How do US equity funds perform when it comes to risk?

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1 How do US quity fund prform whn it com to rik? Atract Thi papr xamin th prformanc of US no-load quity mutual fund. Fund prformanc i drivd uing tochatic frontir analyi for a flxil functional form. Thi analyi allow u to driv paramtric timat of fficincy cor for ach fund in our ampl. Our rult how that US no-load quity fund diplay varying lvl of fficincy ovr tim ut alo dpnding on iz and on invtmnt tyl. A part of a nitivity analyi w unvil th undrlying dynamic of fund fficincy with rpct to rik and oprational charactritic uch a flow, at, and Morningtar tar rating. Panl VAR timation rval that th rpon of fund fficincy to a hock in rik i poitiv and utantial. Som vidnc of rvr cauality i alo orvd. Finally, w xtnd our analyi to invtigat th rlationhip twn fund prformanc and ky covariat acro ugroup dfind y iz. Kyword: US fund prformanc, tochatic frontir analyi, panl VAR, rik. EL Claification: G11, G12, G14, G23. 1

2 1. INTRODUCTION On of th gratt dvlopmnt in th modrn financial markt i thir domination y intitutional invtor. Mutual fund ar proaly th mot important mmr of intitutional invtor managing a ignificant part of aving and channling thm to profital invtmnt. Dpit thir appal to rtail invtor offring numrou advantag uch a acc to profional managmnt, rik divrification and liquidity thr xit cot that com with th advantag. Such cot ar utifid y th aility of fund managr to achiv th optimal allocation of availal capital, aiming at conitntly uprior rik-adutd rturn compard to a paiv nchmark or it pr. Fundamntally, th iu of whthr activ fund managr add valu, from a prformanc point of viw, to thir portfolio ntail important invtmnt and policy implication for th fund managmnt indutry. Thi papr offr for th firt tim in th litratur paramtric maurmnt of fund prformanc uing tochatic frontir analyi. Accurat maurmnt of fund prformanc ha n a rathr challnging tak and ha attractd th focu of th acadmic litratur ovr th pat 40 yar with th main finding ing that on avrag mutual fund undrprform rlativly to thir paiv nchmark approximatly y th iz of cot chargd to thir harholdr (Grur 1996, Carhart 1997, Fama and Frnch 2010). Rcnt attmpt of a mor rlial prformanc maurmnt includ among othr th tudi of Homma & Pigorch (2012) and Anglidi t al (2013). Hnc th kill of fund managr a a whol to offr uprior rik adutd rturn hav n riouly diputd. Although thr i utantial vidnc againt th xitnc of managrial aility, mauring th prformanc of fund managr rmain a hot topic in th litratur. Traditional prformanc maur compar th rturn of th xamind portfolio to th rturn of an unmanagd portfolio of comparal rik ( following ction of tylizd fact for an xtniv dicuion). Svral drawack of th mtric uch a thir inaility to incorporat fund tranaction cot or th iu of lcting th propr nchmark hav fuld th introduction of prformanc maur that rly on frontir analyi in th pirit of Koopman (1951) and Farrll (1957). Following th minal work of Koopman (1951), and Farrll (1957), thr i a urgoning litratur that mploy frontir analyi for th purpo of invtmnt fund prformanc valuation. 2

3 Bfor w procd with th rlvant litratur, it would uful to ditinguih twn th two main path of frontir-ad mthodologi that appar in th rlvant tudi: paramtric approach and nonparamtric approach. Brgr and Humphry (1997) pointd out that th crucial diffrnc twn th two approach rt on th implicit aumption t on data with rpct to (i) th functional form of th t practic frontir (ii) allowanc / non-allowanc of random rror which may produc tranitory poitiv or ngativ dviation in output, input, cot, or profit, and (iii) in ca whr random rror i allowd, th ditriutional aumption impod on it to ditinguih th ffct from th infficinci and th random dituranc. Anothr ignificant dicrpancy twn th mthod li in th form of th cravd fficincy. In particular, nonparamtric modl ar uually mployd for mauring tchnical fficincy whil paramtric modl ar adoptd for gauging ovrall fficincy (Baur, Brgr, Frrir, and Humphry 1998). Morovr, in th contxt of mauring fficincy y man of data nvlopmnt analyi (DEA) rarchr gnrally mploy mutual fund cot and rik varial a input and a wll-dfind indicator of rturn a on of th output ( Murthi t al and Murthi and Choi, 2001, and Bao and Funari, 2001, Lozano and Gutirz, 2008). Andron t al. (2004) analyzd th fficincy of ral tat fund mploying a ri of input uch a load, variou cot and a tandard maur of fund rik (th tandard dviation) and raw rturn a output. Daraio and Simar (2006) addd to thir modl a a nw input th fund iz. Thy uggtd a rout non-paramtric prformanc maur ad on th prmi of ordr-m frontir. A for markt outid US, mauring th prformanc of Italian fund y man of variou DEAad modl wa th focu of. Thy mployd multipl rik maur and al charg in plac of input whra fund man rturn and th numr of priod that th fund wa not dominatd rvd a output. Galagadra and Silvapull (2002) analyzd rlativ prformanc of Autralian mutual fund mploying load, xpn, minimum initial invtmnt and portfolio rik a input and gro prformanc a output. It hould notd that portfolio rik and fund gro prformanc wr calculatd for varying holding priod. Prformanc valuation of hdg fund y man of DEA-ad modl ha attractd th intrt of Grgoriou (2003) and Grgoriou t al. (2005). Employing an xtniv ampl of US and Europan mutual 3

4 fund along with a ri of frontir timator Krtn t al (2011) propod th u of th hortag function a an fficincy maur which thy livd accommodat gnral invtor prfrnc. Mor rcntly, Prmachandra t al (2012) rponding to th lin of criticim facd y tandard DEA-modl appald to th u of an innovativ two-tag DEA modl that dcompo th ovrall fficincy of a dciion-making unit into two componnt, an oprational managmnt fficincy and portfolio managmnt fficincy. For dmontration purpo, th author ad th rlativ prformanc of 66 larg mutual fund famili in th US ovr th priod On th othr hand, fund prformanc valuation tudi that rly on tochatic frontir analyi ar xtrmly limitd. Annart t al (2003) mployd a Europan ampl of quity mutual fund. Thy concludd that iz and pat prformanc ar ignificant prdictor of fund fficincy. In particular, largr fund appard mor fficint than mall fund indicating th prnc of conomi of cal, ut it may alo rlatd to rlativly largr capital inflow into uccful fund. Unlik th two charactritic, fund ag appard to irrlvant for fund fficincy. Finally, thir finding rvald that undrprformr tnd to l fficint in a uqunt priod. Rlatd mpirical vidnc can found in th tudy of Santo t al (2005) who valuatd th prformanc of 307 Brazilian tock mutual fund mploying tochatic frontir. Thy documntd a poitiv rlationhip twn fund fficincy and managmnt kill to at th markt whil portfolio with low volatility appard to mor fficint. To thi nd, th purpo of our tudy i thrfold. Firt, w attmpt to roadn th finding of th rlativly fw tudi mauring fund prformanc uing tochatic frontir analyi for th firt tim in th litratur for an up to dat t concrning US no-load mutual fund. Scond, in ordr to account for poil tim variation in fficincy cor, w provid fficincy cor ovr tim. Third, w opt for a novl mthodology whr iu rlatd to ndognity and dynamic ar takn into account within a panl-vctor Autorgrion (panl-var thraftr) modl. Within thi modl all varial ntr a ndognou, whilt du to th vctor autorgrion th dynamic of fund fficincy ar conidrd. W offr an analyi that allow u to orv th dirction of cauality twn US no-load fund prformanc a 4

5 maurd y fficincy and om ky varial uch a rik, flow and iz. Finally, w liv that in th contxt of our VAR analyi w provid novl finding with rpct to managr rik hifting haviour givn th inconcluiv hatd dat in th litratur ( intr alia Brown, Harly and Stark 1996, Chvallir & Ellion 1997, Bo 2001, Huang t al 2011, Schwarz (2012) and Culln t al 2012). Thr ar a numr of raon that contitut US no-load quity fund an intrting ca to xamin. No-load fund hav rcivd utantial popularity among rtail and intitutional invtor during th lat yar. Thir popularity ha utantially contriutd to th hrinkag of xpn and f in th US mutual fund indutry in gnral. According to th Invtmnt Company Intitut no load har cla hav attractd ignificant inflow compard to thir countrpart charging load ovr th lat yar. In particular, total nt at of long-trm fund in no-load har cla hav rachd in 2010 USD 5.16 trillion from 1.98 trillion in 2002, an atonihing growth of almot 160%. A nick rviw of our rult rval a poitiv rlationhip twn fund prformanc and rik. Examining th rvr cauation w infr that th rpon of fund rik to fficincy innovation i ngativ. Th rt of th papr i organizd a follow: Sction 2 outlin th main hypoth to ttd. Sction 3 dcri th mployd mthodology and data whil Sction 4 dicu mpirical rult. Finally, Sction 5 provid om concluding rmark and policy implication. 2. Hypoth to ttd Hypothi 1: An incra in fund rik cau an incra in fund fficincy. Managr rik havior and thir rpon to rik incntiv ha n a cntral topic in th proc of undrtanding th agncy rlatd prolm that charactriz mutual fund indutry. Rtail invtor opt for a fund that mploy it rourc in th mot ffctiv mannr to maximiz rik-adutd rturn. Contrary to invtor prfrnc mutual fund compani ar motivatd y thir own profit and whn action of mutual fund compani ar not alignd to tho aiming at maximizing xpctd rik-adutd rturn thn w xpct om infficinci to ari. Thrfor, managr can ngag into rik hifting tratgi of thir portfolio acting a if thy ar compting in a 5

6 tournamnt (Brown, Harlow and Stark 1996, BHS hraftr) intrprting th flowprformanc rlationhip a an implicit incntiv contract (Chvallir and Ellion 1997). In particular, according to BHS tournamnt modl fund managr that wr lor in th firt priod wr likly to incra fund volatility in th lattr part of th valuation priod to a gratr dgr than intrim winnr and thi i xactly what thy found. Evidnc againt BHS claim wr provid y Chvallir and Ellion (1997) and Qui (2003) who argud that it i winnr rathr than lor who gaml. In a rlatd tudy Huang t al (2011) mploying a holding-ad maur of rik hifting how that highly riky fund prform poorly compard to fund with tal rik xpour. In gnral, fund managr ar xpctd to hift th dgr of rik in thir portfolio o a to manipulat thir prformanc and thu rap a gratr portion of invtor flow. Hypothi 2: An incra in fund fficincy cau an incra in fund rik lvl. Following th moral hazard hypothi of Gorton and Ron (1995) w claim that managr of fficint financial intitution ar mor inclind to adopt an xpanionary tratgy that could uquntly provd rathr riky. In othr word, rlatd to rational of Brk and Grn (2004) managr of uccful fund ar willing to aum gratr rik in ordr to attract largr inflow and thrfor incra thir atad compnation. Sinc fund ar pricd at th nt at valu th mot killd managr ar xpctd to rciv largr compnation through managing mor at. Th mor fficint a fund com th mor flxil i to ngag in a rikir invtmnt tratgy. In addition to th aov hypoth, w alo xamin th rlationhip twn fund at iz and prformanc. To thi nd, two additional hypoth ar of rlvanc. Hypothi 3: An incra in fund at iz rult in an incra in fund fficincy. Thi hypothi ha n havily xamind in th rlvant litratur with contradictory rult o far. On th on hand, thr i a lin of argumnt that ha n put forward y Chn, t al. (1992) and Indro, t al., (1999) linking th notion of at growth in fund managmnt indutry with th poitiv ffct of conomi of cal. In othr word, largr fund oprat mor fficintly than mallr du to ttr 6

7 and mor ffctiv allocation of th availal rourc. Largr fund hav ttr kill in procing availal information whra can achiv utantially lowr trading commiion du to th lock of trad that charactriz thir tranaction. A a rult, lowr xpn lad to ttr prformanc and incrad fficincy. Hypothi 4: An incra in fund at iz rult in a dcra in fund fficincy. Dparting from th hypothi of conomi of cal liquidity conidration coupld with organizational tructur friction prnt in th fund managmnt indutry could ditort fund prformanc rndring largr fund with a diadvantag compard to thir mallr countrpart. Statd diffrntly, according to Chn t al (2004) mallr fund could mor flxil and could plac all thir availal moni into thir t ida achiving thu uprior rik-adutd rturn. 3. Empirical mthodology and data. 3.1 US fund data Our ampl conit of mor than 500 no-load domtic US quity mutual fund that wr in xitnc for at lat on yar undr th priod of analyi Only no-load fund hav n includd in our analyi o a to avoid th complxity of th varity of xpn chargd in diffrnt fund har cla. Indx fund, xchang tradd fund (ETF) and othr non-traditional mutual fund uch a targt dat fund hav n xcludd from th currnt ampl. Th ourc of input-output data varial i th comprhniv Morningtar Dirct dataa whra th macroconomic varial hav n rtrivd from Thomon Datatram. Within th 9-yar priod w hav collctd annual raw rturn, total yar-nd at and variou fund oprational charactritic including xpn ratio, turnovr ratio and 3-yar fund tar rating. A thorough rviw of th availal data for rporting rror, outlir and othr dicrpanci lav u with an unalancd panl of orvation which includ a total of 507 ditinct fund. 7

8 For th timation of fund prformanc w follow th rlvant tudi conductd in a non-paramtric framwork namly Murthi t al (1997), Bao and Funari (2001, 2003), Daraio and Simar (2006) that mploy a input varial fund cot and man fund rturn a output. In particular, in ordr to maur fund fficincy w pcify two input xpn ratio and turnovr ratio and on output man rturn. Fund harholdr ar chargd with variou cot that ar aociatd with managing, adminitrativ, oprating, advrtiing or markting xpn uch a 12-1 f. Thrfor, a typical maur of a fund xpn i th annual xpn ratio that i xprd a a portion of fund avrag at. Turnovr ratio i conidrd a an additional input varial (Murthi t al 1997) and gag th information-inducd trading activity of a fund managr during a yar. Th ucc of a fund otain whn it managr achiv uprior portfolio rik-adutd rturn through uying and lling curiti in a cot-ffctiv mannr. Although, a high turnovr ratio indicat an activ managr that ngag into markt timing or/and tock picking tratgi in th puruit of profital invtmnt opportuniti thi might ntail incrad cot that ultimatly rod fund rturn (Elton t al., 1993, Indro t al., 1999). In th contxt of th cond tag analyi w includ fund rik, total at undr managmnt, Morningtar tar rating and normalizd flow. Annualizd tandard dviation of fund rturn ha n includd a rik varial. Star rating i an innovativ rik-adutd, pr-group fund prformanc valuation ytm that ha n provd to xrt ignificant influnc on rtail mutual fund invtor (Dl Gurcio and Tkac FQA, 2008). To control for th rikin of th fund rlativ to th markt w opt for an annual markt-adutd rturn of th fund. Th annual markt adutd rturn i calculatd a th dviation of fund rturn from th mdian rturn (DMR) of th whol ampl. Finally, w hav computd annual flow for ach fund at yar t following th prcntag at growth rat nt of apprciation, namly ( TNA t (1 rt ) TNAt 1 ) / TNAt 1, whr TNA t rprnt th fund total at at th nd of yar t and r t i it rturn ovr yar t. Our ampl pan 20 diffrnt invtmnt catgori dfind y Morningtar. 8

9 3.2 Stochatic frontir pcification for US fund fficincy Studi that attmpt to maur oprational fficincy ar ranchd into two path that i paramtric approach incorporating conomtric modl (Stochatic Frontir Approach, Thick Frontir Approach, and Ditriution Fr Approach) and nonparamtric approach applying linar programming tchniqu (Data Envlopmnt Analyi and Fr Dipoal Hull Analyi). Yt, no connu ha n rachd aout th appropriat timation mthodology. In thi papr w opt for th paramtric timation a in Aignr t al. (1977). To thi nd, w mploy a function for US fund rturn that tak th form: R it = f ( N it, Z it ) v it u it (1) whr R it dnot orvd fund rturn for i at yar t, N i a vctor of fund pcific varial affcting thi rturn and Z i a vctor of control varial. N includ two input: xpn ratio and turnovr ratio and on output man rturn. Z compri th CBOE implid volatility indx VIX that rflct markt prcption of th futur rturn and a ond quality prad maur that i calculatd a th diffrnc twn BAA-ratd ond and AAA-ratd ond. W hav includd th two varial o a to captur oth havioral conidration and markt-wid crdit rik condition that ar crucial for portfolio managr dciion. Th lat componnt of quation 1 ar of particular intrt for thi papr a v it corrpond to random fluctuation and i aumd to follow a ymmtric normal ditriution around th frontir whra u it account for th fund fficincy compard to th t-practic lvl within th indutry and follow a half-normal ditriution. Th aov pcification ha n applid in th litratur, ut in th contxt of nonparamtric analyi (DEA) whr fund rturn i conidrd th ky output varial ( Murthi t al and Murthi and Choi, 2001, and Bao and Funari, 2001, Lozano and Gutirz, 2008). To thi nd, th prnt functional form of Equation (1) rprnt th undrlying production function of a typical fund. 9

10 In addition, in th mpirical timation w fit a flxil tranlog pcification that tak into account non-linariti. Th tranlog function tak th form:!"!! =!!!!!"!! 1 2!!"!"#!!"#!!!!!!!"#! 1 2!!"!"#!!"#! 1 2!!"!"#!!"#!!!!!!!!! 1 2!!!!!!!!"#!!!!!"#!!!!!!!!!!!! ±!! (2)!,whr a aov whr R it dnot orvd fund rturn for i at yar t, N i a vctor of fund pcific varial affcting thi rturn and Z i a vctor of control varial. Standard linar homognity and ymmtry rtriction in all quadratic trm of th tranlog pcification ar impod, whilt w alo includ dummi to captur any diffrnc acro pcific group (clutr) of US fund and tim ffct. Th tochatic frontir modl of Equation (2) i timatd via a maximum liklihood procdur paramtrizd in trm of th varianc paramtr 2 σ = 2 ε σ 2 u σ and λ = v σ / u σ. ε 3.3 US fund fficincy cor Tal 2 prnt th avrag fficincy cor of US fund ovr th priod xamind. W alo rport th volution of man fficincy cor of our ampl fund for th priod of analyi. 10

11 Tal 2: US fund fficincy ovr tim. Yar Man Std. Dviation Max Min Avrag Not: timation of US fund fficincy uing a tochatic frontir analyi. Th fficincy cor ar drivd from paramtr timat of a tranlog function pcification. Sourc: Author timation. Th rult highlight that with th xcption of two yar, 2002 and 2008, a yar which wa markd y th ffct of th gloal financial crii throughout th financial ytm, fund man fficincy rmain at rlativly high lvl. Th avrag fficincy cor acro all US fund i 74%, a quit high valu. Anothr intrting fatur i rvald y th diprion of fficincy cor, which rach it hight valu during 2002 and 2008 a prviouly indicating utantial htrognity of fund in trm of fficincy. Thi do not com a a urpri givn th cataclymic ffct in financial markt if th rcnt crdit crunch. Thr i alo om fficincy variaility acro US no-load mutual fund. In light of th influntial tudi of Sharp (1992) and Brown and Gotzmann (1997) that provid vidnc of th importanc of tyl on fund prformanc man fficincy cor acro diffrnt catgori of fund ar rportd in Tal 3. Prliminary vidnc on a poitiv rlation twn at iz and fficincy otain from th lat column of Tal 3 inc fund that long to th thr Larg catgori (Larg Blnd, Larg Valu and Larg Growth) xhiit th hight avrag fficincy cor. On th othr hand, Tchnology Fund xhiit th lowt lvl of fficincy a rult that contradict th finding of Sngupta (2003). Finally, it appar that portfolio of no-load fund invtd in Financial Sctor hav prformd rlativly wll conidring th unfavoural vnt that unfoldd during 2008 crii in th particular ctor. Th lattr could proaly crditd to kilful managmnt on th part of mutual fund managr of th pcific 11

12 catgory. Tal 3: US fund fficincy pr invtmnt catgory Morningtar catgory Avrag Communication Conumr Dicrtionary Conumr Stapl Equity Enrgy Financial Halth Indutrial Larg Blnd Larg Growth Larg Valu Mid-Cap Blnd Mid-Cap Growth Mid-Cap Valu Micllanou Sctor Small Blnd Small Growth Small Valu Tchnology Utiliti Natural Rourc No. of orvation Not: timation of US fund fficincy uing a tochatic frontir analyi. Th fficincy cor ar drivd from paramtr timat of a tranlog function pcification. Sourc: Author timation. Th aov fficincy cor ar drivd from a tochatic frontir analyi and to th t of our knowldg ar rportd for th firt tim in th litratur, a prviou fund fficincy cor hav n ad on non-paramtric mthod. Murthi t al. (1997) wr th firt to apply th DEA mthod to fund prformanc, whilt Murthi and Choi (2001) followd imilar mthodology. Efficincy cor ar imilar to our, though thy ar not ntirly comparal du to diffrnc in th ampl. Morovr, Sngupta (2003) focu on portfolio prformanc and rportd that 70% of th xamind portfolio wr rlativly fficint, ut with ignificant dviation dpnding on th catgory of fund. Othr tudi focuing on US fund includ Andron t al. (2004) who xamind th fficincy of ral tat fund. Grgoriou (2003) and Grgoriou t al. (2005) focu on th hdg fund, whilt Krtn t al 12

13 (2011) hav mployd a larg dataa of US and Europan mutual fund. In a rcnt papr Prmachandra t al (2012) opt for a mi-paramtric two-tag DEA modl that dcompo th ovrall fficincy of a dciion-making unit into two componnt and dmontratd it applicaility y aing th rlativ prformanc of 66 larg mutual fund famili in th US ovr th priod In trm of fund prformanc in othr part of th world, Bao and Funari (2001) xamind th rlativ fficincy of Italian fund mploying DEA-ad modl, whilt Bao and Funari (2003, 2007) hav alo mployd DEA modl for analyzing th prformanc of thical mutual fund. Galagadra and Silvapull (2002) opt for DEA formulation to a th rlativ prformanc of Autralian mutual fund a Waton and Wickramanayak (2009) did in a rcnt papr. Annart t al (2003) mployd a Europan ampl of quity mutual fund. Uing Spanih fund data Lozano and Gutirz (2008) alo timatd fficincy cor uing DEA, whilt Garcia (2010) mploy Portugu pnion fund. Rlatd mpirical vidnc can found in th tudy of Santo t al (2005) who valuatd th prformanc of 307 Brazilian quity mutual fund mploying tochatic frontir. 3.4 Rvaling th undrlying dynamic: a Panl-Var modl Having drivd US fund prformanc w turn nxt our attntion to it main undrlying dtrminant whilt w tackl iu rlatd to undrlying dynamic and ndognity that hav not n addrd in th litratur 1. To thi nd, w xamin th undrlying cauality link twn US fund fficincy and om ky varial pcific to th indutry uch a fund flow, iz, rik and Morningtar rating. W opt for a vctor autorgrion (VAR) modl for a panl data t. Th VAR pcification fit th purpo of thi papr, givn th anc of 1 An important drawack of timating caual rlationhip twn fficincy and it main dtrminant that hav not n dalt in th litratur i th rultd ndognity ia quation (6) du to u a tandard OLS. W tackl ndognity ia hr y mploying a mor flxil framwork uing a panl-var analyi that will alo rval undrlying hort run dynamic. Entially all varial in th panl-var ar ntring a ndognou o a to al to rolv th cauality among thm. 13

14 concrt prior knowldg of which Hypoth propod y th litratur, and dicud aov, hold in th ca of US fund, and thry it dal with th iu of ndognity of th varial. Such a modl tak th form 2 : X it = µ i!x it"1 it, i =1,, N, t=1,,t. (3), whr X it i a vctor, for xampl in thi particular ca, of four random varial. Namly, X it i a vctor could includ th fficincy (EFF it ), flow (flow it ), at (at it ) and mot importantly (rik it ). Thu, Φ i an 4x4 matrix of cofficint, µ i i a vctor of m individual ffct and i,t ar iid ridual. A an xtnion to th 4x4 panl VAR pcification w would alo includ a fifth varial in our modl that i ithr rik or dviation of mdian rturn (DMR). In om dtail th ytm of quation (3) uild on th minal work of Sim (1980) Vctor Autorgriv (VAR) mthodology. Thi mthodology ( Lütkpohl, H., 2005) allow all varial within a ytm of quation to ntr a ndognou, hilt alo th hort run dynamic rlationhip could rvald. Entially, th VAR would allow u to xplor th undrlying caual rlationhip twn our main varial: fficincy and ky fund pcific varial. In thi typ of modl thr ar no rtriction impod concrning th dirction of cauality. For xampl, w would al to orv whthr fund fficincy impact upon, for xampl, fund iz or would it th ca of vic vra, ut alo a i-dirctional on. In th firt mpirical application of th panl-var, w opt for th following form: 2 For purpo of implicity of th xpoition w prnt a firt ordr 4x4 panl-var. 14

15 EFF flow rik it it it at = µ it = µ 10 = µ 20 = µ = 1 = 1 α EFF 11 = 1 α EFF = 1 21 α EFF it it α EFF it it 12 = 1 = 1 = 1 α α = 1 α 22 α 42 flow 32 flow flow it flow it it it α at α at 23 it = 1 = 1 α at 33 it = 1 = 1 α at 43 it = 1 = 1 α rik 13 it 14 = 1 = 1 α rik it α rik 24 it α rik it it 1i, t 2i, t 3i, t 4i, t (4) Th moving avrag (MA) form of th modl t EFF it, flow it, at it and rik it qual to a t of prnt and pat ridual 1, 2, 3 and 4 from th panl-var timation: EFF flow rik it it it at = γ = γ it = γ = γ = 1 = 1 = 1 = it 21 1it 31 1it 41 1it = 1 = 1 = 1 = it 22 2it 32 2it 42 2it 13 3it = 1 = it = 1 = it = 1 = it = 1 = it 24 4it 34 4it 44 4it 1i, t 2i, t 3i, t 4i, t (5) Undr th ndognity aumption th ridual will corrlatd and thrfor th cofficint of th MA rprntation ar not intrprtal. A a rult, th ridual mut orthogonal. W orthogonaliz th ridual y multiplying th MA rprntation with th Cholky dcompoition of th covarianc matrix of th ridual. Th orthogonalizd, or tructural, MA rprntation i: EFF = δ it it it at rik it = δ = δ 10 flow = δ = 1 = 1 = 1 β ε = it β β 21 1it β 31 1it ε ε ε 41 1it = 1 = 1 = 1 β = it β β 22 2it β ε 32 2it ε ε ε 42 2it 13 3it = 1 = it = 1 = 1 β ε 33 3it = 1 = 1 β β β ε ε ε 43 3it = 1 = 1 β 14 4it β β ε 24 4it β 34 4it ε ε ε 44 4it (6) 15

16 with β11 β12 β13 β14 β 21 β 22 β 23 β β31 β32 β33 β β 41 β 42 β 43 β = ε1 ε 2 P ε 3 ε 4 it it it it = P 1 1it 2it 3it 4it (7), whr P i th Cholky dcompoition of th covarianc matrix of th ridual: Cov( Cov( Cov( Cov( 1it 2it 3it 4it,, 1it,, 1it 1it 1it ) Cov( ) Cov( 1it ) Cov( ) Cov( 2it 3it 4it,, 2it,, 2it 2it 2it ) Cov( 1it ) Cov( ) Cov( ) Cov( 2it 3it, 4it 3it,,, 3it 3it ) Cov( 1 it, 4it ) ) Cov( 2it, 4it ) = ) ( 3, 4 ) PP Cov it it ) Cov( 4, 4 ) it it 3it 1 (8) Uing th aov panl-var individual htrognity in th lvl i nurd y introducing fixd ffct in th modl, dnotd µ i. Varial within th panl-var ar forward man-diffrncd uing th Hlmrt procdur (Lov and Zicchino, 2006). In addition, tandard rror of th impul rpon function ar calculatd and confidnc intrval gnratd with Mont Carlo imulation (Lov and Zicchino, 2006). 4. Empirical Rult of panl-var. 4.2 Do rik impact upon fund fficincy? Nxt w rport th Impul Rpon Function (IRF thraftr). IRF plot th rpon of ach varial within th panl VAR framwork to it own innovation and to th innovation of th othr varial. 16

17 From th firt row of Figur 1, right hand id cornr, w orv that a on tandard dviation hock of rik on fficincy i poitiv. It i worth noting that th impact follow an upward path that prit throughout th priod of analyi. In ffct thi finding indicat that th caual rlationhip run from rik to fund prformanc and carri a poitiv ign. Fund that tak larg t ar mor likly to finih with a uprior prformanc. Our finding provid vidnc in favor of Hypothi 1. Thi rult i of om importanc a it rval th dynamic rpon of fund prformanc to rik. Focuing on a tatic framwork could ia rult. Huang t al (2011) in a tatic long run modl how that fund that incra thir rik impd thir prformanc. Figur 1: Impul Rpon Function; th impact of rik. Impul-rpon for 1 lag VAR of ff at dmr rik (p 5) at at (p 95) at (p 5) rik rik (p 95) rik rpon of ff to ff hock rpon of ff to at hock (p 5) at at (p 95) at rpon of ff to dmr hock rpon of ff to rik hock (p 5) rik rik (p 95) rik rpon of at to ff hock rpon of at to at hock (p 5) at at (p 95) at rpon of at to dmr hock rpon of at to rik hock (p 5) rik rik (p 95) rik rpon of dmr to ff hock rpon of dmr to at hock (p 5) at at (p 95) at rpon of dmr to dmr hock rpon of dmr to rik hock (p 5) rik rik (p 95) rik rpon of rik to ff hock rpon of rik to at hock rpon of rik to dmr hock Error ar 5% on ach id gnratd y Mont-Carlo with 10 rp rpon of rik to rik hock Sourc: Author timation. Not: ff: fund SFA fficincy cor, t: fund total, nd-yar at, dmr: fund dviation from mdian rturn, rik: fund annualizd tandard dviation of rturn. Each diagram how th rpon of a varial to it own hock of on tandard dviation and hock of on tandard dviation of th rt of th varial. 17

18 Ovrall, th undrlying dgr of rik mrg a an important lmnt of fund prformanc, pcially in light of th incrad volatility that ha accompanid th outurt of th rcnt financial turmoil. Examining th rvr cauation w infr that th rpon of fund rik to fficincy innovation i ngativ, ignificant and ig in magnitud. According to Gorton and Ron (1995) an incra in fficincy cau an incra in rik lvl that i Hypothi 2, w find vidnc againt thi hypothi and in lin with Huang t al (2011). Thi rult i quit powrful and rval that fund y improving thir prformanc achiv uquntly lowr lvl of rik through ffctiv rik divrification. Howvr, it i intrting to not that during th firt two yar th impact of fficincy on rik i hrinking ut grow in th third priod whra it divrg away from quilirium thraftr. Thi variaility highlight th complxiti involvd in th rlationhip twn rik and fund prformanc, and in particular th undrlying hift in th dirction of cauality and th cinc of covarianc. Thr i an xtndd litratur that focu alo on rik ( Sngupta, 2003, Andron t al., 2004, Grgoriou, 2003, Grgoriou t al., 2005, Bao and Funari, 2001, yt it i for th firt tim that US fund fficincy i dirctly rlatd to rik in thi framwork. Morovr, in contrat to Murthi t al. (1997) hypothi that fficincy i ngativly corrlatd with fund ytmatic rik w find vidnc that th rpon of US fund fficincy to rik i poitiv. Thi finding rml th argumnt y Brk and Grn (2004) tating that managr of uccful fund aum highr rik in ordr to attract largr inflow and thrfor incra thir at-ad compnation. Howvr, th prnt vidnc go furthr to uggt that riky managr ar alo highly fficint. Tal 4 rport varianc dcompoition (VDC). Morovr, from th firt row, lat column, w orv that 19.2% of th forcat rror varianc of US fund fficincy i xplaind y rik. Thi i a quit dominant rult and highlight with grat mphai that US fund fficincy i prdominantly dtrmind y rik. On th othr hand and imilarly, 17.3% of th forcat rror varianc of rik i xplaind y fficincy, whilt 11.6% of rik forcat rror varianc i xplaind y at iz. To 18

19 thi nd, it i worth noting that oth US fund prformanc and at xplain portfolio rik. Rik hifting (Brown, Harlow and Stark 1996, Chvallir and Ellion 1997) may motivatd ithr y agncy iu or y tock lction/timing ailiti of fund managr. In th lattr ca, rik hifting may provd nficial for invtor whn activ managr trad in ordr to xploit thir uprior kill and prform ttr. Following thi conctur fund that incra thir rikin would dlivr uprior prformanc to thir invtor. It hould alo notd that th impact of a tim varying rik tratgy i trongly rlatd to th motivation of uch a tratgy. Thi would imply that whn fund managr ar ngaging into rik hifting tratgi purrd y lf-intrtd motiv thn w hould xpct no uprior prformanc. Tal 4: Varianc Dcompoition; th impact of rik. Eff At DMR Rik Eff At DMR Rik Eff At DMR Rik Sourc: Author timation. Not: ff: fund SFA fficincy cor, at: fund total, nd-yar at, dmr: Fund dviation from mdian rturn, Rik: Fund annualizd tandard dviation of rturn. W opt for a imulation of 10 and 20 priod ahad, notd y. Th tal rport th forcat rror varianc dcompoition of ach varial in th panl-var. 4.2 Do at iz, dviation from mdian rturn and Morningtar rating mattr? Figur 2, firt lin of diagram, rport th rpon of fficincy to hock of on plu/minu tandard dviation in at; fund dviation from mdian rturn; and latly Morningtar 3-yar tar rating. Figur 1 rport thr additional lin of diagram of th rpon of th rmaining varial in th panl-var. Thi th firt tim in 19

20 th litratur that vidnc i providd for th rlationhip twn ratting and fund prformanc. Figur 2: Impul Rpon Function: fund fficincy, at, dviation from rturn and Morning 3-yar rating. Impul-rpon for 1 lag VAR of ff at dmr rat (p 5) at at (p 95) at (p 5) rat rat (p 95) rat rpon of ff to ff hock rpon of ff to at hock (p 5) at at (p 95) at rpon of ff to dmr hock rpon of ff to rat hock (p 5) rat rat (p 95) rat rpon of at to ff hock rpon of at to at hock (p 5) at at (p 95) at rpon of at to dmr hock rpon of at to rat hock (p 5) rat rat (p 95) rat rpon of dmr to ff hock rpon of dmr to at hock (p 5) at at (p 95) at rpon of dmr to dmr hock rpon of dmr to rat hock (p 5) rat rat (p 95) rat rpon of rat to ff hock rpon of rat to at hock rpon of rat to dmr hock Error ar 5% on ach id gnratd y Mont-Carlo with 10 rp rpon of rat to rat hock Sourc: Author timation. Not: ff: fund SFA fficincy cor, at: fund total, nd-yar at, dmr: fund dviation from mdian rturn, rat: Morningtar 3-yar tar rating. Each diagram how th rpon of a varial to it own hock of on tandard dviation and hock of on tandard dviation of th rt of th varial. Contrary to th finding of Annart t al (2003) for th whol ampl w documnt ngativ rlationhip twn fund fficincy and at iz, firt rοw, cond u-diagram from th right. That i to ay th rpon of fficincy on on tandard dviation hock in at i ngativ, ut only in th vry hort run a it convrg to zro thraftr. Thi finding provid om vidnc in favor of Hypothi 2 and i conitnt with prviou tudi intr alia Chn t al (2004) documnting th xitnc of a ngativ ffct of at on fund prformanc. 20

21 From th firt row of Figur 2 w orv that a on tandard dviation hock of th fund dviation from mdian rturn on fficincy i poitiv in th firt priod ut thn thr i om markd fluctuation for convrging. Intrtingly th impact of Morningtar rating on US fund fficincy i pritntly ngativ ovr th whol priod, though it main impact tak plac within th firt two yar and convrg gradually thraftr. Thi i an important rult a it dmontrat that a hock in Morningtar rating, lt ay a downgrad, will rult in a dclin in fficincy of US fund. Similarly, th impact of a hock in fund fficincy on Morningtar rating i poitiv, and ig in magnitud, ovr th whol priod ( lat row, firt diagram from th lft). Thi finding rml th hypothi of Murthi t al (1997) who argu that fficincy i ngativly corrlatd with fund ytmatic rik indicating that high-rik fund ar charactrizd with low fficincy. In th litratur, it i for th firt tim that th Morningtar rating i linkd to US prformanc a maurd y SFA fficincy coring. Yt in th litratur thr ar tudi, Sharp (1998), that xamind th proprti of Morningtar maur and howd that th rik-adutd rating (RAR) gnratd y Morningtar catr rult imilar to th wll-known xc rturn Sharp ratio. Blak and Mory (2000) alo ttd th hypothi that th Morningtar rating ytm provid information on futur mutual fund prformanc for a ampl of US domtic quity fund and rachd wak vidnc that Morningtar hight-ratd fund outprform th nxt-tohight and mdian-ratd fund. In addition, Dl Gurcio and Tkac (2008) documntd a ignificant inflow for 5-tar fund and a rmarkal nitivity of invtor to tar upgrad or downgrad that i gaugd y inflow and outflow xprincd y fund. Nxt w provid mor dtail into th undrlying rlationhip twn th varial of th panl-var y man of varianc dcompoition (VDC), Tal 5. In particular, varianc dcompoition indicat th prcntag of th variaility in th varial of intrt, i.. US fund fficincy, that i attriutd to anothr varial, i.. Morningtar rating. W rport th ovrall aggrgatd ffct ovr 10 and 20 yar. From th firt row, lat column, w orv that 3.8% of th forcat rror varianc of US fund fficincy i xplaind y Morningtar rating. At and fund dviation 21

22 from mdian rturn art a much lowr contriution. On th othr hand, 4.8% of th forcat rror varianc of Morningtar rating i xplaind y US fund fficincy, ininuating a two-way caual rlationhip, in lin with th finding of th IRF aov. Tal 5: Varianc Dcompoition; th impact of Morningtar rating. ff at dmr rat ff at dmr rat ff at dmr rat Sourc: Author timation. Not: ff: fund SFA fficincy cor, at: fund total, nd-yar at, dmr: Fund dviation from mdian rturn, Rat: Morningtar 3-yar tar rating. W opt for a imulation of 10 and 20 priod ahad, notd y. Th tal rport th forcat rror varianc dcompoition of ach varial in th panl-var. 4.3 Do th flow affct fund fficincy? Studi focuing on fund flow rang from invtor raction to fund prformanc, to th rlationhip twn markt movmnt and fund flow and to th intraction twn fund cot and fund flow. To our t of knowldg, no tudy for ha xplicitly addrd th rlationhip twn fund flow and fficincy undr thi framwork. It i alo worth noting that th panl-var dimnion in thi intanc i 5x5. From th firt row, cond diagram from th lft, of Figur 3 w orv that a on tandard dviation hock of flow on fficincy i poitiv. It i worth noting that th impact follow an upward path in th firt two priod ut thn convrg to zro, whilt it magnitud i alo low. On th othr hand, th impact of fficincy on flow i ngativ which contradict arlir finding of Smith (1978), Ippolito (1992) and othr that improvd prformanc attract nw mony to fund. Howvr, orving th rpon of flow to a hock on fficincy (row 2, firt lft hand id, Figur 3) w can again infr that 22

23 th ngativ ffct i only tranitory and thn fad away. Thi could ut th rult of th ignificant outflow xprincd y mutual fund in light of th outurt of financial crii and thi proaly rquir furthr xploration. Figur 3: Impul Rpon Function; th impact of flow Impul-rpon for 1 lag VAR of ff flow at dmr rik (p 5) at at (p 95) at (p 5) rik rik (p 95) rik rpon of ff to ff hock rpon of ff to flow hock rpon of ff to at hock rpon of ff to dmr hock rpon of ff to rik hock (p 5) at at (p 95) at (p 5) rik rik (p 95) rik rpon of flow to ff hock rpon of flow to flow hock rpon of flow to at hock rpon of flow to dmr hock rpon of flow to rik hock (p 5) at at (p 95) at (p 5) rik rik (p 95) rik rpon of at to ff hock rpon of at to flow hock rpon of at to at hock rpon of at to dmr hock rpon of at to rik hock (p 5) at at (p 95) at (p 5) rik rik (p 95) rik rpon of dmr to ff hock rpon of dmr to flow hock rpon of dmr to at hock rpon of dmr to dmr hock rpon of dmr to rik hock (p 5) at at (p 95) at (p 5) rik rik (p 95) rik rpon of rik to ff hock rpon of rik to flow hock rpon of rik to at hock rpon of rik to dmr hock Error ar 5% on ach id gnratd y Mont-Carlo with 10 rp rpon of rik to rik hock Sourc: Author timation. Not: ff: fund SFA fficincy cor, flow: fund prcntag inflow/outflow t: fund total, nd-yar at, dmr: fund dviation from mdian rturn, rik: fund annualizd tandard dviation of rturn. Each diagram how th rpon of a varial to it own hock of on tandard dviation and hock of on tandard dviation of th rt of th varial. Tal 6 rport varianc dcompoition (VDC). Morovr, from th firt row, lat column, w orv, onc mor, that 19.2% of th forcat rror varianc of US fund fficincy i xplaind y rik. Thi i th dominant rult, whilt flow xplain littl of th forcat rror varianc of US fund fficincy. 23

24 Tal 6: Varianc Dcompoition; th impact of flow. Eff Flow At DMR Rik Eff Flow At DMR Rik Eff Flow At DMR Rik Sourc: Author timation. Not: ff: fund SFA fficincy cor, at: fund total, nd-yar at, flow: fund prcntag inflow/outflow, dmr: Fund dviation from mdian rturn, rik: rund annualizd tandard dviation of rturn. W opt for a imulation of 10 and 20 priod ahad, notd y. Th tal rport th forcat rror varianc dcompoition of ach varial in th panl-var. 4.4 Routn analyi; a gnral panl-var A part of tting th routn of our rult w opt in thi ction a gnral panl- VAR pcification with dimnion 6x6. To thi nd, Figur 4 rport th IRF rulting from a panl-var formulation incorporating all varial of intrt. Th rult ar in lin with th on rportd aov and provid furthr vidnc favoring th importanc of rik in xplaining th variation of fund fficincy. Etimatd IRF ar conitnt with Hypothi 3 and 4. 24

25 Figur 4: Impul Rpon Function for a 6x6 panl-var. Impul-rpon for 1 lag VAR of ff flow at dmr rik rat (p 5) at at (p 95) at (p 5) rik rik (p 95) rik (p 5) rat rat (p 95) rat rpon of ff to ff hock rpon of ff to flow hock rpon of ff to at hock (p 5) at at (p 95) at rpon of ff to dmr hock rpon of ff to rik hock (p 5) rik rik (p 95) rik rpon of ff to rat hock (p 5) rat rat (p 95) rat rpon of flow to ff hock rpon of flow to flow hock rpon of flow to at hock (p 5) at at (p 95) at rpon of flow to dmr hock rpon of flow to rik hock (p 5) rik rik (p 95) rik rpon of flow to rat hock (p 5) rat rat (p 95) rat rpon of at to ff hock rpon of at to flow hock rpon of at to at hock (p 5) at at (p 95) at rpon of at to dmr hock rpon of at to rik hock (p 5) rik rik (p 95) rik rpon of at to rat hock (p 5) rat rat (p 95) rat rpon of dmr to ff hock rpon of dmr to flow hock rpon of dmr to at hock (p 5) at at (p 95) at rpon of dmr to dmr hock rpon of dmr to rik hock (p 5) rik rik (p 95) rik rpon of dmr to rat hock (p 5) rat rat (p 95) rat rpon of rik to ff hock rpon of rik to flow hock rpon of rik to at hock (p 5) at at (p 95) at rpon of rik to dmr hock rpon of rik to rik hock (p 5) rik rik (p 95) rik rpon of rik to rat hock (p 5) rat rat (p 95) rat rpon of rat to ff hock rpon of rat to flow hock rpon of rat to at hock rpon of rat to dmr hock rpon of rat to rik hock Error ar 5% on ach id gnratd y Mont-Carlo with 10 rp rpon of rat to rat hock Sourc: Author timation. Not: Eff: fund SFA fficincy cor, At: Fund total, nd-yar at, Flow: Fund prcntag inflow/outflow, DMR: Fund dviation from mdian rturn, Rik: Fund annualizd tandard dviation of rturn Each diagram how th rpon of a varial to it own hock of on tandard dviation and hock of on tandard dviation of th rt of th varial. Similarly, Tal 7 rport VDC that provid vidnc in lin with th on rportd aov. Onc mor, rik i th dominant dtrminant of US fund fficincy a 28.7% of th lattr i xplaind y th formr. Morningtar rating alo play an important rol a 4.1% of fficincy i xplaind y th rating. Intrtingly w orv that for longr horizon th variaility of US fund fficincy attriutd to rik amount to 46.32%. 25

26 Tal 7: Varianc Dcompoition Eff Flow At DMR Rik Rating Eff Flow At DMR Rik Rating Eff Flow At DMR Rik Rating Sourc: Author timation. Not: Eff: fund SFA fficincy cor, Flow: Fund prcntag inflow/outflow, At: Fund total, nd-yar at, DMR: Fund dviation from mdian rturn, Rik: Fund annualizd tandard dviation of rturn, Rating: Morningtar 3-yar tar rating. W opt for a imulation of 10 and 20 priod ahad, notd y. Th tal rport th forcat rror varianc dcompoition of ach varial in th panl-var. 4.5 IRF and VDC for fund groupd according to iz At iz rmain a fundamntal iu in th proc of profional mony managmnt. Svral tudi hav highlightd th rlationhip twn fund iz and prformanc intr alia Grinlatt and Titman (1989), Brk and Grn (2004), Chn t al (2004) all raching contradictory rult. In om ca, mallr fund achiv uprior prformanc cau thy can uy/ll curiti without affcting advrly thir pric. On th othr hand, a fw rarchr (Golc 1996) liv that mallr fund may confrontd with highr tranaction cot rulting from diconomi of cal that rod prformanc. Thrfor, w t off to hypothiz a diffrnt rlationhip twn th varial undr xamination acro variou fund iz. Murthi t al (1997) found that fund fficincy cor drivd from a DEA approach wr not rlatd to at iz. To thi nd, w divid our ampl into four group (quartil) on th ai of fund iz and rport th rlvant IRF and VDC for ach ugroup. 26

27 Figur 5 to 8 prnt IRF for fund that long to th variou at group whil Tal 8 ummariz th rpctiv VDC. From th firt row of Figur 5 w infr that th ffct of on tandard dviation hock of rik on fund fficincy i poitiv and rlativly larg in magnitud for mallr fund. Th pak rpon of fficincy to a hock in rik occur aftr two yar whil it convrg to quilirium thraftr. Howvr, if w xamin th rpon of rik to a hock in fficincy w orv that i ngativ implying a rvr fdack. Thi man that a hock that would incra fund fficincy rduc portfolio rik. Figur 5: Impul Rpon Function, Small Fund Impul-rpon for 1 lag VAR of ff flow dmr rik (p 5) rik rik (p 95) rik rpon of ff to ff hock rpon of ff to flow hock rpon of ff to dmr hock rpon of ff to rik hock (p 5) rik rik (p 95) rik rpon of flow to ff hock rpon of flow to flow hock rpon of flow to dmr hock rpon of flow to rik hock (p 5) rik rik (p 95) rik rpon of dmr to ff hock rpon of dmr to flow hock rpon of dmr to dmr hock rpon of dmr to rik hock (p 5) rik rik (p 95) rik rpon of rik to ff hock rpon of rik to flow hock rpon of rik to dmr hock Error ar 5% on ach id gnratd y Mont-Carlo with 500 rp rpon of rik to rik hock Sourc: Author timation. Not: Eff: fund SFA fficincy cor, Flow: Fund prcntag inflow/outflow, DMR: Fund dviation from mdian rturn, Rik: Fund annualizd tandard dviation of rturn. Each diagram how th rpon of a varial to it own hock of on tandard dviation and hock of on tandard dviation of th rt of th varial. A for th rt varial, a larg part of fund flow variation i xplaind y chang in th total rikin of th portfolio pcially for th iggt fund. Thi finding i rlatd to th conctur of Chvallir and Ellion (1997) who argu that fund flow- 27

28 prformanc rlationhip could rv a an implicit incntiv chm for managmnt compani to incra or dcra rikin with th aim of attracting nw mony. So, in light of th wll-documntd rlationhip twn flow and rik w from lin 2, th diagram on th right hand id, of Figur 5 that a on tandard dviation hock in rik on fund flow i poitiv and larg in magnitud for mall fund. Howvr, it i intrting to not that for th othr catgori of fund, namly mall mdium, mdium-larg, and larg ( Figur 6-8) w orv a ngativ rpon of flow to rik. Thi man that an incra in fund total rikin rduc flow. Thu, fund flow rpond to rik (Chvallir and Ellion 1997) ut not in uniqu way, a th iz of fund i dtrimntal. Figur 6: Impul Rpon Function, Small- mdium fund Impul-rpon for 1 lag VAR of ff flow dmr rik (p 5) rik rik (p 95) rik rpon of ff to ff hock rpon of ff to flow hock rpon of ff to dmr hock rpon of ff to rik hock (p 5) rik rik (p 95) rik rpon of flow to ff hock rpon of flow to flow hock rpon of flow to dmr hock rpon of flow to rik hock (p 5) rik rik (p 95) rik rpon of dmr to ff hock rpon of dmr to flow hock rpon of dmr to dmr hock rpon of dmr to rik hock (p 5) rik rik (p 95) rik rpon of rik to ff hock rpon of rik to flow hock rpon of rik to dmr hock Error ar 5% on ach id gnratd y Mont-Carlo with 500 rp rpon of rik to rik hock Sourc: Author timation. Not: Eff: fund SFA fficincy cor, Flow: Fund prcntag inflow/outflow, DMR: Fund dviation from mdian rturn, Rik: Fund annualizd tandard dviation of rturn. Each diagram how th rpon of a varial to it own hock of on tandard dviation and hock of on tandard dviation of th rt of th varial. 28

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