Contrarian and momentum strategies in China stock market:

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1 Contraran and momentum strateges n Chna stock market: Joseph Kang *, Mng-Hua Lu, Xaoyan N Nanyang Busness School, Nanyang Technologcal Unversty, Sngapore Abstract Usng A shares accessble only to local nvestors (who account for 99% of stock nvestors n Chna), ths paper tests f short-horzon contraran and ntermedate-horzon nvestment strateges generate abnormal profts. We fnd statstcally sgnfcant abnormal profts for both the arbtrage portfolo-nvestment strateges. Detaled analyss ndcates that: () an absolute domnance of non-nsttutonal nvestors leads to an envronment of excessve speculaton and hence excessve overreacton to frm-specfc nformaton; () the overreacton to frm-specfc nformaton s the sngle most mportant source of the shortterm contraran proft; (3) the stock returns n the ntermedate horzon exhbt lagged overreacton to common factors; and (4) the lead-lag overreacton to common factor s the major reason behnd the ntermedate-term momentum proft. These fndngs are robust, among other thngs, to bd-ask spread and nonsynchronous tradng. JEL classfcaton: G4; G5 Keywords: Momentum and contraran strateges; Chna stock market; overreacton and underreacton; frm-specfc nformaton; common factor; lead-lag structure.. Introducton An extensve body of fnance lterature documents that past stock returns can predct the future stock returns n short-term, ntermedate, and long-term horzons, although the predctablty weakens over longer horzons. For example, Jegadeesh (990) and Lehmann (990) fnd return reversals n relatvely short-term horzons (one month and sx months, respectvely). Jegadeesh and Ttman (993) document return contnuatons n ntermedate horzons (three to twelve months) where past wnners contnue to outperform, on average, past losers. DeBondt and Thaler (985 and 987) report long-term (e.g., three to fve years) prce reversals where past long-term * Correspondng author. Emal: acskang@ntu.edu.sg; Tel (65) ; Fax (65) We would lke to thank for ther valuable comments Lllan Ng, Andrew Chen, Joseph Wllams, Qan Sun and Jack Chen as well as partcpants of the CREFS semnar at the Nanyang Busness School n Sngapore and the 3 th PACAP/FMA Annual Fnance Conference n Seoul, Korea. We also acknowledge that an earler verson of ths paper receved the best paper award at the 3 th PACAP/FMA Annual Fnance Conference.

2 losers outperform past long-term wnners. Gven such tme-seres patterns n cross-sectonal stock returns, one can formulate two arbtrage portfolo-nvestment strateges: contraran and momentum strateges. Under the contraran strategy, past losers are bought and past wnners are shorted. Under the momentum strategy, past wnners are bought and past losers are shorted. Abnormal returns of these strateges are documented n the lterature cted above. Abnormal profts of the momentum and contraran strateges are also documented n non-us equty markets. For example, Ahmet and Nusret (999) fnd abnormal returns of long-term contraran strateges n the stock markets of seven non-us ndustralzed countres. Chang, McLeavey and Rhee (995) fnd abnormal returns of short-term contraran strateges n Japan stock market, whereas Hameed and Tng (000) fnd the same n Malaysa stock market. Rouwenhorst (998) fnds momentum profts n twelve European equty markets, whereas Rouwenhorst (999) fnds abnormal returns of momentum strateges n sx (out of twenty) emergng equty markets. Hameed and Yuanto (000) fnd that a (dversfed country-neutral) momentum strategy generates small but statstcally sgnfcant returns n sx Asan stock markets. Schereck, DeBondt and Weber (999) fnd abnormal returns for both ntermedateterm momentum strategy and short- and long-term contraran strateges n Germany equty market. Fama (99) notes that the predctablty of stock returns over tme s among the most controversal ssues on stock market effcency. The controversy led to varous explanatons on the possblty and the sources of abnormal profts of contraran and momentum strateges. The explanatons nclude: one based on behavoral rratonalty of nvestors and the other based on stock market effcency. In these studes, losers are those stocks whose returns are smaller than market ndex returns whereas wnners are

3 The most frequently-cted explanaton of the abnormal profts of contraran strateges s: market s over-reacton to frm-specfc nformaton and the subsequent correcton. For example, Mun, Vasconcellos and Ksh (999), and Bacmann and Dubos (998) post that an overreacton to frm-specfc nformaton s the prmary reason behnd the abnormal profts of short-term contraran strateges. DeBondt and Thaler (985) argue that nvestors overreacton to recent past events also can lead to long-term contraran profts. Lo and MacKnlay (990) demonstrate that return reversal s not the only source of contraran profts and dentfy second potental source of contraran profts that arses when some stocks react more quckly to nformaton than others. The alternatve source of contraran profts s referred to as lead-lag structure because the returns of some stocks lead the returns of others. Jegadeesh and Ttman (995) and Boudoukh, et al. (994) show that the lead-lag structure rather arses from nvestors overreacton or delayed reacton to common factors and also show that both the overreacton and underreacton (or equvalently delayed reacton) of prces to nformaton can n theory contrbute to contraran profts. Another explanaton s that short-term (and long-term) contraran profts can result from tme-varyng common factors. For example, Conrad and Kaul (998) argue that, even n frctonless markets, short-term stock returns can be auto- or cross-correlated. They argue that both the negatve autocorrelaton n short-term ndvdual stock returns and the negatve crosssectonal autocorrelaton are consstent wth tme-varyng common factor. the stocks whose returns are larger than market ndex returns. The school of thoughts based on market effcency also lsts, as the reasons of long-term contraran profts, meanrevertng expected market returns (e.g., Chan, 988; Ball and Kothar, 989), frm sze effect (see Zarown, 990), and measurement error due to bd-ask bounce, non-synchronous tradng, or llqudty (see Park, 995; Ball, Kothar and Wasley, 995; Conrad, Gultekn and Kaul, 997). 3

4 The market-effcency camp argues that tme-varyng common factors (or tme-varyng expected returns) and/or data mnng lead to the exstence of ntermedate-term momentum profts. Accordng to ths explanaton, the abnormal returns of momentum strateges are attrbutable to common factors that are not accounted for n CAPM or three-factor model. As Jegadeesh and Ttman (993) pont out, to the extent that hgh past returns are partly due to hgh expected returns, wnner portfolos wll contan hgh-rsk stocks that would also generate hgher expected returns n the future. Conrad and Kaul (998) examne ths possblty and conclude that momentum profts can be explaned by cross-sectonal dfferences n expected returns. Chorda and Shvakumar (000) also show that momentum profts can be drven by tme-varyng expected returns that are n turn related to the state of economy. In contrast, the behavorsts argue that the exstence of momentum profts s a strong evdence of market neffcency and t results from stock prces under- and over-reacton to nformaton as well as nvestors herdng behavor. Barbers et al. (998), Danel et al. (998), and Hong and Sten (997) develop models that appeal to behavoral bas and hence explan the stock-return contnuatons. In these papers, cogntve bas leads nvestors to ether under-react to nformaton or nvestors follow postve feedback strateges that lead to delayed overreacton to nformaton. Another behavoral explanaton s herdng. The tendency to herd among fund managers s a well-documented fact and t contrbutes to the profts of ntermedate-term momentum strateges. See, e.g., Grnblatt, Ttman and Wermers (995) and Lakonshok, Shlefer and Vshny (994). In ths paper, we nvestgate the short-term contraran and ntermedate-term momentum strateges n Chna stock market. Chna s an mportant emergng economy that has just joned the WTO. 3 Although the predctablty n stock returns and ts mplcatons on 3 It has the largest populaton (. bllon) n the world. Its nomnal GDP (US$.0 trllon) s the second largest n Asa (after Japan) and the real GDP growth rate of about 8% s among the hghest n the world. Its total trade s near 4

5 portfolo nvestment have been extensvely nvestgated n many emergng stock markets, Chna stock market stll remans among the most mportant emergng markets awatng such nvestgatons. 4 The lack of such nvestgaton s manly due to both the short hstory of equty tradng n Chna and the lack of nterests among global nvestors (who can nvest only n the small and llqud B shares market. 5 The persstence of negatve correlaton between Chna and the Unted States as well as other developed equty markets wll, however, ncreasngly attract the attenton of global nsttutonal nvestors. Hence, the nvestgaton of momentum and contraran strateges n Chna stock market s not only tmely to global nvestment professonals but also nterestng to fnance academcs dong research n the area of stock market effcency. As stated n Hu (999), the tradng practce, composton, behavor of nvestors and regulatory envronment n Chna stock market are very dfferent from those n other markets. 6 Perhaps, the most nterestng nsttutonal feature n Chna stock market s the absolute domnance of ndvdual nvestors as the man composton (99%) of stock market nvestors. See Shenzhen Stock Exchange Fact Book (999). 0.5 trllon US dollars whch s about 60% of Japan s equvalent. See Chna Securtes and Futures Statstcs Yearbook (00). 4 In 000, Chna s one of the two countres whose stock markets are negatvely correlated wth the US stock market. See, e.g., Economst (6- December 000, p. 90). 5 Currently, there are two stock exchanges: Shangha and Shenzhen Stock Exchanges. Snce ther establshments n early 90s, the respectve exchange has seen sharp ncreases both n the number of lsted companes and n the amount of market captalzaton. As at January 00, there were about,000 companes lsted on the two exchanges wth total captalzaton of about US$590 bllon. Each exchange has two sectons that are currently segmented: namely, A share and B share sectons. The A shares are denomnated n Chnese currency and ssued only to (and traded only by) domestc nvestors. On the other hand, the B shares are denomnated n US or Hong Kong dollars and ssued only to (and traded only by) foregn nvestors. The A shares account for 99% of total market captalzaton as at January 00 and are actvely traded. But, the B shares are not actvely traded. Snce February 00, local nvestors are allowed to trade the B shares. But, under the current regulatons on exchange control, local nvestors are stll prohbted from convertng ther local currency to US or Hong Kong dollars for the purpose of B share nvestment. Gven the current speed of lberalzaton takng place n Chna stock market and the entry nto WTO, however, the segmentaton between A and B shares may dsappear n not-dstant future. 6 There are studes (e.g., IPO study by Sun and Tong, 000) that document specal features of Chna stock market. 5

6 There are several reasons behnd the domnance of ndvdual nvestors. Stocks and shares, long consdered as fnancal nstruments n captalst economc system, have been taboos n socalst Chna untl recently. In early 990s, the Chna government set up two stock exchanges as an experment for economc reform. The experment s yet to be completed before the stock market s ready for unlmted nvestment by fnancal nsttutons. Another reason for the domnance s that too much money chases too few stocks. The nadequate socal securty system n Chna has led to ndvduals savngs rate that s among the hghest n the world. Due to lack of ther access to treasury securtes or corporate bonds, ndvdual nvestors have no choce but to resort to bank deposts, stocks or propertes. The bank depost rates are often kept below the market equlbrum rate for the purpose of economc development,. Untl recently, prvate ownershp of propertes was strctly regulated by the government. Hence, stocks are the favorte wealth-buldng nstrument most preferred by Chnese ndvdual nvestors. There are a lmted number of shares that ndvdual nvestors can buy. Snce state-owned enterprses (often, heavly ndebted) account for the majorty of total market captalzaton, there are only a handful of prvate companes beng lsted. Wth the state ownershp beng the corner stone of the socalst system, prvatzaton s stll an deologcally senstve ssue n Chna. As a consequence, there are tradng bans on about two-thrds of the shares of lsted state-owned enterprses to ensure that these companes reman state-owned. In Chna, corporate fnancal data are not relable (sometmes even fabrcated), and the stock market s not transparent. Corporate bankruptces are rare and standards of corporate governance are very low. Wth lttle knowledge of or lmted experences n stock nvestments, most ndvdual nvestors/stockbrokers select stocks accordng to both past return performances of and current rumors on companes. Ths practce s commonly known 6

7 as str-fryng stocks. Indvdual stock prces are therefore often pushed too hgh (or too low) and then are quckly corrected. The consequence of str-fryng stocks s a stock market mana where stock prces can be pushed up by several hundred tmes and quckly corrected later on. 7 The rumor-based str-fryng nvestment by ndvdual nvestors n Chna market suggests a pattern of return reversals. It also suggests a herdng behavor that s unque n the sense that t s the herdng among unnformed ndvdual nvestors. Insttutonal nvestors herdng behavor n emergng market s well documented. As a consequence, return contnuaton can be the norm n these markets. Whether the unque herdng behavor leads to return contnuaton n the Chna stock market s an nterestng emprcal queston. The man objectves of ths paper are two-fold: () to see f return reversal or return contnuaton exsts n Chna stock market and to test f contraran and momentum strateges can generate abnormal profts and () to dentfy the man sources of the abnormal profts of the two nvestment strateges. The remander of ths paper s organzed as follows. Secton frst dscusses data and the methodology employed for portfolo formaton. Then t reports the patterns of stock returns and abnormal returns of contraran and momentum strateges. Secton 3 examnes the sources of the contraran and momentum profts. Fnally, Secton 4 concludes the study.. Data and Methodology.. Data and Sample Selecton 7 For example, durng December 990 and December 993, the composte ndex of Shangha Stock Exchange ncreased from 00 to 834. But, wthn the next seven months, the ndex dropped to

8 Stock prces are obtaned from Datastream (the verson of 000). Usng closng prces, we compute the log of relatve prce for contnuously-compounded stock returns. Our sample perod ranges from January 993 to January 000. We select January 993 as the startng pont because the year993 s the startng year for socalst Chna to have a szable number of lsted stocks. Snce new stocks frequently experence rregular returns around the tme of ntal publc offerngs (see Sun and Tong, 000), the returns of newly lsted stocks n the frst week after lstng are excluded n the sample. The total number of stocks n the sample s 48 for year 993, 63 for year 994 and 68 for the perod between 995 and Portfolo Formaton To test whether return reversal or return contnuaton exsts, we follow the method of Jegadeesh and Ttman (993). Frst, we rank n an ascendng order the stock returns n the past F weeks (the portfolo formaton perod). Based on the rankng, fve equal-sze quntle portfolos are formed. The quntle portfolo wth the hghest stock returns s the wnner portfolo, whereas the quntle portfolo wth the lowest return s the loser portfolo. Then, an equally-weghted average return for each quntle over the next H weeks (the holdng perod) as well as the dfference between returns of the loser and the wnner portfolos durng the H weeks s calculated. If the average return of wnner portfolo n a holdng perod s hgher than that of loser portfolo, then a return contnuaton s observed durng the holdng perod. If t s lower, then a return reversal s observed. We consder eght dfferent horzons (.e.,,, 4, 8,, 6, 0, and 6 weeks) for both formaton ( F ) and holdng ( H ) perods. To see f our results are consstent across dfferent perods we consder more tme perods than Jegadeesh and Ttman (993) dd. As there are eght perods for both formaton ( F ) and holdng ( H ) perods, we have 64 (= 8 x 8) dfferent 8

9 nvestment strateges. The number of observatons for strateges -H and F- ranges from 359 to 334, whereas that for strateges 6-H and F-6 ranges from 334 to 309. In order to avod bases that can arse from the bd-ask spread, prce pressure, and nonsynchronous data, we skp one tradng day between the portfolo formaton and holdng perods for all nvestment strateges (for smlar treatment, see Chan et. al., 999; and Lehmann, 990). For the formaton perod, a week s taken to begn on Wednesday and end on Tuesday (f the day s a non-tradng day, then the next tradng day). For the holdng perod, a week s taken to begn on Thursday and end on Wednesday (f the day s a non-tradng day, then the next tradng day). To ncrease the power of the test, we also consder the nvestment strateges for overlappng holdng perods. Therefore, n any gven week t, an nvestor can hold certan quntle portfolos that are formed n the current as well as prevous H weeks and can lqudate the quntle portfolos formed n the prevous H weeks..3. Return Performance Table reports average monthly returns of the loser and wnner portfolos across varous holdng perods (and ther dfferences) for the 64 strateges. 8 There are eght parts n the table, each wth same portfolo formaton perod. The frst row n each part s the specfc strategy. For example, Strategy -8 represents the strategy that stocks are ranked accordng to ther prevous one-week returns and then held for the next eght-weeks. To examne whether contraran or momentum profts exst, we then calculate the holdng-perod (monthly) returns of wnner and loser portfolos and the dfference between ther monthly returns (L-W). If the dfferences between 8 Here, we do not adjust the portfolo returns for market returns. The dfference between returns of the loser and wnner portfolos remans the same regardless of whether the portfolo s returns are adjusted for market returns or not. 9

10 losers return and wnners return are statstcally sgnfcantly larger than zero, then there are contraran profts. If t s negatve, then momentum profts exst. Otherwse, nether profts exst. INSERT TABLE HERE The dfference between monthly returns of loser and wnner portfolos (L-W) s reported n the second last row for each part n Table. The results show that, although not all strateges generate statstcally sgnfcant momentum or contraran profts, both momentum and contraran profts are observed. Statstcally sgnfcant contraran profts emerge among the strateges whose formaton perods are,, 4, 8, and weeks. Among the strateges whose formaton perods are, 6, 0, and 6 weeks, ten strateges that hold stocks for more than weeks generate statstcally sgnfcant momentum profts. For portfolos formed accordng to prevous one-week return, loser s returns are larger than wnner s returns for one- to 0-week holdng perods. However, they are not statstcally sgnfcant at 0% level except the case of one-week holdng perod. For the two-week formaton perod, there are contraran profts for -, 8-, -, 6-, 0- and 6-week holdng perods, among whch the 8-, - and 6-week holdng perods generate statstcally sgnfcant contraran profts. For portfolos formed accordng to prevous four-week stock returns, contraran profts are postve for 4-, 8-, and -week holdng perods. For the eght-week portfolo formaton perod, most strateges generate postve contraran profts except the strateges of 0-and 6- week holdng perods. The magntude of contraran profts s hghest for the eght-week formaton perod. For the -week portfolo formaton perod, contraran profts are not so obvous unlke those of the strateges wth 8-week holdng perod. Only the strateges wth 4-, 8-0

11 and -week holdng perods generate statstcally sgnfcant contraran profts. But, when the momentum profts begn to manfest for the holdng perod of 6 weeks, wnners outperform losers by 0.35% per month. For the portfolos formed accordng to prevous 6-, 0-, and 6- week returns, contraran profts no longer exst. However, momentum profts are observed. The longer the formaton and holdng perods, the larger the momentum profts. For the 6-weeks portfolo formaton perod, momentum profts are statstcally sgnfcant for strateges of 0- and 6-week holdng perods. For the 0-week formaton perods, momentum profts exst for strateges wth 6-, 0- and 6-week holdng perods. In the longest formaton perod of 6 weeks, momentum profts are the most dstnct. Momentum profts can be observed for strateges wth holdng perods from to 6 weeks. Durng the sample perod, contraran profts are observed f we form portfolos accordng to prevous -, -, 4-, 8- and -week returns and hold them for not longer than 6 weeks. Losers tend to become wnners, whereas wnners tend to gan much less than losers n the holdng perods. For portfolos formed accordng to prevous and 8- week returns, the longer the formaton perod, the larger the contraran profts. When the portfolo formaton perods are longer than twelve weeks and, at the same tme, holdng perods are at least as long as twelve weeks, momentum profts emerge. Losers reman as losers and wnners do so as wnners. For portfolos formed accordng to prevous and 6-week returns, the longer the portfolo formaton perod, the larger the momentum profts. When there are contraran profts, the larger losses that the loser portfolos ncurred n the formaton perod, the larger gans they wll obtan n the holdng perod. Such tendency becomes weaker, however, as we go up the ladder of fve quntle portfolos. When there are momentum profts, the more profts that the wnners generated n the formaton perod, the more profts they tend to generate n the holdng perod. Such tendency becomes weaker, however, as we go down the ladder of fve quntle portfolos.

12 3. Sources of Contraran and Momentum Profts Contraran or momentum profts may be due to: () measurement error; () tme varyng rsks; (3) overreacton; and (4) lead-lag structure. In ascertanng the man sources n Chna stock market, we follow Jegadeesh and Ttman (993) to focus on three strateges; namely -, 8-8 and We frst examne whether short-term contraran and ntermedate-term momentum profts n Chna stock market are due to measurement errors or tme-varyng rsks. Then, we nvestgate f they are due to overreacton to frm-specfc nformaton or the lead-lag structure n stock returns. 3.. The Effect of Measurement Errors Accordng to Lehmann (990), Park (995), and Conrad, Gultekn and Kaul (997), short-term contraran profts may be spurous because they can be drven by bd-ask spread. When both the bd and the ask prces are used n computng portfolo returns, short-term contraran profts are magnfed than they truly are. Stocks appear to be wnners (losers). Ths s so because the ntal transacton of sellng wnners (buyng losers) s done at the bd (ask) prce and the correspondng transacton at the end of holdng perod s done at the ask (bd) prce wll tend to exhbt proft to short (long) postons. Lehmann (990) controls for the bas due to bd-ask spread by skppng one tradng day between portfolo formaton and holdng perods. Followng the conventon, the portfolo formaton perod n the current analyss ends on Tuesday, whereas the holdng perod begns on Thursday and ends on Wednesday.

13 To check whether skppng one-day suffcently corrects for the bas due to bd-ask spread, we also skp one-week and calculate the dfference between monthly returns of loser and wnner portfolos for the 3 strateges (.e., Strateges -, 8-8, and 0-0). When we do that for - strategy, the average dfference between monthly returns of the loser portfolo and the wnner portfolo s (close to zero). For 8-8 and 0-0 strateges, the result s not much dfferent from the case of skppng one-day. When one week s skpped, the average dfference between monthly returns of the loser and wnner portfolos are (wth t = 3.) for the 8-8 strategy, whereas the dfference for 0-0 strategy s (wth t = -3.7). Gven these results, we cannot exclude the possblty that the contraran proft for - strategy may be spurous because t could have resulted from the measurement error. But, for 8-8 and 0-0 strateges, the bd-ask measurement bas s not a problem. In the followng analyses on the effect of tme-varyng common factors and the lead-lag structure n stock returns, we skp only one day for the purpose of controllng for the bd-ask spread bas. 3.. The Effect of Tme-varyng Common Factors Chan (988) proposes that common factors for the wnner and loser stocks are not constant over tme. Allowng for tme-varyng common factor, he fnds only small abnormal returns for contraran strateges. He fnds that, n contraran strateges, losers stocks tend to be rsker and wnners stocks tend to be less rsky n the perods after portfolos are formed. He also fnds that, when there are momentum profts, the correct strategy s to choose the stocks wth hgh rsk as the wnner stocks and the stocks wth low rsk as the losers stocks. Followng Chan (988), we use CAPM model to nvestgate whether tme-varyng market rsk plays an mportant role n explanng contraran or momentum profts: 9 The frst two portfolos represent short-term contraran strateges and the thrd portfolo represents an ntermedate- 3

14 r Pt r = α + β ( r r ) + ε P ( W, L) () ft Mt ft t r Lt r = ( ) ε () Wt c c α + β rmt rft + t r Wt r = ( ) ε (3) Lt m m α + β rmt rft + t where rlt s the return of loser portfolo at tme t, r Wt s the return of wnner portfolo at tme t, and r Mt s the market ndex return at tme t. As the portfolos are made up of stocks from both the Shangha and Shenzhen exchanges, we use a smple arthmetc average of the two ndex returns as the return on the market ndex. The correlaton coeffcents among market ndex return ( r Mt ) and two ndex returns are over 95%, respectvely. Wnner and loser returns for three strateges (.e., Strateges -, 8-8 and 0-0) are tested by Eq. (). Eq. () and Eq. (3) apply to the dfference between returns of loser and wnner portfolos. Eq. () examnes contraran profts for - and 8-8 strateges, whereas Eq. (3) tests momentum profts for 0-0 strategy. Table shows that the market beta rsk explans a substantal porton of the varaton n the returns of wnner and loser portfolos. However, the varatons n the dfference between returns of the loser and wnner portfolos are not solely explaned by the beta rsk. For Strateges - and 8-8, whch generate contraran profts, there are negatve abnormal returns for wnners and postve abnormal returns for losers. The dfference between betas of the wnner and loser portfolos s not sgnfcantly dfferent from zero. For Strategy 0-0 that generates momentum profts, the dfference s not statstcally sgnfcant although the wnner s beta s larger than the term momentum strategy. 4

15 loser s beta. Therefore, f beta rsk s used as a measure of the market rsk, then contraran profts are not due to beta rsk. In other words, the beta rsk s not the sole reason for momentum profts. INSERT TABLE HERE 3.3. The Effect of Overreacton to Frm-specfc Informaton and the Lead-lag Structure n Stock Returns Stock prces move as nvestors react to two dfferent knds of nformaton: frm-specfc nformaton and unexpected realzaton of common factors. If stock prces overreact to frmspecfc nformaton and later correct, then contraran profts are generated. On the other hand, f stock prces underreact to frm-specfc nformaton, then momentum profts wll emerge. However, we cannot draw the same concluson for over- or under-reacton to common factors because stocks react to common factors dfferently. Some stocks react more quckly to common factors than others do. Then, the returns of some stocks lead those of others because the lead stocks have larger than average contemporaneous betas. Ths lead-lag structure can lead to ether contraran or momentum profts. In ths secton, we follow Jegadeesh and Ttman (995) and nvestgate whether momentum or contraran profts result from over- (under-) reacton to frmspecfc nformaton, the lead-lag structure, or both. We conduct the nvestgaton by decomposng the stock returns nto respectve component that s the result of ether frm-specfc nformaton or common factors One-Factor Model 5

16 Frst, we use one-factor asset prcng model to analyze stock-prce reacton to a common factor and frm-specfc nformaton. We then decompose the sources of contraran and momentum profts n the context of one-factor model. The followng one-factor model of stock returns allows stock prces to react to common factor both currently and wth a one-perod lag: µ (4) t t r, t = + b0, ft + b, f t + e, t where µ s the uncondtonal expected return of stock, f t s the unexpected common-factor realzaton at tme t, b. 0 and b, are the senstvtes of stock to contemporaneous and lagged common factors, respectvely. We assume that the factor senstvtes are uncorrelated wth factor realzatons, that s, t E t ( b0, ft, ft ) = b0, t and E t ( b, ft, f t ) = b,. Followng Jegadeesh and Ttman (993 and 995), we use a demeaned market ndex return ( r, ) n Eq. () as the common factor. We assume that, snce f t s defned as an unexpected factor realzaton, M t cov( f, ) = 0 and t f t E = σ. Snce the comovement n stock returns s entrely captured by ( f t ) f the common factor, we assume that cov( e, t, e j, t ) = 0, j, and cov( e t, e, t ) = σ,. Gven the return-generatng model, the cross-seral covarance between the returns of and j s cov(r,t, r j,t- ) = cov[ E ( b t t t b0 j )] σ f, whereas the cross-seral covarance between the returns of and j s cov(r,t-, r j,t ) = cov[ E ( b t t t 0, b, j )] σ f. 0 The return-generatng model allows for the crossseral covarances to be asymmetrc. For nstance, f j reacts nstantaneously to f t but reacts 0 The dervaton of cross-seral covarance requres, among other thngs, the orthogonaltes between the factor realzatons at dfferent tmes and between the unexpected factor realzaton and the factor senstvtes of and j. 6

17 t t partally wth a delay to f t, that s, f b 0 and b 0, then cov(r,t, r j,t- ) > 0 but cov(r,t-, r j,t ) = j = > 0. In ths case, j leads snce j s return predcts s return but the reverse s not true. Ths aspect of lead-lag structure (that s, the pattern of the cross-seral covarance mpled by the return-generatng model) does not necessarly lead to ether contraran or momentum profts. Ths s because the effect of the overall aspects of the lead-lag structure (that s, the sgn of crosssectonal average of the cross-seral covarance) should also depend on the way that the contraran and momentum nvestment strateges are structured. The property of the cross-seral covarance s dscussed here to facltate the dentfcaton of the sources of the contraran and momentum profts that depend manly on the covarance structure of the nvestment strateges. The cross-seral covarance s an essental component of the lead-lag structure and, together wth autocovarance component, characterzes the covarance structure of returns of the nvestment strategy. An overreacton of stock prces to frm-specfc nformaton wll nduce negatve auto-covarance n e. If stock prces move n the absence of nformaton and later correct, t wll also nduce a negatve auto-covarance n the error term. An overreacton to frm-specfc nformaton always contrbutes postvely to contraran profts, whereas an under-reacton to frm-specfc nformaton always contrbutes postvely to momentum profts. If stock prce reacts to common factor wth a delay, then b, > 0. If stock prce overreacts to common factor, then b, < 0. The effect of over- or under-reacton to common factor on the contraran and momentum profts s In short, the postve effect of lead-lag structure on the proft of contraran strategy can be ascertaned from the negatve of the sgn of the cross sectonal average of the covarance between contemporaneous and lagged betas (namely, sgn of [cov(b 0j, b )]). In contrast, the postve effect of lead-leg structure can be ascertaned from the sgn of the cross-sectonal average of the covarance between contemporaneous and lagged betas (namely, sgn of [cov(b 0, b j )]). To apprecate ths pont, we need to explan the Jegadeesh and Ttman (995) decomposton of contraran and momentum profts. 7

18 dfferent from the effect of over- or under-reacton to frm-specfc nformaton. Ths s so because over- or under-reacton to common factor s entangled wth the effect of the lead-lag structure n stock returns. By examnng the sgn of cross-seral covarance of contemporaneous and lagged betas, (namely, sgn of cov( b, b 0 ) ), we can determne whether the lead-lag structure contrbutes to ether contraran or momentum profts. Suppose stock A always leads stock B. As long as the lagged beta of lead stock (Stock A) s larger than that of lagged stock (Stock B), namely A B b b >, then the cross autocovarance of beta s postve and the lead-lag structure generates momentum profts. On the other hand, f the lagged beta of lead stock (Stock A) s lower than that of lag stock (Stock B), namely A B b b <, then the cross-autocovarance of beta s negatve and the lead-lag structure leads to contraran profts. Ths result holds regardless of whether there s over- or under-reacton to common factor (see Fgure ). INSERT FIGURE HERE If stocks over-react to common factor, namely b < 0, then the lead-lag structure wll generate momentum profts provded that the correcton for overreacton of lead stock s less than that of the lag stock. Ths s so because, although A B b b >, the absolute value of A b s less than that of B b. On the other hand, contraran profts wll emerge f lead stock s correcton for overreacton s larger than that of lag stock. When stocks under-react to common factor ( b > 0 ), the lead-lag structure wll nduce momentum profts f lead stock s more senstve to the lagged common factor. Ths s so because A B b b > s also true n absolute value. If lag stock s more responsve to the lagged common factor, then the lead-lag structure generates contraran profts Decomposton of Contraran and Momentum Profts 8

19 3.3.. The weghtng scheme. In Secton, contraran and momentum profts are calculated by an equally-weghted average stock returns. In order to decompose the contraran or momentum proft nto respectve component that s the result of stock prces reacton to frm-specfc nformaton or lead-lag structure, Jegadeesh and Ttman (993 and 995) calculate momentum and contraran profts by weghtng each stock by the dfference between ts past return and past equally-weghted ndex return. Ths weghtng scheme provdes a tractable framework for examnng the sources of momentum profts and for evaluatng the relatve mportance of the respectve source. Followng Lehmann (990), we calculate contraran profts for strateges - and 8-8 by weghtng all stocks n the sample by the quantum that s computed as the past equally-weghted average stock returns after subtractng the past ndvdual stock return. For 0-0 strategy, every stock return (that s weghted by ts past returns less the past equally-weghted average stock returns) generates momentum proft. Our evdence also shows that, for contraran (momentum), the more a stock loses (gans) n the portfolo formaton perod, the hgher weght the stock gets n the holdng perod. 3 For - and 8-8, the weghtng s: w = (, t r, t rt ) (5) N c whereas actual average contraran proft s: = T N π ( r, t rt ) r, t (6) T t= N = For 0-0, the weghtng s: w = (, t r, t rt ) (7) N Lehmann (990) also computes contraran profts by weghtng all stocks by a quantum that s computed from the past equally-weghted ndex after subtractng the past ndvdual stock return. He then demonstrates that the source of contraran profts can be easly dentfed. Hs weghtng scheme s based on the fndng that the more a loser loses n the portfolo formaton perod, the more t gans n the holdng perod when contraran profts are statstcally sgnfcant. Wth momentum profts, the hgher the wnner gans n the formaton perod, the hgher t gans n the holdng perod. 3 Although the negatve weghtng should not apply to Chna stock market (snce short-sellng s not allowed), we apply t here because our objectve s to dscern the source of contraran/momentum profts. 9

20 m whereas actual average momentum proft s: = T N π ( r, t rt ) r, t (8) T t= N = In the decomposton, rt s the average return of all stocks at tme t. To make contraran (momentum) profts under the weghtng scheme comparable to contraran (momentum) proft generated by equally-weghted returns, we also use overlappng data n computng the average proft for 8-8 and 0-0 strateges. The tme perod between t and t s one week for the three strateges. The number of tme-seres observatons s 369, 345, and 35 for the respectve strateges. Average profts for -, 8-8, and 0-0 strateges are 0.34 x 0-3,.96 x 0-3, and 6.39 x 0-3, respectvely. The correlaton coeffcent between profts under the weghtng scheme and the equally-weghted return dfferences of loser and wnner quntle s 0.88, 0.94, and 0.9 for the three respectve strateges. These hgh correlaton coeffcents suggest that we can use the weghtng scheme for the purpose of nvestgatng the sources of contraran and momentum profts Decomposton of Contraran or Momentum Profts. We decompose contraran and momentum profts usng the weghtng scheme nto components attrbutable to frm-specfc nformaton and common factor. If stock returns are generated by the one-factor model n Eq. 4 and every stock s weghted by the dfference between ts own return and the average return of all stocks, then the expected contraran (momentum) profts can be decomposed as follows (for mplcatons, see Jegadeesh and Ttman, 995): E (9) N c ( π ) = E ( r, t rt ) r, t = σ µ Ω δσ f N = 0

21 E (0) N m ( π ) = E ( r, t rt ) r, t = σ µ + Ω + δσ f N = where N σ µ = ( µ µ ) () N = Ω N cov( e, t, e, t ) N = () N δ t ( b0, b 0 )( b, b ), δ E( δ t ) (3) N = where b 0 and b are the cross-sectonal averages of b, t b,. 0 and t The expected contraran profts (Eq. (9)) and momentum profts (Eq. (0)) have three components. The frst component ( σ ) s the cross-sectonal varance of expected returns. If µ stocks wth hgher expected returns tend to experence hgher-than-average returns durng both portfolo formaton and holdng perods, ths component wll reduce contraran profts and ncrease momentum profts. The second component ( Ω ), namely the cross-sectonal average seral covarance of dosyncratc component of ndvdual stock returns, s determned by stockprce reactons to frm-specfc nformaton. If stock prces overreact to frm-specfc nformaton and correct the overreacton n the followng perod, Ω wll be negatve and hence t wll contrbute to contraran profts. If stock prces under-react to frm-specfc nformaton, on the other hand, Ω wll be postve and t wll ncrease momentum profts. The last component ( δσ ) s the component of contraran or momentum profts attrbutable to the lead-lag structure. If δ < 0 (.e. the cross autocorrelaton of contemporaneous and lagged betas s less than zero), the leadlag structure contrbutes postvely to contraran profts and negatvely to momentum profts. The reverse wll hold f δ > 0. f

22 INSERT TABLE 3 HERE Table 3 reports the regresson results for three components for each of the three strateges, the actual average profts under the weghtng scheme, and the expected profts under the one-factor model. The tme perods between t and t k are, 8 and 0 weeks, respectvely, for the three strateges. Wth eght years data and for the 8-8 strategy, the number of observatons used for estmatng µ, b 0, b n Eq. (4) and cov( e, t, e, t ) vares from 37 to 44 (as t depends on lstng dates). For Strategy 0-0, the number of observatons ranges from 4 to 7. For relable results, we also make full use of the over-lappng data. For example, for each stock n 8-8 strategy, we compute eght estmates for respectve parameter of µ, b 0, b, and cov( e, t, e, t ). We then compute the average for respectve parameter. Smlarly, for Strategy 0-0, we estmate those parameters 0 tmes and then compute ther respectve averages. The results n Table 3 show that the cross-sectonal average of ndvdual stock s senstvty to the lagged common factor, b (.e. the average of lagged beta) s postve for - strategy and negatve for 8-8 and 0-0 strateges, although the absolute value s small. When we gnore the measurement error, the postve lagged beta n short term and negatve lagged beta n longer terms ndcate that stocks on average underreact to common factor n one-week perod but overreact n longer perods. In other words, stocks on average overreact to common factor n a lagged manner.

23 The cross-sectonal varance of expected returns ( σ ) contrbutes 3%, -0%, and 344% to the -, 8-8, 0-0 strateges, respectvely. The longer the tme perod, the more mportant the role t plays. Snce the cross varance of expected return ( σ ) arses from the fact that hgher expected returns tend to experence hgher-than-average returns durng both portfolo formaton and holdng perods, t can serve as an addtonal rsk factor that s not captured by contemporaneous and lagged betas n the one-factor model. Gven the magntude of ts contrbuton, common factors that are not captured by beta rsk appear to play an mportant role n generatng the momentum proft. µ µ The second component, the average cross-sectonal auto-covarance of the dosyncratc component n stock returns ( Ω ) s negatve for all three strateges. It s the only component that contrbutes postvely to contraran profts. Snce Ω s determned by stock prce s reactons to frm-specfc nformaton, the result suggests that stocks heavly overreact to frm-specfc nformaton. The negatve average seral covarance can also arse from the fact that stocks prces are pushed too hgh or too low by rumors at frst but then they are corrected when the rumors are cleared. However, there s a puzzle here. That s, f stocks overreact to frm-specfc nformaton n one- week perod and the prces are corrected n the subsequent week, then n longer tme perods (e.g., 8 or 0 weeks), the auto-covarance ( cov( e, t, e, t ) ) should tend to be zero (or at least ts magntude should decrease). But, our results also ndcate that the absolute value ncreases for both 8-8 and 0-0 strateges. Therefore, the magntude of negatve autocovarance for 0-0 strategy s larger than that for 8-8 strategy. One possble explanaton s that the negatve autocovarance for - strategy s due to measurement error (namely, the bases from the bd-ask spread and non-synchronous data). The fndng n Secton 3. shows that, when one week s skpped, the contraran profts for - strategy dsappear. Ths fndng ndcates that the 3

24 one-day skppng between portfolo formaton and holdng perods s not suffcent to mtgate the bas of measurement error. Another reason may be that dfferent types of frm-specfc nformaton affect stock-prce s overreacton dfferently. If the rumors generate the negatve autocovarance, then the stock prces may be corrected n a relatvely short perod. If the stock prce s pushed too hgh or too low by nvestors overreacton to earnngs forecast, on the other hand, t may take longer tme to correct the dstorted prce. 4 The lead-lag component ( σ f δ ) s postve for all three strateges. The contraran profts decrease and the momentum proft ncreases due to the lead-lag structure. It contrbutes -7% and -% to the contraran profts of - and 8-8 strateges, whereas t contrbutes 7% to the momentum proft of 0-0 strategy. The fndng that the lead-lag structure contrbutes to momentum proft and decrease the contraran proft s dfferent from those of Lo and MacKnlay (990) and Jegadeesh and Ttman (993 and 995). These fndngs n the US market suggest that the leadlag structure would ncrease contraran proft and t s not the man reason for momentum proft. The current fndng also ndcates that the average of covarances between contemporaneous and lagged betas (δ ) s postve. Ths fndng therefore suggests that some frms tend to have hgherthan-average betas wth respect to both contemporaneous and lagged common factor. In other words, contemporaneous and lagged betas are postvely correlated and the lead-lag structure reduces the contraran proft but ncreases the momentum proft. Snce the average lagged beta s postve for - strategy and the cross-sectonal betas exhbt a postve cross autocorrelaton, the weekly lead-lag structure decreases the contraran proft. Table 3 shows that stocks underreact to common factor and lead stocks are also more senstve to the 4 Companes n Chna are requred to report corporate earnngs only semannually. 4

25 lagged common factor than lagged stocks. The negatve lagged beta and postve crossautocorrelaton for 8-8 and 0-0 strateges ndcate that stocks overreact to common factor n longer perods (see Table 3). In ths lead-lag structure, the lead stocks lagged betas are stll hgher than average lagged beta, but the lead stocks lagged betas are lower than lag stocks lagged betas n absolute value. In other words, when stocks prces move later to an opposte drecton (n correctng the overreacton), the magntudes of the reverse moves of lead stocks are less than those of lag stocks. Ths asymmetry contradcts our ntuton. Note that, f stock prces are corrected to ther ntrnsc value durng the reverson, then t s the lag stock (not the lead stock) that should overreact more ntensely to the common factor n the prevous perod. If we aggregate the stock returns n the formaton and holdng perods, then lead stocks wll generate hgher aggregate returns than lag stocks do when the market s up. If there s negatve common factor, then lead stocks wll lose more than lag stocks. Therefore, we can regard lead stocks as the rsker stocks and lag stocks as less rsky ones. The last two rows of Table 3 shows that expected contraran or momentum profts ( E (π ) ) generated from the decomposton are qute close to actual average profts for - and 8-8 strateges under the weghtng scheme, π. For Strategy -, the expected proft s.46 x 0-4, whereas the actual average proft s.34 x 0-4. For Strategy 8-8, the expected proft s.375 x 0-3, the actual proft s.96 x 0-3. But, for Strategy 0-0, the expected proft ( E (π ) ) s , whle the actual observed momentum proft s x 0-3. The relatvely large dfference may be due to the fact that, gven the lmted sample perod (only eght years), the number of observatons s too small to obtan relable estmates for the parameters and/or that the asset prcng model s not sutable to Chna stock market. The 0-week lagged common-factor realzaton s no longer a statstcally sgnfcant ndependent varable n explanng the stock returns. But, the dfference between expected and actual profts should not mpede us from 5

26 drawng a qualtatve nference about the relatve contrbuton of σ µ, Ω, and σ f δ to momentum profts. In absolute value, the total contrbuton of the three components ranges from 7% to 485%. In order to substantate the argument that the lead-lag structure contrbutes postvely to momentum profts, we also use the method suggested by Jegadeesh and Ttman (993). We then examne the relatonshp between the lead-lag effect and the momentum profts. Jegadeesh and Ttman (993) demonstrate that, f the momentum profts result entrely from the lead-lag structure, then the magntude of the proft should be postvely related to the square of common-factor unexpected realzaton n the prevous perod. 5 The cross-sectonal average of stocks senstvtes to lagged common factor,.e., the average of lagged betas, s postve for strategy - but negatve for strateges 8-8 and 0-0 although the absolute value s small. If we gnore measurement error, the postve lagged beta n the short term and negatve lagged beta n the longer term ndcate that on average stocks underreact to common factor wthn one week but fnally overreact to common factor n longer tme perod. Hence, on average, stocks overreact to common factor n a lagged manner. 6 5 For the nvestgaton, we use the followng model: r Wt rlt = α + θf mt, 0 + u (4) t where rwt rlt s the equally-weghted wnner returns less loser returns, f mt, 0 s the demeaned return on the value-weghted ndex n the weeks t 0 through t. The estmates of θ and the correspondng autocorrelatonconsstent t-statstc over the sample perod are 3.69 and.4, respectvely. Ths postve relatonshp ndcates that the lead-lag structure plays an mportant role n generatng the momentum proft. A B b b 6 For all three strateges, the lagged beta of lead stock s larger than that of lag stock,.e., > (n other words, the cross-autocovarance of beta s postve). The lead-lag structure ncreases the momentum profts and decreases the contraran profts regardless of whether there s over- or under-reacton to common factor. Ths fndng follows from the followng summary table. Strategy b Cross autocorrelaton Effect on contraran/momentum proft (Underreacton) Postve decrease contraran proft (Overreacton) Postve decrease contraran proft (Overreacton) Postve ncrease momentum proft 6

27 4. Dscussons Our results show that short-term return reversals and ntermedate-term return contnuatons are observed n Chna stock market. Statstcally sgnfcant contraran profts emerge from the strateges that evaluate stock returns accordng to prevous one- to twelve-week returns and they persst untl the next 6 weeks. In contrast, momentum profts occur for strateges that evaluate stock returns accordng to prevous twelve- to 6-week returns. Lke n the U.S. and other markets, short-term contraran and medum-term momentum can be observed n Chna stock market. Short-term contraran profts tend to exst for one month n the U.S. and other markets. But, n Chna, the contraran profts persst up to three months. Regardless of tme horzon, the beta rsk cannot explan the abnormal returns of short-term contraran strateges. Stocks prces overreacton to frm-specfc nformaton appears to be the sngle most mportant source of the contraran profts. The current analyss ndcates that there are two sources for the momentum proft n Chna market: namely, the cross varance of uncondtonal expected returns and the lead-lag structure. Cross-varyng expected return contrbutes to the momentum proft. Ths fndng suggests that the rsk not captured by beta can explan a non-neglgble porton of momentum proft. Stocks that have hgher expected returns tend to experence hgher-than-average returns durng both the portfolo formaton and holdng perods. That the lead-lag structure s the source of contraran and momentum profts n our study s dfferent from the fndng n the US market. Our results show that the lead-lag structure s the major source of momentum proft and contrbutes negatvely to contraran proft. However, studes n the U.S. market, for example, Lo and MacKnlay (990) and Jegadeesh and Ttman (995), fnd that the leadlag structure ncreases the contraran profts. Furthermore, Jegadeesh and Ttman (993) 7