On the Style Swtchng Behavor of Mutual Fund Managers Bart Frjns Auckland Unversty of Technology, Auckland, New Zealand Auckland Centre for Fnancal Research Aaron Glbert Auckland Unversty of Technology, Auckland, New Zealand Auckland Centre for Fnancal Research Remco C. J. Zwnkels* Erasmus School of Economcs, Erasmus Unversty Rotterdam, The Netherlands Auckland Centre for Fnancal Research We would lke to thank semnar partcpants at Monash Unversty for ther useful comments and suggestons. *Correspondng author. Erasmus Unversty Rotterdam, Erasmus School of Economcs. P.O.Box 1738, 3000DR, Rotterdam, The Netherlands. E: zwnkels@ese.eur.nl; T: +31 10 408 1428; F: +31 10 408 9165. - 1 -
On the Style Swtchng Behavor of Mutual Fund Managers Ths Verson: July 2012 Abstract Ths paper develops an emprcally testable model that s closely related to theoretcal model for style swtchng behavor of Barbers and Shlefer (2003). We mplement ths model to examne the style swtchng behavor of US domestc equty mutual fund managers. Usng monthly data for 2,044 mutual funds over the perod 1961-2010, we fnd strong evdence for style swtchng behavor: on average nearly 53% of the funds n our sample engage n style swtchng. Overall, we fnd that growth funds tend to behave more as postve feedback (momentum) traders, whereas value funds tend to behave more as negatve feedback (contraran) traders. Lnkng the style swtchng behavor to fund characterstcs, we typcally fnd that funds that engage more aggressvely n style swtchng tend to be younger and have hgher total expense ratos. Lnkng the style swtchng behavor to rsk-adjusted performance, we fnd no evdence of the ablty of style swtchng to generate postve alpha. JEL Codes: C22; C58; G11 Keywords: Mutual Fund Managers; Style Swtchng; Feedback Tradng. - 2 -
1. Introducton One of the great success stores n fnance s the development of the mutual fund ndustry. Ths ndustry has seen tremendous growth n the past decades, both n terms of nvested captal and number of funds. Wth ths enormous growth n number and dversty, many funds classfy themselves nto nvestment styles to provde nvestors wth some nformaton on the asset allocaton of the fund. These styles have flown out of the popularty of certan nvestment strateges among mutual fund nvestors, such as growth or value stocks and small or large cap stocks (Teo and Woo, 2004). Gven that these strateges are selected for ther perceved ablty to produce postve alpha, pursung such a strategy should play a major role n determnng the returns that a fund produces from followng the strategy. However, as Barbers and Shlefer (2003) pont out, the returns to partcular styles are not constant and can be thought of as followng a lfe cycle, where returns may go from outperformng ntally to underperformng as market condtons change or the characterstc s prced out of the market. As such, returns for funds dentfyng wth a partcular style wll be drven, to a large degree, by the performance of the style. Of nterest s the effect that such changes n style performance have on funds that are commtted to a partcular style. Competton between mutual funds for fund flow s ferce and s largely drven by the recent performance of the fund (Srr and Tufano, 1998). As a result, there are consderable ncentves for funds to outperform other funds wthn the same asset style. 1 As fund returns are largely drven by the proclamed nvestment style of the fund, one way to acheve outperformance s by strategcally (and temporarly) devatng from the 1 Brown, Harlow, and Starks (1996), for nstance, show that mutual funds engage n so-called tournament behavor, where funds take on addtonal rsks n later evaluaton perods f they are beng outperformed by peers. - 3 -
proclamed nvestment style and ncreasng exposure to styles that are expected to perform better. Ths has become known as style tmng or style swtchng. In ths paper, we examne the style swtchng behavor of US mutual fund managers usng the framework of Barbers and Shlefer (2003). Barbers and Shlefer (2003) propose a theoretcal model of style nvestng, where ndvdual nvestors classfy assets nto styles and allocate ther nvestments at the style level. Barbers and Shlefer (2003) further propose a mechansm of how nvestors allocate money to partcular nvestment styles and suggest that nvestor act as feedback traders, comparng the relatve past performance of the dfferent nvestment styles. Ths model can explan several stylzed facts observed n fnancal markets, such as style momentum and excess comovement of assets wthn a style. The emprcal predctons of the model proposed by Barbers and Shlefer (2003) have been valdated by several studes, e.g. Teo and Woo (2004) and Froot and Teo (2008). However, we are not aware of any study that estmates an emprcal model along the lnes of Barbers and Shlefer (2003). Based on Froot and Teo (2008), who fnd that nsttutonal nvestors also allocate more at the style level than at the ndvdual stock level, we postulate that fund managers dsplay smlar behavor as ndvdual nvestors n terms of ther asset allocaton to dfferent styles, and actng as feedback traders. As such, we connect to several lnes of lterature, such as style nvestng, style swtchng, as well as and nvestor behavor. We mplement the model of Barbers and Shlefer (2003) emprcally usng the framework proposed by Brock and Hommes (1997). Brock and Hommes (1997) consder a market for a sngle asset, where nvestors can swtch between dfferent tradng strateges over tme condtonal on ther relatve performance n recent perods. Swtchng between these strateges occurs by means of a multnomal choce functon. Ths functon has several - 4 -
desrable features. Frst, t ntroduces contnuous tme-varyng exposures to dfferent nvestment styles and therefore allows us to modfy a model wth statc exposures nto a dynamc one. Second, ths functon s very flexble and can nclude any varable that may trgger fund managers to change ther nvestment style. We use relatve past performance, followng Barbers and Shlefer (2003) and Brock and Hommes (1998), to assess whether fund managers engage n feedback tradng. Thrd, ths functon leads to a parsmonous model specfcaton, whch (n the smplest specfcaton) only consumes one addtonal degree of freedom compared wth a statc specfcaton. We use the survvorshp-free CRSP mutual fund database over the perod December 1961- September 2010 to examne the swtchng behavor n US domestc equty funds. We classfy funds nto dfferent styles based on ther Lpper Classfcaton code based on sze (Large, Mult, Md, and Small cap) and value-growth orentaton (Value, Centre, and Growth). Ths produces a 4 3 matrx of 12 dfferent styles. To assess the swtchng behavor of fund managers, we obtan four benchmark portfolos/styles: large-value, small-value, largegrowth, and small-growth from Kenneth French s webste. 2 The selecton of these four styles allows us to examne the swtchng behavor of fund managers n both the sze and valuegrowth dmensons jontly and separately. We fnd strong evdence for feedback-nduced style swtchng n our sample, over 50% of the funds n our most basc specfcaton. These results corroborate the fndngs of Froot and Teo (2008), who also fnd strong support for style-level tradng by US domestc equty fund managers. Interestngly, we fnd that fund managers not only act as postve feedback or 2 Data are avalable from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ndex.html. The selecton of these four styles allows for swtchng n the sze and value-growth dmenson. - 5 -
momentum traders (as suggested by Barbers and Shlefer, 2003), but there s also a consderable number of fund managers that act as negatve feedback or contraran traders. 3 Ths fndngs has also been observed n the tradng behavor of ndvdual nvestors n ndex funds (Goetzmann and Massa, 2002) and style funds (Blackburn et al., 2011), but to date has not been documented n the tradng behavor of fund managers. Consstent wth Froot and Teo (2008) and along the lnes of Barbers and Shlefer (2003), we fnd strong support for the exstence of so-called twn styles, 4 where nvestors swtch between styles at opposte ends of the spectrum. For the funds that engage n style swtchng, the majorty tends to do so n both the value-growth and the sze dmenson. In addton, we fnd that the style swtchng behavor,.e. beng a postve or negatve feedback trader hghly depends on the nvestment style, where managers of growth funds tend to base ther swtchng strategy on a postve feedback rule (.e. ncreasng exposure to styles that have performed relatvely well n the recent past), whereas managers of value funds tend to base ther swtchng strategy on a negatve feedback rule (.e. ncreasng exposure to styles that have performed relatvely poor n the recent past). Ths has been observed n the tradng behavor of ndvdual nvestors (Blackburn et al., 2011) but has not yet been documented n the behavor of nsttutonal nvestors. When we examne the relatonshp between fund characterstcs and swtchng behavor n a cross-sectonal test, we fnd that younger mutual funds and mutual funds wth hgher total 3 We follow Goetzmann and Massa (2002) n our defntons of momentum and contraran traders, where a momentum trader s defned as a trader who buys after a recent prce ncrease and a contraran trader buys after a recent prce decrease. 4 Twn styles refer to the asset allocaton decson, where an ncrease n the allocaton to, say, value stocks s fnanced by a decrease n the allocaton to ts twn style, growth stocks, etc. - 6 -
expense ratos engage n more aggressve swtchng behavor. For funds that swtch aggressvely n the sze dmenson, we also fnd a sgnfcantly postve relatonshp wth the turnover of the fund. Fnally, we evaluate whether style swtchng leads to ncreased outperformance for mutual funds. 5 We do ths by obtanng rsk-adjusted outperformance (alpha) from the Carhart (1997) 4-factor model and regress ths alpha on the degree by whch funds swtch and several other fund characterstcs. Consstent wth Brown et al. (2011), we fnd that style swtchng does not lead to outperformance. We do, however, fnd that when funds that apply a postve feedback rule n the short run (1 to 6 months), there s no sgnfcant mpact on alpha. However, when fund managers apply such a strategy n the long run (7 to 12 months) there s a sgnfcant deteroraton n outperformance. In contrast, fund managers that apply a negatve feedback tradng rule n the short run see a sgnfcant deteroraton n outperformance, whereas those that apply such a strategy n the long run see no effect on outperformance. Our work s related to several emprcal studes on style nvestng. It closely relates to Froot and Teo (2008), who examne style nvestng for nsttutonal nvestors (US domestc equty funds) and show that nsttutonal nvestors ndeed allocate ther nvestments at the style level. They also provde emprcal evdence for allocatons beng made accordng to the twn-styles conjecture of Barbers and Shlefer (2003), where ncreased allocatons towards 5 Several studes have examned style tmng n mutual funds, however, evdence of whether ths style tmng s proftable s mxed. For example, Swnkels and Tjong-A-Tjoe (2007) examne three styles, market tmng, value-growth and sze, and fnd proftable swtchng wth regards to market tmng and value-growth but not sze. Budono and Martens (2009) test a model wth all three styles, market tmng, value-growth and sze, and fnd that managers that tme styles generate sgnfcant outperformance. Grnblatt et al. (1995) fnd outperformance of momentum traders compared to other funds. By contrast, Brown, Harlow, and Zhang (2011) shows that funds swtch aggressvely,.e. have hgh style volatlty, underperform relatve to fund wth less style volatlty on a rsk adjusted bass. - 7 -
small caps tend to be fnanced by decreased allocatons towards large caps, etc. We confrm ths fndng of Froot and Teo (2008) and extend ther work by showng that fund managers engage n twn style tradng ether as postve or negatve feedback traders. Ths largely depends on the nvestment style of the fund. In addton, our paper relates to Brown et al. (2011) who study style swtchng (measured by style volatlty) and relate ths to rsk-adjusted outperformance of mutual funds. In lne wth Brown et al. (2011), we confrm that funds that swtch aggressvely between styles have lower rsk adjusted performance. We extend ther work by showng that style volatlty can be explaned by postve and negatve feedback tradng and show that both these strateges have a dfferent mpact on rsk adjusted outperformance (postve feedback tradng beng worse when used wth longer look back perods and negatve feedback tradng beng worse when used wth shorter look back perods). Wermers (2012) further notes that style drft, for a sgnfcant part, s caused by actve management. In addton, Wermers (2012) fnds that managers tend to be style chasers ; ths s n lne wth our fndngs of feedback tradng at the style level. Fnally, ths paper s closely related to several studes on nvestor behavour (.e. feedback tradng). An mportant contrbuton n ths respect comes from Grnblatt, Ttman and Wermers (1995), who fnd that 77% of mutual funds have a tendency to buy past wnnng stocksbange (2000) shows that stock portfolo adjustments of ndvdual nvestors reflect past market movements, consstent wth postve feedback tradng. In addton, Kem and Madhaven (1995) document both momentum and contraran tradng by nsttutonal nvestors. Choe, Kho, and Stulz (1999) and Froot, O Connell, and Seasholes (2001) report feedback tradng by nsttutonal nvestors at the country level. Goetzmann and Massa (2002) - 8 -
examne the tradng behavour of ndvdual nvestors n ndex funds and fnd that some nvestors act as postve feedback traders (who they label momentum traders ) and some as negatve feedback traders (who they label contraran traders ). In an extenson, Blackburn et al. (2011) study the tradng behavour of ndvdual nvestors n style and mult-style funds (value, growth and value-growth funds). They fnd that nvestors adopt dfferent tradng strateges dependng on the characterstcs of the assets beng traded, where growth nvestors tend to follow momentum buy strateges and value nvestors tend to follow a contraran buy strategy. We contrbute to ths lterature by showng that nsttutonal nvestors also follow momentum and contraran tradng strateges, and, n lne wth Blackburn et al. (2011) we fnd that managers of growth funds follow more momentum strateges, whereas managers of value funds follow more contraran strateges. The remander of the paper s organzed as follows. Secton 2 presents our feedback tradng model. In Secton 3, we explan the data and methodology appled to estmate the model, and Secton 4 presents the results. Secton 5 concludes. 2. Model Barbers and Shlefer (2003) propose a model of style nvestng, where the market s populated by nvestors who can swtch between nvestment styles based on the past relatve performance of these styles (referred to as swtchers) and fundamental traders, who act as arbtrageurs. In ths secton, we develop an emprcally testable model along the lnes of Barbers and Shlefer (2003), where, nstead of ndvdual nvestors, mutual fund managers swtch between nvestment styles based on the styles relatve past performance. - 9 -
Accordng to Barbers and Shlefer (2003), swtchers allocate more captal to a partcular style f t performed relatvely well n the recent past and fnance ths by allocatng less to styles wth relatvely poor past performance. These swtchers are assumed to have a specfc look-back perod over whch they compare the relatve performance of the dfferent nvestment styles. They further have a specfc degree of style persstence (.e. how senstve they are to dfferences n relatve past performances of the nvestment styles). A further feature s that although nvestors are wllng to swtch between styles, they are less wllng to swtch between asset classes,.e. nvestors may be wllng to swtch between value and growth, but are less wllng to swtch between, e.g., equtes and bonds. Ths mples that the swtchng between styles s mostly self-fnanced wthn a specfc asset class. Fnally, Barbers and Shlefer (2003) suggest that swtchers choose to swtch between so-called twnstyles, where an ncreased allocaton to growth stocks s fnanced by a decreased allocaton to value stocks and an ncreased allocaton to small-cap stocks s fnanced by a decreased allocaton to large-cap stocks, etc. We emprcally mplement the model of Barbers and Shlefer (2003) usng a dscrete choce model along the lnes of Mansk and McFadden (1981) and concepts of the adaptve ratonal equlbrum framework proposed by Brock and Hommes (1997). Brock and Hommes (1997) propose a model where economc agents use predctors (whch are functons of past nformaton) and choose between these predctors usng a dscrete choce model, selectng the predctor (or puttng more fath n the predctor) that has produced the hghest proft or the lowest forecast error n the recent past. Ths generates a dynamcs where, over tme, agents swtch between dfferent predctors and adjust ther demand for assets accordngly. 6 The 6 See Brock and Hommes (1998) for the complex dynamcs that such a model can generate n asset prces. - 10 -
degree to whch these agents swtch between dfferent predctors s controlled by a so-called ntensty of choce parameter, and captures the agents senstvty to dfferences n the profts or forecast errors of the dfferent predctors. At each pont n tme, fund managers examne the past performance of K dfferent nvestment styles, where k = 1,, K. We defne the past performance of style k as, k t1 J r, (1) j1 k t j where k rt s the return on nvestment style k n perod t, s the past performance measure of nvestment style k n perod t 1, and j s the number of perods that the fund manager looks back ( j = 1,, J). 7 k t1 Followng Brock and Hommes (1997, 1998), we assume that the swtchng between styles follows a multnomal swtchng rule whch compares the relatve performance of the varous nvestment styles. Accordng to ths swtchng rule, the weghts that a manager puts on nvestment style k s defned as k w t t1 exp{ ( exp{ k k t1 k ( t1 )} )} 1 lk 1 exp{ ( l t1 k t1, (2) )} 7 Barbers and Shlefer (2003) use a geometrc decay process to capture the memory of nvestors. We apply a dscrete measure followng Blackburn et al. (2011). - 11 -
where k wt t 1 s the weght fund manager puts on strategy k at tme t, condtonal on tme t 1 nformaton, and γ s the ntensty of choce parameter, whch captures the manager s senstvty to the past profts of dfferent nvestment styles and determnes the aggressveness by whch the fund manager swtches between dfferent nvestment styles. For nstance, f = 0, the fund manager does not respond to dfferences n relatve proftablty, and n ths case w w k k t t1. At the other extreme, f the fund manager wll fully allocate hs nvestments to the style that has had the hghest relatve performance. A postve value for γ ndcates that the fund manager puts more weght on the style that performed relatvely well n the recent past and therefore behaves as a postve feedback (momentum) trader. A negatve value for γ ndcates that the fund manager acts as a negatve feedback (contraran) trader. 8 The swtchng rule defned n Equaton (2) has several emprcal advantages. Frst, t ensures that weghts add up to unty. In other words, f a certan style performs better than another, captal s added to the former at the expense of the latter (ths conforms wth Barbers and Shlefer (2003), who suggest that the swtchng between styles s self-fnanced wthn a specfc asset class). Second, the multnomal swtchng rule guarantees that each weght s bounded between zero and one, mplyng that fund managers cannot swtch from a long to a short poston and vce versa. Ths s a reasonable assumpton as we are examnng US domestc equty funds, whch generally only enter nto long postons. 9 8 See also Goetzmann and Massa (2002) and Blackburn et al. (2011) who use a smlar defnton of momentum and contraran traders and dentfy the presence of both types of traders among ndvdual nvestors. 9 In addton, ths specfcaton only consumes one addtonal degree of freedom whereas several alternatves typcally consume one addtonal degree of freedom per style; see e.g. Swnkels and Tjong-a-Tjoe (2007). - 12 -
Based on the stated nvestment style of the fund and the past performance of all styles, the fund manager allocates captal. The return of the fund can be explaned by the returns on the dfferent styles and the exposures the fund manager has to each nvestment style,.e., r t K k1 w k k 1 rt, (3) k t t t where r t s the return of fund at tme t, α captures the out- or underperformance over the nvestment styles, and k captures the uncondtonal exposure to each nvestment style k. We nclude uncondtonal exposures n ths equaton as fund managers typcally classfy themselves nto a partcular nvestment style. For example, f a fund classfes tself as a growth fund, then we expect that, uncondtonally, there wll be a greater exposure to the k growth nvestment style than to other styles. Includng n Equaton (3) therefore allows a fund to take an uncondtonal exposure to ts stated nvestment style, whereas k wt t 1 allows for devatons from these uncondtonal exposures. 3. Data We estmate the model presented n Secton 2 usng data from the CRSP Mutual Fund Database. Ths s a survvorshp bas free database that contans monthly mutual fund data from 1961 onwards. Our data run from December 1961 to September 2010. We collect data for retal funds wth more than 10mln USD assets under management that have a Domestc Equty focus and exclude Index trackng funds. We remove funds wth less than 36 observatons to ensure that we can obtan meanngful estmates of our coeffcents. Before - 13 -
estmatng the model, we classfy funds nto nvestment styles based on the Lpper classfcaton code. We focus on twelve styles: large cap value equty (LCVE); large cap core equty (LCCE); large cap growth equty (LCGE); mult cap value equty (MLVE); mult cap core equty (MLCE); mult cap growth equty (MLGE); md cap value equty (MCVE); md cap core equty (MCCE); md cap growth equty (MCGE); small cap value equty (SCVE); small cap core equty (SCCE); small cap growth equty (SCGE). Next, we check whether a fund s nvestment style s consstent wth ts Lpper classfcaton. To do ths we follow Annaert and van Campenhout (2007). For each fund, we estmate a regresson of the fund s excess returns on the excess returns of the market, the SMB factor and the HML factor. 10 For ths regresson, we requre the R 2 to be at least 50%, and we requre the factor loadngs to be consstent wth the fund style (.e. postve exposure to the excess market return, and a postve loadng on SMB f the fund classfes tself as small cap, or a negatve loadng f t classfes tself as large cap, etc.). Ths leaves us wth 2,044 unque US domestc equty funds. 11 INSERT TABLE 1 HERE In Table 1, we report summary statstcs for the mutual funds n our sample. As can be seen, all fund types are well represented, wth md cap value equty havng the least number of funds n the sample (96) and mult cap centre equty havng the greatest number of funds n the sample (326). The medan average return shows consderable varaton over the varous nvestment styles wth large cap growth equty havng the lowest average return per month of 0.530% (about 6.5% p.a.), and small cap centre equty havng the hghest average return of 10 We use the data provded on Kenneth French s webste. 11 We also flter all duplcate funds from our sample. Typcally, these are dentcal funds but wth dfferent fee structures (A, B, C funds). - 14 -
1.024% per month (about 13% p.a.). The pattern n returns clearly reveals the presence of a sze effect, where small cap funds generally outperform larger cap funds. The growth effect s less pronounced n ths table, n two of the sze classes (large and md cap) value outperforms growth, whle t s the reverse n the other two sze classes. The standard devatons also show consderable varaton over the dfferent nvestment styles, and we generally fnd that the nvestment styles wth hgher rsk also yeld hgher average returns. Mnmum and maxmum values reveal that returns can vary wdely over tme, wth a lowest mnmum return of - 26.89% and a hghest maxmum return of 20.71%. These numbers also hghlght that there s some negatve skewness n our data. The last column shows the medan number of observatons (months) per fund. These medan values range between 7 to 10 years of data. In addton to return data, we also obtan data on fund characterstcs. We obtan Total Expense Rato, Fund Age, Total Net Assets, and Turnover from the CRSP mutual fund database. INSERT TABLE 2 HERE In Table 2, we report summary statstcs on several fund characterstcs. The average Total Expense Rato (TER) for all funds n the sample s 1.41%. In general, we observe that growth funds have hgher TERs than value funds (ths was also documented by Carhart (1997)), and that small cap funds charge hgher TERs than large caps (a fndngs also observed by Brown et al., 2011). The average Age of the funds n our sample s 14.24 years, but agan we note some varaton across the dfferent fund styles. Frst, we note that centre equty funds tend to be younger than value or growth funds. Second, we note that small cap funds tend to be younger than large cap funds. - 15 -
The average sze of the funds n our sample s $418.5 mllon, although there s consderable varaton n the sze of funds. In general, large cap funds tend to be larger than small cap funds. For value-growth, we note that growth funds are larger for the large cap funds, and that value funds are larger for the small cap funds. When we look at the Turnover of funds, we fnd an average Turnover rato of 83.30%, whch s agan broadly n lne wth the ratos presented by Carhart (1997) and Brown et al. (2011). In lne wth these studes, we also fnd varaton n Turnover rato by style, where growth funds have hgher Turnover ratos than value funds, and small cap funds have hgher turnover ratos than large cap funds. To examne the style swtchng behavor of mutual fund managers, we compare the performance of each mutual fund wth the performance of benchmark portfolos. These benchmark portfolos are obtaned from Kenneth French s data lbrary. 12 Instead of usng the usual style factors, such as SMB and HML, we use the ndvdual portfolos to construct these factors as our nvestment styles. In partcular, we use the large-value (LV), large-growth (LG), small-value (SV), and small-growth (SG) portfolos. 13 INSERT TABLE 3 HERE In Panel A of Table 3, we present descrptve statstcs on the benchmark portfolos. The mean returns show qute some varaton across the dfferent styles, whch s consstent wth 12 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_lbrary.html 13 For more detals on the constructon of these portfolos, see Kenneth French s webste. - 16 -
the lterature (e.g. Fama and French, 1993). The hghest return s observed for the SV benchmark portfolo, wth an average return of 1.424% per month, whle the lowest return s observed for the LG portfolo (an average return of 0.816% per month). We observe that the value effect n returns s more promnent n the small-cap portfolos than n the large-cap portfolos. Standard devatons also dffer consderably across the benchmark portfolos, where the hghest standard devaton s observed for the SG portfolo (whch has the second lowest average return) and s lowest for the LV portfolo. We also fnd some notable dfferences n the skewness of the dfferent benchmark portfolos, where large cap frms have more negatvely skewed returns than small caps, and value frms have more negatvely skewed returns than growth frms. In Panel B, we report the correlatons between the dfferent benchmark portfolos. Snce the benchmark portfolos are not long-short strateges whch are market rsk neutral such as SMB and HML, the correlatons are qute hgh, but not so hgh that they wll cause multcollnearty ssues. The hghest correlaton s between SV and SG (0.8838) and lowest between the SG and LV portfolos (0.7117). 4. Results In ths secton, we present the results of the model presented n Secton 2. We start by presentng results for a specfcaton wth constant style exposures. Next, we report the results for two models where fund managers can 1) swtch between all four styles (and e.g. could fnance nvestments n growth stocks by sellng small caps), and 2) swtch between twn styles,.e. between value-growth and large-small separately. We then examne whether the - 17 -
swtchng behavor of fund managers s related to fund characterstcs, and whether the style swtchng behavor affects the rsk-adjusted performance of mutual funds. 4.1 Uncondtonal Fund Exposures To examne whether funds ndeed follow ther stated nvestment style, we run a regresson of the excess returns of a fund on the dfferent nvestment styles,.e., r t SV SV SG SG LV LV LG LG r r r r, (4) t t t t t where r, r, r, r are the returns on the small-value, small-growth, large-value and SV t SG t LV t LG t large growth portfolos, respectvely. We run ths regresson for each ndvdual mutual fund. INSERT FIGURE 1 HERE In Fgure 1, we plot the uncondtonal loadngs on the dfferent nvestment styles. Ths plot clearly shows two patterns emergng. Frst, we observe that when movng from value to centre to growth, the loadngs on LV and SV decrease, whle the loadngs on LG and SG ncrease. Ths suggests that the dfferent nvestment styles ndeed capture the value-growth classfcaton of the funds. Second, when movng from large- to mult- to md- to small-cap we observe that the loadngs on LV and LG decrease, whereas loadngs on SV and SG ncrease. Ths also suggests that the dfferent nvestment styles capture the sze classfcaton of the funds. The fndngs n Fgure 1 suggest that, uncondtonally, funds ndeed behave accordng to ther stated nvestment style. - 18 -
4.2 Style Swtchng Behavor of Fund Managers To examne the style swtchng behavor of mutual fund managers, we estmate the model descrbed n Secton 2. Emprcally, we do ths n two ways. We frst estmate a model where fund managers can swtch between all styles, and could, e.g., ncrease ther exposure to the LG style, by lowerng ther exposure to e.g. the SV style. We refer to ths as sngle swtchng. Second, we estmate a model where swtchng occurs accordng twn-styles (see Barbers and Shlefer, 2003),.e. fund managers can swtch wthn the value-growth dmenson and n the small-large dmenson. We refer to ths as double swtchng. For the sngle swtchng model, we estmate the followng equaton, r t w SV SV SG SG SG LV LV LV LG LG LG 1 rt wt t1 rt wt t1 rt wt t1 rt, (5) SV t t t where the weghts are computed accordng to Equaton (2), and profts are computed as J J J SV SG LV kt1 SVt j kt1 SGt j, kt1 LVt j, j1 j1 j1, LG kt1 J j1 LG t j. (6) The model defned n Equatons (5) and (6) assumes that fund managers swtch between the four dfferent strateges mentoned above. To examne the relevance and exstence of twn styles we further estmate a double swtchng model, where we allow the swtchng to occur over sze and/or book-to-market,.e., - 19 -
r t w (1 w SIZE t t1 ) w SIZE t t1 w BM t t1 BM t t1 3 SV w 1 LV (1 w t t SIZE t t1 SIZE t t1 (1 w )(1 w BM t t1 BM t t1 ) SG 2 ) LG 4 t t, t (7) where SIZE wt t 1 s the condtonal weght on a small cap style and BM wt t 1 s the condtonal weght on the value style. These weghts are based on the proftablty of each style measured as, LARGE kt-1 SMALL kt-1 VALUE kt-1 = = = GROWTH kt-1 1 j =1 1 1 j =1 1 2 j =1 2 = J J J J 2 j =1 2 LV SV LV t- j t- j 1 1 t- j 2 LG + LG + SG + SV t- j 2 t- j t- j 1 t- j 2 1 + SG t- j 2, (8) LARGE SMALL where s the proftablty of the large cap nvestment style, s the proftablty kt-1 VALUE of the small cap nvestment style, s the proftablty of the value nvestment style and kt1 kt1 GROWTH kt1 s the proftablty of the growth nvestment style. The weghts are agan computed accordng to Equaton (2), but snce Equaton (7) has two dfferent weghts, we also estmate two dfferent ntensty of choce parameters (γ SIZE and γ BM ). We estmate Equaton (7) n three ways. Frst, we set γ SIZE equal to 0 (ths allows for swtchng only n the value-growth dmenson). Second, we set γ BM equal to 0 (ths allows for swtchng only n the sze dmenson). Fnally, we allow for swtchng n both drecton smultaneously. In Equatons (6) and (8), we select the optmal lag length n the proft functon, by estmatng the Equatons for j = 1 to 12 and choose the optmal value, j*, by selectng the specfcaton - 20 -
wth the hghest log-lkelhood. We estmate the swtchng models ntroduced n Secton 2 for all funds n our sample. However, before presentng the cross-sectonal results we frst examne one partcular fund n detal to better understand the mechansms of the model. 4.2.1 The Case of the Oppenhemer Man Street Opportunty Fund To provde some ntuton on the underlyng dynamcs generated by our model, we present detaled results for one partcular mutual fund. We select the Oppenhemer Man Street Opportunty Fund, CRSP fund number 23076. The fund s classfed as mult-cap core-equty, and has data from September 2000 to the end of our sample n September 2010, yeldng 120 monthly observatons. At the end of the sample perod, the fund had $11.6mln assets under management and, as such, s a relatvely small fund. From the group of funds that have sgnfcant swtchng parameters t s a random choce. INSERT TABLE 4 HERE Table 4 presents the results for the Oppenhemer fund for the statc, the sngle swtchng, the value and sze twn styles and the double twn styles swtchng models. The estmates for the statc model reveal that the fund has sgnfcant exposures to the LG and SV portfolos, and, to a lesser extent, the SG portfolo. Both the mult-cap and the core-equty character are therefore well represented n ths fund. To nterpret the magntude of the β s, we need to dvde the estmated values by 4, because n the statc model, γ = 0, gvng each weght a value of 0.25. Hence, a 1% return n the LG portfolo results n, on average, 1.574/4 = 0.3935% return to the fund. - 21 -
The second column of Table 4 presents the estmaton results for the sngle swtchng model (Equatons (5) and (6)). The results for the β s reman roughly the same, although β SG becomes nsgnfcant n ths model. Most mportantly, the ntensty of choce parameter, γ, s postve and sgnfcant. A Lkelhood Rato test (LR STATIC ) confrms that the ft of the swtchng model s sgnfcantly better than the statc model. 14 The fact that γ s postve suggests that the manager of the Oppenhemer Man Street Fund follows a postve feedback (momentum) strategy. In the best fttng model, the manager ranks the performance of the four benchmark portfolos over the past 12 months, j* = 12, and allocates captal n accordance wth ths rankng. In the next three columns of Table 3, we present the results for the double swtchng models (Equatons (7) and (8)). The estmated uncondtonal exposures are relatvely unchanged compared wth the statc model. For the model where we only allow for swtchng n the value-growth dmenson, we fnd a postve and sgnfcant coeffcent, ndcatng that the fund manager acts as a postve feedback trader. The sgnfcance s confrmed by the Lkelhood rato test versus the statc model, whch produces a LR statstc of 5.52. For the swtchng n the sze dmenson, we fnd an nsgnfcant coeffcent and also the LR statstc of 1.78 s nsgnfcant. Ths suggests that there s no swtchng behavor of ths fund n the sze dmenson. In the last column, we nclude the double twn style model, where swtchng can occur n both drectons. In ths model, we agan observe that γ BM s sgnfcant and γ SIZE s not. The double twn style model performs sgnfcantly better than the statc model wth a LR statstc of 8.10. Fnally, we report the LR statstcs of the double twn style model versus 14 Note that because of the nonlnearty n the model a t-test may not always ndcate whether there s sgnfcant evdence for swtchng. However, a sgnfcant ncrease n the lkelhood provdes ths evdence. - 22 -
the value and sze twn style. The tests show that the double twn style model does not mprove sgnfcantly on the value twn style model, but does mprove sgnfcantly on the sze twn style model. Ths leads us to conclude that ths fund only dsplay swtchng behavor n the value-growth dmenson and follows a postve feedback tradng rule to do ths. INSERT FIGURE 2 HERE In Fgure 2, we plot the relaton between the performance dfference for book-to-market and sze (π VALUE - π GROWTH and π LARGE - π SMALL ) versus the weght put on value and large cap stocks (w VALUE and w LARGE ) for the double swtchng model. For both relatons, we observe an upward slopng curve. Ths s because of the postve values for γ BM and γ SIZE, leadng to a postve relaton between past performance and current exposure. The lne for the sze swtchng s steeper than for the book-to-market swtchng, because γ SIZE > γ BM. From Fgure 2, we can deduce that f the value benchmark under- or outperform the growth benchmark by 40% n the past year, the manager changes the weght on value from about 0.4 to 0.6. In the sze dmenson a smlar under- or outperformance between large and small caps leads to a change n the weght on large cap from about 0.25 to 0.75. An nterestng observaton from Fgure 2 s that the value weghts are concentrated n the upper rght corner, whle the sze weghts are concentrated n the lower left corner. Ths mples that over ths perod value, on average, outperformed growth, whereas small caps outperformed large caps. INSERT FIGURE 3 HERE - 23 -
Fgure 3 shows the proft dfferences and the weghts n a tme seres plot, where the upper part of the graph shows the weghts, w VALUE and w LARGE, and the lower part shows the performance dfference (π VALUE - π GROWTH and π LARGE - π SMALL ). Clearly, there s substantal tme varaton n the book-to-market and sze weghts, rangng roughly from 0.2 to 0.8. Durng the years 2001 and 2002, value frms outperformed growth frms, causng the weght on value frms to be hgh. For the remanng years, the value premum stays slghtly postve, causng the book-to-market weght to be slghtly above 0.5, on average. The sze premum s closer to zero throughout the sample perod. An nterestng excepton s the peak n 2001, causng the fund manager to ncrease the weght on large stocks. In addton, from late 2003 to md 2004 large cap stocks clearly underperform small cap stocks, resultng n a decrease of the weght on large cap stocks to ts low of approxmately 0.2. INSERT FIGURE 4 HERE Fgure 4 presents a tme seres plot of the condtonal exposures to the four benchmark portfolos, gven by the tme varyng weghts w t multpled by the uncondtonal exposures β k. The top-left plot shows the condtonal beta on the large value portfolo. As observed from Table 3, the uncondtonal exposure to the LV portfolo was small, and although there s qute some varaton n the condtonal beta, n absolute terms the exposure remans low. The top-rght plot shows the condtonal beta for the LG portfolo. Uncondtonally, the loadng on ths portfolo was largest, and we observe that ths portfolo also has the largest absolute varaton. Over tme the exposure to LG ranges from a low of about 0.25 n late 2001- early 2002 and agan n early 2004 to a hgh of 0.9 around the start of 2008. Ths suggests that there are large shfts n the exposure of ths fund to the LG portfolo. The bottom-left plot shows the condtonal beta of the SV portfolo. Agan, we note consderable varaton n the - 24 -
condtonal exposure, where the exposure peaks from the mddle of 2001 to the mddle of 2002 and troughs at the start of 2008. Fnally, the bottom-rght plot shows the condtonal exposure for the SG portfolo. The condtonal exposure on the SG portfolo bottoms at the start of 2001 and peaks n the perod 2003-2004. Agan, ths plot show consderable tme varaton n the condtonal exposure to the SG portfolo. 4.2.2 Do Mutual Funds Swtch? We estmate the sngle and twn style swtchng models for all mutual funds n our sample and present summary statstcs n Table 5. We frst report the percentage of funds for whch the lkelhood of the sngle γ model ncreases sgnfcantly at the 5% level compared wth the statc model (Panel A). We report the percentage of funds wth postve and sgnfcant γ and negatve and sgnfcant γ. Overall, we fnd consderable mprovements n the model ft when allowng for swtchng behavor of fund managers. We fnd that there s sgnfcant swtchng for about 53% (30% + 23%) of the funds n our sample. Most sgnfcance n swtchng s reported for the Md Cap Value Equty funds (68%), whereas the least sgnfcance s found for the Large Cap Growth Equty funds (44%). INSERT TABLE 5 HERE We splt out the percentage of sgnfcant swtchng nto postve sgnfcant swtchng (.e. where we observe sgnfcant postve feedback or momentum tradng) and negatve swtchng (where we observe sgnfcant negatve feedback or contraran tradng). The results reveal several nterestng patterns. We observe that, for all sze groups, there s consderably more postve feedback tradng as we go from value to growth funds. When we look at the results for negatve feedback tradng, we observe the opposte pattern,.e. for value funds we - 25 -
fnd most evdence for negatve feedback tradng, whch then decreases for centre and decreases more for growth funds. Ths clearly suggests that the style swtchng behavor s style dependent. Ths fndng s nterestng n the lght of results of Blackburn et al. (2011). Blackburn et al. (2011) fnd that ndvdual nvestors follow postve feedback strateges when buyng growth funds, but negatve feedback strateges when buyng value funds, suggestng that ndvdual nvestors follow dfferent strateges for dfferent styles. Our results suggest that ths s not only the case for ndvdual nvestors, but also for fund managers. In Panel B of Table 5, we present the results for the double twn-style swtchng model, where we allow for two dfferent swtchng parameters. Ths Panel presents the percentage of funds for whch the double swtchng model yelds a sgnfcantly hgher lkelhood than the statc model. In total, we fnd sgnfcant swtchng for about 76% of the funds n the sample. Ths number s consstent wth Grnblatt et al. (1995), who fnd that 77% of funds buy stocks that were past wnners. When lookng at the dfference between postve feedback tradng and negatve feedback tradng, we agan observe several patterns. For the swtchng n the sze dmenson, we observe that, except for large-cap funds, there s more postve feedback tradng for growth funds than for value funds, and more negatve feedback tradng for value funds than for growth funds. For the swtchng n the value dmenson we fnd that there s more postve feedback tradng for growth funds across all sze styles and more negatve feedback tradng n value funds than growth funds. In Panel B3 of Table 5, we report results on sngle versus double twn style swtchng. The frst row n ths panel reports the percentage of funds for whch the value twn style swtchng model s the best. Overall, we observe that most of the funds that swtch do so n both the value-growth dmenson and the sze dmenson nstead of just n one sngle drecton. - 26 -
Growth funds engage more often n double swtchng than do value funds. Interestngly, n the majorty of cases funds are not consstent n ther choce of applyng postve or negatve feedback tradng wth respect to BM and sze swtchng. Ths result s consstent wth Blackburn et al. (2011), who conclude that postve or negatve feedback tradng s not a character trat of nvestors, but determned by the style they are nvestng n. 4.3 Style Swtchng and Fund Characterstcs Secton 4.2 reports evdence of style swtchng behavor of mutual fund managers. In ths secton, we examne whether the style swtchng behavor s related to fund characterstcs, specfcally, the total expense rato, age, sze and turnover of the fund. We obtan these fund characterstcs from CRSP. We run a cross-sectonal regresson of the absolute style swtchng parameters on several fund characterstcs,.e. 1 Log Age ) 2Log( TNA ) 3Turnover 4TER 5 ( Lag StyleDummy, (9) where Log(Age ) s the log of the medan age of the fund, Log(TNA ) s the log of the begnnng of perod sze of the fund, 15 Turnover s the medan share turnover of the fund, TER s the total expense rato of the fund, Lag s the number of lags j * that s used to estmate γ, and StyleDummy are dummy varables to control for the nvestment style of fund. 15 Note that we nclude begnnng of perod Total Net Assets of the funds nstead of average fund sze to avod endogenety ssues. - 27 -
In Table 6, we present the results for Equaton (9) usng the dfferent γ s,.e. γ SINGLE, γ BM and γ SIZE, and report Whte corrected t-statstcs n parentheses. 16 The frst column of Table 6 shows the results for γ SINGLE. We fnd a postve and sgnfcant relatonshp wth TER, suggestng that funds that swtch more charge hgher expense ratos. We further fnd a negatve and sgnfcant relatonshp wth age, suggestng that older funds tend to swtch less aggressvely. There s also a negatve and sgnfcant relatonshp wth Lag, suggestng that more aggressve swtchng occurs at shorter look-back perods. In the next two columns of Table 6, we separate γ SINGLE nto postve and negatve values. We do ths to assess whether postve or negatve feedback tradng s affected by specfc fund characterstcs. We frst note that when we splt γ SINGLE nto postve and negatve, TER s no longer sgnfcant for the postve feedback traders, but remans sgnfcant for negatve feedback traders. The negatve sgnfcance of age remans for both postve and negatve feedback tradng. We further observe a postve and sgnfcant relatonshp between postve feedback tradng and turnover, but an nsgnfcant relatonshp between negatve feedback tradng and turnover. Ths suggests that funds that engage n postve feedback tradng trade more actvely than negatve feedback traders. Fnally, we fnd that the sgnfcant relatonshp between swtchng behavor and lag observed n the frst column s drven by the negatve feedback tradng funds. Negatve feedback traders swtch more aggressvely based on shorter look-back perods. INSERT TABLE 6 HERE 16 We report the results, where we have used the absolute value for gamma for all funds n the sample. We have also run ths regresson only for funds wth sgnfcant swtchng. However, the results are almost dentcal to those reported n ths paper. - 28 -
In the next set of columns, we report the results for γ BM. The frst column n ths block shows that swtchng n the value-growth dmenson s postvely related to TER. We further observe sgnfcantly negatve relatonshps wth Age and Lag. When splttng the swtchng parameter nto postve and negatve feedback tradng, we observe that TER s only related to postve feedback tradng. The negatve relatonshps of γ BM wth age and lag are observed n both postve and negatve feedback tradng. The last block of columns of Table 6 reports the regresson results for γ SIZE. In the frst column, we observe that γ SIZE has a negatve and sgnfcant relatonshp wth Age,.e. older funds swtch less aggressvely n the sze dmenson. We further fnd a sgnfcant postve relatonshp wth Turnover, suggestng that funds that swtch more aggressvely n the sze dmenson have a hgher turnover of stocks n ther portfolo. When splttng γ SIZE nto postve and negatve feedback tradng, we fnd that the relatonshp between γ SIZE and Age s drven by the negatve feedback tradng funds,.e. older funds engage n less negatve feedback tradng (there s no sgnfcant relatonshp between postve feedback tradng and age). The relatonshp between turnover and γ SIZE s drven by the postve feedback tradng funds. We further fnd a sgnfcantly negatve relatonshp between lag and postve feedback tradng n the sze dmenson, suggestng that fund managers that follow a momentum strategy n the sze dmenson trade more aggressvely at shorter look-back perods. 5.4 Outperformance and Style Swtchng The next ssue we address s whether the style swtchng behavor of fund managers s related to the outperformance of the fund. To address ths queston, we compute Jensen s α for each mutual fund usng the four factor Carhart (1997) model, and use ths α n the followng crosssectonal regresson, - 29 -
c 1 1 Lag 2 2 Lag FundControls StyleDummy, (10) where α s the constant of the four factor Carhart (1997) model; and are the style swtchng parameters for postve feedback tradng and negatve feedback tradng, respectvely; Lag s the number of lags that s used to estmate γ; FundControls account for dfferent fund characterstcs that may lead to outperformance; and StyleDummy are dummy varables to control for the nvestment style of fund. We nclude an nteracton term between γ and Lag as dfferent tradng strateges may work better at dfferent look-back perods,.e. postve feedback (momentum) tradng may work better f t s based on swtchng rules that look back for only a few months (n whch case lag s low), whereas negatve feedback (contraran) tradng, may work better f the look back perod s longer (n whch case lag s hgh). INSERT TABLE 7 HERE In Panel A of Table 7, we report the results for Equaton (10). The frst column of Panel A shows the results for the sngle swtchng parameter. We fnd a postve and sgnfcant relatonshp between γ+ and α, suggestng that more aggressve postve feedback tradng leads to greater rsk-adjusted performance. The nteracton term of γ+ wth lag has a sgnfcantly negatve sgn, whch suggests that as the look-back horzon gets longer, the proftablty of postve feedback tradng decreases. Ths s n lne wth e.g. Jegadeesh and Ttman (1993) and Rouwenhorst (1998) (amongst many others) who fnd that momentum strateges work better when based on short look back horzons. Next, we consder the results - 30 -
for γ-. We fnd a postve sgnfcant mpact of γ- on the α of the fund. Ths suggest that the lower (more negatve) γ- s (.e. the more aggressvely the fund manager acts as a negatve feedback trader), the lower the rsk-adjusted performance of the fund s. The nteracton term of γ- wth lags yelds a negatve coeffcent, suggestng that the coeffcent on γ- decreases as the look-back horzon ncrease. The loadng on γ- becomes negatve from 4 lags and onwards. Ths mples that when fund managers follow a contraran strategy, ther strategy starts to have a postve mpact on rsk-adjusted performance f they base ther swtchng behavor on longer look-back horzons. For the fund-level control varables, we fnd a negatve relatonshp between α and Age, Fund Sze, Turnover and a negatve relatonshp between α and TER. All these results are consstent wth the lterature (see e.g. Carhart, 1997). In the second column of Table 7, we show the results for the swtchng n the value-growth dmenson. We fnd that the mpact of postve feedback tradng n ths dmenson, n general, s postve. However, there s no mpact of lags or negatve feedback tradng. In the thrd column, we report the results for the regresson of rsk-adjusted performance on the swtchng n the sze dmenson. Ths column shows the opposte result of the swtchng n the value dmenson. In ths regresson, we fnd a negatve relatonshp between postve feedback tradng and rsk-adjusted performance. As for the fund controls, there an no notable dfference wth the results presented n the frst column. In Panel B of Table 7, we report the results of a regresson smlar to Equaton (10), but now splt the postve and negatve swtchng parameters nto quartles based on ther look-back horzon. We defne 1, 2, 3, 4, and 1, 2, 3, 4 as the postve and negatve - 31 -