Stock mispricing induced by an outdated stock market index

Transcription

1 Sock mispricing induced by an oudaed sock marke index KOTARO MIWA 1 Tokio Marine Asse Managemen Co., Ld 1-3-1, Marunouchi, Chiyoda-ku, Tokyo, Japan phone: fax: miwa_fk@cs.c.u-okyo.ac.jp KAZUHIRO UEDA Inerfaculy Iniiaive in Informaion Sudies, The Universiy of Tokyo / CREST, Japan Science and Technology Agency, 3-8-1, Komaba, Meguro-ku, Tokyo, Japan phone: fax: ueda@gregorio.c.u-okyo.ac.jp Biographical noes: Koaro Miwa, Ph.D., is Quaniaive Analys in Tokio Marine Asse Managemen Co., Ld., Japan. Kazuhiro Ueda, Ph.D., is Professor in Inerfaculy Iniiaive in Informaion Sudies, Universiy of Tokyo, Japan. 1 Corresponding auhor. 1

2 Sock mispricing induced by an oudaed sock marke index July 2014 Absrac Alhough a capializaion-weighed sock marke index is regarded as an adequae index o measure he performance of he marke, some oher oudaed indexes, e.g., a price-weighed sock marke index, remain influenial and represenaive. In his sudy, we show ha he oudaed weighing sysem of he marke index causes significan mispricing. As an influenial, albei oudaed sock marke index, we focus on he Nikkei 225. We find ha overweigh socks, i.e., index consiuens wih high share prices, experience excessively srong buying (selling) pressure when sock marke surges (falls), and experience srong price correcion afer such periods of change. Conrarily, we find ha non-consiuen socks wih high share prices do no experience such rading pressure. In addiion, he sudy s resuls sugges ha a consiuen selecion sysem does no induce mispricing. Our findings suppor he view ha he oudaed weighing sysem of he index causes significan mispricing when he marke moves. JEL classificaion: G2, G14, G17, G23 2

3 1. Inroducion Capializaion-weighed, or cap-weighed, indexes have been considered adequae o evaluae he performance of he broad marke for more han 50 years (Markowiz, 1952, 1959; Sharpe, 1965; Arno e al., 2005). Thus, cap-weighed indexes are regarded as represenaive in many sock markes, mos invesors rade cap-weighed marke porfolios o increase or decrease heir exposure o he marke. However, in some sock markes, e.g., he Japanese sock marke, he oudaed price-weighed index is sill influenial; invesors no only consider he price-weighed index as a represenaive marke index, hey also rade he index porfolio o change heir exposure o he sock marke. Capializaion-weighing assigns he greaes weighs o he larges companies. These companies are ypically among he larges in erms of sales, book value, cash flow, dividends, and oal employmen (Arno e al., 2005). Conversely, price-weighing seeks o assign he greaes weighs o high share price socks, even hough higher share price does no necessarily equae o a firm having a higher conribuion o he economy. In addiion, while larger cap socks are likely o have higher liquidiy, socks wih higher share price do no always have higher liquidiy. Thus, he price-weighing sysem is a a much greaer disadvanage han he cap-weighing sysem in erms of reducing price impac from ransacions of he index porfolio. Considering ha even ransacions of cap-weighed marke porfolios have a cerain price impac (Barberis, e al., 2005, and Boyer, 2011) 2, i is highly likely ha ransacions of he price-weighed index porfolio causes an excess price impac, especially on socks excessively weighed on he price-weighed index, also known as overweigh socks. Specifically, when a sock marke surges (falls), increased (decreased) demand for index porfolio can be observed; hus, overweigh socks could experience excessive buying (selling) pressure ha resuls in significan mispricing, when a sock marke surges (falls). Thus, in his sudy, we explore sock mispricing induced by he price-weighing sysem of he influenial sock marke index. As an oudaed bu influenial marke index, we focus on he Nikkei 225, he bes-known price-weighed index covering he Japanese sock marke 3. Since he Nikkei 225 fuures can be raded no only on he Japanese marke bu also on he CME and SGX, Nikkei 225 fuures are raded much more frequenly by invesors o increase or decrease heir exposure o he Japanese sock marke han are TOPIX fuures (he fuures on he cap-weighed sock index 2 These sudies show ha socks end o commove more (less) wih index socks afer hey are added o (deleed from) he S&P 500 index (Barberis, e al., 2005) and S&P/Barra syle index (Boyer, 2011). 3 The Dow Jones Indusrial Average is also a well-known marke index. However, he index is less influenial han S&P 500 because mos invesors rade S&P 500 index fuures o conrol heir exposure o U.S. sock markes raher han Dow Indusrial Average fuures. On he oher hand, rading Nikkei index fuures are regarded as a firs choice o increasing or decreasing invesors exposure o he Japanese sock marke. 3

4 covering he Japanese sock marke) 4. I is highly possible ha sock marke movemen could be accompanied by considerable ransacions of he Nikkei 225 porfolio specifically hrough Nikkei 225 fuures rading. In his sudy, in order o es our predicion, we examine wheher he oudaed weighing sysem of he Nikkei 225 induces mispricing when he marke reurns move significanly. To our bes knowledge, only Greenwood (2008) has invesigaed he effec of he weighing sysem of he Nikkei 225. The findings show ha a price of overweigh sock commoves o ha of oher index consiuens, and sugges ha he Nikkei 225 weighing sysem affecs comovemen wihin Nikkei index consiuens. Since his excess comovemen migh indicae mispricing, hese findings migh suppor our predicion ha he price-weighing sysem of he sock index causes mispricing when he marke moves. However, we canno deny he possibiliy ha sock fundamenals are more correlaed wih he index consiuens. In addiion, he comovemen analysis does no ell us when prices diverge from heir fundamenal values and wheher and when he divergence is correced. Thus, heir findings (i.e., he associaion beween overweighing and sock price comovemen) canno provide an evidence on wheher he price weighing sysem of he sock index causes mispricing during periods of significan marke movemen. In his sudy, o es our predicion, we firs analyze he cross-secional associaion beween overweighing and sock reurns. Then, we examine wheher he ime-varying associaions are correlaed wih concurren and lagged marke reurns. Since significan marke movemen could be accompanied by rading pressure for index shares, overweigh socks could ouperform (underperform) when he sock marke rises (falls). In oher words, he cross-secional associaions beween overweighing and sock reurns should be posiively associaed wih concurren marke reurns. In addiion, hose socks would experience a price correcion, i.e., hey would underperform (ouperform) in a subsequen period of marke surge (fall). Thus, if he oudaed weighing sysem causes significan mispricing, he cross-secional associaions beween overweighing and reurns should be negaively associaed wih lagged marke reurns. Consisen wih our predicion, we find ha overweigh socks experience higher sock reurns when a marke reurn is higher, and hose socks experience lower reurns in a subsequen period. The resuls also reveal ha non-consiuen socks wih high share prices do no experience such rading pressure during periods of significan marke movemen, supporing ha he above-effec on cross secional reurns is induced by ransacions of Nikkei 225 shares. In addiion, he resuls reveal ha he effec of an inclusion in he Nikkei 225 consiuens is no affeced by lagged marke reurns, which indicaes ha he mispricing during periods of significan marke movemen is caused by he price weighing sysem raher han by he consiuens selecion rules. The res of his paper proceeds as follows: Secion 2 presens he developmen of our 4 During he invesigaed period (Sep Dec.2013), average daily rading value of Nikkei fuures is approximaely 300 imes as much as ha of TOPIX fuures. 4

5 hypoheses; Secion 3 concerns our sample and descripive saisics; Secion 4 describes an analysis of sock mispricing induced by he oudaed price-weighing sysem; Secion 5 offers robusness ess for he resuls; finally, we summarize our findings in Secion Hypohesis developmen Since Nikkei 225 fuures are raded no only on he Japanese sock marke bu also on he CME and SGX, a Nikkei 225 fuures ransacion is considered he fases and easies way o change exposures in he Japanese sock marke. In fac, Nikkei index fuures are raded much more frequenly by invesors han are TOPIX fuures. Since arbirageurs long (shor) he 225 index porfolio and shor (long) Nikkei fuures if here is a price dispariy beween he spo and fuure, buying (selling) pressure for he Nikkei fuures resul in buying (selling) pressure for he Nikkei 225 index shares. Thus, he index porfolio is raded by invesors according o an increase or decrease in heir exposure o he Japanese sock marke. Sock marke movemen could reflec changes in invesors demand for aking marke exposure; specifically, marke surge (fall) could reflec increased (decreased) demand for aking he marke exposure. Thus, marke surge (fall) could be accompanied wih increased (decreased) demand for he Nikkei 225 porfolio. Hence, we predic ha overweigh socks, i.e., socks ha are excessively overweighed on he Nikkei 225, experience srong buying pressure when he Japanese sock marke rises and srong selling pressure when he sock marke falls. Since sronger buying (selling) pressure resuls in higher (lower) sock reurns, we formulae he firs hypohesis as follows. Hypohesis 1. Overweigh socks ouperform (underperform) when he sock marke rises (falls). These reurn differences beween overweighed and oher socks during periods of significan marke movemen canno be jusified by a cross-secional difference in a sock s fundamenals. Therefore, i is highly possible ha overweigh socks are overvalued when sock marke surges and are undervalued when he marke falls; rading pressure induced by he weighing sysem of he Nikkei 225 during periods of significan marke movemen could resul in sock mispricing. Since overvalued socks are likely o experience price correcions in a subsequen periods, overweigh socks could experiences lower (higher) sock reurns especially afer a marke rise (fall). This leads o he second hypohesis. Hypohesis 2. Overweigh socks underperform (ouperform) ohers afer a marke rise (fall). We hen examine wheher high-priced non-consiuen socks experience excess rading pressures during periods of significan marke movemen as high-priced index consiuens (overweigh socks) do. If hey do no, we can say ha he observed rading pressures for overweigh 5

6 socks are aribued o ransacions of Nikkei 225 shares. Hence, we examine wheher non-consiuens reurns are affeced by he price-weighing facors, i.e., weighs esimaed on he basis of he price-weighing sysem of he Nikkei 225, no as high-priced index consiuens do. Specifically, we es wheher he effec of he price weighing facors is no posiively associaed wih concurren marke reurns and no negaively associaed wih lagged marke reurns, wihin non-consiuens. This leads o he hird hypohesis. Hypohesis 3. Wihin non-index consiuens, he effec of he price weighing facors is no posiively associaed wih concurren marke reurns and no negaively associaed wih lagged marke reurns. The original index feaure of he Nikkei 225 is no only price-weighing bu also he consiuen selecion rule; 225 consiuen securiies are seleced from he TSE (Tokyo Sock Exchange) Firs Secion based on liquidiy, wih consideraion of indusry allocaion. Thus, we finally examine wheher he consiuen selecion rule causes mispricing. We predic ha he selecion rule is less likely o cause mispricing han is he weighing sysem, since here is a cerain raionaliy for he selecion rule under which high liquidiy socks, which end o be large socks, are seleced as consiuen securiies. In addiion, since liquidiy is higher for Nikkei 225 consiuens han for non-consiuens, a difference in rading pressure beween consiuens and non-consiuens can be absorbed by he high liquidiy of index consiuens. Thus, i is unlikely ha he consiuens selecion rule causes sock mispricing, i.e. overvaluaion of consiuens socks when he marke is up and undervaluaion of consiuens socks when he marke is down. Specifically, a correcion of mispricing induced by he consiuens selecion rule, i.e. underperformance of consiuens socks afer a marke rise and ouperformance of consiuens socks afer a marke fall, canno be observed. This leads o he final hypohesis. Hypohesis 4. The effec of an inclusion in he Nikkei 225 on sock reurns is no negaively associaed wih lagged marke reurns. 3. Daa and definiions 3.1 Sample consrucion We obain our sample from he TSE (Tokyo Sock Exchange) daabase service (hisorical daa is available from he end of July 1993). We collec daa from TOPIX consiuen securiies, which cover all domesic common socks lised on he TSE Firs Secion. We uilize daily daa from he end of July 1993 o he end of We divide he sample ino hree sub-periods (July 1993 o 1999, 2000 o 2006, and 2007 o 2013) and perform sub-period analysis. On average, here are 6

7 approximaely 1500 firms in our sample for each day. For marke reurns, we use capializaion-weighed reurns of TSE Firs Secion socks. Marke reurns coincide wih TOPIX reurns unil he end of Ocober Afer he end of Ocober 2005, TOPIX ransiioned o a free-floa weighing index. To mainain consisency regarding he definiion of he marke index, we calculae unadjused capializaion-weighed index reurns from he beginning of November 2005 as marke reurns Effec of he price-weighing sysem The value of he Nikkei 225 is deermined by adding he sock prices of is consiuens, divided by he presumed face value FV 5, imes a consan, dividing he oal by he index divisor 6. Thus, he index weigh w N225 is proporional o share prices divided by he face value as follows: w N 225 i, P FV P 225 i, i, /50 i1 FV /50 To evaluae he effec of he price-weighing sysem on cross-secional reurn, following he sudy of Greenwood (2008), we firs calculae he raio of each sock s weigh in he Nikkei 225 o is weigh in a capializaion-weighed index. Then, we define overweighing (denoed as OW) as he log of one plus he raio. As discussed in Greenwood (2008), his is no only an inuiive measure of he overweighing relaive o weigh in he cap-weighed index, bu also ha of he price impac from ransacions of index porfolio since sock capializaion is posiively associaed wih liquidiy. Then, we evaluae he effec of he weighing sysem of he Nikkei 225 on cross-secional sock reurns by regressing sock reurns on one-day lagged OW (OW a he previous working day). Since Nikkei index weigh is zero for non-consiuens securiies, OW is zero for approximaely 80% of socks. Thus, OW migh capure no only he effec of he price-weighed sysem bu also he effec of he consiuen selecion sysem of he Nikkei 225 (he reurn spread beween Nikkei index consiuens and non-consiuens). As a resul, when we evaluae he effec of he weighing sysem (he price impac of OW), we conrol for he effec of an inclusion in he Nikkei 225 (he effec of he consiuen selecion sysem) by including a binary variable (denoed as NK) ha has a value of 1 if a sock is included in he Nikkei 225 consiuens, and 0 oherwise. We also include a cap-weighing facor which is defined by he log of one plus weigh of cap-weighed index (denoed as MW) o conrol for he effec of he denominaor of OW (and size effec). In addiion, we conrol for he liquidiy effec and measuremen errors in prices, i.e., bid-ask 5 Mos socks have a face value of 50 (JPY). Bu, some socks have 500, 5000, or Since 2001, he index used he deemed face value which is esimaed by considering pas face value, corporae evens, capializaion changes, and so on. 6 Index divisor is a parameer o adjus sock spli, capializaion changes, and so on. 7

8 spreads in securiies in he following ways. To conrol for he liquidiy effec, we include an illiquidiy indicaor of Amihud (2002),denoed as ILLIQ, which is defined by an average of he absolue value of sock reurn denominaed by million yen rading volume 7 over he one monh, 8 as one of he conrol variables. When here is considerable fund flow o/from he Japanese sock marke, illiquid socks could receive sronger price impac. Thus, cross-secional differences in illiquidiy could resul in cross-secional variaion in sock reurns, especially when he sock marke moves. Furhermore, o conrol for he effec of he bid-ask bounce, we include he bid-ask spread (denoed as SPREAD) as a conrol variable. Since he bid-ask spread daa of Japanese socks for he enire sudied period is no available, we calculae he esimaed bid-ask spread following he mehodology of Corwin and Schulz (2012). Several sudies (e.g., Roll 1984, Akins and Dyl, 1990) demonsrae and sugges ha a daily cross-secional paern is parly aribued o he exisence of bid-ask spreads in securiies. Especially, when he sock marke surges (falls), he closing price is deermined by he ask price (bid price) because of srong buying (selling) pressure. Thus, an effec of bid-ask spread on cross-secional reurns could be srong especially when he sock marke moves. Therefore, o evaluae he effec of he price-weighed sysem on sock reurns for each day, he daily reurns are regressed on no only lagged OW bu also on he above-menioned four variables (lagged NK, MW, ILLIQ, and SPREAD) as: R i, 1, OW i, 1 NK i, 1 β MW i, 1 βilliq 1, ILLIQ i, 1 β SPREAD OW1, NK1, MW1, SPREAD1, i, 1 (1) 1, i, denoes one-day reurns for sock i over he day. and can be regarded as a proxy for he effec of he price weighing sysem on sock reurns and he effec of an inclusion in he Nikkei 225 (he effec of he consiuen selecion sysem). In addiion, for a robusness check, we include book-o-price raio (denoed as BP) 9 and price momenum variables, he reurn over he preceding six monhs (MOM) o conrol for he momenum and value effecs. We run he following regression: R i, 2, OW OW 2, i, 1 NK NK 2, i,1 β ILLI 2, ILLIQ i,1 β SPREAD2, β SPREAD MW 2, i,1 β MW BP2, i,1 BP i,1 β MOM 2, MOM i,1 2, i, (2) The descripive saisics for marke reurn, and each coefficien of Eq. (1) and Eq. (2) are shown in Table 1. During his period, average daily marke reurn is no significanly posiive, 7 Original definiion of Amihud illiquidiy is defined by he absolue value of sock reurn divided by dollar rading volume (Amihud 2002). However, o reduce currency effec on evaluaing illiquidiy, he denominaor is se o be yen rading volume. 8 Specifically, we ake 21 rading days average of he raio. 9 BP is defined as he book value of oal common equiy a he end of he mos recen quarer, deflaed by price. 8

9 reflecing Japanese weak growh. As is consisen wih he sudy by Iwaisako (2007), an auocorrelaion of marke reurns on a one-day window is quie weak (0.03). In addiion, and are neiher significanly posiive nor negaive indicaing ha he price-weighing sysem and he consiuens selecion sysem do no have long-run (coninuous) effecs on cross-secional reurns. 4. Hypohesis esing 4.1. The associaion wih concurren marke reurns In his secion, we show he analysis o es Hypohesis 1 regarding he associaion beween he effec of he weighing sysem of he Nikkei 225 (he price impac of a ransacion of he index shares) and concurren marke reurns. Firs, we simply divide he days based on wheher he sock marke rises or falls (marke reurn is eiher higher han zero or no). Moreover, we examine wheher he effec of he weighing sysem in regression models (1) ( ) is significanly posiive when he marke is up and negaive when he marke is down. Second, we run he following regression o analyze he associaion beween marke reurn and he effec of he weighing sysem: (s=1,2) (3) OW a b MR s As As e, As, Coefficien b As (s=1, 2) is esimaed using he weighed leas squares (WLS) mehod, where he values for he reciprocal of he square of he sandard error of coefficien s in regression models (1) and (2), respecively, are used as weighs. A posiive coefficien in Equaion 3 (b A >0) indicaes ha overweigh socks experience sronger buying pressure when he Japanese sock marke rises and experience sronger selling pressure when he Japanese sock marke falls. Specifically, he posiive coefficien indicaes ha a price impac caused by he price weighing sysem is posiively associaed wih concurren marke reurn. The resul is shown in Table 2, and in he whole period. However, s s (s=1, 2) is neiher significanly posiive nor negaive are significanly posiive when he marke is up and negaive when he marke is down, indicaing ha overweigh socks ouperform (underperform) when he marke is up (down). In addiion, Table 2 (b) shows ha s is significanly, posiively associaed wih marke reurns. This resul can be undersood ha he effec of he price-weighing sysem is posiively associaed wih marke reurns. These findings srongly suppor Hypohesis The associaion wih lagged marke reurns In his secion, we examine Hypohesis 2. If his is he case, overweigh socks are likely o be 9

10 overvalued (undervalued) during he periods of up marke (down marke). To his end, we firs divided days based on wheher he sock marke had risen or fallen in he previous working day. Since mispricing could be correced gradually, we also divide days based on wo- and hree-day lagged marke reurns o examine he associaion beween he price correcion and wo- and hree-day lagged marke movemen. If he price-weighing sysem causes mispricing during periods of significan marke movemen, overweigh socks will experience price correcion especially afer hese periods; specifically, overweigh socks would underperform afer a marke rise, and ouperform afer a marke fall. Thus, we examine wheher he effec of he weighing sysem on sock reurns ( ) is significanly negaive afer a marke rise and posiive afer a marke fall. In addiion, we analyze wheher he effec of he weighing sysem is negaively associaed wih lagged marke reurns, by running he following regressions: a b MR b MR b MR b MR e (s=1, 2) (4) OW s, Bs B0s B1s 1 B2s 2 B3s 3 The coefficiens for he models are esimaed using he WLS mehod, where he reciprocal of he square of he sandard error of coefficien 2 1 B in regression model (1) and ha of coefficien in regression model (2) are used as weighs. We include concurren marke reurn M as a conrol variable since here is a srong posiive associaion beween concurren marke reurn and he price impac of he overweighing (as shown in he previous secion). Furhermore, we include no only M 1 bu also M 2 and M 3 as independen variables, considering he possibiliy of gradual price correcion. We examine wheher negaively associaed wih M 1, M 2, or M 3. The resul in Table 3 (a) reveals ha is sill posiively associaed wih M and is significanly negaive when one-day lagged OW marke reurn is posiive and significanly posiive when one-day lagged marke reurn is negaive. This resul indicaes ha overweigh socks underperform (ouperform) one-day afer a marke rise (fall). In addiion, Panels (b1) and (b2) show ha is significanly, negaively associaed wih OW one-day-lagged marke reurns (M 1 ). This negaive associaion beween he effec of he price-weighing sysem and he lagged marke reurn can be observed in each sub-period. On he oher hand, OW is posiively associaed wih wo-day-lagged marke reurns ( M 2 ) and hree-day-lagged marke reurns (M 3 ). However, since hese average coefficiens are much smaller han hose of M 1, he associaion wih wo- and hree-day-lagged reurns is quie weak, compared wih he associaion wih one-day lagged marke reurns. In sum, hese resuls indicae ha alhough overweigh socks ouperform (underperform) when he marke is up (down), he performance is oally reversed in a subsequen day. This resul can be undersood from he view ha overweigh socks experience srong rading pressure, which causes significan mispricing, especially during periods of significan marke movemen, and he mispricing is correced on a subsequen day. Alhough he mispricing does no las for more han wo days, our resuls clearly 10

11 suppor he possibiliy ha he price-weighing sysem causes periodic bu significan mispricing when he sock marke moves. 4.3 Effec of he price weighing facors wihin non-consiuens In his secion, we es he predicion ha non-consiuen socks wih high share prices do no experience he same rading pressure during periods of significan marke movemen. As such, we es Hypohesis 3, which posis ha wihin non-consiuens, he effec of he price-weighing facors is no posiively associaed wih concurren marke reurns and no negaively associaed wih lagged marke reurns. To calculae he price-weighing facors, we should esimae weighs for non-index consiuens based on he price-weighing sysem of Nikkei 225. As explained in Secion 3, he weigh is basically deermined by a share price denominaed by is face value. However, since 2001, he Japanese socks have no had official face value. Thus, he deemed face value, which is prediced by considering pas face value, corporae evens, and oher index consiuens, has been used o calculae he Nikkei 225. Since he deemed face value is affeced by oher index consiuens and by qualiaive judgmen made by index disribuors, we hardly esimae face value for non-consiuens socks. Therefore, we calculae he non face-value adjused weigh for non-consiuens: we simply calculae he weighs ha are correlaed wih heir share price 10. Alhough we do no adjus he weigh by heir face value, he unadjused weighs are likely o be highly correlaed wih face-value adjused weighs; he unadjused weighs for Nikkei 225 consiuens have an approximaely 0.8 correlaion wih he official index weighs. Similar o he definiion of he overweighing facor for Nikkei 225 consiuens, we hen calculae he raio of he weigh o is weigh in capializaion-weighed index; finally, we define a price-weighing facor PF as he log of one plus he raio 11. To evaluae he effec of a price-weighing facor PF, for each day, daily reurns are regressed on PF in addiion o he four conrol variables (NK, MW, ILLIQ, and SPREAD), as: R i, 3, PF i, 1 NK NK i, 1 βmw MW i, 1 βilliq 3, ILLIQ i, 1 β SPREAD PF1, 3, 3, SPREAD3, i, 1 (5) 3, i, R i, 4, PF PF 2, i, 1 NK NK 4, i,1 β ILLIQ 4, ILLIQ i,1 β SPREAD4, β SPREAD MW 4, i,1 MW β i,1 BP4, BP i,1 β MOM 4, MOM i,1 4, i, (6) 10 We also calculae he weigh based on logged share price o reduce an excessive influence of high-priced socks. When we use his measure, he resuls regarding he associaion beween he effec of he pricing facors and marke reurns go hrough as before. The deails of he resuls are available upon reques. 11 PF have a value of zero for Nikkei 225 consiuens. 11

12 PF can be regarded as he effec of he price-weighing facor on cross-secional reurns. We examine wheher MR, or 2 3 PF s, is posiively associaed wih PF MR and negaively associaed wih MR, 1 MR by regressing on concurren and lagged marke reurn as: PF a b MR b MR b MR b MR e (s=1,2) (7) C s C0s C1s 1 C2s 2 C3s 3 The coefficiens for model (7) are esimaed using he WLS mehod, where he values for he reciprocal of he square of he sandard error of coefficien PF s, and (6), respecively, are used as weighs. In addiion, we calculae average up, when he marke is down, and afer hese periods. The resuls in Table 4 reveal ha marke is down. Furhermore, PF reurns. The resuls also reveal ha marke is up (down), and PF PF C (s=1, 2) in regression models (5) PF when he marke is is negaive when he marke is up and posiive when he is significanly, negaively associaed wih concurren marke PF is significanly posiive (negaive) when one-day lagged is significanly posiively associaed wih one-day lagged marke reurn. No resuls suppor he possibiliy ha he effec of he price-weighing facor is posiively associaed wih concurren marke reurns and negaively associaed wih lagged marke reurns. Thus, hese resuls suppor Hypohesis 3. I is likely ha observed rading pressures for overweigh socks is aribued o ransacions of he Nikkei Effec of he consiuen selecion sysem The price impac of he Nikkei 225 shares ransacion can be divided ino he impacs aribued o he price-weighing sysem and hose aribued o he index consiuens selecion sysem. In his sudy, we predic ha he mispricing is caused by he price-weighing sysem raher han he index consiuens selecion sysem. To es our predicion, we es Hypohesis 4, which posis ha he effec of he index consiuens selecion sysem, i.e., he effec of an inclusion in he Nikkei 225 on sock reurn, is no associaed wih lagged marke reurns. If he hypohesis is suppored, we can conclude ha he index consiuens selecion sysem does no cause mispricing when he sock marke moves. To his end, we firs examine wheher he effec of an inclusion in he Nikkei 225 ( ) is significanly negaive afer a marke rise and posiive afer a marke fall. As he second sep, and in order o analyze he associaion beween he effec of an inclusion in he Nikkei 225 and lagged marke reurns, we run he following regressions: a b MR b MR b MR b MR e (s=1, 2) (8) NK s, Ds D0s D1s 1 D2s 2 D3s 3 The coefficiens for model (8) are esimaed using he WLS mehod, where he reciprocal of he D square of he sandard error of coefficien ( 1 ) in regression model (1) and ha of coefficien 12

13 ( 2 ) in regression model (2) are used as weighs. We examine wheher ( ) is negaively associaed wih MR, 1 MR, or 2 MR. 3 The resul in Table 5 (a) reveals ha NK negaive when he marke is down. Panels (b1) and (b2) show ha concurren marke reurns ( is significanly posiive when he marke is up and NK is posiively associaed wih MR ). I seems ha he consiuens selecion sysem affecs cross-secional sock reurns when he sock marke moves. However, we canno observe any price correcion afer hese periods. Table 5 (a) reveals ha NK is no significanly negaive afer a marke rise and no significanly posiive afer a marke fall. Panels (b1) and (b2) show ha no significanly associaed wih MR and 1 MR. Alhough he whole periods regression analysis 2 shows ha NK migh be negaively associaed wih hree-day lagged marke reurns, sub-period NK analysis shows ha he associaion is no robus. In summary, hese resuls suppor Hypohesis 4, which posis ha he effec of an inclusion in he Nikkei 225 on sock reurn is no associaed wih lagged marke reurns, indicaing ha he consiuens selecion rule of he Nikkei 225 does no cause mispricing when he marke moves. is 5. Robusness 5.1 Analysis wihin Nikkei 225 consiuens As menioned in Secion 2, since he Nikkei index weigh is 0 for non-consiuens securiies, OW is 0 for approximaely 80 % of domesic common socks lised on he TSE Firs Secion. Thus, OW migh capure no only he price impac caused by he rade of Nikkei 225 shares bu also he effec of an inclusion in he Nikkei 225. Thus, in he previous secion, when we evaluae he effec of he price-weighing sysem, i.e., he price impac of OW, we conrol for he effec of an inclusion in he Nikkei 225 by including a binary variable NK as one of he conrol variables. However, we can also conrol i by limiing our analysis o Nikkei 225 consiuens. Therefore, in his secion we examine he effec of he price weighing sysem wihin Nikkei 225 consiuens. Specifically, we run he regression model wihin Nikkei 225 consiuens for each day, as: R i, 5, OW i, 1 βmw MW i, 1 βilliq 5, ILLIQ i, 1 β SPREAD OW3, 5, SPREAD5, i,1 5, i, (9) R i, 6, β BP6, OW 4, BP i,1 OW β i, 1 β MOM 6, MW 6, MOM MW i,1 i,1 β 6, i, ILLIQ 6, ILLIQ i,1 β SPREAD6, SPREAD i,1 (10) We calculae average β OW3 and β OW4 when he marke is up and when he marke is down, and afer hese periods. In addiion, we examine wheher β OW3 and β OW4 are posiively associaed 13

14 wih MR and negaively associaed wih 1 MR, MR, or 2 MR, by regressing β 3 OW3 and β OW4 on lagged marke reurns ( MR, 1 MR, or 2 MR ) and concurren marke reurn ( 3 MR ) as follows: a b MR b MR b MR b MR e (s=3,4) (11) OW s, E s E0s E1s 1 E2s 2 E3s 3 The coefficiens for model (11) are esimaed using he WLS mehod, where he values for he reciprocal of he square of he sandard error of coefficien (s=3, 4) in regression models (9) s and (10), respecively, are used as weighs. The resuls are shown in Table 6 and follow as before: marke is up (down) and OW E is posiive (negaive) when he is posiively associaed wih concurren marke reurns. Furhermore, is negaive (posiive) 1 day afer a marker rises (falls) and OW is negaively associaed wih 1 day lagged marke reurn. These resuls also suppor he view ha he price weighing sysem causes periodical bu significan mispricing when he marke moves. 5.2 Financial leverage Modigliani and Miller (1958) sugges ha afer conrolling for asse risk, equiy beas should be posiively relaed o he degree of financial leverage. Alhough Hech (2002) ess his proposiion using U.S. daa and he daa do no confirm i, Greenwood (2008) finds ha leverage is posiively relaed o he comovemen of sock reurns wihin he Nikkei consiuens. Thus, we examine wheher overweigh socks sensiiviy o marke reurn is aribued o he effec of financial leverage. To his end, we also include financial leverage raio (LEV) he raio of long-erm deb o common equiy o conrol for a financial leverage facor. We run he following regression: R i, 7 OW OW 5, i, 1 NK NK 7, i,1 β SPREAD7, SPREAD i,1 β LEV 7, LEV β i,1 MW 7, MW 5, i, i,1 β ILLIQ 7, ILLIQ i,1 (12) R i, 8, OW OW 6, i, 1 NK NK8, i,1 β SPREAD8, SPREAD i,1 β BP8, BP i,1 β β MW 8, MW MOM8, i,1 MOM β i,1 ILLIQ 8, β ILLIQ LEV 8, i,1 LEV i,1 8, i, (13) Then, OW is regressed on lagged marke reurns ( 1 marke reurns ( MR ) as follows: OW s, F s F0s F1s 1 F 2s 2 F3s 3 MR, MR, or 2 MR ) and concurren 3 a b MR b MR b MR b MR e (s=5, 6) (14) The coefficiens for model (14) are esimaed using he WLS mehod, where he values for he reciprocal of he square of he sandard error of coefficien F (s=5, 6) in regression models (12) OW s and (13), respecively, are used as weighs. We examine wheher β OW5 and β OW6 are posiively associaed wih MR and negaively associaed wih 1 MR, MR, or 2 MR. In addiion, we 3 14

15 calculae average β OW5 and β OW6 when he marke is up and when he marke is down and afer hese periods. The resul is shown in Table 7 where is posiive (negaive) when he marke is up (down) and is posiively associaed wih concurren marke reurn. Furhermore, is negaive (posiive) one day afer a marke rise (fall) and is negaively associaed wih one-day lagged marke reurn. Thus, he effecs of financial leverage do no accoun for our resuls. 5.3 Alernaive measuremen of index overweighing In his secion, o es he robusness of our resuls, we uilize anoher measure of overweighing and examine wheher he effec of he price weighing sysem, evaluaed by he alernaive measuremen of overweighing, is also posiively associaed wih wih MR, 1 MR, or 2 MR. 3 MR and negaively associaed The measure of index overweighing used hroughou he paper is log(1+w N225/w MV). As discussed in Greenwood (2008), his is an inuiive measure of he overweighing of he sock and he price impac from ransacions of index porfolio since sock capializaion, which deermine w MV, is posiively associaed wih liquidiy. An alernaive liquidiy measure would be he illiquidiy measure of Amihud (2002). Ideally, his would capure sock price sensiiviy o uninformed demand. Since a rading value from an index porfolio s ransacion is correlaed wih index weigh, index weigh muliplied by he illiquidiy measure would capure a price impac from ransacions of index porfolio. Thus, he following measure (denoed as AOW) can be regarded as an alernaive measuremen of overweighing: AOW i, ILLIQ i, w N 225 i, 225 i1 ILLIQ i, w N 225 i, To evaluae he effec of he price weighing sysem, i.e., he price impac of AOW, for each day, daily reurns are regressed on AOW and conrol variables as: R i, 9, OW AOW i, 1 NK i, 1 βilli ILLIQ Q i, 1 β SPREAD 7, NK9, 9, SPREAD9, i, 1 (15) 9, i, R i, 10, OW AOW 8, i, 1 NK NK10, i,1 β MW10, MW i,1 β BP10, BP i,1 β MOM10, β ILLIQ 10, MOM i,1 ILLIQ i,1 10, i, β SPREAD10, SPREAD i,1 (16) (s=7, 8) can be regarded as an alernaive measure for he effecs of he price-weighed OW s sysem. Then, (s=7, 8) is regressed on lagged marke reurns ( OW s 1 concurren marke reurns ( MR ) as follows: OW s, Gs G0s G1s 1 G2s 2 G3s 3 MR, MR, or 2 MR ) and 3 a b MR b MR b MR b MR e (s=7, 8) (17) G 15

16 The coefficiens for model (17) are esimaed using he WLS mehod, where he values for he reciprocal of he square of he sandard error of coefficien (s=7, 8) in regression models (15) OW s and (16), respecively, are used as weighs. In addiion, we calculae average β OW7 and β OW8 when he marke is up, when he marke is down, and afer hese periods. The resuls are shown in Table 8. When we use his measure of overweighing, we obain he same resuls as before: (s=7, 8) is posiive (negaive) when he marke is up (down) and OW s OW is posiively associaed wih concurren marke reurns. Furher, afer a marke rise (fall) and OW OW is negaive (posiive) one day is negaively associaed wih one-day lagged marke reurns. 6. Summary Alhough a cap-weighed sock marke index has been regarded as an adequae index o measure he performance of he marke, some sock indexes ha apply oudaed price-weighing sysems are sill influenial and represenaive. In his sudy, we examine wheher an oudaed sock price index causes mispricing. To es his possibiliy, we focused on he Nikkei 225 index. No only is his price-weighed index regarded as a represenaive index for he Japanese sock marke, bu invesors also rade he index porfolio o increase or decrease heir exposure in he Japanese sock marke. Buying (Selling) pressure for he Nikkei 225 index porfolio could be higher (lower) when marke reurn is higher (lower). Thus, socks ha are more overweighed on he Nikkei 225 experience more buying (selling) pressure when sock marke surges (falls). This rading pressure for overweigh socks is aribued no o heir fundamenals, bu o he oudaed weighing sysem of he index. In addiion, overweigh socks do no always have higher liquidiy o absorb higher rading pressure han ohers. Thus, hese excessive rading pressures during periods of significan marke movemen could resul in significan mispricing for hose socks. Consisen wih our predicion, we firs find ha overweigh socks significanly ouperform (underperform) when he marke is up (down). The findings sugges ha overweigh socks could experience significan rading pressure when he sock marke moves considerably. Second, hey significanly underperform (ouperform) afer he periods, i.e. heir performance is reversed. The resuls suppor he view ha he overweigh socks are significanly overvalued (undervalued) when sock marke surges (falls). In addiion, we find ha non-consiuen socks wih high share prices do no experience such rading pressure, no as index consiuens do; his resul suggess ha observed rading pressures for overweigh socks is aribued o ransacions of Nikkei 225. Finally, we find ha he consiuen selecion sysem of he Nikkei 225 does no cause mispricing during periods of significan marke movemen. In sum, hese findings srongly suppor he view ha he price weighing sysem of he Nikkei 225 causes periodical bu significan mispricing when he sock 16

17 marke moves. Our resuls no only uncover mispricing, which is aribued o he oudaed weighing sysem of he marke index, bu hey also suppor he demand heory in which correlaed invesor demand for securiies causes periodic and widespread mispricing (De Long e al., 1990; Pindyck and Roemberg, 1993; Vijh, 1994; Hardouvelis, e sl., 1994; Morck e al., 2000). Our sudy shows ha unusual (oudaed) weighing sysem causes unusual correlaed demand for securiies, which resuls in mispricing when he marke moves. In addiion, our sudy raises anoher problem for using he price-weighed index as a sock marke index. A price-weighed marke index has been regarded as a less adequae index o measure he performance of he marke, since socks wih higher share price do no always mean greaer conribuion o he marke. In addiion o his problem, our analyses show ha he index value could be disored by mispricing which is induced by he index weighing sysem. Specifically, when he marke is up, he index value could be upwardly biased due o overvaluaion of overweigh socks, while when he marke is down he index value could be downwardly biased due o undervaluaion of overweigh socks. Thus, he daily reurns of he price-weighed index are biased by no only an inadequae evaluaion of marke movemen bu also mispricing induced by he weighing sysem. References Amihud, Y., 2002, Illiquidiy and sock reurns: Cross-secion and ime series effecs, Journal of Financial Markes, 5, Arno, D., J. Hsu, and P. Moore, 2005, Fundamenal indexaion, Financial Analyss Journal, 61, Akins, A. and E. Dyl, 1990, Price reversals, bid ask spreads, and marke efficiency, Journal of Financial and Quaniaive Analysis, 25, Barberis, N., A. Shleifer, and J. Wurgler, 2005, Comovemen, Journal of Financial Economics, 75, Boyer, B., 2011, Syle relaed comovemen: Fundamenals or labels? Journal of Finance 66, Corwin, A. and P. Schulz, 2012, A simple way o esimae bid-ask spreads from daily high and low prices, Journal of Finance, 67, De Long, J. Bradford, A. Shleifer, L. Summers, and R. Waldmann, 1990, Noise rader risk in financial markes, Journal of Poliical Economy, 98, Greenwood, R., 2008, Excess comovemen: evidence from cross-secional variaion in Nikkei225 weighs. Review of Financial Sudies, 21, Hech, P., 2002, Do equiy covariances reflec financial leverage? Working Paper, Harvard Business 17

18 School. Hardouvelis, G., R. La Pora, and T. Wizman, 1994, Wha moves he discoun on counry equiy funds? in Jeffrey Frankel (ed.), The Inernaionalizaion of Equiy Markes (Chicago, The Universiy of Chicago Press). Iwaisako, T, 2007, Sock index auocorrelaion and cross-auocorrelaions of size-sored porfolios in he Japanese marke, Hiosubashi Journal of Economics, 48, Markowiz, H., 1952, Porfolio selecion, Journal of Finance, 7, Markowiz, H., 1959, Porfolio Selecion: Diversificaion of Invesmens, New York: John Wiley & Sons. Modigliani, F. and M. Miller, 1958, The cos of capial, corporae finance and he heory of invesmen, American Economic Review, 48, Morck, R., B. Yeung and W. Yu, 2000, The informaion conen of sock markes: Why do emerging markes have synchronous sock price movemens? Journal of Financial Economics, 58, Pindyck, R., and J. Roemberg, 1993, The comovemen of sock prices, Quarerly Journal of Economics, 108, Roll, R., 1984, A simple implici measure of he effecive bid-ask spread in an efficien marke, Journal of Finance, 39, Sharpe, W., 1965, Risk-aversion in he sock marke: Some empirical evidence, Journal of Finance, 20, Vijh, A., 1994, S&P500 Trading sraegies and sock beas, Review of Financial Sudies, 7,

19 Table 1 Descripive Saisics Table 1 shows descripive saisics of he coefficiens of Eqs. (1) and (2). The Mean row shows he ime series average. Max / Min / SD show he maximum value/minimum value/sandard deviaion. Prob{X>=0} and Prob{X<0} show he probabiliy ha he value is more han or equal o 0 and he probabiliy ha he value is negaive, respecively. The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. Mean SD Min Max Prob{X>=0} Prob{X<0} MR 0.01% (0.52) 1.34% -9.57% 13.51% 50.6% 49.4% βow1-0.02% (1.12) 1.45% % 8.12% 49.6% 50.4% βow2-0.01% (0.39) 1.45% -8.98% 8.71% 50.7% 49.3% βnk1 0.02% (1.65) % 51.0% βnk2 0.02% (1.90) % 51.3% βmv1-6.56% (2.64) *** % 52.4% βmv2 5.48% (1.08) % 50.9% βbidask1-0.24% (1.95) % 53.0% βbidask2-0.38% (3.44) *** % 52.7% βilliq1 3.35% (1.24) % 49.3% βilliq2-2.21% (0.96) % 50.9% βbp % (2.86) *** % 43.2% βmom % (3.39) *** 3.29% -18.6% 201.9% 45.9% 54.1% 19

20 Table 2 The associaion wih concurren marke reurns Table 2(a) shows he averages of β OW1 and β OW2 when he marke is up (shown in he column of MR 0 ), when he marke is down (shown in he column of MR < 0 ), and he enire invesigaed period (shown in he column of Whole period ). Weighed leas squares regression resuls for Eq. (3) are shown in Table 2 (b). The regression resuls for he periods , , , and he enire invesigaed period are shown in he columns , , , and Whole period, respecively. The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. (a) Average values when he marke is up & down βow1 βow2 (b) Regression analysis βow1 βow2 Whole period MR >=0 MR < % 0.131% *** % *** (1.08) (6.31) (9.08) % 0.162% *** % *** (0.36) (7.81) (9.17) Whole period *** *** *** 0.21 *** (11.88) (4.20) (6.25) (13.24) *** *** *** 0.22 *** (11.62) (5.10) (7.38) (14.09) 20

21 Table 3 The associaion wih lagged marke reurns Table 3(a) shows he averages of β OW1 and β OW2 one day afer a marke rise (shown in he column of MR 1 0 ), one day afer a marke fall (shown in he column of MR 1 < 0 ), wo days afer a marke rise (shown in he column of MR 2 0 ), wo days afer a marke fall (shown in he column of MR 2 < 0 ), hree days afer a marke rise (shown in he column of MR 3 0 ), hree days afer a marke fall (shown in he column of MR 3 < 0 ), during he whole invesigaed period (shown in he column of Whole period ). Weighed leas squares regression resuls for Eq. (4) in he ex are shown in Panels (b1) and (b2). The columns of MR, MR 1, MR 2, and MR 3 show he average coefficiens of MR, MR 1, MR 2, and MR 3, respecively. The regression resul for he period from 1993 o 1999, he period from 2000 o 2006, he period from 2007 o 2013, and he whole invesigaed period are shown in he row of , , , and Whole period, respecively. The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. (a) Average values when he marke is up & down βow1 βow2 Whole period MR -1 >=0 MR -1 <0 MR -2 >=0 MR -2 <0 MR -3 >=0 MR -3 < % % *** 0.217% *** % % 0.005% % ** (1.08) (13.30) (10.34) (0.92) (1.25) (0.25) (2.41) % % *** 0.233% *** 0.011% % 0.024% % (0.36) (12.41) (11.18) (0.54) (1.27) (1.20) (1.87) (b1) Regression analysis for OW1 (b2) Regression analysis: OW 2 21

22 Table 4 The effec of he weighing sysem for non-consiuens Table 4(a) shows he averages of β PF1 and β PF2. Weighed leas squares regression resuls for Eq. (7) in he ex are shown in Panels (b1) and (b2). The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. (a) Average values when he marke is up & down βpf1 βpf2 Whole period MR >=0 MR <0 MR -1 >=0 MR -1 <0 MR -2 >=0 MR -2 <0 MR -3 >=0 MR -3 < % % *** 0.061% 0.073% *** % *** % % *** % % *** (1.57) (16.25) (1.18) (7.01) (3.73) (1.32) (4.39) (1.65) (2.90) % % *** 0.163% *** 0.084% *** % *** 0.019% % *** 0.001% % ** (1.16) (18.67) (16.22) (8.68) (10.45) (1.87) (4.22) (0.08) (2.45) (b1) Regression analysis: PF1 (b2) Regression analysis: PF 2 22

23 Table 5 The effec of he consiuens selecion sysem Table 5(a) shows he averages of β NK1 and β NK2. Weighed leas squares regression resuls for Eq. (8) in he ex are shown in Panel (b1) and (b2). The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. (a) Average values when he marke is up & down βnk1 βnk2 Whole period MR >=0 MR <0 MR -1 >=0 MR -1 <0 MR -2 >=0 MR -2 <0 MR -3 >=0 MR -3 < % 0.178% *** % *** 0.048% *** % % 0.040% *** 0.005% 0.033% *** (1.65) (15.39) (13.41) (4.28) (0.92) (0.12) (3.56) (0.39) (3.08) 0.021% 0.144% *** % *** 0.041% *** 0.000% 0.004% 0.038% *** 0.014% 0.027% *** (1.90) (12.80) (10.03) (3.83) (0.01) (0.38) (3.51) (1.25) (2.62) (b1) Regression analysis: NK1 (b2) Regression analysis: NK2 23

24 Table 6 The effec of he weighing sysem wihin he index consiuens Table 6(a) shows averages of β OW3 and β OW4. Weighed leas squares regression resuls for Eq. (11) in he ex are shown in Panels (b1) and (b2). The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. (a) Average values when he marke is up & down βow3 βow4 Whole period MR >=0 MR <0 MR -1 >=0 MR -1 <0 MR -2 >=0 MR -2 <0 MR -3 >=0 MR -3 < % 0.048% ** % *** % *** 0.167% *** % % 0.010% % ** (0.90) (2.11) (4.33) (9.50) (7.66) (0.91) (0.88) (0.48) (2.29) 0.000% 0.113% *** % *** % *** 0.172% *** 0.014% % 0.034% % (0.01) (5.05) (5.60) (7.94) (7.79) (0.68) (0.69) (1.62) (1.61) (b1) Regression analysis: OW 3 (b2) Regression analysis: OW 4 24

25 Table 7 The effec of he weighing sysem afer leverage adjusmen Table 7(a) shows he averages of β OW5 and β OW6. Weighed leas squares regression resuls for Eq. (14) in he ex are shown in Panels (b1) and (b2). The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. (a) Average values when he marke is up & down βow5 βow6 Whole period MR >=0 MR <0 MR -1 >=0 MR -1 <0 MR -2 >=0 MR -2 <0 MR -3 >=0 MR -3 < % 0.155% *** % *** % *** 0.220% *** % % 0.002% % ** (1.25) (7.32) (11.00) (13.52) (10.33) (0.72) (1.80) (0.10) (2.56) % 0.190% *** % *** % *** 0.236% *** 0.016% % 0.023% % (0.41) (9.17) (10.66) (12.72) (11.32) (0.78) (1.62) (1.16) (1.93) (b1) Regression analysis: OW 5 (b2) Regression analysis: OW 6 25

26 Table 8 Alernaive measuremen of index overweighing Table 8(a) shows he averages of β OW7 and β OW8. Weighed leas squares regression resuls for Eq. (17) in he ex are shown in Panels (b1) and (b2). The figures in parenheses are simple -saisics. ** and *** indicae wo-sided saisical significance a 5% and 1%, respecively. (a) Average values when he marke is up & down βow7 βow8 Whole period MR >=0 MR <0 MR -1>=0 MR -1<0 MR -2>=0 MR -2<0 MR -3>=0 MR -3< (1.37) (4.75) *** (7.96) *** (13.16) *** (9.69) *** (0.78) (3.59) *** (0.16) (2.83) *** (2.19) ** (4.67) *** (7.00) *** (14.77) *** (5.63) *** (1.05) (4.02) *** (1.35) (3.50) *** (b1) Regression analysis: OW 7 (b2) Regression analysis: OW 8 26