IBIMA Publishing Journal of Financial Sudies & Research hp:// www.ibimapublishing.com/journals/jfsr/jfsr.hml Vol. 0 (0), Aricle ID 494, pages DOI: 0./0.494 Profiabiliy of Momenum Sraegies in Emerging Markes: Evidence from airobi Sock Exchange Josepha Lisiolo Lishenga, Peerson Obara Maguu, Joseph Lumumba Barasa and Cliff Ouko Onsongo 3 Deparmen of Accouning and Finance, School of Business, Universiy of airob airobi Kenya Deparmen of Managemen Science, School of Business, Universiy of airob airobi Kenya 3 School of Business, Jomo Kenyaa Universiy of Science and Technology, airobi Kenya Absrac This paper ess he profiabiliy of momenum sraegies in Kenya, an emerging marke for he period 99 o 00. Boh relaive srengh sraegies (RSS) and (weighed relaive srengh sraegies (WRSS) are employed o implemen momenumbased rading sraegies. Analysis revealed ha airobi Sock Exchange (SE) exhibi medium erm reurn coninuaion over he enire sample period and he subperiods. We used RSS resuls o evaluae he influence of ransacion coss, calendar effecs, risk facors and oher repored momenum characerisics on momenum profiabiliy. We employ WRSS resuls o discriminae beween he wo diamerically opposed causes for he profiabiliy of momenum sraegies: behavioral facors (imeseries coninuaion in he firmspecific componen of reurns), and risk facors (crosssecional variaion in expeced reurns and sysemaic risks of individual securiies). Our resuls show ha, consisen wih he evidence elsewhere, momenum is an anomaly; he evidence is consisen wih momenum being driven by coninuaion in he idiosyncraic componen of individualsecuriy, raher han by crosssecional differences in expeced reurn and risks. Keywords: Profiabiliy, Momenum Sraegies Emerging Markes, airobi Sock Exchange Inroducion General Background The concep of Efficien Marke Hypohesis (EMH) appeared in 960s and reached such a heigh of dominance around 90s ha any deviaion in financial markes has been called anomaly. The 980s winessed he proliferaion of repored anomalies. Among hem, mediumerm coninuaion of equiy reurns, also called momenum sraegy, is he mos inriguing phenomenon. I has no been raded away, despie being well known as public informaion for many years now. Jegadeesh and Timan (993, 99) are he firs o repor mediumerm profi momenum. Upon examining a variey of momenum sraegies in he Unied Saes sock marke over he sample period 96 o 989, hey Cind ha sraegies ha buy winning socks (socks wih high reurns over he previous hree monhs o one year) and sell losing socks (socks wih low reurns over he same period) earn profis Copyrigh 0 Josepha Lisiolo Lishenga, Peerson Obara Maguu, Joseph Lumumba Barasa and Cliff Ouko Onsongo. This is an open access aricle disribued under he Creaive Commons Aribuion License unpored 3.0, which permis unresriced use, disribuion, and reproducion in any medium, provided ha original work is properly cied. Conac auhor: Josepha Lisiolo Lishenga, e mail: lishengajl@yahoo.com
Journal of Financial Sudies & Research of abou percen per monh for he following year. Since is very firs appearance as an anomaly o he EMH, momenum has been criicized by many as he produc of a daa snooping process. Bu ou of sample esing has vindicaed he widespread exisence of he momenum phenomenon. Jegadeesh and Timan (00) exend he original sample period o he period of 990 o 998, and concirmed he same level of profis repored in heir seminal paper. Grundy and Marin (00) furher exend he sample period and documen ha momenum profis are remarkably sable across subperiods pos 96. Besides, oher researchers have checked sock markes of differen regions over differen ime periods using various mehods, and have consisenly repored posiive reurns by implemening hese sraegies. Rouwenhors (998) for insance, documens momenum profis for several European markes, of similar magniude o hose in he USA. In he Asian markes, Chui e al. (000) repors evidence of momenum profiabiliy. There is evidence ha invesors employ momenum sraegies in making decisions. Grinbla e al. (99) repor ha, abou % of he invesors in heir sample, have recourse o momenum sraegizing. The proponens of EMH argue ha he momenum resuls can be accouned wihin he framework of risk facor models. Zarowin (990) aribues hem o he size facor effec: Small socks, ofen losers, have higher expeced reurn han large socks. Chan e al. (996) show ha mediumerm performance coninuaion can be parly explained by underreacion o earnings informaion, bu price momenum is no subsumed by earnings momenum. Fama and French (996) ry o accoun for he crosssecion sock reurn predicabiliy wih heir mulifacor model, bu fail o explain mediumerm reurn coninuaion. Chopra e al. (99) show ha losers would have o have much higher beas han winners in order o jusify he reurn differences, and he bea in he CAPM framework canno accoun for i. Grundy and Marin (00) Cind ha neiher indusry effecs nor crosssecional differences in expeced reurns are he primary cause of he momenum phenomenon, and he sraegy s average profiabiliy canno be explained by Fama and French s hreefacor model. Some behavioral models have been suggesed o explain he momenum sraegy. Grinbla and Han (00) argue ha he disposiion effec accouns for a large percenage of he momenum in sock reurns. The concaviy (convexiy) of he value funcion in he gains (losses) region makes invesors willing o sell (hold) a sock which has earned hem capial gains (losses). And his may iniially depress (inflae) he sock price, generaing higher (lower) reurns laer. Hirshleifer and Shumway (003) aribue he momenum o he fac ha low reurns on a sock pu he invesors of he sock in a negaive, criical mood. This bad mood may in urn cause skepical and pessimisic inerpreaion of subsequenly arriving informaion. People will no fully foresee heir negaive inerpreaion of fuure informaion, causing a endency oward coninuaion of he drop in price. Oher behavioral models include Barberis e al. (998), Daniel e al. (998), and Hong and Sein (999). In his response o he criiques of he EMH, Fama (998) argues ha he reurn anomalies should sand up o ouofsample ess. If he conclusions derived from developed markes are robus, we should find similar effecs in developing markes. Since Kenyan marke can be considered o be independen of he developed world, findings of a momenum paern in Kenya should conribue evidence ha pus o res he fears of daa snooping. The objecives of he sudy are fourfold. Firsly, we es he pervasiveness of profiabiliy of momenum sraegies using daa from he SE. Secondly, we check wheher ransacion coss and risk facors can significanly dissipae momenum profis when aken ino accoun. Thirdly, we examine wheher he characerisics of momenum profis repored in he
3 Journal of Financial Sudies & Research lieraure, such as calendar effec, apply o he SE. And fourhly, we decompose he momenum profis, using he framework of Conrad and Kaul (998) and evaluae he relaive imporance of he behavioural componen (ime series predicabiliy) versus he riskbased componen (crosssecional variaion). We find ha Winners ouperform Losers in he mediumerm horizons for nearly all holding periods. The ouperformance lass for abou one and half years. Furher ess show ha he momenum reurns canno be explained by he FamaFrench hreefacor model. Differen from developed markes (USA), we do no observe he January effec a he SE. Furhermore, ransacion coss do no rule ou he profiabiliy of he momenum sraegies for a majoriy of he holding periods. Conrary o Conrad and Kaul (998) who repor a negligible role of he imeseries predicable componens in he Unied Saes marke, we find ha he expeced profis are highly predicable for mos of he rading sraegies from he imeseries. Besides, he crosssecional variance of mean reurns of individual securiies increases wih he rading horizon, bu he magniude of he increase is much smaller han he random walk hypohesis predics. airobi Sock Exchange (SE) Daily prices of socks lised a he SE obained covering he period 99 o 00. The prices were used o derive average monhly prices which were adjused for sock splis and bonus issues. Wih hese daa, we calculae profis of various momenum sraegies from January 996 o December 00. The daa for 99 were mainly used in consrucing he beginning relaive srengh porfolios. Par of our ess employed Fama and French hreefacor model, i was necessary o collec daa on relevan variables. We used he SE_0 index as proxy for he marke. To calculae excess marke reurn, he risk free rae of reurn will be esimaed from The Governmen Treasury Bill rae which is obained from he Cenral Bank of Kenya. The rends, once noing in Table, are for he averages of he marke reurn and he riskfree rae. The reurn on he SE 0 index (proxy for he marke porfolio) averages approximaely 0.0% for he whole sample period. The subperiod 99 00 was characerized by a decline in he index, wih markes monhly reurns regisering.04%. In conras, he subperiod ha followed beween he years 003 o 00, coincided wih and exuberan mood among invesors wih he consequence ha monhly marke reurns averaged.4%. The riskfree rae experiences opposie rends o he marke reurn. For he subperiod 9900, he Treasury bill rae spiked up, regisering a monhly average reurn of.9%. In his period he governmen of he day raised he ineres on reasury bills so as o arac domesic finance o bridge a gap lef by inernaional donors who reneged on he aid pledges. The subperiod 00300 sees a drasic fall in he average monhly riskfree rae o 0.0%, reclecing a phase of pruden financial managemen and he unlocking of donor funds, mainly because of he change in poliical power dispensaion a he end of 00. Table also repors he SMB and HML facors of FamaFrench for he sample markes. To calculae hese facor values, we follow he mehod described in Fama and French (993) o form he 6 sizebe/me sock porfolios based on all he equiies a he airobi Sock Exchange.
Journal of Financial Sudies & Research 4 Table : Descripive Saisics of Equiies in he Sample and SubSamples Time period Whole sample Subsample Subsample 9900 9900 00300 Average number of socks 4.4 48.88 4.40 Reurn on SE0 index (Rm) Mean 0.0049 0.003 0.044 Sd. Dev. 0.0408 0.0483 0.04 Riskfree ineres rae (Rf) Mean 0.00968 0.089 0.00 Sd. Dev. 0.00 0.00 0.00 Mean 0.0044 0.049 0.06 Sd. Dev. 0.04 0.04688 0.034 Mean 0.0333 0.063 0.0064 Sd. Dev. 0.4069 0.49 0.0394 Mean 0.06 0.09 0.030 Sd. Dev. 0.968 0.8066 0.030 This able gives he monhly descripive saisics of he se0 index (a proxy for he marke), and he FamaFrench facors for he airobi sock Exchange for he whole sample period and subsamples. To calculae hese values he mehod of Fama and French (993) was followed by forming 6 sizebme sock porfolios based on all equiies lised. Daa Analysis, Findings and Discussions Profis of Relaive Srengh Sraegy (RSS) Firs, we form he relaive srengh porfolios as described in Jegadeesh and Timan (993). A he end of each monh, all socks are ranked in descending order on he basis of heir pas J monhs reurns (J = 3, 6, 9, or ). Based on hese rankings, he socks are assigned o one of five quinile porfolios. The op quinile porfolio is called he Winner, while he boom quinile called he Loser. These porfolios are equally weighed a formaion, and held for K subsequen monhs (K=3, 6, 9, and ). See Appendix I in appendices. To undersand he noion of sraegic human resource managemen, i is necessary o appreciae he concep of sraegy upon which i is based. Johnson and Scholes (999) decine sraegy as he direcion and scope of an organizaion over he long erm which achieves advanage for he organizaion hrough configuraion of resources wihin a changing environmen, o mee he needs of markes and fulfill shareholders expecaions. Minzberg e al (988) sugges ha sraegy can have a number of meanings namely; a plan or somehing equivalen a direcion; a guide or cause of acion; a paern ha is consisency in behavior over ime; a perspecive, an organizaions way of doing hings; a play, a specific maneuver inended o ouwi an opponen or a compeior. Pearce and Robinson (000) recommend hree criical ingrediens for he success of a sraegy. Firs, he sraegy mus be consisen wih condiions in he compeiive environmen. I mus ake advanage of exising or projeced opporuniies and minimize he impac of major hreas. Second, he sraegy mus place realisic requiremens on he firm s resources. The firm s pursui of marke opporuniies mus be based no only on he exisence of exernal opporuniies bu also on compeiive advanages ha arise from he firm s key resources. Finally, he sraegy mus be carefully execued. To minimize smallsample biases and o increase he power of he es, we implemen rading sraegies for overlapping holding periods on a monhly frequency. Therefore, in any given monh, he sraegies hold a series of porfolios ha are seleced in he curren monh as well as in he previous K monhs. This is equivalen o a composie porfolio in which /K of he holding is replaced each monh. To avoid he poenial survival biases, we do no require all securiies included in a paricular sraegy in he formaion period
Journal of Financial Sudies & Research o survive up o he end of he holding period. If a securiy i survives for less han J periods, we use a (Jj) period in calculaing reurns, where j is he period of delising. If a securiy does no survive he formaion period, i is dropped from he paricular sraegy. Appendix I shows he average monhly buyandhold reurns on he composie porfolio sraegies implemened during differen periods a he SE. For each sraegy, he able liss he reurns of he Winner and he Loser, as well as he excess reurns (and sa) from buying Winner and selling Loser. For insance, as Panel A shows, during he period 99600 buying Winner from a 3monh/3monh sraegy earns an average reurn of.3 percen per monh, 0.8 percen higher han buying Loser in he same sraegy, which reurns 0.46 percen. The excess reurn is signicican a he percen level of significance, wih a sa of.4 For he enire period 99600, among he sixeen sraegies implemened, significanly posiive excess reurns are observed a he percen level for nine sraegies. Specifically, he excess reurns of buying Winner over buying Loser range from 0.8 for he 3by sraegy o. percen per monh for he 9by9 sraegy (wih a mean of 0.4 percen). The porfolio reurns of boh subperiods are in sark conras. The subperiod 996 o 00 is characerized by a complee lack of momenum in he reurns. Of he 6 sraegies implemened over he period, only four show significan momenum profiabiliy. Of he remaining porfolios, significanly negaive reurns are experienced for 8 sraegies. The average WinnerLoser reurn for he period is virually zero percen (0.09 percen). The period 003 o 00 is responsible in large measure for he momenum effec winessed in our overall sample. Fifeen of he sraegies during his period exhibi posiive momenum profis ha are signicican a he % level. Average monhly momenum procis are a.3 percen, and ranging beween 0.6 percen o 3. percen per monh. We include he subperiods o invesigae he robusness of he momenum a he SE. The evidence from our analysis is mixed. While in one period, momenum is no discernible, a laer period provides unmisakable evidence of he coninuaion phenomenon. In sum, he balance of evidence dips on he side exisence of momenum effec. Characerisics of Momenum Sraegies (wih RSS) RiskAdjused Reurns This subsecion explores he relaionship beween he reurns of momenum porfolios and FamaFrench risk facors, namely, he overall marke facor (he valueweighed SE0 index minus he riskfree rae), he size facor (SMB, small socks minus big socks), and he bookomarke facor (HML, high minus low bookomarke socks). We regress he monhly reurns of he momenum sraegy in excess of he riskfree ineres rae, on he excess reurn of he SE0 index over he riskfree ineres rae, and he FamaFrench SMB and HML facors over he sample periods. The regression akes he form below: (4.) Where R RSS, T =Average reurn of he relaive srengh sraegy for he monh. rf, The risk free rae of reurn observed a he beginning of he monh,. RM, Average monhly reurn on he overall marke facor. SMB The monhly difference beween he reurns of a porfolio of small socks and he porfolio of big socks.
Journal of Financial Sudies & Research 6 HML The monhly difference beween he reurns of a porfolio of high BE/ME socks and he porfolio of low BE/ME socks α The inercep in he regression equaion β SMB The sensiiviy of he size facor o relaive srengh sraegy (RSS) profis β M The sensiiviy of RSS profis o he overall marke facor β HML The sensiiviy of RSS profis o he B M facor ε The error erm of he regression Table : Risk Adjused Excess Reurns of Momenum Porfolios (α) ( ) ( 996 00 996 00 003 00 0.009 4. 0.306. 0.06 0.6 0.06 0.68 0. 03 0.00 0.63 0.64 0.0 0.08 0.646 0. 0.9 0.6 0.0 3.83 0.89.846 0.0.0 0.03 0.46 0.0 8 This able provides he resuls from regression he monhly reurns of he 6monh/6monh momenum sraegy in excess of he riskfree ineres rae on FamaFrench hreefacors: ( ),, and m F R HML over he sample period: R r R SMB β ( β β R RSS r = α + f m R M r ) + f smbr + SMB hmlr +,,,,, HML, l R is he coefficien of deerminaion adjused for degrees of freedom; ( ) is he relaed coefficien divided by is sandard error. signicican a %: signicican a %. Table repors he resuls of he regression for he whole period and he wo subperiods. As is shown in column 4, all he marke facor coefficiens ( β m) are negaive, indicaing ha he losers are somewha more sensiive o he marke risk facor han he winners. A closer look a column shows ha coefciciens for he whole sample and 99600 subperiod are significanly differen from zero, meaning ha marke beas for winners and losers differ signicicanly. Columns 69 reveal he effec of he size facor coefficiens ( ) and bookomarke facor coefficiens ( ). The signs are mosly negaive and he significan levels are mixed. This indicaes ha he losers are riskier han he winners because hey are relaively more sensiive o all hree FamaFrench facors. The second column of Table repors he alpha (α) of he various momenum porfolios esimaed by regressing he monhly momenum reurns on he Fama French facors. The alphas for hese riskadjused porfolios are abou he same as he raw reurns, wih he only excepion of he 9900 subperiod which regisers alpha significanly equal o zero. The las column of he able presens he R square of each regression, ranging from 0.08 o 0.0.6. In sum, he FamaFrench hreefacor model canno explain he profis of he momenum sraegies in mos of he cases. Seasonaliy Effec Jegadeesh and Timan (993, 00) Cind an ineresing seasonaliy in momenum profis in he Unied Saes. They documen ha he Winners ouperform he Losers in all monhs excep January, when he Losers
Journal of Financial Sudies & Research ouperform he Winners. Grundy and Marin (00) also repor similar resuls in he U.S., where he momenum porfolio earns significanly negaive reurns in Januaries and significanly posiive reurns in monhs oher han January. Migh his seasonaliy be a saisical fluke? We examined he performance of he sraegy in January and nonjanuary monhs o see wheher he January effec applies a SE. Table 3 repors he average monhly momenum porfolio reurns and he percenage of monhs wih posiive reurns for January as well as nonjanuary monhs. Column 3 in he able is he associaed saisics. Differen from earlier findings in he Unied Saes marke, he momenum profis in January a SE show significan posiive reurns. This resul is consisen wih he Cindings of Wang (008) on he markes of UK, Germany, Japan, and China. Table 3: Momenum Reurns in January and Ouside January Monh Average saisic Percen posiive Overall 0.09.809 68.06 January 0.034.8006 Ohers 0.0 4,008 6.44 JanuaryOhers 0.00 0.8469 This able repors he average monhly momenum porfolio reurns, associaed saisic, and he percenage of posiive reurns for January as well as nonjanuary monhs. The momenum porfolios are formed based on previous sixmonh reurns and held for six monhs. The able also repors he difference beween he January monhly reurns and he nonjanuary monhly reurns. SigniCican a % level. SigniCican a % level. Table 3 also repors he es of he difference beween he average monhly January reurns and he average monhly nonjanuary reurns. o surprisingly, he difference is insignifican. Posholding Period Cumulaive Profis o he Momenum Sraegy In his subsecion we examine he resuls of momenum porfolios over various holding ime horizons (K) o check he behavior of he momenum reurns over ime. This provides informaion on he duraion of he coninuaion effec and he exen o which i is permanen. Table 4 gives he monhly average momenum porfolio reurns and associaed saisics in he firs five years afer porfolio formaion based on previous sixmonh reurns. The reurns are nearly posiive in he firs year, afer which hey urn negaive. These resuls are very similar o Jegadeesh and Timan (993) for he Unied Saes, who repor dissipaion and reversal of momenum profis afer one year, in he Unied Saes.
Journal of Financial Sudies & Research 8 Table 4: Posholding Period Reurns Monh Average saisic 0.003 0.33 0.06.0 3 0.09 3.,4638 4 0.00. 0.0. 6 0.00.809 0.04.63 8 0.009.43 9 0.008 0.6649 0 0.004 0.83 0.00 0.36 0.008 0.38 0.00098 0.3006 8 0.0006 0.04 0.000 0.06 4 0.0034 0. 0.0033 0.60 30 0.00309 0.4 33 0.0039 0.389 36 0.0040 0.393 39 0.009 0.43389 4 0.0030 0.334 4 0.0089 0.49986 48 0.0066 0.399 0.004 0.438 4 0.0046 0.88 0.0086 0.338 60 0.0090 0.66 This able repors he average monhly momenum porfolio reurns and associaed saisic over a 60 monh posformaion period... The momenum porfolios are formed based on previous sixmonh reurns. The number in bold means significanly, differen from zero a % level. Compared o oher markes, momenum a he airobi sock exchanged, is apparenly a very shorlived phenomenon, lasing only for only 8 monhs. Saring from he 9h holding monh, momenum persiss bu no a a signicican magniude. By he 4 h monh momenum has peered ou and mild reversal is observed up o he 60 h holding monh. Appendix II depics he evoluion of he cumulaive momenum profis over an even ime of 60monh posformaion period. Cumulaive momenum profis increase monoonically in he firs wo years unil hey reach he peaks beween 0 and 0 percen. The SE shows a degree of reversal bu mainains a profi level of above %. These resuls are consisen wih he behavioral models ha predic ha momenum profis will be reversed evenually. See appendix II, Cumulaive Momenum Profis. This figure presens cumulaive momenum porfolio reurns of RSS over a 60monh pos formaion period. The sample socks cover over 9 percen of he marke capializaion in each counry. The momenum porfolios are formed based on previous sixmonh reurns. Transacion Coss Transacion coss of implemening he momenum sraegies may cancel ou all or par of he momenum profis documened.
9 Journal of Financial Sudies & Research Transacion coss for a single ransacion a he SE amoun o % in form of brokerage commissions and various fees and levies paid o he sock exchange and relaed regulaory agencies This implies roundrip ransacion cos of 4 per cen. Assuming a ransacion frequencyof 40 percen, his cos per ransacion is reduced o.6 % per ransacion. For momenum rading o earn abnormal profis, i mus reurn a rae significanly higher han.6 percen. Does our 6 monh/ 6 monh sraegy mee his minimum condiion? The 6 monh/6 monh sraegy requires four rades per six monh period (opening and closing posiions for boh he Winner and loser porfolios. Our sraegy repored earlier in Appendix I, resuls in sixmonh average reurn of.0%. Wih a requiremen of four ransacions o close he posiion, his delivers a reurn of.8 percen per ransacion. This reurn compares unfavourable wih ransacion coss of.6 percen. Even if one revises he adaped rading frequency which should lower for illiquid markes like he SE, he level of comfor for hese sraegies is sill marginal. This is because, while his simple approximaion accouns for he dynamics of he rading sraegy by incorporaing he ransacion coss when hey occur, i neiher considers marke fricions induced by rading (i.e., a price impac) nor aemps o accoun for poenial differences in rading coss associaed wih differen socks or sock characerisics. For simpliciy, we jus assume ha ransacion coss for buying and selling winner socks as well as selling shor and buying back loser socks are of equal size. Lesmond e al. (004) have indeed shown ha many of he socks included in relaive srengh sraegies are illiquid and exreme, and require disproporionaely high levels of ransacion coss o rade. Wheher momenum sraegies are anomalous, may ulimaely depend on he answers surrounding he coss of rading Grundy and Marin (00) repor an average 40 percen of urnover for boh he winner and he loser porfolios. he sraegies. I appears eviden ha ransacion coss when properly modelled and incorporaed in he analysis have he poenial o ea away ino any illusory abnormal profis. The efficien markes hypohesis ha has been rereaing in he face of he relenless march of behavioural scienis may find here saving grace and be evenually vindicaed as he foundaion of asse pricing. From he analysis, we conclude ha momenum sraegies remain highly profiable also when ransacion coss are accouned for. Though we acknowledge ha he preceding analysis provides only a crude approximaion o he effec of ransacion coss on he profiabiliy of our momenum sraegies, i is paen ha momenum sraegies may be very profiable, a leas no o he degree oued by proponens. everheless, as shown by Appendix II, he absolue value of cumulaive momenum procis signicicanly exceeds a.6 percen ransacion cos for holding periods beween and 36 monhs. I appears plausible ha long horizon holding periods which need less frequen rading can be profiable. This noion underlies he resuls of Wang (008) finding for four markes: ha he momenum profis obained in each marke remain significanly differen from zero afer considering he ransacion coss. Decomposiion of he Profi Sources (wih WRSS) To enable us decompose momenum profis we generae hem using he weighed relaive srengh mehod of Conrad and Kaul (998). As in he secion under relaive srengh sraegies, he es period is divided ino Jmonh formaion period (from ime o ) and kmonh holding Jegadeesh and Timan (993) repor a correlaion as high as 0.9 for he 6 monh/6monh sraegy in he Unied Saes. Wang (008) reveals, in his sudy of UK, Germany, Japan, and China markes, ha he e reurns of RSS and WRSS are evidenly posiively correlaed.
Journal of Financial Sudies & Research 0 period (from ime o ). Following Conrad and Kaul (998), he weigh of each securiy in he rading porfolio in he holding period is deermined by he relaive performance of he securiy o he equalweighed marke porfolio in he formaion period. Specifically, w ( k) = + [ ( J ) ( J )],,, R i i Rm (4.) 3 where w is he fracion of he rading sraegy porfolio devoed o securiy in holding period, R is he reurn of securiy i in he formaion period, and R is he equalweighed m, marke porfolio reurn in he formaion period. is he number of securiies in he porfolio a ime, and i=. By consrucion, he porfolio is an arbirage porfolio since he weighs of securiies sum o zero. And he oal invesmen posiion (long or shor) is given by: I = = w ( k) (4.3) The profi in he holding period for he sraegy is: π = wi i= ( ) ( k), k R (4.4) For he 6by6 sraegy he resuls of he WRSS sraegy range from 0.0 o0.09, wih a mean of 0.0. The correlaion beween he RSS resuls and he WRSS resuls is high a 0.84. Afer generaing he WRSS reurns, we nex decompose he profis of weighed relaive 3 The plus sign in he equaion emphasizes ha we will implemen a momen sraegy, i.e., going long in a securiy if i ouperforms he equalweighed marke porfolio and going shor in a securiy if i underperforms he marke porfolio. srengh sraegies (WRSS) and invesigae he source of he momenum profis. To decompose he WRSS profi, we assume ha he realized reurn of sock i is expressed as: R u ( + i k) = ( k) ( k), µ (4.) where µ ( k) is he uncondiional expeced u i k, reurn of sock i and ( ) is he unexpeced reurn a ime. Then he momenum profis in Eq. (4.) can be decomposed ino componens based on expeced and unexpeced componens of reurns as follows: +σ = C ( k) + ( k) [ ( k)] O µ = P ( k) +σ Where ( ) C k (4.6) is he firsorder auocovariance of he reurns on he marke porfolio, O ( k ) is he average of he firsorder auocovariances of he individual socks in he zero cos porfolio, µ ( k) = µ ( k), and m. i= σ is he crosssecional variance of expeced reurns 4. In calculaing he componens of he rading porfolio profis, we assume ha individual sock reurns are mean saionary. Eq. (4.6) decomposes he oal expeced profis ino wo componens: P (k ) ; he 4 Lo and MacKinlay (990) originally propose his decomposiion. Jegadeesh and Timan(99), and Conrad and Kaul (998) have furher reamen of his decomposiion and is economic inerpreaion.
Journal of Financial Sudies & Research imeseries predicable componens in asse reurns, and [ µ ( k )]; he profis σ generaed by crosssecional variance of he mean reurns. The equaion indicaes ha any crosssecional variaion in expeced reurns conribues posiively o momenum profis. Since realized pas reurns are posiively correlaed wih expeced reurns, if a large par of realized reurns is due o expeced reurns, pas Winners (Losers) will, on average, coninue o earn higher (lower) han average reurns in he fuure. Following Conrad and Kaul (998), we assume ha he serial covariances and he crosssecional variances of mean reurns of individual socks are ime dependen. Then, ( k ), ( ) C O k, and σ esimaed as: T ( k ) C ( k) = ( k), T ( k) C Where C m, ( k ) = m, [ Ri, i= are (4.) ( k) = ( k) ( J) + ( k) + ( k) ( J) ( J)],. µ µ O R m R T ( k ) ( k) = ( k), T ( k) O ( k ) = R (4.8) Where O ( k) = [ R ( k) ( J ) J, µ ( )] i= And T ( k ) σ = ( k) T ( k) σ Where σ ( k ) = ( k) = µ [ µ ( J) m, ( J)] i= (4.9) T (k) is he oal number of overlapping reurns in he sample period for a rading sraegy of holding period k. µ ( J), m, µ ( J ) are he esimaed expeced reurns of sock and marke porfolio a ime. µ is esimaed hrough average realized reurns of each sock: µ Tii Ri = Ti =, Where T i (4.0) is he number of observaions available for sock i. Then, µ ( k) = m. i= (4.) Table presens he resuls of he conribuion of imeseries predicabiliy and crosssecional variaion of sock reurns over differen holdings k for he enire sample period, where k ranges from 3 o monhs. For breviy, we only lis sraegies for which he lengh of he formaion period J and he fuure holding period k are idenical. Their resuls are represenaive for oher sraegies wih differen formaion and holding periods. π The columns 4 repor, E[ ( k)], P(k), and σ. To faciliae evaluaion of he relaive imporance of he profi sources, he percenage conribuions of P(k), and σ o he oal profis, E[ π ( k)], are repored in column and column 6, respecively. σ There are several noable findings in Table. Firs, is σ significan in all cases, given he fac ha ( k) is he crosssecional variance ofµ, i. The P (k) is negaive bu insignificanly differen from zero. Second, he magniude of P(k) increases monoonically wih ime. The percenage conribuion of P(k) dominaes ha of σ in nearly all sraegies.
Journal of Financial Sudies & Research Table : The Decomposiion of Average Profis o WRSS % % 3monh 0.06 0.0 0.04 68.6 68. (sa) 0. 0.86 6.83 6monh 0.4 0. 0.08 64.4 3. (sa).36 0.88.94 9monh 0.0 0.9 0.3 36.4 6.43 (sa) 0.4 0. 33.4 monh 0.44 0.63 0.0 4.04 4.0 (sa)..63 38.6 This able repors he decomposiion of average profis o rading sraegies and associaed saisics (wih idenical formaion and holding period during is enire sample period. The decomposiion is given by E[ ( k)] = P( k), where P(k) and represen he imeseries and crosssecional π +σ σ predicable pars, respecively. All proci esimaes are muliplied by 00. and denoe signicicance a % and 0%, respecively. The resuls are revealing in wo ways. Firs, he expeced profis are highly predicable for mos of he rading sraegies from he imeseries componens, since P(k) σ conribues more of he profis han does. This finding is differen from he Unied Saes marke resuls by Conrad and Kaul (998). Second, he resuls do no suppor he random walk hypohesis. Alhough he magniude of σ does increase wih he rading horizon, he magniude of he increase is much smaller han he random walk hypohesis indicaes. In sum, hese resuls reveal marke inefficiencies. Conclusions This paper documens reurns of momenum sraegies a he SE during he period 99 o 00. Following he framework developed by Jegadeesh and Timan (993) and Conrad and Kaul (998), we measure he momenum profis of WRSS. I urns ou ha he pas Winners ouperformed he pas Losers for mos of he periods. Furher ess show ha he momenum reurns canno be explained by risk models such as he FamaFrench hreefacor model. Differen from he Unied Saes marke, we do no observe he January effec in our sample markes. The concaviy of he cumulaive momenum profis over various holding periods show ha he behavioral models are suppored. When rading, coss are considered, however, relaive srengh sraegies profiabiliy is significanly viiaed especially for a majoriy of shor horizon holding periods of over monhs. We decompose he expeced profis of he momenum sraegies ino wo differen sources: Timeseries profiable componen and crosssecional variance of mean reurns of individual securiies. We find ha he expeced profis are highly predicable for mos of he rading sraegies from he imeseries componens. In addiion, he crosssecional variance of mean reurns of individual securiies increases wih he rading horizon, bu he magniude of he increase is much smaller han he random walk hypohesis predics. These resuls cas doubs on marke efficiencies. References Barberis,., Shleifer, A. & Vishny, R. (998). A Model of Invesor Senimen, Journal of Financial Economics, 49, pp. 30343. Chan, K., Jegadeesh,. & Lakonishok, J. (996). Momenum Sraegies, The Journal of Finance,, pp. 683. Chopra,., Lakonishok, J. & Rier, J. R. (99). Measuring Abnormal Performance: Do Socks Overreac?, Journal of Financial Economics, 3, pp. 368.
3 Journal of Financial Sudies & Research Chu A., Timan, S. & We K. (000). Momenum, Ownership Srucure, and Financial Crises: An Analysis of Asian Sock Markes, Universiy of Texas a Ausin Working Paper. Conrad, J. & Kaul, G. (998). An Anaomy of Trading Sraegies, The Review of Financial Sudies, pp. 4899. Daniel, K., Hirshleifer, D. & Subrahmanyam, A. (998). Invesor Psychology and Securiymarke Under and Overreacions, The Journal of Finance 3, pp. 839886. DeBond, W. F. M. & Thaler, R. (98). Does he Sock Marke Overreac?, The Journal of Finance 40, pp. 9380. DeBond, W. F. M. & Thaler, R. H. (98). Furher Evidence on Invesor Overreacion and Sock Marke Seasonaliy, The Journal of Finance 4, pp. 8. Fama, E. F. (998). Marke Efficiency, Longerm Reurns, and Behavioral Finance, Journal of Financial Economics, 49, pp. 83 306. Fama, E. F. &French, K. R. (996). Mulifacor Explanaions of Asse Pricing Anomalies, The Journal of Finance, pp. 84. Grinbla, M. & Han, B. (00). The Disposiion Effec and Momenum, UCLA Working Paper. Grundy, B. D. & Marin J. S. (00). Undersanding he aure of he Risks and he Source of he Rewards o Momenum Invesing, The Review of Financial Sudies 4, pp. 98. Hirshleifer, D. &Shumway, T. (003). Good Day Sunshine: Sock Reurns and he Weaher, The Journal of Finance 8, pp. 00903. Hong, H. and Sein, J. C. (999). A Unified Theory of Underreacion, Momenum Trading and Overreacion in Asse Markes, The Journal of Finance 4, pp. 4384. Jegadeesh,. & Timan, S. (993). Reurns o Buying Winners and Selling Losers: Implicaions for Sock Marke Efficiency, The Journal of Finance 48, pp. 69. Jegadeesh,. & Timan, S. (99). Overreacion, Delayed Reacion and Conrarian Profis, The Review of Financial Sudies 8,pp. 93993. Jegadeesh,. & Timan, S. (00). Profiabiliy of Momenum Sraegies: An Evaluaion of Alernaive Explanaions, The Journal of Finance, 6, pp. 6990. Lo, A. & MacKinlay, A. C. (990). When are Conrarian Profis Due o Sock Marke Overreacion?, The Review of Financial Sudies 3, pp. 08. Rouwenhors, K. G. (998). Inernaional Momenum Sraegies, The Journal of Finance, 3, pp. 684. Wang, D. (008). "Are Anomalies Sill Anomalous? An Examinaion of Momenum Sraegies in Four Financial Markes," Working Paper, WP., Universiy of avarre. Zarowin, P. (990). Size, Seasonaliy, and Sock Marke Overreacion, Journal of Financial and Quaniaive Analysis,, pp. 3.
Journal of Financial Sudies & Research 4 Form aion Perio d (J) Porfoli o 3 Winner (W) Loser( L) APPEDICES Appendix I: Average Profis o Relaive Srengh Sraegies (RSSs) 99600 Holding period (K) 99600 holding Period 00300 holding period 3 6 9 3 6 9 3 6 9.03 3.004 6 WL.008 6 Winner (W) (sa). Loser( L).08.006 9 WL.0 9 9 Winner (W) (sa) 3.46 Loser( L).03.04 6 WL.000 (sa) 0.0 Winner (W).0 4 0.0 64 0.0 404.00 4 0.0 6 0.0 08.00 4 0.0 9 0.08 86.008 8.0 6 0.00.00 9.004 0.00 63.0080 8.9 0.9....0 9.006 9.0.8.0.03 88.03 0.0 3.06 8 Loser( L).03 46.03 4 WL.03.00 4 (sa) 0.3.8.0 89.0 3.00 8 0.6.06 6.000.0 9 4.8.000 88.09 9.0608.00 8 0.3.006.0069.006.0069.009 6.0000.009.00 9.00.003 8.93.06.008.0043.0043.0038 9.48.08.004.00.063.08 9.0043 3.00.0094.03.8.09.0.0006 6.064 3.00 3.00.000.06.0040.00 99.0498.09 9.030.04 83.030 4.0 43.9.8.048.06 6.0 9.048.06 6.0 9.043..036 68.006 9.9.048 6.036 33.0.6.3 3..90 3.000 36.0089.00 63.0048.00 86.0448 4.034 9.03.98. 0..39.08 4.030.003.000 84.00.034 6.0009.04..00 8.000.004.090 006 0.00.00 3 8 0.6.00 0.3.6.3.68.036 6.04 8.034 3.008 08.8.038 9.03.033.0066.00 6 9.046 69.0 6.03 09.98.043.034 0.009 04 0.68 0.8 6.3 /.040.04.00..0466.0404.008 0.839.006.036.0384.9.00.039.068.8
Journal of Financial Sudies & Research The able shows average procis o relaive srengh sraegies (RSS) a he SE beween 99 o 00, and wo subperiods o disinguish a markedly bullish posr00 period from he earlier period. A he end of each monh, all socks a he sock marked are ranked in descending order on he basis of heir J monhs pas reurns. Based n hese rankings he socked are assigned o each of he equally weighed quinile porfolios. The op quinile porfolio is called he Winner, while he boom quinile porfolio is called he Loser. These equally weighed porfolios are held for K subsequen monhs. saisic is he average reurn divided by is sandard error. represens signicicance a he % level and signicican a % level. Appendix II: Cumulaive Momenum Profis 0..3 0. 0. Cumulaive Reurns 0 0. 0. 0 0 30 3 40 4 0 60 Even monh 0.3