividing he eimaed alpha by a high eimaed andard error when he fund ha a hor life or underake riky raegie. 5 To illurae, for boorap b = 1, uppoe ha he fir imeerie drawing i monh 37, hen he fir e of peudo reurn incorporaing zero abnormal performance for hi boorap i found by deducing i from ( Ri,37 rf37 ) for every fund i ha i in he ample for monh 37. Suppoe ha he econd imeerie drawing i monh 92, hen he econd e of peudo reurn i found by deducing i from ( Ri,92 rf92) for every fund i ha i in he ample for monh 92. Afer T drawing, he fir boorap i compleed. 6
7 reurn. 6 There are wo oher difference beween he wo boorap mehod a The mo imporan difference beween he wo boorap mehod i ha he KTWW boorap aume independence beween he reidual acro differen fund and ha he influence of he common rik facor i fixed hiorically. In oher word, he KTWW boorap aee fund manager kill conrolling only for he effec of nonyemaic rik. By conra, he FF boorap preerve he crocorrelaion of reurn acro boh fund and common rik facor. Thi implie ha he FF boorap aee fund manager kill conrolling for boh yemaic and nonyemaic rik. Thi i becaue, wih he FF boorap, he facor loading repreening yemaic rik are reeimaed wih every boorap, whil preerving he crocorrelaion of fund implemened in he wo udie. KTWW include fund in heir analyi wih more han 60 monhly obervaion in he daae, wherea he fund incluion crierion wih FF i 8 monh. The KTWW boorap ue 1,000 imulaion, wherea he FF boorap ue 10,000 imulaion. FF repor ha he diribuion of acual ( ˆ ) value i o he lef of ha of he b luck diribuion of he boorapped ( ) value, paricularly for fund wih negaive alpha, bu alo for mo fund wih poiive alpha. FF conclude ha here i lile evidence of muual fund manager kill. Thi conra wih KTWW who conclude ha here are a mall number of genuinely killed ar fund manager. FF poin ou a common problem wih boh mehod. By randomly ampling acro individual fund reidual in he fir mehod and acro individual ime period in he econd, any effec of auocorrelaion in reurn i lo. KTWW (p. 2582) performed a eniiviy analyi of hi iue by reampling in ime erie block up o 10 monh in lengh. They found ha he reul changed very lile. i i 3. Daa The daa ued in hi udy combine informaion from daa provider Lipper, Morningar and Defaqo and coni of he monhly reurn on 561 UK domeic equiy (openended) muual fund (uni ru and OIECS) over he period January 1998 Sepember 2008, a oal of 129 monh. The daae alo include informaion 6 FF argue ha he KTWW boorap failure o accoun for he join diribuion of join reurn, and of fund and explanaory reurn, biae he inference of KTWW oward poiive performance (p. 1940). 7
8 on annual managemen fee, fund ize, fund family and relevan Invemen Managemen Aociaion (IMA) ecor. We include in our ample he primary ecor clae for UK domeic equiy fund wih he IMA definiion: UK All Companie, UK Equiy Growh, UK Equiy Income, UK Equiy & Growh, and UK Smaller Companie. The ample i free from urvivor bia (ee, e.g., Elon e al., 1996; Carpener and Lynch, 1999) and include fund ha boh were creaed during he ample period and exied due o liquidaion or merger. We impoe he rericion ha fund in he ample mu have a lea 20 conecuive monhly reurn. Thee crieria reul in a final ample of 516 fund which will be ued in our boorap analyi. Gro reurn are calculaed from bidobid price and include reinveed dividend. Thee are repored ne of ongoing operaing and rading co, bu before he fund managemen fee ha been deduced. 7 We alo compue ne reurn for each fund by deducing he monhly equivalen of he annual fund managemen fee. We have complee informaion on hee fee for 451 fund. For each of he remaining 65 fund, each monh we ubrac he median monhly fund managemen fee for he relevan ecor cla and ize quinile from he fund gro monhly reurn. A in KTWW and FF, we exclude iniial and exi fee from our definiion of reurn. Table 3.1 provide ome decripive aiic on he reurn o and he ize of he muual fund in our daae. The average monhly gro reurn acro all fund (equally weighed) and monh in he daae i 0.45% (45 bai poin), compared wih an average monhly reurn over he ame period of 0.36% for he FTAll Share Index. 8 The overall andard deviaion of hee reurn i 4.82%, and he diribuion of reurn alo emphaie ha here i ome variabiliy in hee reurn. In he ubequen regreion analyi, we require a minimum number of obervaion o underake a meaningful aiical analyi, and we impoed he requiremen ha ime erie fund parameer are only eimaed when here were 20 or more monhly gro reurn for ha muual fund. We alo repor he diribuion of gro reurn for he ubample of 516 muual fund wih a minimum of 20 imeerie obervaion, and hi can be compared wih he diribuion of reurn acro he whole ample o 7 Operaing co include adminiraion, recordkeeping, reearch, cuody, accouning, audiing, valuaion, legal co, regulaory co, diribuion, markeing and adveriing. Trading co include commiion, pread and axe 8 Noe ha he FTAll Share Index reurn i gro of any co and fee. 8
9 confirm ha he ubample i indeed repreenaive. 9 Overall, hee reul indicae ha urvivorhip bia i very low in hi daae. The mean monhly ne reurn i 0.35%, implying ha he monhly fund managemen fee i 0.11%. The mean reurn i now very cloe o he mean reurn of 0.36% for he FTAll Share Index. Thi provide iniial confirmaion ha he average muual fund manager canno bea he marke (i.e., canno bea a buyandhold raegy inveed in he marke index), once all co and fee have been aken ino accoun. The final column how ha he diribuion of cheme ize i kewed: wih he median fund value in Sepember 2008 being 64 million and he mean value 240 million. I can be een ha 10% of he fund have value above 527 million. 4. Reul We now urn o aeing he performance of UK equiy muual fund over he period The reul are divided ino four ecion. The fir ecion look a he performance of equal and valueweighed porfolio of all fund in he ample again he four and fivefacor benchmark model over he whole ample period. The econd ecion compare he alpha performance of all he fund baed on he acual aiic b ( ˆ ) from he facor model wih he imulaed aiic ( ) generaed by he i boorap mehod of KTWW and FF dicued above. We repor he reul for boh gro and ne reurn. The hird ecion conduc a oal performance comparion baed on he acual and imulaed aiic, ( TM i ) and ( TM i ), for he wo boorap, again uing boh gro and ne reurn. The fourh ecion perform a erie of ochaic dominance e involving pairwie comparion beween he diribuion (of he aiic) under he wo boorap mehod and beween each of he boorapped diribuion and he acual diribuion of boh gro and ne reurn. i b 4.1 Performance again he facor benchmark model Following Blake and Timmermann (1998), Table 4.1 repor he reul from eimaing he four and fivefacor model (2.1) and (2.2) acro all T = 129 imeerie obervaion, where he dependen variable i, fir, he exce reurn on an 9 We choe 20 obervaion a a compromie beween he 8 obervaion ha FF ue which we believe involve oo few degree of freedom in he regreion equaion and he 60 obervaion ued by KTWW which could reul in urvivor bia. Panel A confirm ha he diribuion of ne reurn wih 20 or more obervaion i very imilar o he diribuion wih he full ample of fund. 9
10 equalweighed porfolio p of all fund in exience a ime, and, econd, he exce reurn on a valueweighed porfolio p of all fund in exience a ime, uing aring marke value a weigh. 10 For each porfolio, he fir wo column repor he loading on each of he facor when he dependen variable i baed on gro reurn, while he econd wo column repor he correponding reul uing ne reurn. The loading on he marke porfolio and on he while he loading are negaive bu inignifican on he loading are poiive bu inignifican on he SMB facor are poiive and ignifican, MOM facor. 11 HML facor. The facor The alpha baed on gro reurn differ from he correponding alpha baed on ne reurn by he average level of fund managemen fee. However, he mo imporan poin i ha he alpha ( ) i no ignifican in he fourfacor model and he oal performance meaure ( TM Var R rf p ) i no ignifican in he p p p m fivefacor model. In he laer cae, while p can be ignifican a in he cae of he equalweighed porfolio uing gro reurn a he 10% level hi i more han compenaed for by he ignificanly negaive loading on Rm rf 2. Thi hold wheher he porfolio i equalweighed or valueweighed, 12 or wheher we ue gro reurn or ne reurn. A paricularly inereing finding in Table 4.1 i ha he eimae for p in he fourfacor model i very imilar in ize o he eimae of TM p in he correponding fivefacor model, even hough boh eimae are no aiically ignifican. 13 Again hi i rue wheher we compare on he bai of gro or ne reurn, or an equal or valueweighed porfolio. Thi can only happen, of 10 We ue he monhly FTSE AllShare Index a he marke benchmark for all UK equiie. We ake he exce reurn of hi index over he UK Treaury bill rae. SMB, HML, and MOM are UK verion of he oher facor benchmark a defined in Gregory e al. (2013). 11 Noe ha he eimaed facor loading for he model where he dependen variable i baed on gro reurn are very imilar o hoe in he correponding model where he dependen variable i baed on ne reurn. Thi i becaue he fund managemen fee i fairly conan over ime. While hi will lead o differen eimae of he inercep ( ) in a regreion equaion, i will no lead o ignifican change in p he eimae of he lope coefficien. 12 The lower value of p and TM p in he valueweighed regreion compared wih he correponding equalweighed regreion indicae dieconomieofcalein fund managemen performance. 13 Grinbla and Timan (1994, p. 438) repor he ame reul in heir daae and argue ha he meaure are imilar becaue very few fund uccefully ime he marke. In fac, he meaure are ignificanly differen for hoe fund ha appear o have uccefully imed he marke. 10
11 coure, if he eimae of p in he fivefacor model i lower han he eimae of in he correponding fourfacor model by an amoun approximaely equal o he ize of Var R rf. p m The implicaion of hee reul i ha he average equiy muual fund manager in he UK i unkilled in he ene of being unable o deliver ouperformance (i.e., unable o add value from he wo key acive raegie of ock elecion and marke iming), once allowance i made for fund manager fee and for a e of common rik facor ha are known o influence reurn, hereby reinforcing our finding from our examinaion of raw reurn in Table 3.1. Bu wha abou he performance of he be and wor fund manager? To ae heir performance, we need o urn o he boorap analyi. p 4.2 Alpha performance of reurn uing he KTWW and FF boorap We eimae he fourfacor benchmark model (2.1) acro N = 516 muual fund wih a lea 20 monhly ime erie obervaion beween 1998 and We now have a cro ecion of aiic on alpha which can be ranked from lowe o highe o form a cumulaive diribuion funcion (CDF) of he { ( ˆ ), i 1,..., N} aiic for he acual fund alpha. We alo generae 10,000 KTWW and FF boorap imulaion for each fund a decribed in Secion 2.2 above. For each boorap, hi will generae a cro ecion of aiic on alpha, auming no abnormal performance. The 5.16 million aiic can alo be ranked from lowe o highe o creae a CDF of boorapped luck { ( b ), i 1,..., N; b 1,...,10,000} aiic for each boorap. i We compare he averaged value in eleced percenile range of he CDF of he  aiic on he acual alpha ( ( ˆ )) wih he averaged value of he aiic b derived from he KTWW and FF boorap imulaion ( ( )) in he ame percenile range. We repor he reul of he analyi fir uing gro and hen ne reurn. i Alpha performance baed on gro reurn Panel A of Table 4.2 look a alpha performance baed on gro reurn and Figure 4.1 illurae he reul graphically. The lef ail of he CDF of he acual aiic lie o he lef of ha of boh boorap. For example, in he percenile range , he acual aiic i 1.85, while he KTWW aiic i and he FF aiic i  11
12 1.71. Thi ugge ha hoe fund in he boom of he diribuion are here a a reul of poor kill raher han bad luck. Thi hold for mo of he diribuion of reurn. Only for percenile of he CDF above abou 70% i i he cae ha he acual aiic begin o exceed hoe from eiher imulaion mehod. For example, in he percenile range , he acual aiic i 2.32, while he KTWW aiic i 1.72 and he FF aiic i Thi mean ha hoe fund above he 70 h percenile ouperform heir luck diribuion providing evidence of kill in erm of gro reurn Alpha performance baed on ne reurn Aeing alpha performance uing ne reurn raher han gro reurn raie he performance hurdle, ince we are now aeing wheher fund manager are able o add value for heir inveor afer covering heir operaing and rading co and heir own fee. Subracing fee from gro reurn o derive ne reurn will reduce he value of boh he acual alpha and heir aiic. Figure 4.2 how he conequence of hi graphically: he CDF of he acual aiic of he alpha hif ignificanly o he lef. 14 Thi i confirmed by Panel B of Table 4.2. For example, in he percenile range , he acual aiic i 2.59, down from in Panel A. By conra, here i lile change in eiher he KTWW aiic a or he FF  aiic a Thi paern hold for mo of he diribuion of reurn. Fund need o be ranked above he 95 h percenile before hey generae aiic for acual reurn above hoe of he KTWW boorap. They never exceed hoe of he FF boorap. In oher word, above he 95 h percenile, he acual diribuion lie beween he wo boorap diribuion. 14 However, he CDF for he averaged value of boh he KTWW and FF boorap imulaion do no move ignificanly a all when here i a wich from gro o ne reurn. In he cae of he KTWW boorap, hi can be een if we e i 0 in (2.7) for boh gro and ne reurn and no oher variable on he righhand ide of (2.7) change when we make an allowance for fund manager fee. In he cae of he FF boorap, he influence of fee i broadly cancelled ou in he dependen variable in (2.9), ince Ri will be lower by he i h manager fee and ˆi ample which will be of imilar ize. Figure 1 and 2 in FF have he ame reul. ( R ) ˆ i rf i will be lower by he average fee acro he b 12
13 4.3 TM performance of reurn uing he KTWW and FF boorap We now repea he analyi of he previou ubecion bu ue he fivefacor benchmark model (2.2) and focu on he TM oal performance meaure inead of alpha. 15 We repor he reul of he analyi fir uing gro and hen ne reurn TM performance baed on gro reurn Panel A of Table 4.3 look a TM performance baed on gro reurn. A comparion of he Ac column in hi able wih ha in Panel A in Table 4.2 how a remarkable imilariy in he value of he aiic for he TM and alpha gro reurn performance meaure a he ame percenile. 16 Boh able demonrae ha i i only for percenile of he CDF above abou 70% ha i i he cae ha he acual  aiic exceed hoe from eiher imulaion mehod. For example, in he percenile range , he acual aiic i 2.35 (compared wih 2.32 when he performance meaure i alpha), while he KTWW aiic i 1.71 (compared wih 1.72) and he FF aiic i 1.79 (compared wih 1.80). The regreion analyi in ecion 4.1 produced a imilar finding. We herefore have he ame inerpreaion of hi performance, namely ha only a minoriy of fund are able o generae reurn from ock elecion and marke iming ha are more han ufficien o cover heir operaing and rading co TM performance baed on ne reurn Panel B of Table 4.3 examine TM performance baed on ne reurn. A comparion of he Ac column in hi able wih ha in Panel B of Table 4.2 how he ame imilariy beween he value of he TM and alpha ne reurn performance meaure ha he previou ubecion found when looking a gro reurn. Fund need o be ranked above he 95 h percenile before hey are generaing aiic for he acual reurn above hoe of he KTWW boorap. They only bea he FF boorap above he 96 h percenile. 15 In he cae of he FF boorap, he dependen variable in (2.9) become 2 b ( R ) ˆ ˆ i rf i i Rm rf. 16 For he ame reaon given by Grinbla and Timan (1994, p. 438) in foonoe 13 above. 13
14 4.4 Sochaic dominance e In hi ubecion, we provide a formal comparion of he acual and boorap diribuion uing ochaic dominance echnique. We compare he wo boorap wih each oher and compare each boorap wih he acual diribuion from he relevan facor model of (α) and (TM) for boh gro and ne reurn. Table and Figure revealed a conien paern. Alhough he boorap diribuion for boh (α) and (TM) are very imilar, a low percenile, he KTWW boorapped CDF lie lighly o he righ of he FF boorapped CDF. A high percenile, he relaionhip wiche around. The croover happen beween he 30 h and 40 h percenile in he cae of alpha (for boh gro and ne reurn) and around he 60 h percenile in he cae of TM (again for boh gro and ne reurn). The implicaion i ha he KTWW boorap e a higher hurdle han he FF boorap a he boom of he diribuion, bu a lower hurdle a he op. Thi mean ha he KTWW boorap will idenify marginally more fund in he lef ail of he diribuion a being unkilled compared wih he FF boorap. I alo mean ha he KTWW boorap will idenify marginally more fund in he righ ail of he diribuion a being killed compared wih he FF boorap, i.e., he KTWW boorap will idenify more fund manager ar han he FF boorap. FF uggeed hi reul in heir paper, bu did no formally e i. The momen of he acual (α) and (TM) diribuion (conruced from he 516 facor model) ogeher wih he correponding KTWW and FF boorap diribuion (conruced from he 5.16 million imulaion) are hown in Table 4.4. All he diribuion have zero mean by conrucion. The facor model generae imilar diribuion for boh gro and ne (α) and (TM): wih andard deviaion in he range , mode poiive kewne in he range 0.5 and kuroi in he range 89. The KTWW boorap alo generae imilar diribuion for boh (α) and (TM). The diribuion have (approximaely) uni variance. They are alo fairly ymmeric and have a mode degree of exce kuroi compared wih he normal diribuion. 17 By conra, he FF boorap diribuion ha a larger variance and much faer ail (epecially in he cae of (TM), where he lefkew i alo more prominen). In order o ae wheher hee diribuion are aiically differen 17 Neverhele, all he diribuion decribed in Table 4.4 fail a Jarque Bera e for normaliy (reul no repored). 14
15 from each oher, we will e for ochaic dominance beween: a) he boorap diribuion, and b) he acual and boorap diribuion for gro and ne reurn. Several mehod have been propoed for eing for ochaic dominance and hee can be claified ino wo main group. The fir group of e relie on he comparion of boh diribuion a a finie number of grid poin (e.g., Anderon, 1996; and Davidon and Duclo, 2000). The ue of an inf or up aiic over he uppor of he diribuion i advocaed under he econd approach by McFadden (1989) and Kaur, Rao and Singh (1994, hereafer KRS). The power of uch e ha been udied by a number of auhor. Subequenly, Te and Zhang (2004), Linon e al (2010) and Heahcoe e al (2010) have uggeed ha he performance of uch e, epecially in mall ample, can be improved by he adopion of boorap mehod. Given ha our ample i of coniderable ize, we adop he mehodology of Davidon and Duclo (2000, henceforh DD) baed upon he finding of Te and Zhang (2004, p. 377) who repor ha he DD e dominae he oher. Following he eing procedure decribed in DD, Heahcoe e al (2010) and Te and Zhang (2004), we may e any order of ochaic dominance for any wo random variable (which need no be independen), Y,..., Y and Z,..., Z, wih 1 M 1 M empirical diribuion funcion, Fˆ ( x ) and Fˆ ( x ), by conidering he following e Y Z aiic: T ˆ ( ) ˆ D x D ( x) ( x) (4.1) ˆ V ( x) Y Z where 18 N ˆ ˆ ( 1) 1 1 D ( x) ( ) ˆ ( ) Y D Y dy x Y df Y x Y 0 Y 0 Y i x x 1 1 ( 1)! N( 1)! i1 i a naural eimaor of D ( x) for 2 wih Y Dˆ ( x) Fˆ ( x) (and analogouly for 1 Y Y ˆ D ( x )), where (ince he diribuion are independen) ˆ ˆ ( ) ( ) ˆ V x V x V ( x) Z Y Z i he variance of ˆ ( ) ˆ D x D ( x) Y Z wih 18 x i defined a i x Y i Y max,0. 15
16 N ˆ 1 1 2( 1) ˆ 2 V ( x) x Y D ( x) Y i Y N N(( 1)!) i1 (and analogouly for ˆ V ( x )), and where N i he ample ize. T Z DD how ha, under he null hypohei: ( ) : ( ) H D x D ( x ) 0 Y Z Y Z. x i diribued aympoically a a andard normal variae again he alernaive hypohee: H : D ( x) D ( x) ( Y Z A Y Z H Y Z : A1 H Z Y. : A2 ), bu Y Z and Z Y Y dominae Z ochaically a order if D ( x) D ( x) for all x 0, D ( x) D ( x) for ome x, and ( Y) ( Z), where (.) Y Z diribuion. We denoe hi above a Y Z. Y Z i he mean of he To conrol for he ize of he e, i i convenional o ue he udenized maximum modulu (SMM) whoe criical value are repored in Soline and Ury (1979). The ignificance of he e i deermined aympoically by he criical value of he SMM diribuion wih k and degree of freedom, where k i he number of value of x in he relevan diribuion a which he e i performed. We employ he following deciion rule: If k T ( x ) M j, for all j = 1,, k, accep H, 0 If k T ( x ) M j, for all j and k T ( x ) M j, for ome j, accep H, A1 If k T ( x ) M j, for all j and k T ( x ) M j, for ome j, accep H, A2 If k T ( x ) M j, for ome j and k T ( x ) M j, for ome j, accep H. A Panel A of Table 4.5 preen he ummary reul of our hypohei e a he 5% ignificance level for ochaic dominance beween he diribuion generaed by he wo boorap mehod. H i eed a k (= 19) value of x (i.e., in 20 equally 0 paced grid or bin) in each of he diribuion. 19 The panel how ha he KTWW 19 The criical value for k = 19 and degree of freedom from he SMM diribuion are a follow: (1% ignificance level), (5%), and (10%). 16
17 diribuion ochaically dominae he FF diribuion in erm of (α) and (TM) for boh gro and nereurn. 20 FF pu forward a number of reaon o explain he difference in he diribuion. One reaon wa differen ample period. Anoher wa differen incluion rule: FF argued ha he KTWW rule of only including fund wih a lea 60 monh of reurn produce more urvival bia han heir rule of including all fund wih a lea 8 monh daa (p. 1939). Our udy ue he ame daae and he ame incluion rule of a lea 20 monh in he daae, o hee wo explanaion are no applicable. We are herefore lef wih FF hird explanaion for he difference beween he reul of he wo boorap, namely, he reampling aumpion ued in he imulaion: KTWW independenly reample only he reidual in each fund facor benchmark model, while FF imulaneouly reample acro all he fund reurn and facor. We now urn o he ochaic dominance e beween he acual diribuion and hoe generaed by he boorap for boh gro and nereurn (α) and (TM). If we look acro he whole of hee diribuion a he 5% level, we find (in unrepored reul) ha, for he groreurn (α) and (TM), he acual diribuion appear o be equivalen o boh he KTWW and FF diribuion obained under he null hypohei ha manager poe neiher eleciviy kill nor iming abiliy. Thee reul herefore appear o be in line, qualiaively a lea, wih he concluion reached by FF who documened abence of pecific kill and aribue he inciden of excepional performance o luck. We alo find ha, for he nereurn (α) and (TM), boh boorap diribuion ochaically dominae he acual diribuion. Thi would appear o indicae ha he fund manager were no ju unlucky, hey demonrae no kill ne of heir fee. However, he ruh i more uble han hi if we ake a cloer look a he fund in he upper ail of he diribuion. Following Lean e al. (2008. p.32), we divided he op 10 percen of he diribuion ino 20 equally paced minor grid. The reul are preened in Panel B and C of Table 4.5 a he 1% ignificance level. We find ha, while he ame reul a above hold for he nereurn (α) and (TM), for he groreurn (α) and (TM), he acual diribuion now ochaically dominae boh 20 In mo cae, he order of ochaic dominance i = 2, bu for he nereurn (α), i i = 3. Since he KTWW diribuion ochaically dominae he FF diribuion, i provide a higher overall hurdle acro he diribuion of fund a a whole. I i only for op 5% of fund ha he FF hurdle i higher a hown in Table 4.2 and
18 he KTWW and FF diribuion. Thi uppor he KTWW finding ha here are a mall number of ar fund manager who have ufficien kill o generae reurn enough o cover heir operaing and rading co. Bu and here i one of our key finding hey exrac he full ren from heir kill in he fee ha hey charge. Finally, we noe ha he ochaic dominance e indicae ha, alhough he wo boorap are aiically differen from each oher, he quaniaive difference beween hem i mall. The reul in hi ubecion indicae ha, depending on he pecific hypohei being eed and he pecific ignificance level of he e, he acual diribuion eiher ochaically dominae boh boorap diribuion or i ochaically dominaed by boh boorap diribuion. Figure reveal how viually cloe he boorap are. Thi conra wih he reul in Panel B of Table 4.2 and 4.3 which howed ha, above he 95 h percenile, he acual diribuion lie beween he wo boorap diribuion. 5. Concluion Our paper conribue o he lieraure in hree way. Fir, we ue a new daae of UK equiy muual fund o ae he TreynorMazuy meaure of oal performance (TM) kill of muual fund manager uing facor benchmark model. TM i uperior o an aemen baed on alpha alone, ince i include marke iming kill a well a eleciviy kill; mo exiing udie, including KTWW and FF, only examine eleciviy. Second, we compare direcly he KTWW and FF boorap mehod for aeing muual fund manager performance (boh alpha and TM) uing he ame fund eleced uing he ame incluion crieria over he ame ample period. 21 Third, we employ ochaic dominance o e formally wheher a) he wo boorap diribuion of he aiic of he performance meaure (alpha and TM) and b) he diribuion of hee aiic from he facor benchmark model and each of he correponding boorap are aiically differen from each oher. We conduc he analyi for boh gro and ne (of fund manager fee) reurn. On he bai of a daae of equiy muual fund in he UK over he period , we draw he following concluion. Fir, he average equiy muual fund manager in he UK i unable o deliver ouperformance from eiher ock elecion or marke iming, once allowance i made 21 FF did no reproduce he KTWW boorap mehod on heir daae. They ju ued heir boorap mehod wih he KTWW incluion crierion and ample period o ae he KTWW mehod. 18
19 for fund manager fee and for he e of common rik facor known o influence reurn. Second, 95% of fund manager on he bai of he KTWW boorap and almo all fund manager on he bai of he FF boorap failed o ouperform he boorap imulaion of he nereurn (α) and (TM) aiic. The TM reul, in paricular, indicae ha he va majoriy of fund manager are very poor a marke iming. Any eleciviy kill ha fund manager migh poe and a be only a very mall number of hem do are wiped ou by heir aemp o ime he marke. We noe ha, on he bai of our UK daae, he FF boorap e a marginally higher hurdle han he KTWW boorap for fund manager o jump over before hey can be conidered o be ar. Thi i becaue he FF boorap conrol for he yemaic relaionhip beween a fund reurn and he facor benchmark, while he KTWW boorap ignore hi relaionhip and conrol only for he nonyemaic rik conained in he reidual of he facor benchmark model. Third, and focuing on he upper ail of he diribuion, he ochaic dominance e indicae ha he diribuion of he acual groreurn (α) and (TM) aiic ochaically dominae boh of he boorap diribuion, bu boh boorap diribuion for he nereurn (α) and (TM) ochaically dominae he acual diribuion. Taken ogeher, he above reul prove ha he va majoriy of fund manager in our daae were no imply unlucky, hey were genuinely unkilled. However, a mall group of ar fund manager are genuinely killed and hence able o generae uperior performance (in exce of operaing and rading co), bu hey exrac he whole of hi uperior performance for hemelve via heir fee, leaving nohing for inveor. Our final concluion i ha, while ar fund manager do exi, all he empirical evidence including ha preened here indicae ha hey are incredibly hard o idenify. Furhermore, i ake a very long ime o do o: Blake and Timmermann (2002) howed ha i ake 8 year of performance daa for a e of a fund manager kill o have 50% power and 22 year of daa for he e o have 90% power. For mo inveor, our reul how ha i i imply no worh paying he va majoriy of fund manager o acively manage heir ae. 19
20 Table 3.1: Decripive aiic on UK equiy muual fund Gro reurn Gro reurn ( 20 monh) Ne reurn ( 20 monh) Fund managemen fee ( 20 monh) Size a 30 Sep 2008 ( million) Mean Sd. dev Beween d. dev Wihin d. dev % % % % % Ob. 48,061 47,492 47,492 47,492 No. of fund Noe: he able repor average monhly reurn from February 1998 o Sepember 2008 (129 monh). I alo repor average monhly fund managemen fee over he ame period, a well a he ize of fund a he end of he ample period. 20
21 Table 4.1: Eimae of he fourfacor and fivefacor model for an equalweighed and a valueweighed porfolio of UK equiy muual fund Equalweighed Valueweighed Gro Gro reurn Ne Ne reurn wih Gro Gro reurn Ne Ne reurn wih reurn wih marke reurn marke iming reurn wih marke reurn marke iming iming iming p * (0.20) (1.71) (1.27) (0.49) (0.21) (1.414) (1.62) (0.27) R rf *** *** *** *** *** *** *** *** m (41.53) (40.36) (41.46) (40.3) (41.39) (43.29) (41.39) (43.29) SMB *** *** *** *** *** *** *** *** (9.96) (10.88) (9.96) (10.88) (7.35) (8.33) (7.36) (8.34) HML (1.27) (1.40) (1.26) (1.40) (0.30) (0.42) (0.30) (0.42) MOM (0.99) (0.78) (0.98) (0.78) (0.17) (0.09) (0.17) (0.09) R 2 m rf ** * ** * (2.16) (2.16) (2.15) (2.15) TM p (0.24) (1.28) (0.18) (1.63) R Ob Noe: The reul are baed on (2.1) wihou marke iming and (2.2) wih marke iming. The dependen variable, ( R rf ), i eiher he exce reurn on an equalweighed porfolio or on a valueweighed porfolio p of all fund in exience a ime. The dependen variable i meaured boh gro and ne of fund managemen fee. TM Var R rf ) i alo repored. Relevan aiic eimaed from Whie (1980) robu andard error are The oal performance meaure ( p p p m repored in bracke underneah each parameer eimae: ***, ** and * denoe ignificance a he 1%, 5% and 10% level. p 21
22 Table 4.2: Percenile of he acual and average KTWW and FF boorap cumulaive deniy funcion of (α) in he fourfacor model for boh gro and ne reurn of UK equiy muual fund Panel A: Gro reurn Panel B: Ne reurn Pc Ac Sim (KTWW) Sim (FF) Ac Sim (KTWW) Sim (FF) Noe: The reul are baed on he fourfacor model R rf R rf SMB HML MOM where + ( i 1,...,516) i i i m i i i i he dependen variable i exce gro reurn in Panel A and exce ne reurn in Panel B. The able how he averaged value in eleced percenile range (Pc) of he cumulaive diribuion funcion of he acual (α) aiic for he eimaed alpha (Ac) in hi regreion. The able alo how for he ame percenile range he averaged value of (α) from 5.16 million imulaion of he KTTW and FF boorap (Sim(KTWW) and Sim(FF)). 22
23 Table 4.3: Percenile of he acual and average KTWW and FF boorap cumulaive deniy funcion of (TM) in he fivefacor model for boh gro and ne reurn of UK equiy muual fund Panel A: Gro reurn Panel B: Ne reurn Pc Ac Sim (KTWW) Sim (FF) Ac Sim (KTWW) Sim (FF) Noe: The reul are baed on he fivefacor model + 2 R rf R rf SMB HML MOM R rf i i i m i i i i m i ( i 1,...,516) where he dependen variable i exce gro reurn in Panel A and exce ne reurn in Panel B. The able how he averaged value in eleced percenile range (Pc) of he cumulaive diribuion funcion of he acual (TM) aiic for he eimaed TM (Ac) in hi regreion. The able alo how for he ame percenile range he averaged value of (TM) from 5.16 million imulaion of he KTTW and FF boorap (Sim(KTWW) and Sim(FF)). 23
24 Table 4.4: Momen of he cumulaive deniy funcion of (α) and (TM) from he acual and boorap imulaion baed on boh he gro and ne reurn of UK equiy muual fund Mehod Momen (α) (TM) Gro reurn Ne reurn Gro reurn Ne reurn Acual Mean S. dev Skewne Kuroi KTWW Mean S. dev Skewne Kuroi FF Mean S. dev Skewne Kuroi Noe: The able how key momen of he diribuion of he (α) and (TM) aiic from he acual facor model, he KTWW boorap and he FF boorap for boh gro and ne exce reurn. 24
25 Table 4.5: Sochaic dominance e: Summary of reul Panel A: Te of KTWW v. FF boorap cumulaive deniy funcion 1. Y = KTWW groreurn (α) v. Z = FF groreurn (α): Accep H : Y Z A Y = KTWW groreurn (TM) v. Z = FF groreurn (TM): Accep H : Y Z A1 2 3a. Y = KTWW nereurn (α) v. Z = FF nereurn (α) (econdorder e): Accep H : Y Z, bu Y A Z and Z 2 2 3b. Y = KTWW nereurn (α) v. Z = FF nereurn (α) (hirdorder e): Accep H : Y Z A Y = KTWW nereurn (TM) v. Z = FF nereurn (TM): Accep H : Y Z A1 2 Y Panel B: Upper ail e of acual fourfacor model cumulaive deniy funcion v. boorap cumulaive deniy funcion for (α) 1. Y = Acual groreurn (α) v. Z = KTWW groreurn (α): Accep H : Y Z A Y = Acual groreurn (α) v. Z = FF groreurn (α): Accep H : Y Z A Y = Acual nereurn (α) v. Z = KTWW nereurn (α): Accep H A2: Z 2Y 4. Y = Acual nereurn (α) v. Z = FF nereurn (α): Accep H A2: Z 2Y Panel C: Upper ail e of acual fivefacor model cumulaive deniy funcion v. boorap cumulaive deniy funcion for (TM) 1. Y = Acual groreurn (TM) v. Z = KTWW groreurn (TM): Accep H : Y Z A Y = Acual groreurn (TM) v. Z = FF groreurn (TM): Accep H : Y Z A Y = Acual nereurn (TM) v. Z = KTWW nereurn (TM): Accep H : Z Y A Y = Acual nereurn (TM) v. Z = FF nereurn (TM): Accep H A2: Z 2Y 25
26 Figure 4.1: Groreurn (α) Acual and average KTWW and FF boorap cumulaive deniy funcion of (α) in he fourfacor model baed on he gro reurn of UK equiy muual fund Noe: The verical line indicae he 5 h and 95 h percenile of he diribuion of he boorapped aiic. 26
27 Figure 4.2: Nereurn (α) Acual and average KTWW and FF boorap cumulaive deniy funcion of (α) in he fourfacor model baed on he ne reurn of UK equiy muual fund Noe: The verical line indicae he 5 h and 95 h percenile of he diribuion of he boorapped aiic. 27
28 Reference Anderon G., Nonparameric e of ochaic dominance in income diribuion. Economerica 64, Blake, D., Roi, A., Timmermann, A., Tonk, I., Wermer, R., Decenralized invemen managemen: evidence from he penion fund indury. Journal of Finance, 68(3), Blake, D., Timmermann, A., Muual fund performance: evidence from he UK. European Finance Review 2, Blake, D., Timmermann, A., Performance benchmark for iniuional inveor: meauring, monioring and modifying invemen behaviour. In Knigh, J., Sachell, S., (ed) Performance Meauremen in Finance, BuerworhHeinemann, Oxford, Carhar, M., On perience in muual fund performance. Journal of Finance 52, Cuhberon, K., Nizche, D., O Sullivan, N., UK muual fund performance: kill or luck. Journal of Empirical Finance 15, Davidon, R., Duclo, J.Y.,2000. Saiical inference for ochaic dominance and he meauremen of povery and inequaliy. Economerica 68, Efron, B., Tibhirani, R. J., An Inroducion o he Boorap, Monograph on Saiic and Applied Probabiliy. Chapman and Hall, New York. Fama, E.F., French, K.R., Common rik facor in he reurn on ock and bond. Journal of Financial Economic 33, Fama, E.F., French, K.R., Luck veru kill in he croecion of muual fund reurn. Journal of Finance 65, Feron, W.E., Schad, R.W., Meauring fund raegy and performance in changing economic condiion. Journal of Finance 51, Gregory, A., Tharyan, R., Huang, A., Conrucing and eing alernaive verion of he FamaFrench and Carhar model in he UK, Journal of Buine Finance and Accouning, 40(12), Grinbla, M., Timan, S., A udy of monhly muual fund reurn and performance evaluaion echnique. Journal of Financial and Quaniaive Analyi 29, Heahcoe, A., Brown, S., Wagenmaker, E.J, Eidel, A., Diribuionfree e of ochaic dominance in mall ample, Journal of Mahemaical Pychology 54,
Equity Valuation Using Multiples. Jing Liu. Anderson Graduate School of Management. University of California at Los Angeles (310) 2065861
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